Principles of Code Division Multiple Access (CDMA) · PDF filePrinciples of Code Division...

Principles of Code Division Multiple Access(CDMA)

Professor A. Manikas

Imperial College London

EE303 - Communication SystemsAn Overview of Fundamentals

Prof. A. Manikas (Imperial College) EE303: CDMA 16 Nov 2012 1 / 35

Table of Contents1 Introduction2 Basics of CDMA

Basic Properties of CDMA SystemsDS-CDMA: SynchronizationMobile Cellular Systems: Conventional & CDMAChannel Reuse and Reuse DistanceSignal Overlay

3 Analysis of a Direct Sequence BPSK CDMA SystemModelling and AnalysisSNIRout as a function of EUE, Nc and KBER as a function of EUE, Nc and KBPSK Examples

4 Some Important CDMA System ComponentsPower ControlVoice Activity FactorSectorization


Introduction

(a) SSS: (b) CDMA (K users):


Introduction

The PN signal b(t) is a function of a PN sequence of ±1’s {α[n]}

I The sequences {α[n]} must agreed upon in advance by Tx and Rx andthey have status of password.

I This implies that :F knowledge of {α[n]})demodulation=possibleF without knowledge of {α[n]})demod.=very di¢cult

I If {α[n]} (i.e. “password”) is purely random, with no mathematicalstructure, then

F without knowledge of {α[n]})demodulation=impossible

I However all practical random sequences have some periodic structure.This means:

α[n] = α[n+Nc ] (1)

where Nc =period of sequencei.e. pseudo-random sequence (PN-sequence)


Introduction

Remember

DS-SSS (Examples: DS-BPSK, DS-QPSK):

b(t) = ∑n

α[n].c(t ! nTc ) (2)

where {α[n]} is a sequence of ±1’s;c(t) is an energy signal of duration Tc

FH-SSS (Examples: FH-FSK)

b(t) = ∑nexp {j(2πk[n]F1t + φ[n])} .c(t ! nTc ) (3)

where {k[n]} is a sequence of integers such that

{α[n]} 7! {k[n]} (4)

and {α[n]} is a sequence of ±1’s;c(t) is an energy signal of duration Tc


Basics of CDMA

Basics of CDMABLOCK DIAGRAM


K = number of users

K-1 = multiple access interference

Basics of CDMA

Example: DS-BPSK CDMA System

SISO = Scalar-Input Scalar-Output Channel


SNIRoutSNIRin

Basics of CDMA

SISO Multipath Channel

SISO Multipath channel of the i-th user

In the absence of multipaths the above diagram has only τi1 and βi1terms.

For the simplicity we will drop the second subscript and we will use τiand βi ,and thus the BPSK/DS-CDMA in the absence of multipathsmay be represented as follows:&


Basics of CDMA


Basics of CDMA Basic Properties of CDMA Systems

Basic Properties of CDMA Systems

CDMA is one of the applications of spread spectrum communicationswhich is used in civilian, commercial and military communication.

Two systems: DS-CDMA (i.e averaging system) and FH-CDMA (i.e.avoidance system).In this course only DS-CDMA will be considered.

Assign a specific PN-code to each user

PN-code (having the status of ‘password’) acts like a ‘channel’

DS-CDMA: two main casesI PN-signal period = NcTc = Tcs (known as ‘short codes’ CDMA)I PN-signal period = NcTc % Tcs (known as ‘long codes’ CDMA)


Basics of CDMA Basic Properties of CDMA Systems

DS-CDMA: two main types1 synchronous DS-CDMA8><

>:

i-th user

j-th user2 non-synchronous DS-CDMA8><

>:

i-th user

j-th user


Basics of CDMA DS-CDMA: Synchronization

DS-CDMA: SynchronizationThe Rx requires a replica of the PN code, with the correct clockphase, in order to despread the signal.Therefore, Rx =“synchronization circuits” + “demod. circuits”The process of synchronizing the receiver to the transmitter’s PNcode consists of two stages:

I Acquisition (coarse synchronization).I Tracking (fine synchronization).

Operation: acquisition; tracking + demodulation; loose tracking;acquisition; tracking+demodulation; ......etc..........


Basics of CDMA Mobile Cellular Systems: Conventional & CDMA

Mobile Cellular Systems: Conventional & CDMA

A mobile cellular system consists of base stations, cells (a cell is thearea serviced by a base station) and mobiles (subscribers). When acall originates, the base station negotiates with the mobile on variousaspects (such as the channel used etc.), before establishingcommunications. After this, as the mobile moves from cell-to-cell, theservice is handed (hand-o§ or handover) from one base station toanother.

Only one base station will service a mobile at any one time.

Note:I base station to mobile is known as FORWARD LINKI mobile to base station is known as REVERSE LINK



Type of channels:

UPLINK DOWNLINKTra¢c Channel Tra¢c ChannelAccess Channel Pilot Channel

Synchron.ChannelPaging Channel

Frequency Division Duplex (FDD) and Time Division Duplex (TDD)



Channel Reuse and Reuse Distance

There is interference from other cells sharing the same channels. Thereuse distance D, in these systems, is determined by the worst caseinterference situation.

Current cellular systems = FDMA/TDMAMost of the current cellular systems, such as GSM, use frequencydivision multiplex - time division multiplex (FDM-TDM) technique toimprove the system capacity. In these systems, each user is assignedone time-frequency slot.

I When the system gets larger,

slots 6= unique for each and every user

as this will limit the system capacity. Therefore these slots(time/frequency) have to be reused(reused in cells separated by D (cells), which is the reuse distance ofthe system).



The system capacity could be increased by increasing the number ofchannels available in a single cell, i.e. reducing the reuse distance D.But this reduction is limited by the co-channel interference, (i.e. theinterference from other cells sharing the same channels).The reuse distance D, in these systems, is determined by the worstcase interference situation.



In a CDMA system, the available spectrum and time are not split intodistinct slots. Instead the whole (available) spectrum is used by eachuser.

Since the same frequency channel could be used by all theusers/subscribers, the reuse distance D could be reduced to 1, i.e.

if CDMA then D = 1 (5)



Signal OverlayThe spread spectrum signal, from a CDMA system, has a very low powerspectral density and, therefore, a CDMA system can overlay on top ofexisting narrow-band mobile cellular systems (of the same frequencyband).This is because the interference (due to CDMA signals), added to anarrow-band mobile system channel, is very low and, therefore,the presence of CDMA signal will hardly a§ect the performance of thenarrow-band mobile system.The CDMA system, however, needs to perform some extra processing toreject the narrowband interference due to the presence of the narrow-bandsignals.Comment:The capacity and performance of a mobile cellular system could besignificantly improved by using CDMA techniques. In the paper “On theCapacity of a Cellular CDMA”, IEEE Transactions on VehicularTechnology, Vol.40, 1991 (by Gilhousen et al) the improvement in thecapacity is discussed and it is stated that “no other proposed schemeappears to even approach this (CDMA) performance”.


Analysis of a Direct Sequence BPSK CDMA System

Analysis of a Direct Sequence BPSK CDMA Systemobjective: to relate the BER pe with the total number of users K aswell as with the EUEequ at the receiver.i.e.

pe = f{EUEequ,K} (6)

Main AssumptionsI single cell system of K users,I @ multipathsI PN code period = Nc =PGI System=perfectly power-controlled(all SS signals arrive at the receiver with the same power)

F NB: power control can often be implemented in practice with greataccuracy.

I System = totally asynchronous (there is no common timing referencefor the transmitters/users)

F NB: This is actually an advantage of CDMA over other multiple accesstechniques, because all users can transmit independently and nosignalling information is required.


Analysis of a Direct Sequence BPSK CDMA System Modelling and Analysis

DS/BPSK CDMA System: Modelling and Analysis

Note that the carrier of i th transmitter ispPi . exp (j(2πFc t + ψi ))



i-th user’s data signal mi(t) and PN-signal bi (t):8>>><

>>>:

mi (t) ( ∑nai [n]. c1 (t ! n.Tcs ) ; nTcs < t ) (n+ 1)Tcs

bi (t) = ∑k

αi [k ]. c2 (t ! kTc) ; kTc < t ) (k + 1)Tc

with Tcs = NcTc ;jkNc

k= n;

(7)

The period of each user’s PN-sequence is selected as Nc = TcsTc, and

therefore there is one code period per data bit (or Nc chips per bit).Thus, for the BPSK case, the processing gain PG is:

PG = Nc =TcsTc

(8)

The transmitted signal si (t) of the i-th user is therefore

si (t) =pPi .mi (t).bi (t). exp (j (2πFc t + ψi )) (9)

where Fc is assumed common for all carriers.



Since the transmitters are not time-synchronous, there is a di§erenttime delay τi for each signal si (t) before it reaches the receiver, with0 ) τi < Tcs for i = 1, 2, 3, ...,K . The carrier phases ψi are alsoassumed di§erent so that 0 ) ψi < 2π for i = 1, 2, 3, ...K . Thus,ignoring the band-pass filters at the transmitters and the receiver, thereceived signal r(t) can be described as follows:

r(t) =K

∑i=1

βipPi| {z }

,pP

.mi (t ! τi ).bi (t ! τi ). exp(j (2πFc t + φi )) + n(t)

(10)where

φi = ψi ! 2πFcτi (11)

with n(t) denoting the additive white Gaussian channel noise ofdouble sided power spectral density N0/2



If the transmitted signals are all synchronized, the delays τi , 8i ,areneglected. Synchronizing all transmitted signals requires a commontiming reference and compensation for transmission delays in varioustransmission paths. This complicates the system requirements andhas no clear advantage.

The receiver has a local PN-signal generator as well as a carriergenerator that generate exact replicas of those used in the transmitter.The receiver is in perfect synchronism with the transmitter by usingacquisition and tracking techniques (i.e. τ1, φ1 are known).

Thus, without loss of generality, let us assume that τ1 = 0, φ1 = 0.

The output of the 1-st correlator (desired) at t = Tcs is thus

G1 =1Tcs

Z nTcs

(n-1)Tcsr(t).b1(t). exp(!j(2πFc t)dt (12)


Analysis of a Direct Sequence BPSK CDMA System SNIRout as a function of EUE, Nc and K

SNIRout as a function of EUE, Nc and KAt the ouput of the correlator (i.e. G1) we have:

SNIRout + 2.EUEequ = 2Eb

Nj +N0(13)

However,

Nj = (K ! 1).PBss

= (K ! 1).P.Tc =(K ! 1).

=Ebz}|{PTcs

Nc=(K ! 1).Eb

Nc(14)

Therefore

SNIRout + 2.EUEequ

= 2Eb

(K!1).EbNc

+N0=

1K!12Nc

+ 12 EUE

(15)


Analysis of a Direct Sequence BPSK CDMA System BER as a function of EUE, Nc and K

BER as a function of EUE, Nc and K

We have seen that

SNIRout +,K ! 12Nc

+1

2 EUE

-!1(16)

However,

pe =TnpSNIRout

o(17)

which implies that

pe = Tnp

2EUEequo= T

8<

:1q

K!12Nc

+ 12 EUE

9=

; (18)


Analysis of a Direct Sequence BPSK CDMA System BPSK Examples

BPSK Examples




carrier



Some Important CDMA System Components Power Control

Power Control

In order to achieve the full benefits of using CDMA, the transmittedsignal powers Psi should be controlled in such a way that receivedsignal power, from all the users at a cell, are the same.This makes power control a key feature of CDMA mobile systems.


Some Important CDMA System Components Voice Activity Factor

Voice Activity Factor

Human speech contains a lot of pauses where there is no data totransmit.Thus a speaker is active for about half the time due to listening andpauses in speech.

The fraction of time that a speaker is active is known asthe voice activity factor a

Extensive studies have shown that 0.35 < a < 0.5.A popular value used is a = 3/8 = 0.375The voice activity feature can be taken into account in acommunication system by suppressing the transmission when voice isabsent.Assuming that we have a scheme where the carrier is turned-o§during the speech idle periods then a reduction in interference (by afactor of the voice activity) can be achieved.



implementation of voice activity:

(TDMA/FDMA: very di¢cult

CDMA: very easy

For a large number of users the capacity increases by a factor 1/a.

Therefore, using the voice activity monitoring approach the capacityand the performance of a CDMA system will be improved(this improvement cannot be obtained in FDMA/TDMA systems)

In particular the power of a user’s signal at a specific time instant canbe expressed 1, Puser with probability a and 0, Puser withprobability (1! a).Using voice activity the performance can be improved even more.

BPSK : SNIRout = 2.EUEequ = 2Eb

Nj +N0(19)

where Nj =(K ! 1).Ps .a

Bss(20)



Therefore we can model the “on-o§” activity of each user a binomialdistribution, which implies that the probability that k user (out of K )are active is given as follows:

Pr(k users are active) =6kK

7ak (1! a)K!k (21)

where K is the number of users per cell

Note that as K =")spread of distribution=#Set a threshold Kth , εth such that:

Pr(number of active users > Kth) < εth (22)


Some Important CDMA System Components Sectorization

Sectorization

It is used in TDMA/FDMA and CDMA systems



Sectorization

Sectorization is achieved by using directional antennas instead ofomnidirectional antennas.

Each cell is divided to three sectors using three directional antennaseach having 1200 beamwidth.

Using sectorization the performance can be improved even more.(The expected value of the total interference is reduced by a factor ofs = 3wrt single omnidirectional antenna case)

BPSK : SNIRout = 2.EUEequ = 2Eb

Nj +N0(23)

where Nj =(K ! 1).Ps .s

Bss(24)

In practice: 3 dB<SNIRout < 15dB



A better approach is to use three linear antenna arrays (smartantennas)

antenna array switched beam array system adaptive array system


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