Concept of Software Deﬁned Electronics (SDE): A ...

Geza Kolumban Pazmany Peter Catholic University, Budapest, Hungary

Concept of Software Defined Electronics (SDE):A Revolutionary New Approach for Researching, Building

and Teaching of ICT Systems

Geza Kolumban, Fellow of IEEE, IEEE CAS DLP (2013-14)

Pazmany Peter Catholic University, Faculty of Information Technology, Budapest, Hungary

Adjunct Prof. at Edith Cowan University, Perth, Australia

Ultimate goals:

• Implement every application in SW

• Substitute RF/microwave/optical analog information processing with a low-frequency digital

one and assure the use the lowest sampling rate attainable theoretically

• Use a universal, i.e., an application independent HW device for the transformation

• Use a unified theory everywhere from education to scientific research, from prototyping to

mass production

• Provide step-by-step design rules

• In short: Change the paradigm of teaching, researching, prototyping and manufacturing ICT

systems

ISCAS 2018 PM8 Tutorial, May 27, 2018 Software Defined Electronics (SDE): Page 1


Motivation

(1) TURN YOURMATLAB/LabVIEW/C++/etc SIMULATOR INTO REALWORKING

SYSTEM

• To verify your new idea in real field tests performed by stand alone microwave test equipment

• Evaluate the performance of your new system in a real application environment

• Make prototyping of a new research results easy

(2) SOLVE MAIN CHALLENGES IN OPTICAL/MICROWAVE/RF ENGINEERING

1. High carrier/center frequency requires an extremely high sampling rate

2. To assure high Signal-to-Quantization-Noise Ratio (SQNR), a high resolution and high

speed analog-to-digital converters are required

SQNR ≈ 20 log10(2Q) = 6.02 × Q dB

where Q is the number of quantization bits

(3) IMPLEMENT ALL APPLICATIONS NOT IN HARDWARE BUT IN SOFTWARE



Key issues of SDE concept

• Integration of many subjects into one solution

– Equivalent BB signal processing (mathematical background)– Software defined radio– Virtual instrumentation– Use of OSI BR model developed in computer science and VISA architecture

elaborated in measurement engineering

• Universal HW device is used for transformation

• Integration of different SW platforms into one application

• Implementation as a system embedded into a computing environment

• Exploit idea of HW-SW co-design

• Transformation of the already known and proved HW solutions into SW

An engineering-based approach



What is new in SDE concept?

1. Integration of many many subjects into one unified framework• Theory of complex envelope, mathematical background

• Software Defined Radio (SDE)

• Virtual Instrumentation (VI)

• Embedded operation

2. Concept of equivalent baseband transformation• It offers a unified theory for the design of all RF bandpass systems

• Instead of a case-by-case solution, SDE offers a general and systematic approach

• Transformation is performed by universal application-independent HW devices

3. Implementation and derivation tool• Systematic way for the derivation of BB equivalent

4. A new way of researching, teaching, developing, manufacturing and main-taining of ICT systems. A complete change in ICT paradigm where focus isshifted from circuit design to system level and SW-based approach



Opinion at Stanford

Background required

1. RF circuit & system design

2. Digital signal processing

(DSP and FPGA)

3. Networking

4. + Virtual instrumentation

Main goal of my talk: Elaborate a unified comprehensive framework which pro-vides a systematic approach for the analysis and design



Once upon a time two books written by four GREAT PROFESSORSreshaped our profession completely (1975)

Oppenheim – Schafer Rabiner – Gold

These books provided a comprehensive theory for digital signal processing



Slogan: From education to research, from product development to mass production

Key issues to be discussed:

2 Theoretical background2.1 Concept of complex envelopes

2.2 Derivation of BaseBand (BB) equivalents

3 Key HW component: The universal RF hardware device(Transformation between the analog RF bandpass and digital low-pass BB domains)

4 Embedded operation of universal HW transformer

5 Applications of equivalent baseband information processing5.1 Computer simulations

5.2 Industrial applications

5.3 Application in scientific research

6 Conclusions and acknowledgements



Slogan: From education to research, from product development to mass production

Contents:

1 Motivation and a new way of teaching and researching ICT systems











1 Motivation and a new way of teaching and researching

ICT systems

MOTIVATION:

• Research and prototyping:Universal testbeds are required that offer a very high level of flexibility

• Mass production:Implementation in SW running on the same HW platform

• Education:Should follow this trend, emphasis should be placed on

– system level engineering and– SW-based approach because HW industry is concentrated in a very few

places



TOPICS TO BE DISCUSSED:

1.1 Why SDE?

1.2 Example: Teaching waveform communications via hands-on examples

Classroom demonstrations with a laptop and two USRP units

Application of SDE concept in scientific research will be discussed later



1.1 Why SDE?

(Only the most important reasons)

• Today theory and practice are almost completely separated in teachingand researching ICT systems

• The time is never enough in education and research, we always have verylimited financial resources

• Multifunctionality can be implemented, an important issue in cognitive radioand adaptive systems

• Make changes easy: a very important requirement in research and prototyping

• Reduce the required time to market in industry

• Reconfiguration of already deployed systems can be performed

• · · ·



1.2 TEACHING WAVEFORM COMMUNICATIONS VIA

HANDS-ON-EXAMPLES

Three levels:

(a) Simulation at system level to support the theoretical discussions– Simulation of a BPSK system

– Simulation of a M-ary QAM system

(b) Study of a working radio system and measurement equipment– FM radio receiver with a built-in spectrum analyzer

– RF spectrum monitoring

(c) Study, implementation and testing of a complete radio link– M-ary FSK transmitter

– M-ary FSK receiver

– M-ary FSK radio link

SDE implementations used in the demonstrations have been developed and/or modified by me,

Tamas Krebesz (my PhD student) and National Instruments



Simulation of a BPSK system

(Only system level simulation, not an implementation)

From left to right, upper

row

• Tx output spectrumin RF frequency do-

main

• Noisy received signalin AWGN channel

• Received signal intime domain

From left to right, lower

row

• Noisy received signalat the output of Rx

channel filter

• Eye diagram

• Constellation dia-

gram



Simulation of an M-ary QAM system

(Only simulation. For explanations refer to the labels on the Front Panel)



Insight into the SW side of equivalent BaseBand (BB) implementation

Part of the block diagramof M-ary QAM simulator

where in the complex waveform

• t0 is the start time of waveform (timestamp)

• dt is the time interval elapsed between two consecutive data points, i.e., sampling

time

• data values of waveform, i.e., the real and imaginary parts of complex envelope

Theory of complex envelopes will be discussed in the next section



FM radio receiver with a built-in spectrum analyzer

(Note the dual functionality: A working FM receiver and a spectrum analyzer)



RF spectrum monitoring

(A working implementation where a USRP unit is used to extract the complex envelope)

• Real (I) and imaginary

(I) components of com-

plex envelope are shown

in white and red, re-

spectively

• Note, the duration of

windowing can be set

by the number of Sam-

ples/Frame

• Red line in the Inten-

sity Chart gives the time

instant where the BB

Spectrum of Received

Signal is plotted



A working 4-FSK transmitter with Gaussian Tx filter



A working 4-FSK receiver



Contents:












2 Theoretical background (Part 1)

2.1 Concept of complex envelopes

Goals of equivalent baseband transformation:

• Reduce sampling frequency to its theoretically attainable minimum value

IN SUCH A WAY THAT

• preserve all information available in the original signal without any distortion

• Substitute high-frequency analog signal processing with low-frequency digital one in baseband

Properties of baseband equivalents:

• Each bandpass signal (either deterministic or random) and each bandpass system can be

fully represented by its complex envelope and its complex impulse response, respectively, in

baseband

• RF bandpass analog signal processing can be done in the BaseBand (BB) using low-frequency

equivalent baseband circuits

• RF bandpass analog signals can be fully recovered from the complex envelopes



Elements of system level analysis: • Deterministic signals

• Linear Time Invariant (LTI) blocks

• Random processes


2.1.1 Baseband representation of bandpass signals

2.1.2 Properties of complex envelopes

2.1.3 Transformation between the RF bandpass and and baseband domains

2.1.4 Description of modulations

2.1.5 BB equivalent of Linear Time Invariant (LTI) systems

2.1.6 Baseband representation of bandpass random processes

2.1.7 Block diagram of equivalent BB implementation



To get the lowest sampling rate, RF bandpass signal to be processed has tobe decomposed into product of a complex envelope and a carrier exp(jωct)

x(t) = ℜ [x(t) exp(jωct)]

Method: Steps of derivation of complex envelopes

1. RF bandpass signal

jX(f

)j

jX(f)j

f

�f

f

| {z }

2B

| {z }

2B

Note, sampling rate is

determined by (fc + B)

⇒

2. Pre-envelope

jX

+

(f)j

f

�f

f

2jX(f

)j

| {z }

2B

⇒

3. Complex envelope

f

|X(f)|

2|X(fc)|

fc−fc

︸︷︷︸B

Goal achieved: sampling

rate is determined by B

Note: To perform the transformation a one-sided spectrum has to be generated first



HILBERT TRANSFORM:

The tool used to form a one-sided spectrum

Consider a bandpass signal x(t) with its Fourier transform X(f). The Hilberttransform of x(t) is defined by

x(t) =1

π

∫ ∞

−∞

x(τ)

t − τdτ

Hilbert transform may be rewritten as a convolution

x(t) ⋆ h(t) =

∫ ∞

−∞

x(τ)h(t − τ)dτ =

∫ ∞

−∞

x(τ)1

π(t − τ)dτ = x(t) ⋆

1

πt

and the Hilbert transform becomes a product in the frequency domain

X(f) = −jsgn(f)X(f)



2.1.1 BASEBAND REPRESENTATION OF BANDPASS SIGNALS

Consider a bandpass signal x(t) with a total bandwidth of 2B centered abouta center frequency fc and with its Fourier transform X(f) =

∫ ∞

−∞x(t)e−j2πftdt

Pre-envelope

The pre-envelope, also called analytic signal, is defined by

x+(t) = x(t) + jx(t)

Exploiting Hilbert transform, the spectrum of pre-envelope is obtained as

X+(f) = X(f) + j[−jsgn(f)X(f)] = X(f)[1 + sgn(f)] =

2X(f), f > 0

X(f), f = 0

0, f < 0

Note: Goal achieved, the pre-envelope has one-sided spectrum



COMPLEX ENVELOPE: Shifting the spectrum of pre-envelope to zero

1. RF bandpass signal

jX(f

)j

jX(f)j

f

�f

f

| {z }

2B

| {z }

2B

fsampling > 2(fc + B)

⇒

2. Pre-envelope

jX

+

(f)j

f

�f

f

2jX(f

)j

| {z }

2B

⇒

3. Complex envelope

f

|X(f)|

2|X(fc)|

fc−fc

︸︷︷︸B

fsampling > 2B

Price to be paid:

Complex envelope to be processed is a complex-valued function of time

x(t) = xI(t) + jxQ(t) = x+(t) exp(−jωct)

where xI(t) and xQ(t) are the in-phase and quadrature components of x(t), respectively



2.1.2 PROPERTIES OF COMPLEX ENVELOPE

Recall, definition of complex envelope: x(t) = ℜ [x(t) exp(jωct)]

Canonical form of RF bandpass signal: x(t) = xI(t) cos(ωt) − xQ(t) sin(ωt)

Properties:

In time domain:

A slowly-varyingcomplex-valued signal

x(t) = xI(t) + jxQ(t)

In frequency domain: A low-pass signal

f

|X(f)|

2|X(fc)|

fc−fc

︸︷︷︸B

Note: The only information which is not included in BB equivalent is fc



2.1.3 TRANSFORMATION BETWEEN RF BANDPASS AND BASE-BAND DOMAINS

Generation of in-phase and quadrature components of complex envelope

-2

2

x

Q

(t)

x

I

(t)

sin(!

t)

os(!

t)

x(t)

Processing: • Processing of complex-valued signal is not a problem in SW implementations

because LabVIEW and MATLAB use complex data-flows and arrays, respec-

tively

• In circuit-based analog signal processing two arms have to be used where

frequency responses of I/Q arms have to be tightly matched. Even a small

mismatch error makes the implementation impossible



Reconstruction of a bandpass signal from the I/Q components

Derivation of the canonical form of an RF bandpass signal:

x(t) = ℜ [x(t) exp(jωct)] = xI(t) cos(ωct) − xQ(t) sin(ωct)

x(t)

�+

os(!

t)

sin(!

t)

x

Q

(t)

x

I

(t)

Note: • Except the carrier frequency ωc, the complex envelope carries all information

• RF bandpass signal may be reconstructed from its I/Q components by means of

a quadrature mixer, a standard building block of each IC technology



2.1.4 DESCRIPTION OF MODULATIONS

(Envelope and phase of a bandpass signal)

Complex envelope: x(t) = xI(t) + jxQ(t) = a(t) exp[jφ(t)]

RF bandpass signal:

x(t) = ℜ [x(t) exp(jωct)] = ℜ [a(t) exp (j[ωCt + φ(t)])] = a(t) cos [ωCt + φ(t)]

Envelope of a bandpass signal gives its amplitude modulation (AM)

a(t) = |x(t)| =√

x2I(t) + x2

Q(t)

Phase of a bandpass signal gives its angle modulation (PM and FM)

φ(t) = arctan

[xQ(t)

xI(t)

]= ℑm(ln[x(t)])



2.1.5 BB EQUIVALENT OF A LINEAR TIME INVARIANT BLOCK

Original RF band-pass LTI system

h(t)

x(t) = ℜ [x(t) exp(jωct)] y(t) = ℜ [y(t) exp(jωct)]

Can it be substi-tuted by a base-band equivalent?

h(t)

x(t) 2y(t)

Yes, the complex impulse response of a bandpass LTI block

h(t) = ℜ[h(t) exp(jωct)

]= ℜ{[hI(t) + jhQ(t)] exp(jωct)}

gives the relationship between the input and output complex envelopes

y(t) =1

2

∫ ∞

−∞

h(τ)x(t − τ) dτ =1

2h(t) ⋆ x(t)



Input-output relationship

y(t) =1

2

∫ ∞

−∞

h(τ)x(t−τ) dτ =1

2h(t)⋆x(t) =

1

2[hI(t) + jhQ(t)]⋆[xI(t) + jxQ(t)]

Note: Two complex quantities has to be convolved

hQ(t)

hI(t)

hQ(t)

hI(t)

xI(t)

xQ(t)

2yI(t)

2yQ(t)

The upper and lower arms are referred to as I− and Q−arms, respectively



2.1.6 BB REPRESENTATION OF RANDOM PROCESSES

Recall, both noise and interference are modeled as random processes

Mathematical model of a signal corrupted by noise or interference

White Gaussian noise

r(t)

Observable signalcorrupted by noise or interference

+

+

y(t)

Noise-free signalto be received or analyzed

w(t)

n(t)

RF bandpass random process

RF bandpass filter

2Bnoise

where 2Bnoise is greater or much greater than the RF bandwidth of y(t)



Properties of random process n(t) considered here

• Gaussian random process with zero mean

• n(t) is a bandpass process, its spectrum has a bandwidth of 2B centeredabout the center frequency ±fC

• Power Spectral Density (psd) SN(f) of n(t) is locally symmetric about thecenter frequencies ±fC

Let Rnn(τ) denote the autocorrelation function of RF bandpass noise n(t) tobe modeled



Representation of an RF bandpass random process in baseband

Bandpass random process n(t) can also be represented by its complex envelope

n(t) = ℜ [n(t) exp(jωCt)] = ℜ{[nI(t) + jnQ(t)] exp(jωCt)}

Recall, Power Spectral Density (psd) is used in frequency domain to characterize a randomprocess. Recall, psd of a random process is the Fourier transform of its autocorrelation function

• Let Rnn(τ) denote the autocorrelation function of n(t)

• Let RnInI(τ) and RnQnQ

(τ) denote the autocorrelation function of nI(t)and nQ(t), respectively

Relationship between the autocorrelation function of the RF bandpass randomprocess n(t) and that of the I/Q components of its complex envelope n(t)

Rnn(τ) = RnInI(τ) cos(ωCτ) = RnQnQ

(τ) cos(ωCτ) where RnInI(τ) = RnQnQ

(τ)



Properties of quadrature components of equivalent baseband noise

1. If n(t) is a Gaussian process and is stationary in wide-sense then both nI(t)and nQ(t) are jointly Gaussian and jointly stationary in wide-sense

2. Since n(t) has zero mean, both nI(t) and nQ(t) have zero mean values

3. The correlation functions of nI(t) and nQ(t) satisfy the following equations

RnInI(τ) = nI(t)nI(t + τ) = nQ(t)nQ(t + τ) = RnQnQ

(τ)

RnInQ(τ) = nI(t)nQ(t + τ) = 0 = −nQ(t)nI(t + τ) = RnQnI

(τ)

where overbar symbolizes time-averaging

Note: • first equation shows that the autocorrelation functions of nI(t) and nQ(t) areequal to each other

• second one means that nI(t) and nQ(t) are independent, i.e., orthogonal.

Be careful, two different seeds have to be used in computer simulation!!!



Properties of quadrature components of equivalent baseband noise

(Continuation from the previous page)

4. Relationship between the autocorrelation functions gives the relationshipbetween the power spectral densities measured in the RF and BB domains

Rn(τ) = RnI(τ) cos(ωCτ) = RnQ

(τ) cos(ωCτ) where RnI(τ) = RnQ

(τ)

5. Both the in-phase and quadrature components have the same power spectraldensity which is related to the power spectral density SN(f) of n(t) as

SNI(f) = SNQ

(f) =

{SN(f − fC) + SN(f + fC), −Brand ≤ f ≤ Brand

0, elsewhere

where SN(f) is zero outside of fC − Brand ≤ |f | ≤ fC + Brand and fC > Brand



CONCLUSIONS OF THEORETICAL INVESTIGATIONS:

• Each bandpass signal, either deterministic or random, and each bandpassLinear Time Invariant (LTI) system can be fully represented by its complexenvelope and its complex impulse response, respectively, in baseband

• BB equivalents have a low-pass property where the sampling rate requiredis determined by the half of the bandwidth measured in the RF bandpassdomain

• Except the carrier/center frequency fc, the BB equivalent carries all infor-mation available in the RF bandpass domain

• RF bandpass signal processing can be fully substituted by an equivalentbaseband one using the BB equivalent of the original RF circuit

• RF bandpass signals can be fully recovered from the complex envelopes

• It is a representation and not an approximation, consequently, no distortionoccurs



Rule of thumb: Every RF bandpass property becomes low-pass in base-band

f

−fc fc

2B 2B

0

f

fc−fc B

0

N02

|X(fc)|, |H(fc)|,

|X(f)|

|H(f)|

|SN (f)|

|X(f)|

2|X(fc)|,

SNI(f)= SNQ(f)

|H(f)|

2|H(fc)|, N0



RF bandpass domain and its low-pass BB equivalents

RF bandpass domain BB low-pass domain

Deterministic signal x(t) x(t)

LTI two-port h(t) h(t)

LTI output y(t) y(t)

=∫ ∞

−∞h(τ)x(t − τ) dτ = 1

2

∫ ∞

−∞h(τ)x(t − τ) dτ

Random process n(t) n(t)

Only price to be paid: Complex-valued signals and functions have to be processed



2.1.7 BLOCK DIAGRAM OF EQUIVALENT BB IMPLEMENTATION

EquivalentBB signalprocessing

BaseBand (BB)

BB to RFinverse

transformation

RF domain

RF to BBtransformation

RF domain

Signal analyzer Signal generator

Universal RFHW device

Implementation in SW Universal RFHW device

Demodulator or Modulator or

ADC DAC

I QQI

y(t)

xI [n]

xQ[n]

yI [n]

yQ[n]

x(t)

Remark: Transformation between RF and BB domains is performed by theuniversal RF HW device (discussed in the next section)



2 Theoretical background (Part 2)

2.2 Derivation of BB equivalents

Key issue: How to derive the baseband equivalents?


• Two approaches available for the derivation of BB equivalents

• The engineering approach

• Many examples for the derivation



TWO APPROACHES AVAILABLE FOR THE DERIVATION OF BBEQUIVALENTS

(i) Direct use of mathematical algorithms elaborated in signal processing

• Signal processing consider the topic as a mathematical problem

• Implementation issues are not considered

• Well-known, already proven solutions cannot be re-used

One example: H. Meyr et. al., “Digital Communication Receivers, Synchronization, Channel

Estimation, and Signal Processing ,” Wiley, 1997.

(ii) Concept elaborated in Software Defined Electronics (SDE)

• A step-by-step approach (proposed here) has been elaborated for the deriva-tion of BB equivalents

• Transformation of the already known and proved HW solutions into SW

• Exploit the idea of HW-SW co-design

• An engineering-based approach



Main features of the engineering-based SDE approach discussed here:

• Starts from the already known RF bandpass solution

• A step-by-step systematic approach is provided for the transformation

• The already known, used and proven solutions can be re-used

• Not a pure mathematical but an engineering-based approach

• A systematic use of the theorems of analog and digital signal processing

Most important abbreviations and notations:

BB baseband

BP bandpass

Rx/Tx receiver/transmitter

ZoH zero-order hold

xI(t) in-phase (real) part of complex envelope x(t)

xQ(t) quadrature (imaginary) part of complex envelope x(t)



PROBLEMS SOLVED HERE:

• BB equivalent of an analog FM modulator

• BB equivalent of a QPSK modulator with ZoH pulse shaping

• BB equivalent of a generic QPSK/O-QPSK modulator

• BB equivalent of an AWGN radio channel

• BB equivalent of a two-ray multipath radio channel

• Cascading BB equivalents

• Cancelling RF impairment in baseband

• Implementation and testing of a complete half-sine O-QPSK radio link

We will go from the simplest case to the most complex one



One remark: To get compact equations, a low-pass filtering function is definedhere to express the effect of ideal low-pass filtering

Low-pass filtering is veryfrequently used in SDE.For example, the transfor-mation from RF domain toBB is

2

-2 xQ(t)

x(t) cos(ωct)

sin(ωct)

xI(t)

hLP (t)

xLPin (t) xLP

out(t)

where the impulse response of ideal low-pass filter is

hLP (t) = 2B sinc(Bt) = 2Bsin(2πBt)

2πBt

By definition, function LP(·) of ideal low-pass filtering is

xLPout(t) = hLP (t) ∗ x

LPin (t) =

∫ ∞

−∞

2Bsin[2πB(t − τ)]

2πB(t − τ)xLPin (τ) dτ ≡ LP

[xLPin (t)

]



EXTRACTION OF COMPLEX ENVELOPE

Definition of complex envelope

x(t) = ℜ [x(t) exp(jωct)] = ℜ ([xI(t) + jxQ(t)] [cos(ωct) + j sin(ωct)])

where x(t) denotes the RF bandpass signal

From the equation above we get the RF bandpass signal in canonical form

x(t) = xI(t) cos(ωct) − xQ(t) sin(ωct)

Let us multiply both the LHS and RHS by cos(ωct)

x(t) cos(ωct) = xI(t) cos2(ωct) − xQ(t) sin(ωct) cos(ωct)

Exploiting the well-known “product-to-sum” trigonometric identities we get

x(t) cos(ωct) =xI(t)

2[1 + cos(2ωct)] −

xQ(t)

2sin(2ωct)

Let the spectra of 2nd & 3rd components on the RHS be evaluated by the modulation theorem



Modulation theorem:

Gives the spectrum of a low-pass signal multiplied by a carrier in the time-domain

Spectrum of xI(t)

Spectrum of [xI(t) cos(2ωCt)]

2fC−2fC 0

f

f

1

12

0



Signal before low-pass filtering

x(t) cos(ωct) =xI(t)

2[1 + cos(2ωct)] −

xQ(t)

2sin(2ωct)

Let the low-pass filtering be applied to both sides

LP {x(t) cos(ωct)} = LP

{xI(t)

2[1 + cos(2ωct)] −

xQ(t)

2sin(2ωct)

}=

xI(t)

2

Solution: Extraction of in-phase and quadrature components:

-2

2

x

Q

(t)

x

I

(t)

sin(!

t)

os(!

t)

x(t)



RECONSTRUCTION OF RF BANDPASS SIGNAL

Recall, definition of complex envelope

x(t) = ℜ [x(t) exp(jωct)] = ℜ ([xI(t) + jxQ(t)] [cos(ωct) + j sin(ωct)])

From the equation above we get the RF bandpass signal in canonical form

x(t) = xI(t) cos(ωct) − xQ(t) sin(ωct)

Solution: Reconstruction of RF bandpass signal from the I/Q componentsx(t)

�+

os(!

t)

sin(!

t)

x

Q

(t)

x

I

(t)



EXAMPLE 1

Objective: Derivation of low-pass BB equivalent of an analog FM modulator

Block diagram:

FM MOD sFMRF (t)m(t)

RF bandpass signal

sFMRF (t) = AC cos

[ωCt + 2πkf

∫ t

0

m(τ)dτ

]



Derivation:

Extracting the complex envelope from the FM signal (bandpass RF signal)

cos(ωct)

-2

2

sFMRF

(t) = Ac cos[

ωct+ 2πkf∫ t0 m(τ)dτ

]

sin(ωct)

sFMI (t)

sFMQ

(t)

sMI (t)

sMQ

(t)

Output of the upper in-phase multiplier

sMI (t) = Ac cos

[ωct + 2πkf

∫ t

0

m(τ)dτ

]cosωct

Exploiting the “product-to-sum” trigonometric identity

sMI (t) =

Ac

2

(cos

[2πkf

∫ t

0

m(τ)dτ

]+ cos

[2ωct + 2πkf

∫ t

0

m(τ)dτ

])



Ideal low-pass filter suppresses the sum frequency component

sFMI (t) = 2LP

{sMI (t)

}= Ac cos

[2πkf

∫ t

0

m(τ)dτ

]

Quadrature component is obtained in a similar manner

sFMQ (t) = Ac sin

[2πkf

∫ t

0

m(τ)dτ

]

Block diagram of BB equivalent can be depicted from these equations



Solution: BB equivalent of the analog FM modulator

Generation of complex envelope

AC sin(.)

sFMI (t)

m(t)

AC cos(.)

2πkft∫

0

. dτsFMQ (t)

BB implementation in SW

Reconstruction of RF bandpass

signal

x(t)

�+

os(!

t)

sin(!

t)

x

Q

(t)

x

I

(t)

Universal RF HW device

(transformer)



Application: Analog FM modulator

Lab experiment:

SDE implementation of an Analog FM modulator

Front panel of FM modulator implemented on

USRP-LabVIEW platform

RF spectrum measured by a

stand-alone spectrum

analyzer



EXAMPLE 2Objective: Derivation of BB equivalent of a QPSK modulator with ZoH pulse shaping filter

Recall: Definition of QPSK modulator with ZoH pulse shaping in telecommunications

s

m2

s

m1

++

s

m

(t)

g

1

(t)

g

2

(t)

g1(t)√

2/T cos(ωCt)

g2(t)√

2/T sin(ωCt)

# of symbols 4

sm

√Eb2√Eb2

· · ·

√Eb2

−

√Eb2

Reconstruction of RF bandpass signal

x(t)

�+

os(!

t)

sin(!

t)

x

Q

(t)

x

I

(t)

By inspection:

• Two ZoH circuits are needed to keep

xI(t) and xQ(t) constant for T

• sm1 ∼ xI(t) and sm2 ∼ xQ(t)

• Note the “-” sign



Solution: BB equivalent of the digital QPSK modulator


Pulse Shaping Filter


ZoH

ZoH

ConverterBit2symbol

±1

±1

−

√

EbT

sQPSKI

(t)

sQPSKQ

(t)

√

EbT

bi


Reconstruction of RF bandpass

signal

x(t)

�+

os(!

t)

sin(!

t)

x

Q

(t)

x

I

(t)


(transformer)



EXAMPLE 3

Objective: Derivation of low-pass equivalent of an Offset QPSK with half-sinepulse shaping (used by IEEE 802.15.5 “ZigBee,” 2.4 GHz)

Odd Even

p(t)

+

+

cos(ωct)

sin(ωct)

p(t)Delay

Tc

bi sO−QPSK(t)

±b0, · · ·

±b1, · · ·

where

p(t) =

sin

(π t

2Tc

), 0 ≤ t ≤ 2Tc

0, otherwisewhere Tc denotes the chip duration



Solution by inspection: BB equivalent of generic O-QPSK/QPSK modulator




Delay

ConverterBit2symbol

TS

2

-1

sO−QPSKI

(t)

sO−QPSKQ

(t)

bi


Reconstruction of RF BP signal

x(t)

�+

os(!

t)

sin(!

t)

x

Q

(t)

x

I

(t)


(transformer)

Remarks: • Impulse response of pulse shaping Tx filter and delay have to be set

• Constants fixing Eb are set in the “Bit2symbol Converter”



Application: Generic QPSK/O-QPSK modulator

Lab experiment verifying generic O-QPSK/QPSK modulator:

SDE implementation of QPSK modulator built with raised cosine pulseshaping (Delay = 0, Tx filter = raised cosine)

Front Panel of QPSK modulatorSpectrum measured by

a stand-alone spectrum

analyzer



EXAMPLE 4

Objective: Derivation of low-pass equivalent of a AWGN radio channel

White Gaussian noise

signal

s(t)

Transmitted y(t)

+

+

n(t)

r(t)

ReceivedsignalK

AttenuationFriis formula

Physical transmissionmedium

w(t)

2Bnoise

where 2Bnoise is greater or much greater than the RF bandwidth of s(t)



Derivation

Step #1: Complete RF AWGN with the two transformations (BB=>RF & RF=>BB)

RF BP AWGN

+

+y(t)

w(t)

K

−

+

cos(ωct)

sin(ωct)

sI(t)

s(t)

sQ(t)

2Bnoise

-2

sin(ωct)

cos(ωct)

rI(t)

rQ(t)

2

n(t)

wB(t)

wG(t)

r(t)

Transformation by applying the rules of block diagram algebra

1. Move RF BP AWGN beyond the pickoff point marked by the red circle

2. Exchange the order of RF BP AWGN part moved beyond the pickoff point and the in-phasearm depicted in blue



Step #2: After applying the rules of block diagram algebra

cos(ωct)

sin(ωct)

−

+

cos(ωct)

sin(ωct)

sI(t)

2

s(t)

sQ(t)

LP1

LP1

−2K

2K

cos(ωct)

sin(ωct)

+

+

+

-2

+

LP2

n(t)w(t)

2Bnoise

yI(t)

yQ(t)

rQ(t)

rI(t)

nQ(t)

nI(t)

LP2

wG(t)

Note, the original path of

wB(t) has been substituted

by the green one wG(t)

Note: nI(t) and nQ(t) are the in-phase and quadrature components of complex envelope ofchannel noise n(t) that can be directly generated in baseband



Step #3: Eliminate RF bandpass signal s(t)

−

+

cos(ωct)

sin(ωct)

sI(t)+

yI(t)

rI(t)+

rQ(t)

nI(t)

nQ(t)

yQ(t)

+

+sQ(t)

cos(ωct)

sin(ωct)

−2K

2K

s(t)

Effect of sI(t) on yI(t)

y[sI ]

I (t) = LP[sI(t) cos

2(ωct)

]× 2K = 2K × LP

[sI(t)

1 + cos(2ωct)

2

]= K sI(t)

Effect of sQ(t) on yI(t) is zero because

y[sQ]

I (t) = LP [−sQ(t) sin(ωct) cos(ωct)]︸︷︷︸=0

×2K = 0



Step #4: Add channel noise

rI(t) = yI(t) + nI(t) = K sI(t) + nI(t)

In a similar manner rQ(t) can be expressed as

rQ(t) = K sQ(t) + nQ(t)

Solution: BB equivalent of the AWGN radio channel in the analog domain

K

K

sI(t)

sQ(t)

nI(t)

nQ(t)

yI(t)

yQ(t)

rQ(t)

rI(t)



SDE solution is obtained after digitizing the analog BB signals

Digitized BB equivalent of

AWGN channel

K

K

sI [n]

sQ[n]

yI [n]

rI [n]

nI [n]

yQ[n]

rQ[n]

nQ[n]

Two Gaussian Pseudo Ran-

dom Sequence Generators

(PRSGs) with different

seeds and prescribed vari-

ance have to be used

Spectrum in analog RF

domain

ωc

N0/2

ω−ωc

︸︷︷︸

ωs

︸︷︷︸

ωs

SN (ω)

Parameters:

2Bnoise = fS

var(nI[n]) = var(nQ[n])

= N0fS

Spectrum measured by a

stand-alone spectrum analyzer

Note the direct relationships among the parameters of RF bandpass and BB low-pass models!



Application: AWGN channel

Lab experiment: SDE implementation of an AWGN radio channel

Front panel of AWGN channel sounder implemented on

USRP-LabVIEW platform Measured RF spectrum of

generated channel noise



EXAMPLE 5

Objective: Derivation of low-pass equivalent of a two-ray multipath radiochannel

noiseWhite Gaussian

Transmittedsignal

s(t)

y(t)

mediumPhysical transmission

+

+

n(t)

r(t)

ReceiverinputEffect of

two-ray multipath

Note: • Because of cascading, only the multipath propagation has to be modeled here

• Other effect such as channel attenuation and noise have to be taken into account

by the AWGN channel model



Derivation

Step #1: Complete RF tapped delay line model with the two transformations

(BB=>RF & RF=>BB)

RF BP multipath channel

Gain

k2

Delay

T2

−

+

cos(ωct)

sin(ωct)

sI(t)

sQ(t)

+

+

s(t)r(t)

-2

2

sin(ωct)

cos(ωct)

rI(t)

rQ(t)

Direct relationships between rI(t)–rQ(t) and sI(t)–sQ(t) have to be found

1. Multipath channel is linear, consequently, superposition theorem can be applied

2. Apply the product-to-sum trigonometric identity and

3. Exploit the frequency shifting property of Fourier transform



Equations: Effect of sI(t) on rI(t)

r[sI ]

I (t) = 2 × LP [(sI(t) cos(ωct) + k2sI(t − T2) cos [ωc(t − T2)]) cos(ωct)]

= sI(t) + k2sI(t − T2) cos(ωcT2)

where LP [·], as before, describes the effect of low-pass filtering

Effect of sQ(t) on rI(t) is obtained in a similar manner

r[sQ]

I (t) = 2 × LP [(−sQ(t) sin(ωct) − k2sQ(t − T2) sin [ωc(t − T2)]) cos(ωct)]

= k2sQ(t − T2) sin(ωcT2)

By means of the superposition theorem, rI(t) is obtained as

rI(t) = sI(t) + k2sI(t − T2) cos(ωcT2) + k2sQ(t − T2) sin(ωcT2)

In a similar manner rQ(t) can be expressed as

rQ(t) = sQ(t) + k2sQ(t − T2) cos(ωcT2) − k2sI(t − T2) sin(ωcT2)



Step #2: To get a compact notation, equations given on the previous slide are rewritten as

[rI(t)

rQ(t)

]=

[sI(t)

sQ(t)

]+ k2

[cos(ωcT2) sin(ωcT2)

− sin(ωcT2) cos(ωcT2)

]

︸︷︷︸=D

[sI(t − T2)

sQ(t − T2)

]

Solution: BB equivalent of a two-ray noise-free multipath radio channel

Gain Delay

k2 T2

sI(t)

sQ(t)

Gain Delay

k2 T2

D

rI(t)

rQ(t)



EXAMPLE 6

Objective: Derivation of low-pass equivalent of two two-ports connected incascade in the RF domain

Cascade connection of Block A and Block B in the RF bandpass domain

hA(t) hB(t)x(t) y(t)

Step #1: Complete the two RF blocks with RF=>BB & BB=>RF transformations

-2

sin(ωct)

cos(ωct)

2

hA(t)−

+

cos(ωct) hB(t)−

+

cos(ωct)x(t)

AI(t)

AQ(t)

yI(t)

yQ(t)

BI (t)

BQ(t)

xI(t)

xQ(t)

sin(ωct)

-2

cos(ωct)

2

sin(ωct)sin(ωct)

y(t)



Step #2: Eliminate RF bandpass signals by exploiting superposition theorem

-2

sin(ωct)

cos(ωct)

2

hA(t)−

+

cos(ωct) hB(t)−

+

cos(ωct)x(t)

AI(t)

AQ(t)

yI(t)

yQ(t)

BI (t)

BQ(t)

xI(t)

xQ(t)

sin(ωct)

-2

cos(ωct)

2

sin(ωct)sin(ωct)

y(t)

Effects of AI(t) on BI(t)

B[AI ]

I (t) = LP[AI(t) cos

2(ωct)

]× 2 = 2 × LP

[AI(t)

1 + cos(2ωct)

2

]= AI(t)

Effect of AQ(t) on BI(t) is zero because

B[AQ]

I (t) = LP [−AQ(t) sin(ωct) cos(ωct)]︸︷︷︸=0

×2 = 0



Step #3: Good news — Cascading is preserved in BB!

hA(t)

xI(t)

xQ(t)

AQ(t) = BQ(t)

AI(t) = BI(t)

hB(t)

yI (t)

yQ(t)

Because cascading is preserved in BB

• block diagram of a BB equivalent will be identical with that of the RF blockdiagram

• library elements and libraries can be developed and used



Application of cascading (example #1)

Objective: Derivation of low-pass equivalent of the generation of noisy O-QPSK signal

Block diagram in the RF bandpass domain

Odd Even

p(t)

+

+

n(t)

r(t)cos(ωct)

sin(ωct)

p(t)Delay

Tc

bi

b1, · · ·

b0, · · ·

+

+

K

sO−QPSK(t)

where

p(t) =

sin

(π t

2Tc

), 0 ≤ t ≤ 2Tc

0, otherwise



As library blocks, BB equivalents of both O-QPSK modulator and AWGNchannel are available

Solution:

BB equivalent of the generation of noisy O-QPSK signal

bit2symbolConverter



DelayTS

2

bi

-1

yI(t)

rI(t)

yQ(t)

rQ(t)

nI(t)

nQ(t)

sO−QPSKI

(t)

sO−QPSKQ

(t)

K

K



Application: Half-sine O-QPSK modulator communicating over AWGN channel

Lab experiment:

SDE implementation of half-sine O-QPSK modulator with an AWGNchannel emulator using library blocks

Front Panel of SDE implementing both the

half-sine O-QPSK modulator and AWGN channel

Spectrum measured by


analyzer

Note: • A Gaussian cloud appears around each message point



Application of cascading (example #2)

Objective: Derivation of low-pass equivalent of the O-QPSK modulator and a noisy

multipath channel

Recall, as library blocks, BB equivalents of O-QPSK modulator, multipath propagation and

channel noise are available

Solution: BB equivalent of O-QPSK modulator with noisy multipath channel

bit2symbolConverter



Delay

O−QPSK modulator Multipath propagation AWGN channel

TS

2

bi

Gain Delay

k2 T2

yI(t)

nI(t)

K rI(t)

rQ(t)

yQ(t)

nQ(t)

K

Gain Delay

k2 T2

D

sO−QPSKQ

(t)

sO−QPSKI

(t)

-1



Application: Half-sine O-QPSK modulator communicating over noisy multipath channel

Lab experiment:

SDE implementation of O-QPSK modulator with noisy multipath channel

Front Panel of SDE implementing both the half-sine

O-QPSK modulator and noisy multipath channel

Spectrum measured by


analyzer

Note: • Multipath-related frequency-selective deep fading appears (see the vicinity of carrier frequency)



EXAMPLE 7

Objective: Cancelling RF impairment in baseband

Problem: • Two stand-alone test beds (a 16-QAM Tx and a 16-QAM Rx) were implemented

• Frequency/phase error cancellation algorithms were not robust enough, synchro-

nization was frequently lost

• An external common reference signal was used to eliminate frequency error

• But a phase error introduced by the RF cables was still present and adjustable

microwave phase shifter was not available to cancel the phase error

Block diagram of test bed

External reference

External reference input

Phase shift

External reference input

USRP #1

Tx Rx

USRP #2sI(t)

sQ(t)

rI (t)

rQ(t)

φsignal fc

Question: How to cancel the RF phase error in baseband?



Derivation

Step #1: Mathematical model

C = ?

USRP #1 USRP #2

−

+

cos(ωct)

sin(ωct)

-2

2

cos(ωct+ φ)

sin(ωct+ φ)

sI(t)

sQ(t)

sI(t)

sQ(t)

rI(t)

rQ(t)

Step #2: Effect of sI(t) on rI(t) is obtained as

r[sI ]

I (t) = LP [sI(t) cos(ωct) cos(ωct + φ)] × 2

= 2 × LP

[sI(t)

cos(−φ) + cos(2ωct + φ)

2

]



Exploiting modulation theorem and considering the effect of low-pass filtering

r[sI ]

I (t) = sI(t) cos(φ)

The other components in rI(t) and rQ(t) are obtained in a similar manner

r[sQ]

I (t) = sQ(t) sin(φ), r[sI ]

Q (t) = −sI(t) sin(φ) and r[sQ]

Q (t) = sQ(t) cos(φ)

After applying the superposition theorem and using a compact notation we get

[rI(t)

rQ(t)

]=

[cos(φ) sin(φ)

− sin(φ) cos(φ)

]

︸︷︷︸=A

[sI(t)

sQ(t)

]

Note: Phase shift φ generates a cross-coupling between the in-phase and quadrature arms



Step #3: Compensation of RF phase shift in BB with a matrix C

C

[rI(t)

rQ(t)

]= CA︸︷︷︸

=I

[sI(t)

sQ(t)

]=

[sI(t)

sQ(t)

]

Solution: Cancellation of RF phase shift in BB

C = A−1 =

[cos(φ) − sin(φ)sin(φ) cos(φ)

]



Application: Phase error cancellation in baseband

Lab experiment:

SDE implementation of BB phase error cancellation

Note: Constellation diagram can be rotated by tuning the “Phase shift” knob



EXAMPLE 8

Objective: Implementation and testing a complete radio link

Parts of an RF radio link • TransmitterGeneric QPSK/O-QPSK modulator is available

• Radio channelAWGN, multipath and noisy multipath channelsare available

• Generic QPSK/O-QPSK receiverTo be implemented



Derivation of generic QPSK/O-QPSK demodulator

Generic QPSK/O-QPSK demodulator in the RF domain

Symbol−timing

Receive

Receive

Even OddCarrier

Offset delay

circuitDecision

circuitDecision

r(t)

sin(ωct)

cos(ωct)

RI (t)

RQ(t)

0

−

π2

TS

Threshold

Threshold

Threshold

In-phase channel

Quadrature channel

recovery

filter

filter

recovery

TS

2

bi

Recall, extraction of I/Q

components

-2

2

x

Q

(t)

x

I

(t)

sin(!

t)

os(!

t)

x(t)

BB equivalent of generic QPSK/O-QPSK demodulator is obtained by inspection

Symbol−timing symbol2bit

converter

Offset delay

1

2

circuitDecision

circuitDecision

RI(t)

RQ(t)

TS

−

1

2

rQ(t)

rI (t)

Threshold

Threshold

recovery

TS

2

bi

Note: • For QPSK, offset delay TS/2 has to be set to zero



Test bed developed to implement a complete digital radio link

USRP

# 2

Configuration # 2Receiver

EthernetGigabit

TransmitterConfiguration # 1

EthernetGigabit

USRP

# 1

USB Interface Cable

RF attenuator

20 dB

Coaxial Cable Coaxial Cable

Note: • Two USRP devices and two PCs have been used to implement a stand-alone

transmitter and a stand-alone receiver

• The transmitted data stream is sent via a USB interface for BER evaluation

• Half-sine O-QPSK transceiver communicating over a noisy multipath channel has

been implemented



Application: Testing a complete digital radio link

Lab experiment:

SDE implementation of a half-sine O-QPSK telecommunications radiolink communicating over a noisy multipath radio channel



Contents:












Recall: Universal RF HW device performs transformation between analog RF bandpass and

digital low-pass BB domains

1. Receive/analyzer mode:

Extract I/Q components of complex envelope from an incoming RF bandpass signal

2. Transmit/generator mode:

Reconstruct RF bandpass signal from its complex envelope

EquivalentBB signalprocessing

BaseBand (BB)

BB to RFinverse

transformation

RF domain

RF to BBtransformation

RF domain

Signal analyzer Signal generator

Universal RFHW device

Implementation in SW Universal RFHW device

Demodulator or Modulator or

ADC DAC

I QQI

y(t)

xI [n]

xQ[n]

yI [n]

yQ[n]

x(t)



Transformations to be performed by the universal HW Devices

RF to BB transformation

x(t) ⇒ xI[n] and xQ[n]

ADC

ADC-2

2

sin(ωct)

cos(ωct)x(t)

xI [n]

xQ[n]

xI(t)

xQ(t)

BB to RF transformation

xI[n] and xQ[n] ⇒ x(t)

DAQ

DAQ

−

+

cos(ωct) x(t)

sin(ωct)

xI [n]

xQ[n]

xI(t)

xQ(t)



3 Key HW component: The universal RF hardware device(Transformation between the analog RF bandpass and digital low-pass BBdomains)

Universal RF HW device can be considered as the circuit implementation of mathematical

transformation performed between RF and BB domains

Main requirement: Be universal, i.e., be suitable for the implementation of every communi-

cations and measurement applications without any modification


3.1 Universal Software Radio Peripheral (USRP)

3.2 PXIe-based universal Software Defined (SD) wireless RF platform

3.3 Integrated circuits



3.1 Universal Software Radio Peripheral (USRP)

USRP device:

• Receive path: 14-bit ADC

SQNR ≤ 84 dB

• Transmit path: 16-bit DAC

• Up to 50 MS/s Gigabit

Ethernet Streaming

• RF bandwidth ∼40 MHz

• Low accuracy and stability,

developed for university ed-

ucation and amateurs

Testing a 915-MHz FSK radio link where the USRP device

is used to implement the FSK receiver



Block diagram of the USRP device

Main components: • Main board, includes DACs, ADCs, FPGA

• Exchangeable RF daughter board (up to 6 GHz, analog RF circuits)

PLL VCO

Rx

Con

trol

Tx

Con

trol

Gig

aBit

Eth

erne

t

40 MHz

40 MHzPLL VCO

40 MHz

40 MHz

RF Switch

Drive AmpLNARF Switch

Rx1

Tx1

Rx2

Tx Amp

+

+

ADC

ADC

DAC

DACsample

Up−

Up−

sample

sample

Down−

Down−

sample

Main board

400 MS/s

400 MS/s

100 MS/s

100 MS/s

π2

0

π2

0

Reconstruction of RFbandpass signal

cos(ωct)

sin(ωct)

xI(t)

xQ(t)

x(t)

+

−

Extraction of complexenvelope

-2

2

sin(ωct)

cos(ωct)x(t)

xI(t)

xQ(t)

Important advantage of USRP device: Drivers are available



3.2 PXIe-based universal SDE wireless RF platform

Testing a 2.4-GHz FM-DCSK radio link over an indoor

noisy multipath channel PXI Systems Alliance:

• PCI eXtensions for Instrumenta-tion (PXI) is modular instrumen-

tation architecture developed toimplement test equipment and

automation system

• Many different modules are

available

• Any kind of test beds can be

built from the modules

• PXI provides accuracy and sta-

bility required in measurementengineering and professional ap-

plications

Important advantage of PXIe test bed: Drivers are available



Main components of a PXIe-based test bed

1

2 3.1 3.2

1 Chassis

2 Embedded controller

built with the same ar-

chitecture as a multi-

core PC (on the left)

3 Different modules

3.1 Vector signal ana-

lyzer (in the middle)

Extract I/Q

3.2 Vector signal gener-

ator (on the right)

Reconstruct RF

Operation principle of the PXIe-based universal SD HW platform:

• Heterodyne receive and transmit RF frontends

• ADC and DAC conversions are performed in the IF frequency band



Receive mode: Operation principle of an IF digitizer

Recall:

Extraction of com-

plex envelope

-2

2

sin(ωct)

cos(ωct)x(t)

xI(t)

xQ(t)

Note: • IF bandpass signal is digitized first

• I/Q components of complex envelope are extracted in the digital domain

• Low-pass filtering and decimation of I/Q components are performed

• On-board memory is available for off-line signal processing



Transit mode: Operation principle of an IF arbitrary waveform generator

Recall:

Reconstruction of

RF bandpass signal

−

+

cos(ωct)

sin(ωct)

xI(t)

xQ(t)

x(t)

Note: • Arbitrary waveform is generated from its complex envelope calculated off-line and

uploaded into the Waveform Memory

• RF bandpass signal is reconstructed in the digital domain



3.3 Integrated circuits available on the market• Analog Devices: Analog inputs and outputs, operating from 50 MHz up to 2.2 GHz

• Maxim MAX2769 with built-in analog-to-digital converter

• Analog Devices: AD9361, a complete universal HW RF transformer

Analog Devices: AD8347

Block diagram of AD8347

Note: Low-pass filters are not included

Recall: Extraction of I/Q components

-2

2

sin(ωct)

cos(ωct)x(t)

xI(t)

xQ(t)



Analog Devices: AD8349

Block diagram of AD8349

Recall: Reconstruction of RF signal

−

+

cos(ωct)

sin(ωct)

xI(t)

xQ(t)

x(t)



Maxim IC with built-in digitizer (Price: US$5.00/1 pc or US$3.45/500 pcs)

MAX2769 with digital I/Q outputs

Recall: Extraction of complex

envelope

-2

2

sin(ωct)

cos(ωct)x(t)

xQ(t)

xI(t)

ADC

ADC

xI [n]

xQ[n]



Analog Devices: AD9361, a complete universal HW RF transformer

Main parameters:

• Digital input and output

• Tx: 47 MHz–6GHz

• Rx: 70 MHz–6GHz

• 200 kHz≤BW≤56 MHz, tunable

• 12-bit DACs

• 12-bit ADCs



Contents:













4.1 A similar problem:Architecture of OSI-BR compliant IEEE Std. 802 protocol stack

4.2 Embedded operation of a generic universal HW transformer

4.3 Examples: • USRP device

• PXIe-based universal RF HW platform



4.1 Architecture of IEEE Std. 802 protocol stack

Operation principle is defined

by the Open System Intercon-

nection (OSI) Basic Reference

(BR) model in computer net-

works

Note, two Service Access

Points (SAPs) are defined

(1) PD-SAP:

Physical (PHY) layer Data

(Transmission of data)

(2) PLME-SAP:

Physical Layer Management

Entity (Configuration)



4.2 Embedded operation of a universal HW transformer

SDE protocol stack is similar to that of the IEEE Std. 802

Device

Address Session

Open

Device control chain

Close

SessionUniversal HW transformer

Complex waveform Configuration

BR model

OSI BRApplication Layer

SAP1 SAP2

Universal HW transformer provides services for the upper (application) layer of host computer

Note the two service points:

• SAP1: Upload (Tx) or fetch (Rx) data of complex waveform

• SAP2: Set configuration parameters



4.3 Examples

USRP control chain in Tx mode

Note, icons “NI-USRP” denotes the device drivers

Services offered by the USRP device:

• icon “Configuration”

USRP management service to set the USRP parameters such as carrier frequency, transmit

power, sampling rate, etc.

• icon “Write I/Q Data”

USRP data service to write the I/Q components of complex envelope



Control chain in 4-FSK transmitter discussed in Section 1

Good news: the structure of control chain is the same for each HW transformer:

Select the HW device to be used ⇒ Open session ⇒ Configure HW transformer ⇒ Upload or

fetch complex waveform ⇒ Close session ⇒ Visualize Error Message (if any)



Embedded operation of PXIe-based universal HW transformer

Remarks: • Parts of control chain: (i) Receive (Rx) arm (upper icons), (ii) PXI synchronization blocks(icons in the right middle) and (iii) Transmit (Tx) arm (lower icons)

• Note the two SAPs: (i) PHY Layer Management Service and (ii) Data Service



Contents:












5 Applications of equivalent baseband information processing

5.1 Computer simulations

Goal: Minimize computer simulation time by minimizing sampling rate

BB equivalents are used in each computer simulator

One example from the LabVIEW Modulation Toolkit

Zoom-in the block ofRF bandpass signalreconstruction




Why SDE?

• Implementation in SW offers a huge level of flexibility

• Low prototyping and production cost, minimizing time-to-market

• In many applications adaptivity is a must

• Certain applications such as cognitive radio rely on multifunctional use ofthe same HW platform

• Continuous and rapid change in standards, technology and/or applicationscan be followed, deployed products already in use can be updated andmodernized by changing/updating the SW

• Market demands frequently cannot be identified/predicted in advance beforereleasing a new product. After evaluating the market response, new servicesand applications can be implemented on the already sold devices



5.2.1 RADIO COMMUNICATIONS

CMX994: Direct conversion or zero-IF receiver

Recall:

Generation of BB

I/Q components

-2

2

sin(ωct)

cos(ωct)x(t)

xI(t)

xQ(t)

Note: Complex envelope of received RF bandpass signal are provided as analog BB signals



CC2430: ISM-band SoC O-QPSK transceiver

Direct-conversion transmitter

LNA

DIGITAL

DEMODULATOR

- Digital RSSI- Gain Control

- Image Suppression- Channel Filtering

- Demodulation- Frame

synchronization

DIGITAL

MODULATOR

- Data spreading

- Modulation

AUTOMATIC GAIN CONTROL

TX POWER CONTROL

TXRX SWITCH

ADC

ADC

DAC

DAC

0

90

FREQ SYNTH

PowerControl

PA

FFCTRL

Register bus

CSMA/CA

STROBEPROCESSOR

RADIO

REGISTERBANK

RA

DIO

DA

TA

IN

TE

RF

AC

E

CO

NT

RO

L

LO

GIC

IRQHANDLING

SFR bus

Recall:

Reconstruction of

an RF signal

cos(ωct)

sin(ωct)

xI(t)

xQ(t)

x(t)

+

−



MAX2827: A dual-band IEEE 802.11g/a zero-IF receiver and direct-conversion transmitter



AD9361: A complete universal HW RF transformer includingADC/DAC converters

Main parameters:

• Digital input and output

• Tx: 47 MHz–6GHz

• Rx: 70 MHz–6GHz

• 200 kHz≤BW≤56 MHz, tunable

• 12-bit DACs

• 12-bit ADCs

Recall:

• Resolutions of ADC/DAC convert-

ers limit level of quantization noise

SQNR ≈ 6.02 × resolution



5.2.2 MEASUREMENT ENGINEERING

A close look at a “conventional stand-alone measurement instrument”

SMU200A: A top-quality up-to-date dual vector-signal generator



Note: • Today even the stand-alone type measurement instruments use the idea of virtual instrumentationwhere signal processing is done in BB

• Note the labels “Baseband A/B,” blocks “I/Q Mod A/B,” outputs “DIG I/Q OUT” and “I/Q OUT”

• However, there is no access to the modules of instruments and SW used in BB cannot be changed



5.2.2 OPTICAL COMMUNICATIONS

Note:

I/Q components of complex envelope

of received optical signal are extracted

and all signal processing from chan-

nel equalization to coherent detection

is performed in baseband

Pictures have been taken at the

Lab of Optical Communications

with the permission of Prof. Chao Lu

EIE Dept., The Hong Kong

Polytechnic University



Implementation of a 64-QAM coherent optical receiver in BB

By courtesy of Prof. Lu, EIE Dept., The Hong Kong Polytechnic University

Note the huge potential for standardization:

The same BB 64-QAM demodulator can be used in many different applications




Why to use the SDE approach in research?

• Results of scientific research are verified by computer simulations

• Today BB simulators are used almost exclusively for system level verification

• Goal: Turn the baseband simulator used in the research phase directlyinto a real working system capable of generating and receiving realRF signals

• Perform real field tests without building HW

• Measure physical signals and verify research results by stand-alone testequipment

• Important advantage: SW implementation makes easy and fast to performmodifications required during research and in prototyping

Example discussed here:

• Implementation of a chaos-based FM-DCSK radio communications systems



Generic interface among the different SW/HW components

• Both baseband simulators and universal RF HW transformers process complex envelopes

• Complex envelopes serve as generic interface points among the various SW/HW components

• Approach discussed here can be applied to all simulators which use complex envelopes

Baseband simulator Driver of universal

RF HW transformer

• BB simulator (on the left from

the vertical thick gray line)

generates the complex enve-

lope of FSK signal

• Via the “NI-USRP” driver this

complex waveform is trans-

formed into a real analog RF

bandpass signal by the univer-

sal RF HW device

• Complex waveform includes

timestamp (t0), sampling

time (dt) and complex enve-

lope



Implementation of chaos-based FM-DCSK on an RF PXIe-SDE platform

Goals: • Implement a real FM-DCSK transceiver that can transmit and receive real 2.4-GHz

microwave signals

• Implement (i) Additive White Gaussian (AWGN) and (ii) noisy multipath channel

conditions

• Evaluate the BER performance of FM-DCSK under various channels conditions

• Check all microwave signals with stand-alone test equipment

• Perform a real field test in a real indoor office environment

Main steps: • Develop a MATLAB baseband simulator for the FM-DCSKradio link including the different channel models

• Integrate MATLAB BB simulator into LabVIEWWhy LabVIEW? Because it offers drivers for the blocks of PXI HW platform

• Use PXIe-based universal SDE platform for implementation



Overview of chaos-based FM-DCSK telecommunications system

• Carrier signal is an inherently ultra-wideband chaotic signal

• Chaos-based communications is an alternative solution to spread spectrum communications

where there is no need for an extra spectrum spreading signal

• Typical application: Indoor multipath channels

Modulation scheme

• g(t) is an FM signal where the modulating signal is

provided by a chaotic signal generator

• Each bit is carried by two waveforms of duration Tb/2.

These are reference and information bearing waveforms

• Information is carried by the correlation of reference and

information bearing waveforms

Tb/2

Tb

t

g(t)

g(t− Tb

2) for bit 1

−g(t− Tb

2) for bit 0

Block diagram of FM-DCSK

autocorrelation receiverfilter

Channel

h(t)Delay

circuit

Decision∫τ· dt

r(t) r(t) z(t)

T/2

bi



Step 1: Derivation of MATLAB BB simulator for FM-DCSK radio link

Block diagram of an RF FM-DCSK radio link

Recovered

information

De ision

ir uit

T

Threshold

bi

Delay

T/2

Tele ommu-

ni ations

hannel

Radio hannelFM-DCSK modulator

Binary information

to be transmitted

bi

FM

mod

DCSK

mod

Low − pass

chaotic

signal

m(t)

∫T/2 . dt

Channel �lter FM-DCSK auto orrelation re eiver

z(t)

input

r(t)

Demodulatorinput

r(t)

Receiveroutput

Modulator

s(t)y(t)

Low − passobservation signal

• To get the equivalent BB model, low-pass observation signal z(t) has to be expressed as a

function of low-pass chaotic signal m(t)

• Recall: – Cascading is preserved in baseband

– BB equivalents of many blocks are available as library elements

• BB equivalent of autocorrelation detector has to be derived



Derivation of BB equivalent of autocorrelation detector

t∫

t−T/2

· dτ

z(t)

T

Threshold

Decision

circuit

Delay

T/2

Correlator

r(t)

noisy signal

Received

bi

Estimated

bits

r(t)

Detection algorithm of FM-DCSK receiver

z(t) =

t∫

t−T/2

r(t)r(t −T

2) dt ≈

t∫

t−T/2

r(t)r(t −T

2) dt

where r(t) = rI(t) cos(ωct) − rQ(t) sin(ωct) (canonical form)

Goal: Express z(t) as a function of rI(t) and rQ(t), i.e., the complex envelope of received

noisy signal r(t)

Note: z(t), rI(t) and rQ(t) are all BB low-pass signals



Substitution of the detector input

r(t) = rI(t) cos(ωct) − rQ(t) sin(ωct)

into the detection algorithm

z(t) =

t∫

t−T/2

r(t)r(t −T

2) dt

gives

z(t) =t∫

t−T/2

rI(t)rI(t −T2 ) cos(ωct) cos[ωc(t −

T2 )] dt

−t∫

t−T/2

rI(t)rQ(t −T2 ) cos(ωct) sin[ωc(t −

T2 )] dt

−t∫

t−T/2

rQ(t)rI(t −T2 ) sin(ωct) cos[ωc(t −

T2 )] dt

+t∫

t−T/2

rQ(t)rQ(t −T2 ) sin(ωct) sin[ωc(t −

T2 )] dt



Considering that • ωc T/2 = 2πi where i is an integer and

• exploiting the trigonometric identities

the following equation is obtained

z(t) =t∫

t−T/2

rI(t)rI(t −T2 ) cos

2(ωct) dt − . . .

=t−T/2+Tc/2

∫

t−T/2

rI(t)rI(t −T2 )

1+cos(2ωct)2 dt +

t−T/2+2Tc/2∫

t−T/2+Tc/2

rI(·)rI(·)1+cos(2ωct)

2 dt + . . .

= 12

rI(t)rI(t −T2 )

t−T/2+Tc/2∫

t−T/2

1dt + rI(t)rI(t −T2 )

t−T/2+Tc/2∫

t−T/2

cos(2ωct)dt + . . .

This can be simplified further because the complex envelope is a slowly varying function

z(t) =1

2

[

t∫

t−T/2

rI(t)rI(t −T

2) dt +

t∫

t−T/2

rQ(t)rQ(t −T

2) dt

]



The detection algorithm in baseband

z(t) =1

2

[

t∫

t−T/2

rI(t)rI(t −T

2) dt +

t∫

t−T/2

rQ(t)rQ(t −T

2) dt

]

and the BB equivalent of FM-DCSK autocorrelation detector is obtained as

Delay

Ns/2

Delay

Ns/2 +

+

z[n]

rI [n]

rQ[n]

rI [n]

rQ[n]

n∑

l=n−

Ns

2+1

ADC

ADC

rI(t)

rQ(t)

Ns

bi

Note: • BB equivalent includes only low-pass signals (I/Q components and low-pass signals)

• Effect of digitization is also considered



MATLAB BB simulator of an FM-DCSK radio link

KK

Delay

T/2

Delay

T/2nQ(t)

nI(t)

DCSK

mod

mod

DCSK

yI (t)

yQ(t)

sI(t)

sQ(t)

AWGN hannel

Ac cos(·)

Ac cos(·)

m(t)

1

2hI(t)

1

2hI(t)

∫T/2

(·)dt

∫T/2

(·)dt

1

2

DCSK MOD

2πkft∫

0

(·)dτ bi

rI(t)rI (t)

rQ(t)rQ(t)

z(t)

FM transmitter FM-DCSK auto orrelation re eiverChannel �lter

• MATLAB subroutines have been developed for each block of the FM-DCSK radio link in BB

• Recall: Cascading is preserved in the baseband, consequently library elements can be used

• Even the various propagation condition in radio channel can be implemented in baseband



Step 2:

Integration of MATLAB BB simulator into the PXIe-based SDE platform

Goal and tools available:

• Turn MATLAB BB simulator developed for research into an operatingFM-DCSK radio link without any extra efforts

• Recall, transformation between I/Q sequences given in BB and physical RFanalog bandpass signals is performed by the universal HW device

• LabVIEW offers all drivers required by the universal HW transformers

Solution:

• Integrate MATLAB BB simulator into LabVIEW platform

Method:

• As discussed I/Q components of complex envelope provide the genericinterface between the different SW/HW platforms



Integration of MATLAB BB simulator into the PXIe-based SDE platform

Note: • Observe, both channel filtering and FM-DCSK autocorrelation demodulator are implemented

in MATLAB. See the MATLAB script on the top



Step 3: Implementation on PXIe-based universal SDE wireless platform

• Testing of a 2.4-GHz FM-DCSK radio transceiver in a noisy multipath channel

• Checking by a stand-alone test equipment is always must in verification

Note: The spectra measured in RF bandpass and calculated in BB domains are identical



Unique features of SDE implementation

• Addition to the FM-DCSK transmitter many additional functions and/orsignal processing blocks can be implemented

– Channel noise, multipath propagation, interference, etc

• Any kind of test equipment can be implemented and any kind of measure-ments can be performed

– Multifunctionality can be implemented, for example, signal reception andmeasurement of received spectrum can be done simultaneously

• Automated test beds can be implemented

• Both the system configuration and system parameters can be changed easilyin software



Multifunctionality and flexibility of SDE implementation

Note, the same received waveform is used simultaneously to (i) recover the transmitted

information and (ii) measure the spectrum of received signal



Time consuming measurements can be automatized

(Front panel of PXIe-based Universal Software Defined Wireless Platform)

Note: • Left solid curve: Theoretical value of Bit Error Rate (BER))

• Right solid curve: BER measured in the universal SW defined wireless platform

• Implementation error is about 0.7 dB



Verification of the PXIe-based Universal SD Wireless Platform

Automated BER evaluation:

FM-DCSK, 2B = 17 MHz, T = 2 µs

Theoretical noise performance:

BER =1

22Bτexp

(

−Eb

2N0

) 2Bτ−1∑

i=0

(

Eb2N0

)i

i!

×

2Bτ−1∑

j=i

1

2j

(

j + 2Bτ − 1j − i

)

Legend:

• Solid curve: BER given by the analytical expression

shown above

• ‘+’ marks: BER measured by automated platform

in the 2.4-GHz ISM frequency band

Remarks: • Implementation loss is about 0.7 dB (noise of contribution of universal HW trans-

former, quantization noise, etc)

• Measurement time up to BER= 10−7 is about 3 hours



Automated BER performance evaluation of FM-DCSK in indoor office environment

Spectrum of transmitted

FM-DCSK signal

(Modulation: Random bit

stream)

Spectrum of received signal and BER performance

Effects of multipath related frequency selective deep fadings

are clearly shown in the upper figure



Contents:














6.1 Features of SDE concept

6.2 New challenges for the IEEE Circuits and Systems Society

6.3 A new way of and a new focus in teaching ICT systems

6.4 Acknowledgements



6.1 Features of SDE concept

• HW and SW components are completely separated in SDE and a universal

HW device is used to perform the transformations between the RF and BBdomains

• Every application is implemented entirely in SW, consequently, SDE offersa very flexible solution where every property from the modulation scheme totelecommunications parameters can be changed even dynamically

• Since the transmitted and received signals can be also considered as testsignals, testing of radio transceiver and channel conditions can be performedparallel to radio communications without interrupting the data traffic

• Key issue: The same HW is used in each application

• SDE offers an ideal implementation platform for cognitive radio and recon-figurable adaptive systems



Features of SDE — cont’d

• In research, SDE offers a unified test bed for verification of new theoriesand applications

• In prototyping, SDE reduces the time-to-market considerably

• Application of SDE concept makes the development of RF/microwave/opticalcircuits, the HW components, “unnecessary”

• Provides an easy way for updating the already deployed ICT systems andcomponents

• Because all real analog RF/microwave signals are available, real field tests

can be performed

• Computer simulators can be turned directly (without any modification andextra work) into a working ICT system

• Because SDE systems are embedded systems, they can be integrated intoautomated test beds, calibration systems and manufacturing lines



What is new in SDE concept?

• Integration of many many subjects into one unified framework

– Theory of complex envelope, mathematical background

– Software Defined Radio (SDE)

– Virtual Instrumentation (VI)

– Embedded operation

• Concept of equivalent baseband transformation– It offers a unified theory for the design of all RF bandpass systems

– Instead of a case-by-case solution, SDE offers a general and systematic approach

– Transformation is performed by universal application-independent HW devices

• Implementation and derivation tool– Systematic way for the derivation of BB equivalent

• A new way of researching, teaching, developing, manufacturing and main-taining of ICT systems. A complete change in ICT paradigm where focusis shifted from circuit design to system level and SW-based approach



6.2 New challenges and research possibilities for the IEEE

Circuits and Systems Society

• Time available to detect a symbol in 256-QAM@ 1 Gbit/s is less than 8 ns

• High-speed FPGA devices are resource-limited computing devices

– where fixed-point number representation and fixed-point arithmetics are used

– fixed-point number representation and fixed-point arithmetics have some serious limita-

tions but also offers new opportunities in the algorithm design

– · · ·

• New algorithms optimized for FPGA BB implementation have to be developed

• New design rules for HW-SW co-design should be developed A lot of room for research

and many new challenges for the IEEE CAS Society

We are witnessing a revolution that will make a complete change in the design

paradigm of RF and microwave systems



6.3 A new way of and a new focus in teaching ICT systems

In education and Ph.D. research the change in EE-ICT paradigm is inevitable:

• End-of-roadmap has been almost reached in electrical engineering and ICT

• HW research, design and production are concentrated in a very few placesworldwide

• Except those very few lucky places the market demand worldwide is insystem level design and integration

• SDE approach gives a new chance for researching and developing new ICTsystems everywhere, it needs only a very little financial investment



Consequently, the waste majority of our graduates will work on

systems and system level integration

SDE can help because it can change EE teaching paradigm completely

• Conventional approach:

– Different subjects are taught independently of each other with different terminologies

– Young unexperienced students are expected to learn, understand and do the system level

design and integration themselves without any guidance

• New approach:

– Teach the curriculum in an opposite way

– After laying down the foundations start with system level engineering

– Teach all constituting topics from computer science to microwaves but only in that extent

which is necessary in system level engineering, BUT, in an integrated manner

• A new, integrated approach is badly needed in education

Instead of teaching the different subjects in an isolated manner, a system-level and

SW-based approach should be used everywhere



6.3 Acknowledgments

Many programs used in this tutorial have been developed by

Mr. Tamas Istvan Krebesz, my Ph.D. student

The research presented here has been carried out within the project Thematic Re-search Cooperation Establishing Innovative Informatic and Info-CommunicationSolutions, which has been supported by the European Union and co-financedby the European Social Fund under grant number EFOP-3.6.2-16-2017-00013.



Many thanks for your kind attention


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