Tài liệu CDMA truy cập và chuyển mạch P8 pptx

TheSAD or PAD performance then consists of evaluatingthe additional Signal-to-NoiseRatio SNR needed by either scheme to achieve the same Bit Error Rate BER asthe coherent demodulation...

SE-to user mobility and/or SE-to satellite drift motion, and the temperature variation andventilation conditions at the sites of the various local oscillators that generate thetransmitted signals cause the carrier phase uncertainty.

Coherent demodulation requires the extraction of a reliable (perfect) phase referencefrom the received signal A traditional alternative is the differentially coherentdemodulation that uses the phase of the previous bit (symbol) as a reference, butrequires almost 3dB (for M -ary PSK modulation in AWGN channels, it is less thanthat for BDPSK) of additional signal-to-noise (Eb/N0) in order to achieve the samebit error rate as coherent demodulation This problem is more severe in DS/CDMAsystems, which are limited by other-user interference: the additional cost in dBs ofdifferentially coherent over coherent demodulation increases linearly with the number

of users in the system, so as to render the fully-loaded multi-user system impractical[1] Recently, SAD [2] and PAD [3] have been considered a form of ‘sub-coherent’demodulation In the proposed SAD and PAD schemes, estimates of the channelmultipath phases and amplitudes are extracted by smoothingand interpolation ofthe transmitted known bits in the SAD scheme or the pilot in the PAD scheme TheSAD (or PAD) performance then consists of evaluatingthe additional Signal-to-NoiseRatio (SNR) needed by either scheme to achieve the same Bit Error Rate (BER) asthe coherent demodulation

In this chapter we first present the system model and the design issues of the SADscheme in Section 8.2, and its BER analysis (for the uncoded system) in Section 8.3.Then in Section 8.4 we present the system model, the design and the BER analysis

Copyright © 2001 John Wiley & Sons Ltd ISBNs: 0-471-49184-5 (Hardback); 0-470-84169-9 (Electronic)

188 CDMA: ACCESS AND SWITCHING(for the uncoded system) of the PAD scheme The BER analyses of the coded systemsare presented in Section 8.5 The coded system is based on a proposed new iterativedecodingalgorithm The performance of the coded system of both schemes has beenevaluated via simulations The performance results are presented in Section 8.6.8.2 Symbol-Aided Demodulation

8.2.1 System Model

In symbol-aided demodulation, known symbols are multiplexed with data bearingsymbols The known symbols are multiplexed with the data symbols at a constantratio, so that one known symbol is followed by J− 1 unknown data symbols Thisratio implies a loss in the throughput of 1/J At the receiver the known symbols areused to estimate the channel for other samplingpoints

The system is as shown in Figure 8.1-A The transmitted signal for the first user isgiven by

s1(t) = A

∞

k= −∞

b1(k)a1(t)p(t− kT )

where b1(k) is the binary data sequence, a1(t) is the spreadingcode, which is a periodicsequence of unit amplitude positive and negative rectangular pulses (chips) of duration

Tc, T = N Tc is the symbol duration, and N is the processinggain

The jth code pulse has amplitude aji = ai(t) for jTc≤ t ≤ (j + 1)Tc, and p(t) is aunit energy pulse in the interval 0≤ t ≤ T The received signal is

L

l=1

cml(t− τml)sml(t− τml) + n(t)

where L is the number of paths, n(t) is the AWGN with power spectral density N0

in the real and imaginary parts, and Kuis the number of users The channel complexgain cml(t) represents the Rayleigh or Rician fading for the lth path of the mth user,with an autocorrelation function [4]

Rc(τ ) = σ2g

K

r11(k) = u11(k)b1(k) +

L

l=2

u1l(k)I1l(k)ejφ1l (k)

+

Ku

m=2

L

uml(k)Iml(k)ejφml (k)+ n11(k)

where the Gaussian noise samples n11(k) are white with unit variance, and complexsymbol gain uml(k) has mean

E[uml(k)] =

γs ml

K

K + 1and variance

σ2u

ml= γmls 1

K + 1where the average SNR for path l of user m is given by

γsml= E

s ml

N0and Iml(k) is the interference from path l of user m to path 1 of user 1 For the SADscheme

Esml= Emlb J− 1

Jwhere Ebml is the energy per bit, and

γbml= E

b ml

N0

8.2.2 Design of Modulator and Demodulator

There are several issues that must be taken into consideration for the proper design

of the symbol-aided modulation/demodulation system

The Rate of Aid-Symbols

A proper choice of the value of J is of paramount importance for SAD system design.Increasing J will result in increasingthe throughput, but at the same time it willincrease the processingdelay and the carrier-phase estimation error in both the knownsymbols and the data symbols

Guidelines for the choice of J are given below The value of J is determined fromthe bandwidth, rate of fadingor of Doppler, or in general, from the rate of change ofthe phenomenon that introduces the uncertainty (and change) in the carrier phase

If we assume that the fadingrate (or other rate of change) is Rf, then the samplingperiod Tf s and samplingrate Rf s = 1/Tf s of the channel observations must satisfythe Nyquist condition

Rf s= 1

Tf s ≥ 2RfFor notational convenience, define

Jmax= Rs

2Rfwhere Rs is the symbol rate Jmax corresponds to the samplingof the fadingphenomenon at exactly the Nyquist rate, presented in a more convenient form

190 CDMA: ACCESS AND SWITCHING

Channel AWGN

& Fading

Other User Interf

Rake Receiver

Decision Data

τ

T-Channel Estimation

Delay T-

Channel Estimation

Delay T-

Channel Estimation

Rf << Rsthat is, the rate of change of the carrier phase is much slower than the symbol rate

of the system For example, we may have Rs= 64 kbps (kHz) while Rf = 64 or 128

Hz (or a value in the range of 30 Hz to 200 Hz) Denoting the symbol duration as

Ts= 1/Rs, we have that Tf >> Ts, and define J as the ratio Tf s/Ts, i.e

J = [Tf s/Ts] = [Rs/Rf s]≤ [Rs/(2Rf)] = JmaxTherefore, Jmax corresponds to samplingat exactly the Nyquist rate, and J ≤ Jmaxcorresponds to oversampling; for example J = Jmax/4 corresponds to samplingat fourtimes the Nyquist rate, while J = Jmax/8 corresponds to samplingat eight times theNyquist rate

The idea is to use a sufficiently small J so that oversamplingat rate

R = (J /J )· (2R )

captures the change in the phenomenon and reduces the noise in the estimates ofthe phase (by a factor of Jmax/J through smoothing, as we will see next) but stillmaintains the throughput loss (equal to 1/J ) within acceptable values.

A simple analysis of the SAD technique was presented in reference [5] This

is an approximate analysis assumingperfect filtering, but it provides an intuitiveunderstandingof the problem and it helps identify the optimum J It is done bysimply takinginto consideration the power loss due to reference insertion, expressedas

Lr≈J + 1

J = 1 + 1

Jand the amount of increase in the noise due to the noisy reference (assumingperfectfilteringand interpolation) which is given by

Ln≈ 1 + J

JmaxThus the total loss compared to coherent system is given by

Lt(dB) = Lr(dB) + Ln(dB)The optimum choice of J given Jmax can be obtained by calculatingthe minimumachievable loss; we can easily get

Jopt≈Jmax

Lt(Jopt)≈ (1 +√ 1

Jmax)2Then the conclusion is that the performance of any SAD system can be no better than

Lt dBs below (worse than) the performance of a coherent system (which assumes theperfect knowledge of the fading phase) For example, for Jmax = 50, Jopt ≈ 7, and

Lt≈ 1.15dB

For the SAD scheme, the demodulation will delay the data symbols by J M symbols,where M is half the order of the smoothingfilter Clearly, decreasingJ will produce ashorter delay, but as we mentioned, it will decrease the throughput, and the estimationerror will be increased

The Smoothing Filter

The bandwidth of the smoothingfilter is another important issue This filter is adigital filter that estimates uml(k) of the unknown symbol samples Decreasing J(which is equivalent to oversampling) will enable the filter to better estimate uml(k)

by removingmore noise, and allow easier trackingof the relatively slower fading.Two approaches are addressed here The first is to derive the optimal Wiener filterfor every unknown data point within the frame of length J , which means that filteringand interpolation are done simultaneously (in a slidingwindow manner) The secondapproach is to use a single filter for filtering all the known symbols, which is also aWiener filter, and then to linearly interpolate the resultingoutput in order to obtainall unknown data symbols The difference in performance between the two approaches

is evaluated below

192 CDMA: ACCESS AND SWITCHING8.3 BER Analysis for SAD

The first step for calculatingthe performance is to calculate the interference (see

r11(k) in Section 8.2.1) The best way to proceed is to calculate Iml(k) for a g ivencode selection, and hence calculate the mean square power of the interference averagedover τml A very good approximation is to follow references [6] and [1], and to assume

a random signature sequence of length N This approximation is very accurate if thesystem uses long(period) codes like the IS-95 system [3], and has sufficiently large Nand Ku Followingreferences [6] or [1], we can calculate

8.3.1 Optimum Wiener Filtering

The best performance that can be expected from the SAD technique (for a given filterlength) can be obtained from Wiener filters We will obtain its performance in thissection for multipath Rician fadingchannels Cavers [2] was the first to perform thisanalysis for Rayleigh fading channels The phase reference of the lth path of the mthuser for the unknown symbols is obtained from

vml(k) = h†(k)rml=

M

i=−M

h∗(i, k)r

ml(iJ )

where the dagger denotes conjugate transpose, and rml is the vector formed from

rml(iJ ), the samples of the output of a matched filter of a finger of the rake receiver,

−M ≤ i ≤ M is the index of the known (SAD) symbols, and 1 ≤ k ≤ J − 1 Notethat there will be J− 1 different filters used

The Wiener filter equation will be given by

˜Rh(k) = w(k)where ˜R is the autocorrelation matrix of size 2M + 1 defined by

˜

R = 1

2E[rmlrml]and the J− 1 vectors are

w(k) = 1

2E[u

∗

ml(k)rml]

The channel is Rician as described by Rc(τ ) in Section 8.2.1 Perfect power control

is assumed, such that γb is constant for all users and is denoted by γbL It is assumed

that all the paths are identical, and so

γbL =γbLwhere γb= Lγb

ml is the total average SNR for every bit from all the paths

Now we can obtain ˜R and w(k) from

Rij = γbL

K + 1

J− 1J

P e = Q1(a, b)− I0(ab)e[−1(a2+b2)]+I0(ab)e

xe[− 1(a2+x2)]

I0(ax)dx and µ = σ

2 rv

σvσrwhere for the SAD scheme,

1

K + 1+ 1 + γbL

J− 1J

2[Ku∗ L − 1]

3N

E{v} =

K

K + 1

J− 1

J γbL

194 CDMA: ACCESS AND SWITCHINGwhere Sh(k) = M

i= −Mh(i, k), while for coherent demodulation we have vml(k) =

K + 1γbL

E{r} =

K

K + 1γbLand for differential modulation we have vml(k) = rml(k− 1)

σ2rv= 1

K + 1γbLJ0

π

K + 1γbL

E{r} =

K

K + 1γbLFiltering Followed by Interpolation

The second approach is to design a single filter to filter the known samples and thenlinearly interpolate the output to estimate the channel at the unknown samples AWiener filter can still be used to maximize the effective SNR at k = iJ Followingthe same Wiener optimization approach as before, we can obtain h for k = 0 anduse it

Followingthe filter, the interpolator linearly interpolates the estimates of the carrier(or fading) inphase and quadrature components of the data symbols between each twosuccessive known symbols (0 and J ) We consider the case of 1≤ k ≤ J − 1 withoutany loss of generality We have

v(k) = k

Jv(J ) +J− k

J v(0)The expression for the probability of error Pe (given above) will be used again tocalculate the performance, where now

M

i=−Mh(i)γbL

J− 1J

1

K + 1



K +J− kJ

i= −M

M

j= −Mh(i)h(j)γbL

J− 1J

1

K + 1

$

J− kJ

2

+

kJ

1

K + 1

J− kJ

kJ

2K

2+

kJ

2% 1

+ γbL

J− 1J

2(Ku∗ L − 1)3N



δi,j+ h(i)h(j)J− k

J

kJ

·



1 + γbL

J− 1J

2(Ku∗ L − 1)3N

(δi,j −1+ δi,j+1)

− (E{v})2

The other parameters (E{v}, σ2

r, E{r}, Sh(k)) are like those given in the previoussection for the optimum Wiener filter case

((Apap1(t) + b1(k)a1(t))p(t− kT )

where Ap is the pilot amplitude, ap1(t) is the pilot spreadingcode, and all the otherparameters are as described for the SAD scheme ap1(t) and a1(t) could easily bemade orthogonal through the use of code concatenation The orthogonality will bemaintained for every path because both codes will pass through the same channel

196 CDMA: ACCESS AND SWITCHINGThe received signal will be given by

L

l=1

cml(t− τml)sml(t− τml) + n(t)

The output of the normalizingmatched filter, representingthe finger of the rakereceiver, for the first path of the first user, with impulse response a1(−t)p∗ −t)/(√N0)assuming equal energy pulses and BPSK modulation, will be given by

r11(k) = u11(k)(b1(k) + I11p(k)) +

L

l=2

u1l(k)I1l(k)ejφ1l (k)

+

Ku

m=2

L

l=1

umll(k)Iml(k)ejφm l

+ n11(k)

where the Gaussian noise samples n11(k) are white with unit variance I11p(k) is theinterference from the pilot signal to the data signal from the same path As mentionedabove, each user’s data and pilot codes are assumed orthogonal, and so I11p(k) = 0.For the pilot-aided scheme, for fair comparison, the energy per bit Eb will be thesum of the pilot energy Ep and data energy Ed, which means Eb = Ep+ Ed In thefollowing, we will denote the power in the pilot as a fraction of the power of the datasignal, and so we can write Ep= P Eb

The complex symbol gain uml(k) has mean

E[uml(k)] =

-γd ml

K

K + 1and variance

σu2

ml = γmld 1

K + 1where

γmld = E

d ml

N0and Iml(k) is the interference from path l of user m to path 1 of user 1, includingthe interference from both the data and pilot signals The same expression can beobtained for the pilot fingers of the rake, but with Epreplacing Ed The output of thefirst finger of the first user pilot Rake will be denoted by r11p(k)

8.4.2 Design of Modulator and Demodulator

There are several issues that must be taken into consideration in the proper design of

a pilot-aided modulation/demodulation system

Filter Length

The filter length is of great importance for the performance of the PAD scheme Ifthe fadingis very slow relative to the data rate, an averagingfilter could be used; this

filter will give equal weight to each sample If, on the other hand, the fading is not veryslow, or it is required to have a longfilter, a Wiener filter could be used, and it should

be designed as explained before for the SAD scheme, but ˜R and w will be given by

γdL = Ed

N0 =γdLwhere γp and γd are the average SNRs corresponding to every bit from all the pathsfor the pilot and data, respectively

The Ratio of Powers

The ratio of the power of the pilot to the power of the signal is the other parameter thatshould be studied carefully The choice of this parameter is very similar to the choice

of the parameter J in SAD scheme Increasingthis power will give a better estimate,but the overall performance may be worse There will be an optimum level for thispower that can be obtained with a similar argument to that shown in Section 8.2.2.Again, this is an approximate analysis assuming perfect filtering, but it provides anintuitive understandingof the problem, and figuringout the optimum P It is done

by simply takinginto consideration the power loss due to pilot insertion, expressed as

Lr≈ 1 + Pand the amount of increase in the noise due to the noisy reference (assumingperfectfilteringand interpolation), which is given by

Ln ≈ 1 + 1

P JmaxThus, the total loss compared to coherent system is given by

Lt(dB) = Lr(dB) + Ln(dB)The optimum choice of P given Jmax can be obtained by calculatingthe minimumachievable loss; we can easily get

Popt≈

1

Jmax

Lt(Jopt)≈



1 +√ 1J

2