SIllllllll~lUl l ((1li · The most important system parameter relationships in this report are...

AD-A278 026SIllllllll~lUl l ((1li ~ llliaRL-TR-93-258, Vol II (of two)Final Technical ReportDecember 1993

INVESTIGATION AND SIMULATION OFNONLINEAR PROCESSORS FOR SPREADSPECTRUM RECEIVERS, USERS MANUAL

Illinois Institute of Technology

Donald R. Ucci, William Jacldin, and Jimm Grimm- DTICS ELECTE

APR 11 1994D

\`ýý94- 10819

~~T1Cf- -I ED 3

Rome LaboratoryAir Force Materiel Command

Griffiss Air Force Base, New York

944 8 049

This report has been reviewed by the Rome Laboratory Public Affairs Office(PA) and is releasable to the National Technical Information Service (NTIS). AtNTIS it will be releasable to the general public, including foreign nations.

Although this report references * limited document listed on page 18, no

limited information has been extracted.

RL-TR-93-258, Vol II (of two) has been reviewed and is approved for publication.

APPROVED: +6t

JOHN J. PATTIProject Engineer

FOR THE COMMANDER)JH . RANIERO

Chief Scientist for C3

If your address has changed or if you wish to be removed from the Rome Laboratorymailing list, or if the addressee is no longer employed by your organization,

please notify RL ( C3BB ) Griffiss AFB NY 13441. This will assist us in maintaininga current mailing list.

Do not return copies of this report unless contractual obligations or notices on a

specific document require that it be returned.

REPORT DOCUMENTATION PAGE _-MB No. 0704-0188

go mU ba" W901 temf 8M01A mtl SNO Imm 8"I wua t mu.mu m *wpm& ia Wig WW Sao a '-"1., loco, mý .mw "*w% t MMAW *b:u% to WMM Hoomwom sva~ owwx 9 to n* O0mauu WWRMM& 1215 -dq

cammo SLA 1K MMW% VA =M ad Wome O1= d Me".-wt wW &AUK PIP ~ - PWAOR (0734OI 4. wwI V= DOM=

1. AGENCY USE ONLY (Leave BlanW 2. REPORT DATE J3. REPORT TYPE AND DATES COVEREDDecember 1993 Final Feb 92 - Aug 93

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

INVESTIGATION AND SIMULATION OF NONLINEAR PROCESSORS C - F30602-92-C-0039FOR SPREAD SPECTRUM RECEIVERS, USERS MANUAL PE - 62702F

a. AUTHOR(S) PR - 4519TA - 42

Donald R. Ucci, William Jacklin, and Jimm Grimm WU - PA

7. PERFORMING ORGANIZATION NAME(S) AND ADORESS(ES) & PERFORMING ORGANIZATION

Illinois Institute of Technology REPORT NUMBER

Electrical and Computer Engineering DepartmentChicago IL 60616-3793 N/A

9. SPONSORINGJMONITORING AGENCY NAME(S) AND ADORAESSE) 1. SPONSORING/MONTORING

AGENCY REPORT NUMBER

Rome Laboratory (C3BB)525 Brooks Road RL-TR-93-258, Vol II

Griffiss AFB NY 13441-4505 kof two)

11. SUPPLEMENTARY NOTESRome Laboratory Project Engineer: John J. Patti/C3BB/(315) 330-3615

12a& DISTRIBU1ON/AVALABSITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release; distribution unlimited.

13. ABSTRACT d(n-2mY -,W,

The objective of the recent research effort was to investigate and determine theviability of utilizing Locally Optimal (LO) nonlinear processing to mitigate non-Gaussian interfering signals in a Direct Sequence (DS) SS communications system.

The effort centered on the use of memoryless techniques, as well as techniquesemploying memory, and performance comparisons of many receiver and nonlinearprocessor configurations. The approach used included the analysis and evaluationof several implementation of the various nonlinear processing algorithms. Theanalysis included the study of well known techniques, as well as newly developed

methods. Evaluation was accomplished through the development of software simulationsdesigned to test the algorithms in various signalling scenarios. The resultsillustrate the tradeoffs of each nonlinear processor algorithm for use in a spreadspectrum receiver. This knowledge can be used to determine the most effectiveprocessor for a given interference scenario. The work presented in this report isdirectly in line with the mission of Rome Laboratory (RL) to provide secure, reliablecommunications to the United States Air Force.

14. SUBJECT TERMS I1I NUMBER OF DAGES152

Adaptive Filtering, Nonlinear Processing, Spread Spectrum IPRCE CODE

17. SECURnIY CLASSIFICATION 1& SECURITY CLASSIFICATION 1ig, SECURITY CLASSIFICATION 2o. LMITATION OF ABSTRACtOF REPORT OF THIS PAGE OF ABSTRACT I

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED nU*JSN 75 '- ' St wta=•F ,1'.-g -6 t• 2

P'wgt@0* OV ANSi Sta 9

TABLE OF CONTENTS

Volume II

Section No. Title Page No.

1. Introduction 1

2. The IIT SPW MNPs 1

3. The IIT SPW Systems 4

4. Using the MNPs in an IIT SPW System 6

5. Parameters for IUT SPW Simulations 6

5.1 Parameter Overview 8

5.2 Detailed Parameter Discussion 10

5.2.1 System Parameters Related to the Information Signal

and Gaussian Noise 10

5.2.2 System Parameters Relating the Continuous Wave

Jammer to the Information Signal 12

5.2.3 System Parameters Relating the Partial Band

Jammer to the Information Signal 15

5.2.4 Spread Spectrum System Parameters 17

6. References 18Accesion For

Appendix A NTIS CRA&I A-I

Appendix B DTIC TAB B-iUnannouncedJustification ................................

By .............................------- ------------Distribution !

Availability Codes

Avail and j orDist Special

.. ~ . ...

1. Introduction

This volume of the report serves as a user's guide to the Illinois Institute of Technology

(i)Signal Processing WorksystemT' (SPW) simulations. These simulations consist of nine

modular SPW systems and fifteen Memoryless Nonlinear Processor (MNP) blocks for use with

these systems. A solid understanding of the concepts discussed in Volume I of this report is

essential for using these systems and interpreting the results.

NOTICE TO THE USER:

The most important system parameter relationships in this report aresummarized in three text boxes like this one. It is imperative that thesefundamental constraints are maintained at all times during simulationof the systems. There are no provisions in the systems to automaticallyverify these constraints; it is entirely the responsibility of the user. Ifthese constraints are violated, invalid results may be produced.

2. The liT SPW MNPs

In the current and past research efforts five types of MNPs have been implemented in

the SPW platform: Histogram [Illi93a], Equiprobable Bin Histogram (EBH) [Illi93b], Fourier

Series Approximation (FSA) (Illi93b], Continuous Polynomial Approximation (CPA) [Grim93],

and M Interval Polynomial Approximation (MIPA) [Illi91]. Table 1 summarizes the filenames

for the MNPs' and the linear receiver. These filenames are for reference only since they may

be copied directly from the SPW User Palette [Comd9l] into the desired system.

Filenames of MNM Blocks

N•ONLINEAR RECELV ERS WIHCORRELATOR:

LibravFflenameHISTO/SERIALNONLIN Histogram MNPHISTO/SENONLIN EBH MNPFOURIER/SERIAL NONLIN FSA MNPCPA/SCDF2 NONLIN CPA with Linear Transform MNPCPA/S CDF3_NONLIN CPA with Discontinuous Auxiliary Function MNPCPA/S PDF GT NONLI CPA with Gaussian Tails MNPMIPA/SERIALNONLIN MIPA MNP (for 2! and 4* order: MIPA)LINEARJSERIALUN Linear receiver

NONLINAR RECEIVERS WITHOUT CORRELATOR:

Lib /Filename DescriptionHISTO/SNONUNNC Histogram MNPHISTO/SENONUNNC EBH MNPFOURIER/SNONLINNC FSA MNPCPA/SCDF2_NL NC CPA with Linear Transform MNPCPA/SCDF3_NLNC CPA with Discontinuous Auxiliary Function MN?CPA/S PDF GT NL NC CPA with Gaussian Tails MNPMIPA/SNONUN NC MIPA MNP (for 2T and 4e order MIPA)

Table 1

In this report SPW filenames are written as LIBRARY/FILENAME, where LIBRARY is the

Block Diagram Editor (BDE) library in which the block or system is stored, andFILENAME is the name of the block or system.

2

There are two main categories of MNPs: MNPs with a correlator and MNPs without a

correlator. The MNPs with a correlator implement the entire memoryless Locally Optimal (LO)

algorithm [Illi93b]:

Choose (',S) which maximizes:

N

XEIS~ {..g(rk)cos0,+s(,g(r) sinG4(1Au'

where g(rk)=- + I is the LO Memoryless Nonlinear Transform (MNT).AR(rd) r

Since the correlator performs a decision, these blocks constitute the entire nonlinear receiver,

and may be used in systems such as the conventional Quadrature Phase Shift Keying (QPSK)

[Taub86] systems to be discussed in Section 3. It is important to make the distinction between

the MNT, which is the mathematical formula, and the MNP, which is the block that applies the

MNT.

The MNPs without a correlator only implement the MNT and convert it to rectangular

coordinates as follows:

output = [g, gQ,]T = (s.g(r•) cos0k sg(r•) sinok]T (2)

These blocks may be used in systems where additional post-processing is required after the

MNP, as in the Spread Spectrum (SS) systems to be discussed in Section 3.

3

3. The UIT SPW Systems

Nine modular SPW systems have been designed to incorporate the MNPs previously

discussed. Four of these systems are conventional QPSK systems and five are Direct Sequence

(DS) SS [Taub86] QPSK systems. The conventional systems aid in isolating and characterizing

the performance of the MNPs, and the DSSS systems help analyze the performance of the MNPs

in a spread spectrum environment. Both the conventional and the DSSS systems are based on

QPSK modulation; however, it would be straightforward to modify them to employ alternative

modulation schemes such as Minimum Shift Keying, Quadrature Amplitude Modulation, or M-

ary Phase Shift Keying. The filenames and purposes of the I1T SPW systems are summarized

in Table 2. All systems simulate a communication system with jammers and nonlinear

processing, and each one has certain processing after the nonlinearity that is also listed in the

table.

Figure (1) shows the basic conventional QPSK system, SIM/PE, which calculates the

probability of bit error (Pb) for any of the serial MNPs or the linear receiver. Since QPSK is

a basic form of modulation it was chosen to isolate the effect of the MNP on the overall system

performance. The RL/COMPLEXDATA block generates random QPSK data, and the

JAM/CHANNEL block adds the jammers and Gaussian noise. An MNP or the linear receiver

block must be copied by the user to the designated space in Fig. (1). The

HISTO/PROB OF ERROR block counts the number of errors the receiver makes in decoding the

bits and computes Pb.

The SIM/PES system shown in Fig. (2) is able to calculate Pb for up to three different

receiver configurations simultaneously to facilitate comparisons of the MNPs. The SIM/PE and

SIM/PES simulations may be used in conjunction with the SPW iteration macro (Varn93] to

generate Bit Error Rate (BER) curves as a function of various system parameters.

4

Filenames of lIT SPW Systems

CONVENTIONAL OPSK SIMULATIONS:

Libay/Filename DescriptionSIM/PE Computes P. for any MNPSIM/PES Computes Pb for any three MNPsSIM/HSIGS Computes Pb & plots signals for histogram MNPsSIM/PSIGS Computes Pb & plots signals for polynomial and FSA MNPs

OPSK SPREAD SPECTRUM SIMULATIONS:

Libra/Filename DescriptionSIM/SSyPE Computes Pb for any MNPSIM/SSPES Computes Pb for any three MNPsSIM/DSSSH Computes Pb & plots signals for histogram MNPsSIMIDSSSP Computes Pb & plots signals for polynomial and FSA MNPsSIM/DSSSL Computes Pb & plots signals for linear system

Table 2

The other two conventional systems are SIM/HSIGS and SIM/PSIGS, and are displayed in

Figs. (3) and (4), respectively. HSIGS is an abbreviation of "histogram signals". In addition to

computing Pb, this system outputs all relevant signals for detailed analysis. The SIM/HSIGS

system works for both the histogram and EBH MNPs. PSIGS is short for "polynomial signals",

and the SIM/PSIGS system works for the CPA and MIPA MNPs. SIM/PSIGS also works for the

FSA MNP, even though the FSA is not a polynomial approximation method.

The DSSS systems are shown in Figs. (5) through (9). The basic system, SIM/SSPE, is

shown in Fig. (5). QPSK data is generated by the SPW QPSK SOURCE library block. The

spectral spreading is achieved by multiplying the QPSK data by a Pseudo Noise (PN) sequence,

and the jammers and Gaussian noise are added in the channel. The user must copy an MNP

without a correlator into the designated space. The transformed sequence is multiplied by the

5

same PN sequence to despread the spectrum. A PSK matched filter demodulator library block

is used to receive the message, and the HISTO/PROBOFERROR block is used to compute P,.

4. Using the MNPs in an [iT SPW System

A simple three step process is required to use the MNPs in the UIT SPW simulations.

First, the user enters the Block Diagram Editor (BDE) and loads one of the systems listed in

Table 2 into a viewport. Second, the desired MNP is copied from the User Palette into the

designated space in the system, making sure that all wires are properly connected. The

parameters in the MNP block are already exported to the parameters on the top level of the

system. Finally, the system level parameters are adjusted by the user to their desired settings

and the system is simulated.

5. Parameters for UIT SPW Simulations

There are numerous parameters which specify the configuration of the lIT SPW

simulations. It is not possible to specify every parameter explicitly since some parameter.; are

dependent on others. For example, the symbol rate, R, the sampling frequency, f, and the

number of samples per symbol, N5, are related by R, =f/N,. Thus, specifying any two of these

parameters implies a value for the third. In this manual a parameter which is directly specified

is enclosed in braces {} for clarity. The remaining parameters are considered to be variables,

and their values are a function of the specified parameters. A listing of the parameters of the

IIT SPW simulations is presented in Table 3.

6

[IT SPW System Parameters

SOURCE PARAMETERS: Symbol Name in SPW

Probability of Zero Symbol P. prob zeroSampling Frequency sfreqSamples Per Symbol N, samplespersymbolSymbol Rate R, Rs

ADDITIONAL SOURCE PARAMETERS FOR SPREAD SPECTRUM SYSTEMS:

Samples per Chip N, samples~per.chipProcessing Gain PG pn_gain

CHANNEL PARAMETERS:

Continuous Wave JammerJammer to Signal Ratio J/S JIS, J2_S, J33SFrequency Fraction f,/I? freql, freq2, freq3Jammer Phase •, phasel, phase2, phase3

Partial Band JammerJammer to Signal Ratio JpRIS Jpb_SCutoff Frequency Fraction f/R, pfreq

EG auan NoisBit Energy to Gaussian Noise Power Ratio EVNo EbNoGaussian Noise Power No No

RECEIVER PARAMETERS:

Samples per Correlation N samplesOrder of Approximation P orderNumber of Bins B binsSymbols per Pb calculation Np, symbols.per_caIc

Table 3

7

5.1 Parameter Overview

Several of the parameters in the SPW simulations are interrelated, and certain

relationships between them must be maintained. In addition, the number of iterations per

simulation run is also dependent on certain parameters. It is necessary to choose the correct

number of iterations per simulation to be certain that the desired number of P, values will be

calculated. Do not select run to EOF, because there is no end of file in these systems and they

would run indefinitely.

The nonlinearity in the MNP blocks requires vector operation. In all of the MNPs listed

in Table I the incoming serial data is buffered, operated on by the nonlinearity in vector form,

and converted back to serial form. The length of this vector is N, the number of samples per

correlation. This length also corresponds to the number of samples for each MNT

approximation. The correlation must be based on an integer number of symbols, so N/N, must

be an integer. If NIN, is not an integer correlations after the first one will not be synchronized

to the symbol period and P. will suffer as a result.

Let IQ be the number iterations for a conventional QPSK simulation run and k be the

number of P6 points to be computed. Also, let C be the number of correlations per P.

calculation. This also corresponds to the number of MNT approximations per Pb calculation.

C is an implicit variable which is a function of other parameters. The following three

constraints, (A), (B), and (C), must be maintained at all times:

NM*C-N,, (A,N / N, * C = NA• (A)

IQ = k N * C + N (B)N / N, must be an integer (C)

Fundamental Constraint Box (1)

8

For example, let {N} = 5,000, {N,} = 25 and {N..) = 1,000. (These are the default values

in the lIT SPW systems.) From constraint (A),

(NJ / (N,) * C .5,000125 * C= 1,000

C-5

The number of iterations required for a single Pb data point (k = 1) is determined from

constraint (B) to be 1J = 25,000 + 5,000 = 30,000. To compute three Pb data points requiresla = 3 * 25,(0)0 + 5,000 = 80,000. Note that for both cases C = 5 and (N) / {N,) = 200,

which is an integer as required by constraint (C). When using the SPW iteration macro to

iterate over N, N must be an integer multiple of the least common multiple of all the values of

N,. This insures that constraint (C) is satisfied throughout the iteration.

The additional N term in constraint (B) is a result of buffering requirements. If the

number of iterations for each simulation are chosen to be greater than the required number I0,

more than k Pb values may be computed. Conversely, if the number of iterations is less than

required, fewer than k Pb values will be computed. For the Spread Spectrum systems in this

report, the required number of iterations is Is = IQ + N,, due to time delay in the PSK

demodulator block.

Note: The CPA with Gaussian Tailsnonlinearities (CPA/PDFGTNONLI and

CPA/PDFGTNLNC) must have at least fourbins to function properly.


9

5.2 Detailed Parameter Discussion

This following discussion outlines the reasons why the parameters in Table 3 are the

preferred way to specify the configuration of the SPW systems. In addition, two very important

relationships which are summarized below are discussed:

Maintain R,=f/N, at aD times

For the SS systems, also maintain N,=NPG at all times


The derivations in the following sections are performed in each channel separately.

QPSK modulation may be viewed as Binary Phase Shift Keying (BPSK) in the In-Phase and

Quadrature channels; each QPSK symbol consists of two BPSK bits. The Continuous Wave

(CW) jammer may be viewed as a sinusoid in each channel, and the Partial Band (PB) jammer

may be viewed as a filtered Gaussian signal in each channel. EJNO and AIS are the same for

each channel and for the composite signal. In addition, the bit rate of each channel, Rb, is equal

to R, and the number of samples per bit, Nb, is equal to N,.

5.2.1 System Parameters Related to the Information Signal and Gaussian Noise

Signal EnerM

The energy, E, of a signal s(t) is defined as

EA . Is(t) 12dt (3)

For discrete signals this becomes

10

E=j Is(n)l2 1 (4)

where f, is the sampling frequency. A BPSK bit maintains a constant level ±A for the entire

bit period. The energy of one bit, Eb, is given by

=I A2 A2N A2 (5)

where N, is equal to the number of samples per bit and R, -:L' is equal to the bit rate.

In many analyses it is desirable to compute Pb as a function of E6NO, where No is the

background noise power. This can be achieved by making Eb/No a parameter, {EbINo}, and

making No a parameter, {No}. Thus, for BPSK

{EbI /No} E = - A2 (6){NO} {No}R,

Then the bit amplitude is

A 2 = {Eb/No} {No}f3 (7)N,

Sienal Power

The power, P, of a signal is defined as

PA. I S(t)12dt (8)

where T is the period of the signal. For discrete signals the power is

11

T I Is(n) 121, (9)

For a BPSK signal with amplitude +A the power, S, is

S="E A 2=A 2 (10)

5.2.2 System Parameters Relating the Continuous Wave Jammer to the Information Signal

The power of a CW jammer is

N A12

J = W JA A1 I(~)dt* = (T1

where A, is the jammer amplitude and w, is the jammer frequency. The jammer amplitude can

be found as a function of the parameter {J/No}:

VI/No} =j _ A2/2 (12){No} {No}

AI i 2 {uINo} {Nt} (13)

It is often more useful to write the jammer amplitude as a function of the parameter {JIS}.

fis} ,4 /2 (14)S A2

12

Aj2 - 2A 2{01S)} a2(Eb/1NOJ lnAfi(IS} (1s)

Relationship between CW Jammer Parameters

It is quite straightforward to show that

J

f.}= {N01 (16)

Usually these parameters are specified in deciBels (dB), and the following relationship results:

0144,B) - (JINO} 0 + log10 [{Eb IOI, (17)

Note that in Eq. (17) {Eb/NO} is not in dB.

Choice of CW Jammer Parameters

One of the key assumptions in the LO derivation is that the signal is small compared to

the jammer, i.e. the ratio A/'/A2 is large. From Eqs. (7) and (13) it is seen that if the parameter

{J/No} is used, this ratio becomes

A,2 _ 2J/VIN}

A{E2 /No} (18)

This means that the validity of the small signal assumption is not only dependent on {J/No}, but

also on many other parameters. However, if the parameter {JIS} is used instead of (J/No}, the

ratio A//A2 is determined from Eqs. (7) and (15) to be

13

Aj2 2{Eb/ NO) i'j/4J0ISSA2 N w2{/S} 19

(EbI /NO)NOV

Now the small signal assumption is only dependent on {J/S). For this reason, the use of the

(J/S} parameter is preferred over {J/INO.

renuenav brameters

The message bandwidth is proportional to the bit rate, and R=-.L. If N, is varied, theSNmessage bandwidth will change butf,, the jammer frequency, will not. 7hus, the spectrum of

the message sequence will expand or contract while the spectral position of the jammer will

remain unchanged. As the relative position of the jammer and the message change, the

performance of the system will change dramatically. In order to isolate the performance of the

MNP from the effects of this shift, it is useful to use a frequency ratio, &/R,}, instead of (f,).Using this ratio, the jammer frequency isf,={(f/R,JR,. This wayf! and the message bandwidth

change in the same manner when R, is varied.

Alternatively, the sampling frequency may be set tof,= (N,{R,}. Then if R, is constant,

the message bandwidth will remain constant as N, is varied. The spectral positions of both the

jammer and the message signal will remain constant.

14

5.2.3 System Parameters Relating the Partial Band Jammer to the Information Signal

PB Jammer Power

The autocorrelation function, r.(m), for sampled white Gaussian noise, w(n), is given by

r.(m) = 4:b(m) (20)

where o?. is the variance of w~n) and 6(m) -I M 0 is the Kronecker delta function. The

Power Spectral Density (PSD), Sw(t), is given by

S.(f)fr for all f (21)

The frequency response of an ideal lowpass filter is

H, L 1 <f, (22)Hf 0, f <N~

wheref, is the cutoff frequency (normalized by the sampling frequency,f). The Gaussian noise

PB jammer is constructed by passing white Gaussian noise through the lowpass filter (for

simulation at baseband). Therefore, the PSD of the PB jammer, Sp,(J), is

S 8(f)-- 1 (23)OP , f4< [A< (23

The power of the PB jammer, .4,,, may be found by integrating the PSD over the domain off,

resulting in

15

112

Jp~9 -z _f S(eflv) df (24)

- 2f,

System Parameters

Given the jammer-to-signal ratio parameter (Jr/S), then

A 2s,,= Ira

(EbINJ (NS

2fN

01W

{EbINJ) {N0)f5

To find the required value of oý. for a given {J, 8 S)

a, IJPBIS) {EbI N0) (NO) f,2f~ £(26)

- Jp9/S) (Eb/NO) (NO)R2f, R

16

Iff, is chosen as a fraction of the bit rate, i.e. if VIR,} is used then

2 {J,,/S} (EINo} (NO)"" 2V0, (27)

5.2.4 Spread Spectrum System Parameters

The processing gain, number of samples per chip, and number of samples per symbol

are related by

N=N, PG (28)

R f_Also, since R, =,. then the chip rate, Ro, is equal to

N,

R,..=R, -=R, PG (29)

17

6. References

(Comd9l] Comdisco Systems, Inc., SPW Version 2.8 User's Guide, May 1991.

[Grim93] Grimm, Jimm H. et. al., "Continuous Polynomial Approximation%, to be

published in Proceedings of MILCOM D93, October 1993.

[Illi9l] Illinois Institute of Technology Report, Continuation Study of a Communications

Receiver for Spread Spectrum Signals, RADC Contract No. F49620-88-C-

0053/SB5881-0378, January 31, 1991.

* [Illi93aj Illinois Institute of Technology Report, A Spread Spectrum Communications

Receiver with Nonlinear Processing, RL Contract No. F30602-91-C-0059,

RL-TR-93-50, May 93, ADB174588.

[illi93b] Illinois Institute of Technology Report, Investigation and Simulation of Nonlinear

Processors for Spread Spectrum Receivers Volume I, RL Contract No. F30602-

92-C-0039, RL-TR-93-258, Vol I, Dec 93.

[Taub86] Taub, Herbert and Schilling, Donald L., Principles of Communication Systems

2" edition. McGraw Hill, 1986

[Varn93] Varn, David, "Automatic Parameter Iteration in SPW", WaveForum by Comdisco

Systems, Inc., March 1993.

18

SIMIPE

(z~

-j0r. - w

z S n

0L

~~ LU

L- 4! wLL .g a *

~ IIto a a j a ~

0 LU

C.Cie

U~ =

~J .w

z Figure (1-

SIM/PES

vi l vpI O

!I !:i- | '- -- <-

3W,hi 2 i E h , I 1. 0

5I 5Is! 515

o 4-

I~Zl

w

U

-LJ

o¢ z

I- 0.

o J'!•,- -- --

.<r

9 ' I " i i i I]

z U!.

Q I S o

-•~U .L. -- Z,-• "I, wa snnlml nn i n llnl

42 wI a 1'

w-N

Figure (2)

SIM/HSIGS

S

cu

c

Ii, 1a, 1j 43*

#

1

!I I I

J ill __PA

Figure (3)

SIM/PSIGS

13 fro e

II"L Lh' .

;b? ;13h 4v Jj IL

I d1IkillUa 3U

I 'II

Figure (4

SIM/SS PE

I

c (a I.- i

tA a-

0 C) U

ro cL w- ! lliJ• N...:C_ a-

=00 0 -0

c CO - -LW

S 0 0) C -

00

_0

0r 0 - (

U) CD z

c--

U)-.. a) 0ý

-aPA

~~%A

OA

Figure (5)

SIM/SS-PES

0)~

_0 ai VU

0 w L ow- C

-o.- a) -n -

E0 -U) 4J 44.q.j

LmLo L 0 # l

10T -4 a '

(D-0

Q-) Z LU~

(D

D-0- oH rIrv. 3.v

U)U

n.~ .I

CC-

$IA

Fiur (6) a

SIM/DSSSH

c -0

a) U) -n

OL L

a)k__ 5 -E~n i

aI) 0

II RI

(D - C-)1.*

Q.L 0 6 .. ,. .

a)) 0r CL 1

U La

1A

Figure (7)

SIMID)SSSP

a)

-ACK

Q- w i0 a)

CL a) 13 ,

C -I ISO

(DC 0 c

z I

C,)-. 8 -i0~~ -. _

I - f

a aW aila i

CLb

0 caccl : 0

Fiur (8)

SIMIDSSSL

c "

0 09I,.

ww

us•

WIN

Uw i

Del I *i [] Hi •

(JIf IT

L wL

0~ LI JH ~ ~ i-

U * e.*@ c

C!) a OA

~ i~i~jj1E(I) U U U U$.1A

0V

Fiure (9)

Appendix A

Docgen Listing

This Appendix is an alphabetical listing of the help screens available for each liT SPW

block. In this Appendix the inputs, parameters and outputs of each block are capitalized in the

description of the block to distinguish them from the text. However, in the listing of the inputs,

parameters and outputs, the capitalization matches the capitalization of the actual parameter

names in SPW.

The names of hierarchical blocks are marked with a dagger t. The details of these blocks

are printed in alphabetical order in Appendix B.

A-1

Name:cpa/cdf2t

Description:This hierarchical block generates a Cumulative Distribution Function (CDF) and a Probability

Density Function (PDF) of the magnitude of the input message by applying the ContinuousPolynomial Approximation (CPA) algorithm to a histogram CDF. A vec/heapsort block is usedto sort the data to prepare it for the histo/equi block, which generates the histogram CDF. Thecpa/slopel block computes the derivatives of the histogram needed by the CPA algorithm. Thecpa/coef It block uses the equiprobable bin histogram CDF, its derivatives, and the breakpointsto compute the CPA CDF and PDF.

This block applies the linear transform to the polynomial. Without the linear transform themagnitude values in each bin would range from BP[K-l] to BP[K]. The linear transform shiftseach bin to the origin, so the new magnitude values range from 0 to BP[K]-BP[K-l].

Inputs:data Magnitude of input message sequence

Parameters:bins Number of binssamples Number of samples

Outputs:bp Breakpoints (CDF and PDF interval boundaries)cdf CDF polynomial coefficientspdf PDF polynomial coefficients

See also:vec/heap sort, histo/equi, cpa/slopel, cpa/coef it

Name:cpa/cdf2 nonlint

Description:This is a hierarchical block which applies the nonlinearity to the input signal in vector format.

The histo/rec topolar block converts the two dimensional input signal from rectangular to polarcoordinates, and a CPA of the Probability Density Function (PDF) of the magnitude is computedby the cpa/cdf2 block. The poly/mnt block obtains the Memoryless Nonlinear Transform

A-2

(MNT) from the CPA PDF and applies it to the magnitude of the input message sequence. Theresult is converted back to rectangular coordinates by the histo/polar to rec block using theunmodified phase. The poly/plot block generates a plot of the PDF and CDF from theirpolynomial coefficients.

The coefficients in the cpa/cdf2 block are computed with the linear transform applied, thuseach bin is shifted to the origin.

Refer to the poly/mnt block for more information on the MNT.

Inputs:iUin In-Phase component of input message sequenceq_in Quadrature component of input message sequence

Parameters:samples Number of samples in input vectorsbins Number of bins in the-histogram PDFpoints Number of plot points for PDF and MNT

Outputs:pdf CPA PDFi out In-Phase component of transformed sequenceq_out Quadrature component of transformed sequencemnt Plot of the Memoryless Nonlinear Transformbp Breakpoints (PDF and MNT interval boundaries)

See also:histo/rec_to_polar, cpa/cdf2, poly/mnt, poly/plot, histo/polar to-rec

Name:cpa/cdf3 t

Description:This hierarchical block generates a Cumulative Distribution Function (CDF) and a Probability

Density Function (PDF) of the magnitude of the input message by applying the ContinuousPolynomial Approximation (CPA) algorithm to a histogram CDF. A vec/heapsort block is usedto sort the data to prepare it for the histo/equi block, which generates the histogram CDF. Thecpa/slopel block computes the derivatives of the histogram needed by the CPA algorithm. The

A-3

cpa/coef.ltdaf block uses the equiprobable bin histogram CDF, its derivatives, and thebreakpoints to compute the CPA CDF and PDF.

This block (cpa/cdf3) is identical to the cpa/cdf2 block except that the constraint that the CDFbe continuous has been relaxed. Thus, the equations to determine the coefficient values aredifferent.

Like the cpa/cdf2 block, this block applies the linear transform to the polynomial. Withoutthe linear transform the magnitude values in each bin would range from BP[K-1] to BP[K]. Thelinear transform shifts each bin to the origin, so the new magnitude values range from 0 toBP[K]-BP[K-1].



Outputs:bp Breakpoints (CDF and PDF interval boundaries)cdf CDF polynomial coefficientspdf PDF polynomial coefficients

See also:vec/heapsort, histo/equi, cpa/slopeI, cpa/coef ltdaf

Name:cpa/cdf3_nonlin t


The histo/recto.polar block converts the two dimensional input signal from rectangular to polarcoordinates, and a CPA of the Probability Density Function (PDF) of the magnitude is computedby the cpa/cdf3 block. The poly/mnt block obtains the Memoryless Nonlinear Transform(MNT) from the CPA PDF and applies it to the magnitude of the input message sequence. Theresult is converted back to rectangular coordinates by the histo/polarjto.rec block using the

A-4

unmodified phase. The poly/plot block generates a plot of the PDF and CDF from theirpolynomial coefficients.

The coefficients in the cpa/cdf3 block are computed with the linear transform applied, thuseach bin is shifted to the origin. Also, the constraint that the CDF be continuous is removed.


Inputs:iUin In-Phase component of input message sequenceq.in Quadrature component of input message sequence

Parameters:samples Number of samples in input vectorsbins Number of bins in the histogram PDFpoints Number of plot points for PDF and MNT

Outputs:pdf CPA PDFi out In-Phase component of transformed sequenceq_out Quadrature component of transformed sequencemant Plot of the Memoryless Nonlinear Transformbp Breakpoints (PDF and MNT interval boundaries)

See also:histo/rectopolar, cpa/cdf3, poly/mnt, poly/plot, histo/polar totrec

Name:cpa/coefgt

Description:This block computes the Continuous Polynomial Approximation (CPA)to a function. In this

implementation, the CPA is an approximation of a Probability Density Function (PDF).

The coefficients in this routine are computed with the linear transform applied, thus each binis shifted to the origin. The first and last bins are a Gaussian tail instead of a polynomial. Themean and variance for the Gaussian are taken to be the mean and variance of the received signal.

Note that the value for BINS must be set to a value greater than or equal to 4.

A-5

WARNING:This program modifies the histogram PDF input. If another block is going to also use the

histogram PDF results will be unpredictable.

Inputs:bp Breakpoints (PDF interval boundaries)f Histogram PDFdf First derivative of Histogram PDFmean Average of the received signalvar Variance of the received signal

Parameters:bins Number of bins

Outputs:pdf CPA PDF

Name:cpa/coef It


implementation, the CPA is an approximation of a Cumulative Distribution Function (CDF).

The coefficients in this routine are computed with the linear transform applied, thus each binis shifted to the.origin.

Inputs:bp Breakpoints (CDF and PDF interval boundaries)histo cdf Histogram CDFdf First derivative of Histogram CDFddf Second derivative of Histogram CDF


Outputs:cdf CPA CDFpdf CPA PDF

A-6

Name:cpa/coef ltdaf


implementation, the CPA is an approximation of a Cumulative Distribution Function (CDF).

The coefficients in this routine are computed with the linear transform applied, thus each binis shifted to the origin. Also, the constraint that the CDF be continuous is removed.

Inputs:bp Breakpoints (CDF and PDF interval boundaries)df First derivative of Histogram CDFddf Second derivative of Histogram CDF


Outputs:cdf CPA CDFpdf CPA PDF

Name:cpa/pdfgtt

Description:This hierarchical block generates a Probability Density Function (PDF) of the magnitude of

the input message by applying the Continuous Polynomial Approximation (CPA) algorithm toa histogram PDF. A vec/heapsort block is used to sort the data to prepare it for the histo/equiblock, which generates the histogram PDF. The vec/avebp obtains values of the histogram atthe breakpoints by averaging the values of the adjacent bins. The cpa/slope2 block computesthe derivatives of the histogram needed by the CPA algorithm. The cpa/coef.gt block uses theequiprobable bin histogram, its derivatives, the breakpoints, and the mean and variance of themagnitude to compute the CPA PDF.

The first and last bins are approximated using Gaussian tails instead of polynomials. Becauseof this, the poly/mntgt and poly/plotgt blocks should be used with this block.

A-7

The linear transform is applied to the polynomial bins. Without the linear transform themagnitude values in each bin would range from BP[K-1] to BPWK]. The linear transform shiftseach bin to the origin, so the new magnitude values range from 0 to BP(K]-BP[K-l].

Note that the value for BINS must be set to a value greater than or equal to 4.



Outputs:bp Breakpoints (PDF interval boundaries)pdf PDF polynomial coefficients

See also:vec/heap sort, histo/equi, cpa/slope2, cpa/coef ltdaf, poly/mnt.gt, poly/plot_gt

Name:cpa/pdf gt-nonlin t


The histo/rec topolar block converts the two dimensional input signal from rectangular to polarcoordinates, and a CPA of the Probability Density Function (PDF) of the magnitude is computedby the cpa/pdf gt block. The poly/mnt block obtains the Memoryless Nonlinear Transform(MNT) from the CPA PDF and applies it to the magnitude of the input message sequence. Theresult is converted back to rectangular coordinates by the histo/polar torec block using theunmodified phase. The poly/plot block generates a plot of the PDF and CDF from theirpolynomial coefficients.

The coefficients in the cpa/pdfgt block are computed with the linear transform applied, thuseach bin is shifted to the origin. The first and last bins are a Gaussian tail instead of apolynomial. The mean and variance for the Gaussian are taken to be the mean and variance ofthe received signal.


A-8

Inputs:iUin In-Phase component of input message sequenceq_in Quadrature component of input message sequence


Outputs:pdf CPA PDFijout In-Phase component of transformed sequenceq_out Quadrature component of transformed sequencemnt Plot of the Memoryless Nonlinear Transformbp Breakpoints (PDF and MNT interval boundaries)

See also:histo/rec-to_polar, cpa/pdf gt, poly/mnt, poly/plot, histo/polar-torec

Name:cpa/scdf2_nl nc

Description:This hierarchical block buffers the received data and converts it from serial to vector data and

applies it to the cpa/cdf2_nonlin nonlinearity. This block does not generate the summation partof the LO decision statistic.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLKOUT and HOLDVEC signals. The HOLD VEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLK OUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the cpa/scdf2_nl nc block. The CLKOUT signal has the sameperiod as the CLKIN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the cpa/s.cdf2_nl-nc block,and are used in serial to vector and vector to serial buffering.

A-9

The SAMPLES-PERSYMBOL, NUM-REFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM_REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf .vsource block as "ref/"&substr(" rtype ":model ,2, length(" mtype": model)-2)& "_" &xstring("samples..persymbol ": model)&"spb i'" for the I channel signals and "ref/"&substr("m type":model,2,length("m_type":model)-2) &"_"&xstring("samples..persymbol":model)&"spb q"' for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spbi and /spwdata/ref/bpsk.25spbq.

Inputs:in Input message sequence (complex input)clk-in Clock input for romelib/timing

Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples_per symbol Number of samples per data symbolnum refs Number of reference signalsmtype Modulation type

Outputs:mant Plot of the Memoryless Nonlinear Transformg Complex transformed sequence (vector)out Complex transformed sequence (serial)clk-out Timing signal: goes high when valid data sample is available at the output

of cpa/s cdf2_ninchold vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:cpa/cdf2_nonlin, romelib/timing, rl/inf.vsource, cpa/s cdf2_nonlin

A-10

Name:cpa/s-cdf2_nonlin t


applies it to the cpa/cdf2 nonlin nonlinearity. In addition, the summation in the LO decisionstatistic is formed using the histo/correlator2 block. The output of the correlator is convertedback to serial form.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLKOUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the cpa/scdf2 nonlin block. The CLK OUT signal has the sameperiod as the CLK IN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the cpa/s cdf2_nonlin block,and are used in serial to vector and vector to serial buffering.

The SAMPLESPERSYMBOL, NUMREFS, and MTYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr(" m_type"" model, 2, length (" mrtype": model)-2)&"_" &xstring(" samples.per symbol": model)&"spbi'" for the I channel signals and "ref/"&substr("mtype":model,2,length("mtype":model)-2) &" "&xstring("samples.persymbol":model)&"spbq'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spbi and /spwdata/ref/bpsk_25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples_persymbol Number of samples per data symbolnum refs Number of reference signalsm_type Modulation type

A-11

Outputs:mnt Plot of the Memoryless Nonlinear Transformg Complex transformed sequenceout Decision of nonlinearityclk-out Timing signal: goes high when valid data sample is available at the output

of cpa/s cdf2 nonlinhold vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:cpa/cdf2_nonlin, histo/correlator2, romelib/timing, rl/inf vsource

Name:cpa/scdf3_nl-ncl


applies it to the cpa/cdf3 nonlin nonlinearity. This block does not generate the summation partof the LO decision statistic.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLKOUT and HOLD VEC signals. The HOLD VEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLKOUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the cpa/s cdf3_n nnc block. The CLK OUT signal has the sameperiod as the CLKIN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the cpa/s...cdtjnl-nc block,and are used in serial to vector and vector to serial buffering.

The SAMPLES PER SYMBOL, NUMREFS, and MTYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr(" m_type": model ,2, length(" mrtype": model)-2)&" "&xstring(" samples_per symbol": model)&

A-12

"spb_i'" for the I channel signals and "ref/"&substr("m_type":model,2,length('mtype":

model)-2) &_" &xstring("samplespersymbol":model)&"spbq'" for the Q rhannel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk.25spbi and /spwdata/ref/bpsk_25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples_perjsymbol Number of samples per data symbolnum refs Number of reference signalsm-type Modulation type

Outputs:mnt Plot of the Memoryless Nonlinear Transformg Complex transformed sequence (vector)out Complex transformed sequence (serial)clk out Timing signal: goes high when valid data sample is available at the output

of cpa/s-cdf3_nl ncholdvec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:cpa/cdf3 nonlin, romelib/timing, rl/inf-vsource, cpa/s cdf3_nonlin

A-13

Name:cpa/s cdf3_nonlin'


applies it to the cpa/cdf3_nonlin nonlinearity. In addition, the summation in the LO decisionstatistic is formed using the histo/correlator2 block. The output of the correlator is convertedback to serial form.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLK OUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the cpa/scdf3_nonlin block. The CLK OUT signal has the sameperiod as the CLKIN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the cpa/s cdf3_nonlin block,and are used in serial to vector and vector to serial buffering.

The SAMPLESPERSYMBOL, NUMREFS, and MTYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr("i rtype": model ,2,length(" metype": model)-2)&"_" &xstring(" samplesj.per symbol": model)&"spb i'" for the I channel signals and "ref/"&substr("mtype":model,2,length("mtype":model)-2) &" "&xstring("samples.persymbol":model)&"spblq'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spbi and /spwdata/ref/bpsk_25spbq.

Inputs:in Input message sequence (complex input)clk in Clock input for romelib/timing

Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samplesjper symbol Number of samples per data symbolnum refs Number of reference signalsmetype Modulation type

A-14


of cpa/scdf3 nonlinhold-vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:cpa/cdf3_nonlin, histo/correlator2, romelib/timing, rl/inf vsource

Name:cpa/s pdf gt nl..nct


applies it to the cpa/pdf.gt nonlin nonlinearity. This block does not generate the summationpart of the LO decision statistic.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLDVEC signal holds vector blocks while theserial-data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLK_- OUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the cpa/s_pdf gt nl nc block. The CLK OUT signal has the sameperiod as the CLKIN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the cpa/s._dfgt nl nc block,and are used in serial to vector and vector to serial buffering.

The SAMPLES PER SYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/'&substr(" m_type": model,2, length(" mtype": model)-2)&"_" &xstring(" samples..per..symbol": model)&

A-15

"spb i'" for the I channel signals and "ref/"&substr('mtype*:model,2,length(Om type :model)-2) &"_" &xstring("samples_persymbol" :model)&"spb_q'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spbi and /spwdata/ref/bpsk_25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples_per symbol Number of samples per data symbolnum refs Number of reference signalsmtype Modulation type

Outputs:mnt Plot of the Memoryless Nonlinear Transformg Complex transformed sequence (vector)out Complex transformed sequence (serial)clk.out Timing signal: goes high when valid data sample is available at the output

of cpa/s.pdf gtnlnchold vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:cpa/pdf~gtnonlin, histo/correlator2, romelib/timing, cpa/spdf gt nonli, rl/inf vsource

A-16

Name:cpa/spdf gt_nonlit


applies it to the cpa/pdf gtnonlin nonlinearity. In addition, the summation in the LO decisionstatistic is formed using the histo/correlator2 block. The output of the correlator is convertedback to serial form.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLK OUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the cpa/spdfgt nonli block. The CLKOUT signal has the sameperiod as the CLKIN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the cpals_pdfgt_nonli block,and are used in serial to vector and vector to serial buffering.

The SAMPLES PER SYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUMREFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/infvsource block as "ref/"&substr(" rtype": model, 2, length (" mtype": model)-2)&" _" &xstring(" samplespersymbol": model)&"spb i'" for the I channel signals and "ref/"&substr("m type":model,2,length("mtype":model)-2) &"_"&xstring("samples_persymbol":model)&"spbq'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spbi and /spwdatalref/bpsk_25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples_perjsymbol Number of samples per data symbolnum refs Number of reference signalsmrtype Modulation type

A-17

Outputs:mnt Plot of the Memoryless Nonlinear Transformg Complex transformed sequenceout Decision of nonlinearityclk out Timing signal: goes high when valid data sample is available at the output

of cpa/spdf gtnonlihold vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:cpa/pdfgt.nonlin, histo/correlator2, romelib/timing, rl/inf vsource

Name:cpa/slopel

Description:This block computes the three point derivative of the histogram CDF for use in the CPA

MfNT construction. Extra bins are added to compute the slopes at the endpoints. This is themethod described in Appendix 3 of UiT Final Report 1991, F30602-91-C-0059. This block isused in the cpa/cdf2 and cpa/cdf3 blocks.

Note:The additional derivative at each end is always zero, since

HISTO-CDF(-2j = HISTOCDF(0] =0.0 and HISTO CDF(BINS] =HJSTOCDF[BINS +2] = 1.0.

Inputs:bp Breakpoints (CDF interval boundaries)histo-cdf Histogram CDF


Outputs:df First derivativeddf Second derivative

A-18

Name:cpa/slope2

Description:This block computes the three point derivative of the histogram PDF for use in the CPA MNT

construction. Extra bins are added to compute the slopes at the endpoints. This block is usedin the cpa/pdf gt block.

Note:The additional derivative at each end is always zero, since

HISTO PDF[-2] fHISTO PDF[O] =0.(hndHISTO PDF[BINS] fHISTO PDF[BINS +2] =0.0.

Inputs:bp Breakpoints (PDF interval boundaries)histopdf Histogram PDF


Outputs:df First derivativeddf Second derivative

A-19

Name:fourier/mntt

Description:This block obtains the Memoryless Nonlinear Transform (MNT) from a Fourier Series

Approximation (FSA) of a Probability Density Function (PDF). It is a hierarchical block whichcontains two fourier/rant calc blocks. One of them computes the MNT for each point of themagnitude of the input message sequence, and the other generates a plot of the MNT from theminimum to the maximum magnitude value with the aid of a vec/minmaxjramp block.

This block operates on the magnitude of the two dimensional message signal.

Inputs:a Vector of A coefficients (cosine terms)b Vector of B coefficients (sine terms)T "Period" of the FSA, equal to MAX - MIN (T is computed by the

fourier/pdf block)message Input message sequence (2 dimensional)

Parameters:samples Number of samples in data vectorpoints Number of plot points for MNTP Order of FSA

Outputs:g.val MNT of each data samplemnt Plot of MNT from minimum to maximum data value

See also:fourier/mnt.calc, fourier/pdf, vec/minmax ramp

Name:fourier/mnt calc

Description:This block obtains the Memoryless Nonlinear Transform (MNT) from a Fourier Series

Approximation (FSA) of a Probability Density Function (PDF). The MNT of each point of theinput message sequence is stored in the GVAL output.

A-20

This block operates on the magnitude of the two dimensional message signal.

Inputs:a Vector of A coefficients (cosine terms)b Vector of B coefficients (sine terms)T 'Period" of the FSA, equal to MAX MIN (T is computed by the

fourier/pdf block)message Input message sequence (2 dimensional)

Parameters:samples Number of samples in data vectorP Order of FSA

Outputs:g_val MNT of each data sample

Name:fourier/nonlin'


The histo/recto..polar block converts the two dimensional input signal from rectangular to polarcoordinates, and a histogram approximation of the Probability Density Function (PDF) of themagnitude is computed by the histo/histo block. The fourier/pdf block then constructs a FourierSeries Approximation (FSA) of the PDF based on the histogram. The fourier/mnt block obtainsthe Memoryless Nonlinear Transform (MNT) from the FSA PDF and applies it to the magnitudeof the input message sequence. The result is converted back to rectangular coordinates by thehisto/polar-to-rec block using the unmodified phase. The vec/ramp block computes thebreakpoints for plotting purposes.

Refer to the fourier/mnt block for more information on the MNT.

Inputs:i in In-Phase component of input message sequenceq_in Quadrature component of input message sequence

Parameters:samples Number of samples in input vectorsbins Number of bins in the histogram PDF

A-21

Outputs:pdf Plot of the FSA PDFitout In-Phase component of transformed sequenceqout Quadrature component of transformed sequencemnt Plot of the FSA MNTbp Breakpoints (PDF and MNT interval boundaries)

See also:fourier/pdf, fourier/pdf plot, fourier/mnt, histo/histo, histo/polar-to-rec,

histo/recto_.polar, vec/ramp

Name:fourier/pdf

Description:This block obtains the Fourier Series Approximation (FSA) of a Probability Density Function

(PDF). This FSA method is based on a histogram of the input data magnitude.

Inputs:bins Histogram PDFmin Minimum data valuemax Maximum data value

Parameters:samples Number of samples in data vectorP Order of FSA

Outputs:a Vector of A coefficients (cosine terms)b Vector of B coefficients (sine terms)T "Period" of the FSA, equal to MAX - MIN

A-22

Name:fourier/pdf.plot t

Description:This hierarchical block plots the Fourier Series Approximation (FSA) of a Probability Density

Function (PDF). A vec/minmaxramp block generates a ramp from the minimum to themaximum input values, and the fourier/pdfplot block computes the PDF approximation for eachpoint in the ramp.

Inputs:a Vector of A coefficients (cosine terms)b Vector of B coefficients (sine terms)T "Period" of the FSA, equal to MAX - MIN (T is computed by the

fourier/pdf block)message Input message sequence

Parameters:samples Number of samples in data vectorpoints Number of plot points for PDFP Order of FSA

Outputs:pdf FSA PDF

See also:fourier/pdfplot, vec/minmax ramp

Name:fourier/pdfplot

Description:This block plots the Fourier Series Approximation (FSA) of a Probability Density Function

(PDF). The PDF approximation is computed for each point in the input, which must be a linearramp over the desired plot range.

A-23

Inputs:points Input data vectora Vector of A coefficients (cosine terms)b Vector of B coefficients (sine terms)T "Period" of the FSA, equal to MAX - MIN (T is computed by the

fourier/pdf block)

Parameters:points Number of plot points for PDFP Order of FSA

Outputs:pdf FSA PDF

Name:fourier/s nonlin nct


applies it to the fourier/nonlin nonlinearity. This block does not generate the summation partof the LO decision statistic.

The romelib/timing block generates timing waveforms which enable and disable then,onlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLKOUT and HOLDVEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLK OUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the fourier/s nonlin nc block. The CLK OUT signal has the sameperiod as the CLK IN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the fourier/s nonlin nc block,and are used in serial to vector and vector to serial buffering.

The SAMPLES PER SYMBOL, NUMREFS, and MTYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr(" etype": model ,2, length(" mrtype": model)-2)& "_" &xstring("samples_per..symbol": model)&

A-24

"spbi'" for the I channel signals and "href/"&substr("m typeh":model,2,length(*m_type":model)-2) &"_"&xstring("samples_per symbol":model)&"spb_q'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spbi and /spwdata/ref/bpsk_25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the histogramsamples.pr symbol Number of samples per data symbolnum refs Number of reference signalsm-type Modulation type

Outputs:mnt Plot of the Memoryless Nonlinear Transformg Complex transformed sequence (vector)out Complex transformed sequence (serial)clk.out Timing signal: goes high when valid data sample is available at the output

of fourier/s nonlin nchold vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:fourier/nonlin, romelib/timing, rl/infvsource, fourier/serial nonlin

A-25

Name:fourier/serial nonlin'


applies it to the fourier/nonlin nonlinearity. In addition, the summation in the LO decisionstatistic is formed using the histo/correlator2 block. The output of the correlator is convertedback to serial form.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLKOUT and HOLD VEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLKOUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the fourier/serial-nonlin block. The CLKOUT signal has the sameperiod as the CLK IN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the fourier/serial nonlinblock, and are used in serial to vector and vector to serial buffering.

The SAMPLESPER.SYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr(" rtype ": model, 2, length(" mtype": model)-2)& "_"&xstring(" samples.persymbol": model)&"spb_i'" for the I channel signals and "ref/"&substr("m type":model,2,length('m type":model)-2) &W" &xstring(" samplespersymbol":rmodel)&"spbq" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spb_i and /spwdata/ref/bpsk_25spb-q.


Parameters:samples Number of samples in input vectorsbins Number of bins in the histogramsamplesjper symbol Number of samples per data symbolnum refs Number of reference signalsmtype Modulation type

A-26


of fourier/serial nonlinhold vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:fourier/nonlin, histo/correlator2, romelib/timing, rl/infvsource

A-27

Name:histo/avebp

Description:The histogram is defined only between breakpoints, -leaving values at the breakpoints

undefined. However, some of the polynomial curve fitting algorithms require knowledge of thehistogram values at the breakpoints. This function computes the values at the breakpoints byaveraging the values of the adjacent bins. The first and last values are taken to be the valuesof the first and last bins. The output "histogram" will have one more data point than the inputhistogram.

Inputs:in Input histogram


Outputs:"out Output "histogram"

Name:histo/correk .it )r2

Description:This block implements the matched filter - correlator for a two dimensional system. The input

reference signals, IREF and QREF, are assumed to have all possible signal pairs storedsequentially. The width of each signal is given by SAMPLESPERSYMBOL. The totalnumber of reference signals is given by NUMREFS.

Inputs:i In-Phase component of input message sequenceq Quadrature component of input message sequencei ref I-channel Reference symbolsq.ref Q-channel Reference symbols

Parameters:samples Number of samples in input vectorssamples.per..symbol Number of samples per data symbolnum-refs Number of reference symbols

A-28

Outputs:i decision Decision of In-Phase component of the messageq_decision Decision of Quadrature component of the message

Name:histo/enonlint


The histo/rec topolar block converts the two dimensional input signal from rectangular to polarcoordinates, and the data is sorted by the vec/heapsort block. An equiprobable bin histogramapproximation of the Probability Density Function (PDF) of the magnitude is computed by thehisto/equi block. The histo/mnt2 block obtains the Memoryless Nonlinear Transform (MNT)from the histogram and applies it to the magnitude of the input message sequence. The resultis converted back to rectangular coordinates by the histo/polar to rec block using the unmodifiedphase.

Refer to the histo/mnt2 block for more information on the MNT.

Inputs:i in In-Phase component of input message sequenceq_in Quadrature component of input message sequence


Outputs:pdf Equiprobable bin histogram PDFiLout In-Phase component of transformed sequenceq_out Quadrature component of transformed sequencemnt Plot of the Memoryless Nonlinear Transformbp Breakpoints (PDF and MNT interval boundaries)

See also:vec/heapsort, histo/equi, histo/mnt2, histo/rec-to_.polar, histo/polar-to-rec

A-29

Name:histo/equi

Description:This block generates an equiprobable histogram Probability Density Function (PDF) and an

equiprobable histogram Cumulative Distribution Function (CDF) of the input data sequence.Since The PDF and CDF are equiprobable, the probability of a data point falling in any bin isequal to I/BINS. THE INPUT DATA MUST BE SORTED IN ASCENDING ORDERBEFORE IT IS APPLIED TO THIS BLOCK.

Inputs:data Input data sequence (must be sorted in ascending order)

Parameters:bins Number of bins to generatesamples Number of samples in data vector

Outputs:bp Breakpoints (PDF and CDF interval boundaries)pdf Equi-probable bin histogram PDFcdf Equi-probable bin histogram CDF

Name:histo/histo

Description:This block generates a histogram Probability Density Function (PDF) of the input data

sequence. The width of each bin is (MAX-MIN)/BINS. The output is scaled so that the totalarea of the histogram is equal to 1.

Inputs:message Input data sequence

Parameters:message len Number of samples in data vectorbins Number of bins to generate

A-30

Outputs:bins Probability Density Functionmin Minimum data valuemax Maximum data value

Name:histo/mnt2t

Description:This block obtains the Memoryless Nonlinear Transform (MNT) from a histogram Probability

Density Function (PDF). It is a hierarchical block which contains a histo/mnt calc2 block anda histo/mnt-out2 block. The mnt-calc2 block computes the MNT, and the mnt out2 blockapplies the MNT to each data point of the magnitude of the input message sequence.

This block is a generalized version of histo/mnt iq; it has a breakpoint input so it may be usedfor a histogram with bins of arbitrary width. Thus, it may be used in conjunction with eithera histogram or an equiprobable bin histogram. The MNT of the K* histogram bin is

gK] 1I _ log(PDF[K+1])-log(PDF(K-1])BP[K] BP[K]-BP[K-1]

In the case of a one dimensional data signal, the I/BP(K] term is not included in g[K]. Fora two dimensional data signal, this block operates only on the magnitude.

The G PLOT output is the MNT computed for each histogram bin. Thus, the length of theGPLOT vector must be the same as the BINS vector. The length of the GVAL vector is thesame as the DATA vector.

Inputs:bins Histogram PDFbp Breakpoints (PDF and MNT interval boundaries)data Input message sequence (1 or 2 dimensional)

Parameters:bins Number of bins in the PDFsamples Number of samples in data vectordim Dimensionality of the message sequence (I or 2)

A-31

Outputs:gval MNT of each data samplegjplot Plot of MNT from minimum to maximum data value

See also:histo/mnt-calc2, histo/mnt-out2

Name:histo/mnt-calc2

Description:This function computes the Memoryless Nonlinear Transform (MNT)for a histogram with bins

of arbitrary width. The MNT of the K* histogram bin is

gK] I _ log(PDF[K*I])-log(PDF[K-l])

BP(K] BP[K]-BP[K-1]

In the case of a one dimensional data signal, the I/BP[K] term is not included in g[K]. Fora two dimensional data signal, this block operates only on the magnitude.

Inputs:bins Histogram Probability Density Function (PDF)bp Breakpoints (PDF and MNT interval boundaries)

Parameters:bins Number of bins in the PDFdim Dimensionality of the message sequence (1 or 2)

Outputs:g MNT for each histogram bin

A-32

Name:histo/mnt-calc_2d

Description:This function computes the Memoryless Nonlinear Transform (MNT) for a histogram with

bins of equal width. The MNT of the K* histogram bin is

gK(.] -Iog(PDF[K + 1 ]) -Iog(PDF[K- I])"R WIDTH

where WIDTH = MAX - MIN andR = MIN + K * WIDTH.

This block operates on the magnitude of the two dimensional data signal.

Inputs:bins Histogram Probability Density Function (PDF)min Minimum magnitude of input message sequencemax Maximum magnitude of input message sequence

Parameters:bins Number of bins in the PDF

Outputs:g MNT for each histogram bin

Name:histo/mnt-iqt

Description:This block obtains the Memoryless Nonlinear Transform (MNT) from a histogram Probability

Density Function (PDF). It is a hierarchical block which contains a histo/mnt calc d2 blockand a histo/mnt out block. The mnt-calc_2d block computes the MNT, and the mnt out blockapplies the MNT to each data point of the magnitude of the input message sequence.

This block assumes that each histogram bin has equal width. In addition, , input messagesequence is assumed to be the magnitude of a two dimensional signal. T71 &NT of the K*histogram bin is

A-33

gjf] I - log(PDF[K÷ 1])-log(PDF[K- 1])

K WIDTH

where WIDTH = MAX - MIN andR = MIN + K * WIDTH.

The G PLOT output is the MNT computed for each histogram bin. Thus, the length of theG PLOT-vector must be the same as the BINS vector. The length of the GVAL vector is thesame as the MESSAGE vector.

Inputs:bins Histogram PDFmin Minimum magnitude of input message sequencemax Maximum magnitude of input message sequencemessage Input message sequence (2 dimensional)

Parameters:bins Number of bins in the PDFsamples Number of samples in data vector

Outputs:g_val MNT of each data sampleg.plot Plot of MNT from minimum to maximum data value

See also:histo/mnt-calc_2d, histo/mnt out

Name:histo/mnt out

Description:This block applies the Memoryless Nonlinear Transform (MNT) generated by the

histo/mnt calc_2d block to each sample in the input message sequence. This block assumes thateach histogram bin has equal width. In addition, the input message sequence is assumed to bethe magnitude of a two dimensional signal.

A-34

Inputs:g MNT for input message sequencemin Minimum magnitude of input message sequencemax Maximum magnitude of input message sequencemessage Input message sequence (2 dimensional)

Parameters:bins Number of bins in the Probability Density Functionsamples Number of samples in data vector

Outputs:g_val MNT of each input sample

Name:histo/mnt out2

Description:This block applies the Memoryless Nonlinear Transform (MNT) generated by the

histo/mnt calc2 block to each sample in the input message sequence.This block permits the useof arbitrarily spaced breakpoints.

Inputs:,, MNT for input message sequencebp Breakpoints (MNT interval boundaries)data Input message sequence (I or 2 dimensional)

Parameters:bins Number of bins in the histogramsamples Number of samples in data vector

Outputs:gval MNT of each data sample

A-35

Name:histo/nonlin6t


The histo/recto..polar block converts the two dimensional input signal from rectangular to polarcoordinates, and a histogram approximation of the Probability Density Function (PDF) of themagnitude is computed by the histo/histo block. The histo/mnt iq block obtains the MemorylessNonlinear Transform (MNT) from the histogram and applies it to the magnitude of the inputmessage sequence. The result is converted back to rectangular coordinates by thehisto/polar to rec block using the unmodified phase. The vec/ramp block computes thebreakpoints for plotting purposes.

Refer to the histo/mntiq block for more information on the MNT.

Inputs:i in In-Phase component of input message sequenceq.in Quadrature component of input message sequence


Outputs:pdf Histogram PDFi out In-Phase component of transformed sequenceq_out Quadrature component of transformed sequencemnt Plot of the Memoryless Nonlinear Transformbp Breakpoints (PDF and MNT interval boundaries)

See also:histo/histo, histo/mnt iq, histo/rec-to_polar, histo/polar-to-rec, vec/ramp

A-36

Name:histo/polarto~rec

Description:This block accepts a complex vector in polar coordinates and converts it to a complex vector

in rectangular coordinates as follows:

I = R*cos(A)

Q = R*sin(A)

where R is the magnitude and A is the phase.

Inputs:mag Magnitude of input dataphase Phase of input data

Parameters:samples Number of samples in input and output vectors

Outputs:i In-Phase component of input dataq Quadrature component of input data

Name:histo/prob error'

Description:This hierarchical block computes the Probability of Bit Error (Pb) of a serial data stream.

The number of errors in both the I and Q channel are summed over SYMBOLS PER CALCdata bits in each channel. The Pb is equal to this sum divided by (SYMBOLSPER_CALC*2).

The CLOCK-IN control signal must go high when a sample is present at the input. Thissignal may be generated using the CLKOUT output of the romelib/timing block.

A-37

Inputs:i in Reference signal--I channeli dec Decision of receiver--I channelqcdec Decision of receiver--Q channelq_in Reference signal-Q channelclock in Clock enable

Parameters:symbolsjpercalc Number of symbols per Pb calculationsamplesper.symbol Number of samples per data symbol

Outputs:pe Probability of Bit Errorpe_clock Clock signal for Pb signal sink

Name:histo/recto.polar

Description:This block accepts a complex vector in rectangular coordinates and converts it to a complex

vector in polar coordinates as follows:

R = sqrt(I2 + Q^2)

A =atan(Q/I)

where R is the magnitude and A is the phase.

In the implementation of this block, the phase ranges from -pi/2 to 3"pi/2, instead of the usual-pi to pi. This makes it possible to avoid using an extra IF statement in the program. The twoforms are mathematically equivalent.

Inputs:i In-Phase component of input dataq Quadrature component of input data

Parameters:samples Number of samples in input and output vectors

A-38

Outputs:mag Magnitude of input dataphase Phase of input data

Name:histo/s enonlint


applies it to the histo/enonlin nonlinearity. In addition, the summation in the LO decisionstatistic is formed using the histo/correlator2 block. The output of the correlator is convertedback to serial form.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLKOUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the histo/s enonlin block. The CLKOUT signal has the same periodas the CLKIN signal, thus output samples are produced at the same rate as that of the inputsignal. The remaining romelib/timing signals are internal to the histo/s enonlin block, and areused in serial to vector and vector to serial buffering.

The SAMPLESPER SYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr("m_type": model,2, length(" mtype": model)-2)& "_"&xstring(' samples_persymbol": model)&"spbi'" for the I channel signals and "ref/"&substr("mtype":model,2,length("mtype":model)-2) &" "&xstring("samples_persymbol":model)&"spbq'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spbi and /spwdata/ref/bpsk_25spbq.


A-39

Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples_persymbol Number of samples per data symbolnum refs Number of reference signalsmtýpe Modulation type


of histo/s enonlinholdyvec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:histo/enonlin, histo/correlator2, romelib/timing, rl/inf vsource

Name:histo/s enonlin nct


applies it to the histo/enonlin nonlinearity. This block does not generate the summation part ofthe LO decision statistic.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLDVEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLKOUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the histo/s.enonlin nc block. The CLKOUT signal has the sameperiod as the CLKIN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the histo/s enonlin nc block,and are used in serial to vector and vector to serial buffering.

A-40

The SAMPLESPERSYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUMREFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr(" metype": model, 2, length(" in type": model)-2)&"_" &xstring(" samplespersymbol": model)&"spb i'" for the I channel signals and "ref/"&substr("m_type":model,2,length("m type":model)-2) &"_"&xstring("samples.persymbol":model)&"spb_q'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spb i and /spwdata/ref/bpsk.25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples_persymbol Number of samples per data symbolnumirefs Number of reference signalsie type Modulation type

Outputs:mnt Plot of the Memoryless Nonlinear Transformg Complex transformed sequence (vector)out Complex transformed sequence (serial)clkout Timing signal: goes high when valid data sample is available at the output

of histo/s enonlin ncholdvec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:histo/enonlin, romelib/timing, rl/infvsource, histo/s enonlin

A-41

Name:histo/s nonlin ncl


applies it to the histo/nonlin6 nonlinearity. This block does not generate the summation part ofthe LO decision statistic.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLKOUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the histo/s nonlin nc block. The CLKOUT signal has the sameperiod as the CLKIN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the histo/s nonlin nc block,and are used in serial to vector and vector to serial buffering.

The SAMPLES-PER SYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUMREFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr(" rtype": model, 2, length(" m type'": model)-2)&"_" &xstring(" samplesjper symbol": model)&"spbi'" for the I channel signals and "ref/"&substr("m type":model,2,length("m_type":model)-2) &" "&xstring('samples_per symbol":model)&"spb q'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spb_i and /spwdata/ref/bpsk_25spb q.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samplesj~erjsymbol Number of samples per data symbolnum refs Number of reference signalsm-type Modulation type

A-42

Outputs:mnt Plot of the Memoryless Nonlinear Transformg Complex transformed sequence (vector)out Complex transformed sequence (serial)clk-out Timing signal: goes high when valid data sample is available at the output

of histo/s-nonlin-nchold vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:histo/nonlin6, romelib/timing, rl/inf vsource, histo/serial nonlin

Name:histo/serial nonlint


applies it to the histo/nonlin6 nonlinearity. In addition, the summation in the LO decisionstatistic is formed using the histo/correlator2 block. The output of the correlator is convertedback to serial form.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLDVEC signal holds vector blocks while theserial-data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLKOUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the histo/serial nonlin block. The CLK OUT signal has the sameperiod as the CLK IN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to.the histo/serial nonlin block,and are used in serial to vector and vector to serial buffering.

The SAMPLESPERSYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/"&substr

A-43

("m_type": model,2, length( _type": model)-2)& "_&xstring(" samplesypersymbol": model)&

"Uspb_i'" for the I channel signals and uref/M&substr("m_typeM:model,2,length(t m_type":

model)-2) &" "&xstring("samplesjpersymbol":model)&"spbq'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk.25spbi and /spwdata/ref/bpsk.25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples.per.symbol Number of samples per data symbolnum refs Number of reference signalsmtype Modulation type


of histo/serial nonlinhold vec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:histo/nonlin6, histo/correlator2, romelib/timing, rl/inf vsource

A-44

Name:jam/channel*

Description:This block adds Gaussian noise and jammers to the transmitted data sequence. Currently only

three Continuous Wave (CW) jammers and a Partial Band (PB) are implemented. Any otherinterference blocks may be easily added. (All power parameters are measured in dB)

Inputs:in Transmitted Message

Parameters:JiS Ratio of First CW jammer power to signal powerphase l First CW phasefreq 1 First CW frequencyJ2_S Ratio of Second CW jammer power to signal powerphase2 Second CW phasefreq2 Second CW frequencyJ3S Ratio of Third CW jammer power to signal powerphase3 Third CW phasefreq3 Third CW frequency

JpbS Ratio of PB jammer power to signal powerfilt order Lowpass filter orderatten Passband ripple in dBpfreq Passband 3 dB edge frequencysfreq Stopband 3 dB edge frequency

EbNo Ratio of Bit Energy to Gaussian noise powerNo Gaussian noise power

sfreq Sampling frequencysamplesjperjsymbol Number of Samples per Information Symbol

Outputs:out Corrupted Message

See also:rl/cwjammer, rl/pbjammer

A-45

Name:linear/serial lint


applies it to the histo/correlator2 block. The output of the correlator is converted back to serialform.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLD VEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLK OUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the linear/serial lin block. The CLK OUT signal has the same periodas the CLKIN signal, thus output samples are produced at the same rate as that of the inputsignal. The remaining romelib/timing signals are internal to the linear/serial lin block, and areused in serial to vector and vector to serial buffering.

The SAMPLES PER SYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUMREFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as wref/"&substr("i _type": model, 2, length(" mtype ": model)-2)&" "&xstring(" samplesjpersymbol": model)&"spb i'" for the I channel signals and "ref/"&substr("m type":model,2,length("m type":model)-2) &"_"&xstring("samplesjpersymbol" :model)&"spbq'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk 25spbi and /spwdata/ref/bpsk_25spbq.


Parameters:samples Number of samples in input vectorssamples_persymbol Number of samples per data symbolnum refs Number of reference signalsrntype Modulation type

A-46

Outputs:out Decision of linear receiverclk out Timing signal: goes high when valid data sample is available at the output

of linear/serial finhold vec Timing signal: goes low when vector outputs are available

See also:histo/correlator2, romelib/timing, rl/inf-vsource

A-47

Name:mipalnonlint


The histo/rec_topolar block converts the two dimensional input signal from rectangular to polarcoordinates, and a MIPA of the Probability Density Function (PDF) of the magnitude iscomputed by the mipa/pdf block. The poly/mnt block obtains the Memoryless NonlinearTransform (MNT) from the MIPA PDF and applies it to the magnitude of the input messagesequence. The result is converted back to rectangular coordinates by the histo/polar-to recblock using the unmodified phase. The poly/plot block generates a plot of the PDF from thepolynomial coefficients.


Inputs:in In-Phase component of input message sequence

q.in Quadrature component of input message sequence


Outputs:pdf CPA PDFi-out In-Phase component of transformed sequenceq_out Quadrature component of transformed sequencerant Plot of the Memoryless Nonlinear Transformbp Breakpoints (PDF and MNT interval boundaries)

See also:histo/rec-to-polar, mipa/pdf, poly/mnt, poly/plot, histo/polar-to-rec

A-48

Name:mipa/pdf

Description:This block obtains the M-lnterval Polynomial Approximation (MIPA) of a Probability Density

Function (PDF). The MIPA is a concatenation of polynomial curves, which minimizes thesquared error between the approximation and the actual PDF. This implementation onlysupports 0th, 2nd, and 4th order MIPAs.

Inputs:message Input message sequence

Parameters:bins Number of binssamples Number of samples in input message sequenceorder Order of MIPA

Outputs:bp Breakpoints (PDF interval boundaries)coeff Polynomial coefficients values ao, a,, .. , a.

Name:mipa/snonlin nc*


applies it to the mipa/nonlin nonlinearity. This block does not generate the summation part ofthe LO decision statistic.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLKOUT and HOLDVEC signals. The HOLDVEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing completes and the outputs are available. The CLKOUT signalprovides flexibility for use in multirate systems by pulsing high when a valid data sample isproduced at the output of the mipa/s nonlinnc block. The CLK OUT signal has the sameperiod as the CLK IN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the mipa/s-nonlinnc block,and are used in serial to vector and vector to serial buffering.

A-49

The SAMPLES-PERSYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUMREFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/inf vsource block as "ref/l&substr("imtype ":model, 2, length(" m-type.":model)-2)&"_"&xstring("samples-per-symbo ":model)&"spbji" for the I channel signals and "ref/"&substr("m type":model,2,length("m_type":model)-2) &"-"&xstring("samples.pjersymbol":model)&"spbq'" for the Q channel signals.For example. the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk_25spbi and /spwdata/ref/bpsk_25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samples_persymbol Number of samples per data symbolnumrefs Number of reference signalsre type Modulation type

Outputs:mnt Plot of the Memoryless Nonlinear Transformg Complex transformed sequence (vector)out Complex transformed sequence (serial)clk out Timing signal: goes high when valid data sample is available at the output

of mipa/snonlin ncholdvec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also:mipa/nonlin, romelib/timing, rl/inf vsource, mipa/serial-nonlin

A-50

Name:mipa/serial-nonlin"


applies it to the mipa/nonlin nonlinearity. In addition, the summation in the LO decision statisticis formed using the histo/correlator2 block. The output of the correlator is converted back toserial form.

The romelib/timing block generates timing waveforms which enable and disable thenonlinearity and all subsequent blocks at appropriate times. Of particular interest are theCLK OUT and HOLD VEC signals. The HOLD VEC signal holds vector blocks while theserial data is buffered into vector form. This signal goes low during the simulation iteration inwhich the vector processing complees and the outputs are available. The CLK OUT signalprovides flexibility for use in multtate systems by pulsing high when a valid data sample isproduced at the output of the mipa/serialnonlin block. The CLK OUT signal has the sameperiod as the CLKIN signal, thus output samples are produced at the same rate as that of theinput signal. The remaining romelib/timing signals are internal to the mipa/serial nonlin block,and are used in sekal to vector and vector to serial buffering.

The SAMPLES-PERSYMBOL, NUMREFS, and M TYPE are characteristics of thereference symbols. The reference signals must be created before using this block, and are storedin the /spwdata/ref library. This permits the designer to use any desired signal constellation.The NUM_REFS parameter must be exported to the histo/correlator2 block, and the other twoparameters are exported to the filename of the rl/infvsource block as "ref/"&substr(" m_type": model,2, length(" m_type": model)-2)& " _" &xstring(" samples__per symbol":rmodel)&"spbi'" for the I channel signals and "ref/" &substr(" m_type":rmodel, 2, length ("m_type":model)-2) &"_"&xstring(" samples.per-symbol":model)&" spbq'" for the Q channel signals.For example, the filenames for a Binary Phase Shift Keying (BPSK) signal with 25 samples persymbol would be /spwdata/ref/bpsk 25spbi and /spwdata/ref/bpsk_25spbq.


Parameters:samples Number of samples in input vectorsbins Number of bins in the Probability Density Function (PDF)samplesper symbol Number of samples per data symbolnumrefs Number of reference signalsmrtype Modulation type

A-51


of histo/serial nonlinholdvec Timing signal: goes low when vector outputs are availablepdf Plot of the PDF of magnitudebp Breakpoints (PDF and MNT interval boundaries)

See also"mipa/nonlin, histo/correlator2, romelib/timing, rl/inf vsource

A-52

Name:poly/mnt t

Description:This block obtains the Memoryless Nonlinear Transform (MNT) from a polynomial

approximation to a Probability Density Function (PDF). It is a hierarchical block which contains

two poly/mnt calc blocks. One of them computes the MNT for each value of the magnitude Rof the input message sequence, and the other generates a plot of the MNT from the minimumto the maximum R value with the aid of a vec/minmaxjramp block. This block only operateson the magnitude of the input message sequence. For a PIb order polynomial the MNT is

g.[IR=I a, +2a2R +--÷PaPVR'

R ao+aR+a 2R2 +...apR P

If the LT parameter is set to 1, the linear transform will be applied to the coefficients. Thatmeans that the R values in the K' bin must range from 0 to the width of the K1 bin(BP[K]-BP[K-1]), whereas without the transform the R values in each bin will range fromBP[K-1] to BP[K].

Inputs:bp Breakpoints (PDF and MNT interval boundaries)coeff PDF polynomial coefficients values ao, a,, .. , apdata Input message sequence (I or 2 dimensional)

Parameters:samples Number of samples used to compute MNTbins Number of binspoints Number of plot points in GPLOTorder Polynomial order (number of coefficients - 1)it Linear transform flag

Outputs:gval MNT of input datag-plot Plot of MNT from minimum to maximum data value

See also:poly/mnt.calc, vec/minmax_ramp

A-53

Name:poly/mnt-calc

Description:This function computes the Memoryless Nonlinear Transform (MNT)from a polynomial

approximation to a Probability Density Function (PDF) for each value of the magnitude R of theinput message sequence. For a PI order polynomial the MNT is

grR] . I - a, +2a2R +'..PapR P'-

"R a,+aR+a2R2+...+arRiIn the case of a one dimensional data signal, the I/R term is not included in g[R]. For a two

dimensional data signal, this block operates only on the magnitude R.

If the LT parameter is set to 1, the linear transform will be applied to the coefficients. Thatmeans that the R values in the K" bin must range from 0 to the width of the K1 bin(BP[K]-BP[K-l]), whereas without the transform the R values in each bin will range fromBP[K-l] to BP[K].

Inputs:bp Breakpoints (PDF and MNT interval boundaries)coeff PDF polynomial coefficients values ao, a,, .. , adata Input message sequence (I or 2 dimensional)

Parameters:bins Number of binssamples Number of samples used to compute MNTorder Polynomial order (number of coefficients - 1)dim Dimensions of data signal (I or 2)It Linear transform flag

Outputs:mnt MNT for polynomial

A-54

Name:poly/mnt.calcgt

Description:This function computes the Memoryless Nonlinear Transform (MNT)from a polynomial

approximation to a Probability Density Function (PDF) for each value of the magnitude R of theinput message sequence. For a P1 order polynomial the MNT is

1 a, +2a2R+.'"PaR'-'gil= .=a,+atR+a2R 2÷+...÷+apR P

In the case of a one dimensional data signal, the 1/R term is not included in g[R]. For a twodimensional data signal, this block operates only on the magnitude R.

The first and last bins are fitted with the MNT of a Gaussian PDF instead of a polynomialMNT. THIS BLOCK IS TO BE USED IN CONJUNCTION WITH THE CPA/PDF GTBLOCK.

If the LT parameter is set to 1, the linear transform will be applied to the coefficients. Thatmeans that the R values in the K'" bin must range from 0 to the width of the KI1 bin(BP[K]-BP[K-1]), whereas without the transform the R values in each bin will range fromBP[K-l] to BP[K].

Inputs:bp Breakpoints (PDF and MNT interval boundaries)coeff PDF polynomial coefficients values ao, a,, .. , apdata Input message sequence (1 or 2 dimensional)

Parameters:bins Number of binssamples Number of samples used to compute MNTorder Polynomial order (number of coefficients - 1)dim Dimensions of data signal (I or 2)It Linear transform flag

Outputs:mnt MNT for polynomial

A-55

Name:poly/mnt..gt t

Description:This block obtains the Memoryless Nonlinear Transform (MNT) from a polynomial

approximation to a Probability Density Function (PDF). It is a hierarchical block which containstwo poly/mnt calcgt blocks. One of them computes the MNT for each value of the magnitudeR of the input message sequence, and the other generates a plot of the MNT from the minimumto the maximum R value with the aid of a vec/minmax ramp block. This block only operateson the magnitude of the input message sequence. For a pI order polynomial the MNT is

I a,+2a2 R+'"÷ePapRt'-PR ao+aR+a1 R2÷...÷.aR'

The first and last bins are fitted with the MNT of a Gaussian PDF instead of a polynomialMNT. THIS BLOCK IS TO BE USED IN CONJUNCTION WITH THE CPA/PDF GTBLOCK.

If the LT parameter is set to 1, the linear transform will be applied to the coefficients. Thatmeans that the R values in the K' bin must range from 0 to the width of the K' bin(BP[K]-BP[K-1]), whereas without the transform the R values in each bin will range fromBP[K-11 to BP[K].

Inputs:bp Breakpoints (PDF and MNT interval boundaries)coeff PDF polynomial coefficients values ao, a,, .. , a,data Input message sequence (1 or 2 dimensional)

Parameters:bins Number of binssamples Number of samples used to compute MNTorder Polynomial order (number of coefficients - 1)It Linear transform flag

Outputs:

g val MNT of input datag-plot Plot of MNT from minimum to maximum data value

See also:poly/mnt-calcgt, vec/minmax ramp

A-56

Name:poly/plot

Description:This function plots a piecewise polynomial curve with the number of intervals equal to BINS.

The polynomial in each interval is of the form

y[X] =a,+aX+a2X 2i...+apx

where P is the ORDER. The X value is varied from its minimum to maximum value to generatethe plot. The number of points in this plot is equal to POINTS.

If the LT parameter is set to 1, the linear transform will be applied to the coefficients. Thatmeans that the X values in the K' bin must range from 0 to (BP[K]-BP[K-1]), whereas withoutthe transform the X values in each bin will range from BP[K-1] to BP[K].

Inputs:bp X-axis Breakpoints (interval boundaries)coeff Polynomial coefficients values ao, a,, .. , ap

Parameters:bins Number of binspoints Number of points to plotorder Polynomial order (number of coefficients - 1)it Linear transform flag

Outputs:plot Polynomial curve

Name:poly/plot-gt

Description:This function plots a piecewise polynomial curve with the number of intervals equal to BINS.

The polynomial in each interval is of the form

y[X] =au~aX+a 2X2 +...+apx '

A-57

where P -.s the ORDER. The X value is varied from its minimum to maximum value to generatethe plot. The number of points in this plot is equal to POINTS.

If the LT parameter is set to 1, the linear transform will be applied to the coefficients. Thatmeans that the X values in the K* bin must range from 0 to (BP[K]-BP[K-1]), whereas withoutthe transform the X values in each bin will range from BP[K-I] to BP[K].

The first and last bins are fitted with a Gaussian PDF instead of a polynomial.

Inputs:bp X-axis Breakpoints (interval boundaries)coeff Polynomial coefficients values ao, a,, .. , ap

Parameters:bins Number of binspoints Number of points to plotorder Polynomial order (number of coefficients - 1)It Linear transform flag

Outputs:plot Polynomial curve

A-58

Name:rl/complex.cwt

Description:This block generates a single Continuous Wave (CW) complex sinusoid with a specified

amplitude, frequency, and phase.

Inputs:none

Parameters:amp CW amplitudephase CW phasefreq CW frequencys_freq Sampling frequency

Outputs:cw out Jammer output

Name:rl/complex datal

Description:This block generates a random Quadrature Phase Shift Keying (QPSK) data sequence. A

fundamental relationship exists between the symbol rate and the sampling frequency, namelyS FREQ = Rs * SAMPLESPERSYMBOL. This means that all three of these parametersmay not vary independently, but one must be a function of the other two. For this reason, thesymbol rate parameter is exported as Rs = S FREQ / SAMPLESPERSYMBOL.

Inputs:none

Parameters:amp Bit amplitudeRs Symbol rateprobzero Probability of a bit being zeros_freq Sampling frequency

A-59

Outputs:data out QPSK data stream

Name:rl/cwjammert

Description:This block generates three Continuous Wave (CW) jammers with specified amplitude,

frequency, and phase. Any number of CW jammers up to three may be obtained by setting theamplitude of the undesired jammers to an arbitrarily small value.

Inputs:none

Parameters:ampl First CW amplitudephase l First CW phasefreq 1 First CW frequencyamp2 Second CW amplitudephase2 Second CW phasefreq2 Second CW frequencyamp3 Third CW amplitudephase3 Third CW phasefreq3 Third CW frequencysfreq Sampling frequency

Outputs:cw out Jammer output

See also:rl/complex cw

A-60

Name:rl/hold*

Description:This block generates an output that goes high every SAMPLES iterations. There is no pulse

on the Oth iteration.

Inputs:none

Parameters:samples Number of iterations between pulses

Outputs:hold Output clock

Name:rl/inf vsourcet

Description:This block is identical to the spb/vsource SPW library block except that when an end of file

(EOF) occurs the last output is retained for the remainder of the simulation. This block detectsthe EOF from the spb/vsource and holds the spb/vsource from then on.

Inputs:none

Parameters:same as spb/vsource

Outputs:same as spb/vsource

See also:spb/vsource

A-61

Name:rl/pb jammert

Description:This block generates a baseband Partial Band (PB) jammer by low pass filtering Gaussian

noise with an elliptic lowpass filter. The Passband and Stopband edge frequencies are assumedto be normalized by the symbol rate.

Inputs:none

Parameters:JpbS Ratio of jammer power to signal power in dBflit order Lowpass filter orderatten Passband ripple in dBpfreq Passband 3 dB edge frequencysfreq Stopband 3 dB edge frequencys_freq Sampling frequency

Outputs:pb out Jammer output

Name:rl/psk err cntt

Description:THIS BLOCK DOES NOT WORK CORRECTLY BECAUSE COMM/REALERRCNT

DOES NOT WORK CORRECTLY.

Inputs:X Actual transmitted messageY Decision of receiver

Parameters:

A-62

Outputs:pe Probability of errornumsymbolsresults clk

See also:rl/real err cnt

Name:rl/real err cnt"

Description:THIS BLOCK DOES NOT WORK CORRECTLY BECAUSE COMM/REALERRCNT

DOES NOT WORK CORRECTLY.

Inputs:X Actual transmitted messageY Decision of receiver

Parameters:

Outputs:pe Probability of errornumsymbolsresults clk

See also:ri/real err cnt

A-63

Name:romelib/timing t

Description:This block generates the timing signals for the nonlinear receiver and all subsequent blocks.

In particular, it allows for serial-to-vector conversion of the input data to the nonlinearity blocks,and vector-to-serial conversion at the output. The CLKIN input is provided to facilitate theintegration of the nonlinear blocks into multirate systems. This input should be tied to a timingsource which goes high on every simulation iteration caring which a valid input data sample ispresent. The only parameter for this block, SAMPLES, should be set to the length of the datavector which will be processed by the nonlinear block.

The sequence of output signal states is as follows:a) The HOLD IN output goes low every iteration that the CLKIN input goes high and

indicates when a valid input signal sample is present.b) The LOADOUT output goes high during the simulation iteration when the last of the

SAMPLES samples is available at the input. This is a signal to the circular-buffer blockthat all the required data samples are present and that the data vector is complete.

c) The HOLDVEC output goes low one simulation iteration after the last of the SAMPLESsamples is available at the input. This signal should be tied to the HOLD input of thenonlinearity blocks as well as all vector output sinks/blocks associated with thenonlinearity block, allowing these blocks to go active during the simulation iterationwhen all the required data samples are present in vector form.

d) The LOADIN goes high one simulation iteration after the last of the SAMPLES samplesis available at the input. This signal is used to "latch" the output signal vector of thenonlinearity block for vector-to-serial conversion.

e) The HOLD-OUT signal goes low one simulation iteration after each iteration when theCLKIN input goes high. This signal is provided for clocking the serial blocks locatedafter the nonlinearity block.

f) The CLK OUT output first goes high on the same simulation iteration as theHOLD_ VEC output goes low and the LOADIN output goes high, and then it periodicallygoes high after this with a period equal to that of the CLKIN input signal. TheCLK_OUT signal is used to indicate when a valid serial data sample is present at theoutput of the nonlinearity block.

Inputs:clk_in Synchronizing clock input

Parameters:samples Length of input data vector

A-64

Outputs:hold in Activation signal for serial blocks preceding the nonlinearity blockloadout Indicates when input data vector has been filledhold vec Activation signal for the vector processing/output blocksloadin "Latches" the output data vector for vector-to-serial conversionholdout Activation signal for serial blocks following the nonlinearity blockclk out Synchronizing clock output

A-65

Name:vec/heapsort

Description:This block heap sorts the input data in ascending order. This sort is of order N log (N). For

a description of the heap sort algorithm see Numerical Recipes in C (1988).

Inputs:in Input vector

Parameters:points Number of points in the vector

Outputs:out Sorted vector

Name:vec/minmax

Description:This block finds the minimum and maximum data points in the given data sequence.

Inputs:in Input data vector

Parameters:length Number of points in input vector

Outputs:min Minimum valuemax Maximum value

A-66

Name:vec/stretch nl

Description:This block plots a histogram by copying the value of each bin to the output a number of times

that is proportional to the width of the bin. The total width of the histogram is T WIDTH =BP[BINS] - BP(0], and the width of the K' bin is WIDTH[K] = BP[K] - BP[K-l]. The K* binvalue is copied to the output N times, where N = POINTS * WIDTH(K] / TWIDTH.

The number of breakpoints is one more than the number of input points.

Inputs:bp Breakpoints of histogramin Input histogram

Parameters:bins Number of bins in the input sequencepoints Number of points in the output sequence

Outputs:out Plot of histogram

A-68

Name:vec/minmax-ramp t

Description:This block generates a linear ramp of length RAMP LEN from the minimum to the maximum

values in the given data sequence. If RAMP LEN = I it is not possible to generate a linethrough both min and max unless min = max. In the event that RAMP-LEN 1 1, RAMP isset equal to the average of min and max.


Parameters:data-len Input data vector lengthramplen Ramp vector length

Outputs:ramp Output ramp

See also:vec/minmax, vec/ramp

Name:vec/ramp

Description:This block generates a linear ramp of length POINTS from MIN to MAX. If POINTS = 1

it is not possible to generate a line through both MIN and MAX unless MIN - MAX. In theevent that POINTS = 1, the ramp is equal to the average of MIN and MAX.

Inputs:min Minimum data valuemax Maximum data value

Parameters:points Ramp vector length

Outputs:ramp Output ramp

A-67

Name:vec/var

Description:This block computes the mean and variance of the input data vector as follows:

Le4-1 LEN-I

MEAN iN[i] VAR- = F (IN[if_-MEAN)2MEAN = L .LENE- I V.A


Parameters:len Input vector length

Outputs:mean Mean of the input data sequencevar Variance of the input data sequence

A-69

Appendix B

SPW Block Diagrams

This Appendix is an alphabetical listing of the details of the hierarchical IIT SPW blocks

that were used to generate the results in Volume I of this report.

When the BDE prints a block diagram, the parameters do not reflect their exported

values. Rather, the default values for these parameters are displayed. However, in the actual

simulation the parameter values have all been correctly exported.

B-I

CPA/CDF2

I.

LIa. 1-LLJ

w 0U

L L _r4) a)-- . - , -

c L L L0 0 0

SE Ex 0 00 C cL rz DI J.0. L c- a0. 0 0 0 C 0

<C CL CL 0 -J o0

LL -LL C I£ (- C 0

L L) a.

0 a) a)C L .C -C T

- a)0 c

0~0o -J

0c

00

U 03

h/ia)(I U

0. Li0uCu

E= C (Uj 13

C)

Figure (B-i)

CPA/CDF2-NONUIN

4: ILo U;

00

2%-J 0 ! 2

oo0

0

Q.0U

ILIUU

a. -9

cu

CL -A Car

w -- 0 ItA .l CL A c V 0

____ _M_ _fix

Figure (B-2)

CPA/CDF3

- -_ t .UU

c L L SL

c L L .

0 0 0- L

E E /

X X 0 0 610C C C0. -- -- _

nL Ul 0 0 a

O000-LL LL L.

U C

-- 0 02

-P

0 -

C0j .. V

-L00 __ _

CO

0 m 2

o€

Q.

LL

L) U)

E C (

m, .- 0

Figure (B-3)

CPA/CDF3 NONLIN

Iw

' o

z0

o b L

0 5 t

* C.

y-.

a...

UU

CL(U

C~ ~ 0Jj0

-o jo C. I L

Figure (B34)

CPA/PDF-GT

U 0#2

LL

L

c Lu

o 0 C

0U ID w

L 0n

0. tn0

- 0.

0

In

0

C

0 C

tn

CL

IDInfl

09 V

CLa.0

Figure (B-5)

CPA/PDF GTNONLIN

II

m~ Vl

coL

(Dc

I I- t-J I

o: a - -c (

.0- __

(U

Figurer (B-6

(0(U~~ LL.CDL

a-

<I:

CL 001

-A -vi-

II

T. Ixl I

Figure (B-6)

CPA/SCDF2_NLNC

I.-

10*

cou

00c 0)

II It ,"

'A. 0 a.

(D w

c w

4-

C*CL0o

C 00

Fu (

c-cw-j

Ciue Bo

CPA/SCDF2_NONLIN

g0

LL

111o

la q.

I I'0 -

a.aL ,

C -

FrB

z 0

- -

ai.C1

a-°

S s

Fiur (B-8)

CPA/SCDF3_NLNC

13

og U.,_.;

#A a 0

- xl L

III

r UJ

(LB

2-

ta. (..,C

o -

SC --a- (6.

aca

01

Fgr.. (B-9

)cc-

Zi i o

- 7!!Fiue 49

CPA/S CDF3_NONLLN

j9.

w. as

9 tt•

•" zi

g ! II

0 00

CC

C.)

C .1

F-ig

, UI

Figure (.B. ()

CPA/S PDF GT NL NC

10

€. .

Uxl

U.,

00 0

c 0~

co

•0 --

0 0 a

.x L L .

inILUM o

a.) 0.

Co

C C•- a

0] . ii- iCC

15 UigB1

Fiue(Bo1

CPA/SPDFGTNONLIN

lo

LLL

a m

Ja

IftU

- 0I

M j-• L

cc

0 Ii C

I .CL

Fu (

Fiue(1-2

FOURIER/MNT

cuS

0 0)

$

ol ol*

x

--"i I.'_

C.)CLUL

_ 0

Lo

0.

L JL L:3__ E 0 LR

0 w o -(r a- 0

L - LQ. 4- -

0 0 .

0L LCD CD L

.0 .0 0D

n Lz z

ým 10

Figure (B-13)

FOURIERINONLIN

- -

f i

j V

CL

*!

I

10 230

g ol

0

t o o - o

CL--

00

o In

Figur (B 1)

0 a.

0n 0 0 L

L I D

F (

FOURIER/PDF PLOT

Co

0 "

r'l

CL~

a) L

E (

L in o

(D .. CL )

Ol. -a

SE 0 L_) O 0_ 0

I::] 4- 4- lJ

.2 ooU)

0 - ( 0

CL-

-- ( -(1 (_ a) 0S.. L. L .

"Q.: z z 0 .U) -

Q - 0

L ".

L~L

0

(4-0

.LX.

z\

Figure (B-15)

FOURIER/SNONLINNC

1*(

I it!00

0 A a

a

LL

a. 8

o - 0

S Wi

coo

"00.

C. ,,Xi S

CC

FrB

Fiur-B-6

FOURIER/SERIAL NONLIN

CDu

g.i

~I.-

d ILA-

CD

U)

LL.

i I

Figure (B-1'7)

HISTO/ENONLIN

II i "

11 0

9U'

~0

' .i

0 LL- 0

L

a)•I

-c~c c

0.0,

#A,cU

Figure(B- 18

Fiur CL IA (D

-~~~ ~ AS Ev ,I n••IlIIIl n I I m im o i

HISTO/MNT2

D

CLu6 M

__ CD

Cu

-'I- " I-

0u Cf0'

C L -1

E E

4-- (4,(40- 0~ .0 -

r~~F- <r:- C

L. L )UO

• -- • , U-l,

In C. a

C E E

• 7 Z "zY'ot

o oto

Figure (B-19)

L L L J~)_i

HISTO/MNTIQ

2e0 L.

0

Q .-

E000.2

o -

C -

8 ® -

0- -

*0CL

4. C.-

010.

ou0uC 0

CO

0n L

0-4r00

00

- 0 00 €

L-

W CC

,C -

t-0

Figure (B-20)

I IIF II I I II I II I0

HISTO/NONLIN6

v 0

z

=(UU

131

(S))

W UL CD

r0

-m g I

rn •"

-• o m

m __ -€

2 (4-

WWO %0 1 L

CC

UzzLA2

Cu 0

Figure (B-21)

fi i.

LAI

HISTO/PROB..ERROR

.00

0 LN

U 0)0U

L L

20

nr0

Ln

Fiur (B-22

HISTO/SENONLUN

-Iu

''

4 0,!

M590)

W a 0

O4 (I t I-

0

IoC

3 LU 0

Fiur (,

e-

- 0)

'ii - - I

Figue (-23

HISTO/SENONLINNC

-, nC-

00

CDu

o i

IA

6II

0 -0

II

ca us

(D. 0

C W

IL

C 0oA 3,

wPLb

Fiue(-4

HISTO/SNONLINNC

LIL

U'

III!i,-

I-.. -

o U

0 O 0

z

(az 1 A1 1

Lo

aa

.~.00

I-i

-oj

IAw IliU

Fiue(-25)

HISTOJSERIALsNONLIN

ii

co' I I

F ("- ow.

(.3 iFiue(1-6

JAM/CHANNEL

,ti'a

XE

-i C-

(Lod

L9.

0ý0

40)

W "pz to -

SR i o!

U0 Ui (Ac a S "

I-

U\

LA V

.0i

Wi r -

c- -3LL I -7 . 0. U. .

C -

Fiur B-7

LINEAR/SERLALjLIN

I Id

+ ,,,

usu+O i -

t U0

LCD

cD gym0

L.. IL b 8

lij iiiC j

-J !.

S++++U

!i: i" •i~~it

10Figure'L (B2

MIPAINONUIN

10A~

cu

CLC

0 -J

o z- 0- a.

L

0z

o CL

(M CDL

2C *-MO 0 L C

Figure (B-29)

MIPA/SNONLINNC

Ui LU

L

-C

tI.

0 0 a

Ui -j I

r6-

Ai

t: R

_g_2X

Fiur ( i

Figure (B-30)

MIPA/SERIAL NONUIN

],u

MWM

W; a

0 0

o'U 0 -I

- I.I

II

_u (B-3 1)

1, C

Figure (B-31)

POLY/MNT

-j 8

0. z

0

LL x

CL~

O-2

VE

.C4.

Sl 0

o 4- i- •- -v c_ U._

u•n -a o •

Figure (B-32)

POLYIMNTGT

U (8

-iI /j

_ I_ _D_ =j -

0 m. 2.

o 0- C

O.A-'4. U_.---

w 1- . 0 -

C-)-

O. - -"__ _-w *0

S-r CD-D 0

CDur (B-3)C

'4.)

E06 L

U.I 00) .. (4-.

- as 4-I- L. UA0.- hi c a) c 0E c - - 0COMU - 0 L L

Figure (B-33)

RL/COMPLEXCW

a,N4

xwL~ Lii -

a) i

CLC

r- c u

L -I-

0-

C)C:(DL

(4-L

(Dur ((-U

a))0--

0IIr

0~0L a L

o 0. -

VE L )iDc

Fiur (B34

RL/COMPLEXDATA

0)

cu

wt W

II

T CL

00

SN • m

x

"w WM

-T T

a 0L-

LU N

0 (D

0 0 0

70 0 D

LL

x 4: 0 w

lo w

CL 0 2 nZ . - L (D

E ~x

SC r a! C I.-i (B- 3J

xx

Figure (B-35)

RL/CW-JAMMER

(n0

s 0) 0

0 . -9 -.- -% 0- 0

00

r) L) ..- -r a

xC) 00

U C) U

0 c *U.

C )

U, 0-, a_

ww

x -

a.-

0 nil 0:3

U2

Figure (B-36)

RL/HOLD

0

CDC

IA-

0

Il 2

((D .2C

00Sz-37)

E o

I -

1

Figure (B-37/)

RLIINF-VSOURCE

- a.

Lu -

W UU

=. L

C 3 6- CLS

0 UCo (r U0 .- 0

0 - CL IA

U ~ ~ 5-'w* CC

300

V (3 L U geI&wc0

000

0- -qn cn

0 C L)

* 0 0 -

c

D co 0*-l )

LaFigLure(B-8

RLJPBJAMMER

0

.c0

Og.

0

,,, ....CDu

CD .. O C. a.

CD CsSOJ OJ CDo

(/) .C

L.I 0 0• ._

LiiL

N NWC.T x -

CD (Dr c c- a.

3. -- .-D v) = aU C CL D) D CO

0 M 0

D- elL c 0' z0(D . 0

id D L=L c(1 .LL LL - a)

" "C w _- a) a)0 D .- -0 -0 L •

-LQO aUj U) LCL L133 Z " r, W .JW Li_

D1 .. L .

c 0D O0 0 -0 Xx Co c cc ac LW W3 w0. .- L M W M . QI I---- 0

(_1 V)Lt. . 0.. 0C

J-UOWO

o (- U-' Z -

U (LOLL L L oLO 0 z

IS

IFigure (B-39)

RL/PSK ERR CNT

CA-IJi! i

'/t'J

iLi

_ _ I

8 ---. -J

(DI

Fr (

I-'3o z%

Fiur-('0

RL/REAL ERR CNT

-,C

CLr5-

0-4 :D

0 *

* N U

ZL U

igr (

x. WC..

X jc

N *~ is

x 31

rL

~L

Fiur B-1

ROMELIB/T[MING

a c8cu

1P• - -

- 'ai1 C

#0

U

Fiue(-2

VEC/MINMAXRAMP

CL' -.,

nE

C.

G 0

O0 OD

fD c-

x

0

-C

X(.U

nm

\/cor ( 0

CD O:ý -

-igur (B-43

ROME LABORATORY

Rome Laboratory plans and executes an interdisciplinaryprogram in research, development, test, and technologytransition in support of Air Force Command, Control,Communications and Intelligence (C31) activities for allAir Force platforms. It also executes selectedacquisition programs in several areas of expertise.Technical and engineering support within areas ofcompetence is provided to ESC Program Offices (POs) andother ESC elements to perform effective acquisition ofC31 systems. In addition, Rome Laboratory's technologysupports other AFMC Product Divisions, the Air Force usercommunity, and other DOD and non-DOD agencies. RomeLaboratory maintains technical competence and researchprograms in areas including, but not limited to,communications, command and control, battle management,intelligence information processing, computationalsciences and software producibility, wide areasurveillance/sensors, signal processing, solid statesciences, photonics, electromagnetic technology,superconductivity, and electronicreliability/maintainability and testability.

Date post:	15-Apr-2020
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

SIllllllll~lUl l ((1li · The most important system parameter relationships in this report are...

Documents