Tài liệu Adaptive WCDMA (P13) pptx

13.1 OPTIMAL RECEIVER If user k transmits bit stream b k , with bit interval T , using spreading sequence s k, thenthe low-pass equivalent of the overall signal received in the BS can be

Multiuser CDMA receivers

In this chapter we present a number of methods for multiple-access interference (MAI)cancelation MAI is produced by the presence of the other users in the network, which arelocated in the same bandwidth as our own signal The common characteristic of all theseschemes is some form of joint signal and parameter estimation for all signals present

in the same bandwidth It makes sense to implement this in a Base Station (BS) of acellular system because all these signals are available there anyway At the same timethis concept will considerably increase the complexity of the receiver Although verycomplex, these schemes are being standardized already because they offer significantlybetter performance Details can be seen in Chapter 17 Much simpler but less effectivesolutions feasible for implementations in mobile units are also considered [minimum meansquare error (MMSE) type of algorithms]

13.1 OPTIMAL RECEIVER

If user k transmits bit stream b k , with bit interval T , using spreading sequence s k, thenthe low-pass equivalent of the overall signal received in the BS can be represented as[1,2]

by the second term of equation (13.1) and τ k is the delay of signal from user k On the

basis of the likelihood principle described in Chapter 3, the detector selects the vector of

bits b that maximizes

P[{r t , t ∈ R}|b] = C exp[(b)/2σ2] ( 13.3)

Adaptive WCDMA: Theory And Practice.

Savo G Glisic Copyright ¶ 2003 John Wiley & Sons, Ltd.

ISBN: 0-470-84825-1

where C is a positive scalar independent of b and

In other words, vector b that jointly gives the maximum of equation (13.4) is chosen as a

joint estimate of bits for all users The first term in equation (13.4) can be represented as

where y(i) is a vector with elements y k (i)representing the output of a matched filter for

the ith symbol of the kth user, that is,

Matched filter User 1

Sync K

b1(j )

r (t )

Matched filter User 2

Matched filter User K

OPTIMAL RECEIVER 457

Matched filter User 1

Matched filter User 2

Matched filter User K

Figure 13.4 represents the same results for more realistic code, m-sequence of length

31 One can see that the sequence detector performs almost as though only one user ispresent in the network (single user)

Worst-case conventional detector Best-case conventional detector Upper bound sequence detector Single user

Conventional Worst-case User 1 Worst-case Users 2, 3 Average user 1

Upper bound worst case sequence detector Upper bound average sequence detector Single user

multiuser detectors with three active users employing m-sequences of length 31.

(a)

SNR2/SNR1= −10 dB

Conventional detector Upper bound sequence detector Lower bound minimum distance Single user

12 14

Conventional detector Upper bound sequence detector Single user

Figure 13.5(a) to 13.5(c) presents the same results for different near far ratio (NFR)defined as SNR2/SNR1 From these figures one can see that the impact of using optimaldetector is more evident for larger NFR.

13.2 LINEAR MULTIUSER CDMA DETECTORS

13.2.1 Synchronous CDMA channels

If the signals from different users are received synchronously, equation (13.1) becomes

LINEAR MULTIUSER CDMA DETECTORS 461

The optimum multiuser detector becomes

13.2.2 The decorrelating detector

In the absence of noise, the matched filter output vector is y = Rb The detector will

perform the following operation ˆb = sgn R−1y Note that the noise components in R−1y

are correlated, and therefore sgn R−1y does not result in optimum decisions It is

inter-esting to point out that this detector does not require knowledge of the energies of any

of the active users To see this, let ˜y k = y k /√

E k, that is, ˜y k is the result of

correlat-ing the received process with the normalized (unit-energy) signal of the kth user Then,

we have

sgn R−1y = sgn E −1/2 R−1E −1/2 y

= sgn W −1/2 R−1˜y

where R is the cross-correlation matrix of normalized signals and therefore, the same

decisions are obtained by multiplying the vector of normalized matched filter outputs bythe inverse of the normalized cross-correlation matrix For an iterative solution of theproblem, see Reference [3]

13.2.3 The optimum linear multiuser detector

Linear detector [4] that minimizes the probability of bit error will be referred to asoptimum linear multiuser detector Its operation can be represented as

We will consider the set I (R) of generalized inverses of the cross-correlation matrix R

and analyze the properties of the detector

in the next chapter The special case I (R) = R−1 is referred to as a decorrelatingdetector

13.3 MULTISTAGE DETECTION IN ASYNCHRONOUS CDMA

If the indexing of users is arranged in increasing order of their delays, then the output of

the correlator of user k can be represented as

η (i) k is the component of the statistic due to the additive channel noise In vector notation,

letting z (i) ( 0) = z (i)

1 ( 0), z2(i) ( 0), , z (k) K ( 0)T, we have

z (i) ( 0) = η (i) + R(1)b (i −1) + R(0)b (i) + R(−1)b (i +1) ( 13.18)

13.3.1 The multistage detector

The multistage detector [5] recreates the interfering term for each user on the basis of bitestimations in the previous stage (iteration), subtracts the estimated MAI and then makesthe new estimate of data that can be represented as

The block diagram of multistage multiuser detector (MSMUD) is shown in Figure 13.6

A detailed implementation of the kth M-stage processor where for each m = 1, 2, ,

M − 1, ˆI (i −2m+1)

k (m) denotes the estimate of the MAI reconstructed in the mth stage on

the basis of bit estimates ˆb (i j −2m) (m − 1), ˆb (i −2m+1)

j (m − 1) and ˆb (i −2m+2)

obtained from the other K− 1 processors is shown in Figure 13.7

An example of probability of error curves is shown in Figure 13.8 All parameters areshown in the figure itself One can see that even two-stage detector may significantlyimprove the system performance

MULTISTAGE DETECTION IN ASYNCHRONOUS CDMA 463

Matched filter User 2

M -stage processor User 2

M -stage processor User K

Matched filter User K

Store

bk(i−4)(3)bk (i−5)(3)bk (i−6)(3)

–

Delay 2

Delay 2

In order to further emphasize the role of multiuser detection (MUD) in the presence ofnear far effect, Figure 13.9 presents BER for the case when the cross-correlation is very

high r12= 1/3 One can see that when the second user becomes stronger and stronger theimprovement compared with a conventional detector is more significant

This conclusion becomes more and more relevant if either r12 is increased, as inFigure 13.10, or SNR is increased, as in Figure 13.11

Figure 13.12 demonstrates the same results for five users in the network

One- stage U.B One- stage AV U Two- stage U.B Two- stage AV U Single user

conventional receiver (CR) and the two-stage receiver and the single-user bit error probability:

Aazhang, B (1990) Multistage detection in asynchronous code division multiple access

communications IEEE Trans Commun., 38, 509 – 519, by permission of IEEE.

NONCOHERENT DETECTOR 465

N = 31

K = 2

E2/E1= 3 dB

One- stage U.B.

One- stage AV U Two- stage U.B.

Two- stage AV U Single user

5

Conventional Decorrelator Optimum linear Two-stage (conv) Two-stage (dec) Optimum

r = 1/3 SNR1 = 8 dB

M and Aazhang, B (1991) Near optimum detection in synchronous code division multiple access

systems IEEE Trans Commun., 39, 725 – 736, by permission of IEEE.

13.4 NONCOHERENT DETECTOR

13.4.1 Conventional noncoherent single-user detector – DPSK

A conventional detector for differential phase keying signals is defined by the followingequation

Conventional Decorrelator Optimum linear Two-stage (conv) Two-stage (dec) Three-stage (dec) Optimum

Varanasi, M and Aazhang, B (1991) Near optimum detection in synchronous code division

multiple access systems IEEE Trans Commun., 39, 725 – 736, by permission of IEEE.

r = 0.7 SNR1= 8 dB

Conventional Decorrelator Optimum linear Two-stage (conv) Two-stage (dec) Optimum

NONCOHERENT DETECTOR 467

SNR1 = 8 dB

Active Users: 1,2,3,4,5

Conventional Decorrelator Two-stage (dec) Three-stage (dec) Four-stage (dec)

M and Aazhang, B (1991) Near optimum detection in synchronous code division multiple access

systems IEEE Trans Commun., 39, 725 – 736, by permission of IEEE.

where f m (t) is the signal matched filter function In the trivial case it is the signalspreading code only The block diagram is shown in Figure 13.13

13.4.2 Noncoherent linear multiuser detectors – DPSK

In general, a noncoherent linear multiuser detector for the mth user, denoted by a nonzero

transformation h (m) ∈ C K, is defined by the decision

A noncoherent decorrelating detector for user m is defined by the decision with the linear

transformation h = d where d denotes the complex conjugate of the mth column of a generalized inverse R I of R If the mth user is linearly independent, it can be shown that

Rd = u m is the mth unit vector If all the signature signals are linearly independent, R−1exists and the decorrelating transformation d is uniquely characterized as the complex conjugate of the mth column of the inverse of R The receiver block diagram is shown

in Figure 13.14

For illustration purposes, four users, using Gold sequences from Figure 13.15(a), areconsidered Performance results with MU detector are shown in Figure 13.15(b) [7]

13.4.4 Noncoherent detection in asynchronous multiuser channel

The z-transform of equation (13.18) gives

b ˆ 2

b ˆ k

NONCOHERENT DETECTOR 469

+1

−1 +1

−1 +1

−1 +1

assigned to the four users of a four-user DS-SSMA system (b) Bit-error rate of first user as a function of the first user’s signal-to-noise ratio These error rates are independent of interfering

signal energies and phases.

1

) Re(

) Re(

Differential encoder

.

where

S (z) = R(−1)z + R(0) + R(1)z−1 ( 13.24)

and Z (z), ˆ D (z) and N (z) are the vector-valued z-transforms of the matched-filter output

sequence, the sequence{ ˆd(l) = A(l)d(l)} and the noise sequence {n(l)} at the output of

the matched filters If we define

13.5 MULTIUSER DETECTION IN FREQUENCY

NONSELECTIVE RAYLEIGH FADING CHANNEL

Topics covered in the previous chapter are now repeated for the fading channel Previouslydescribed algorithms are extended to the fading channel by using as much analogy as

MULTIUSER DETECTION IN FREQUENCY NONSELECTIVE RAYLEIGH FADING CHANNEL 471

possible in the process of deriving the system transfer functions In frequency-selectivechannels, decorrelators are combined with the RAKE type receiver in order to furtherimprove the system performance A number of simulation results are presented in order

to illustrate the effectiveness of these schemes The concept of this chapter is based onproper understanding of the channel model, which is covered in Chapter 8 The overallsystem model, including the channel model for frequency-nonselective fading, is shown

in Figure 13.17

Parameters c k (i) are, for fixed i, independent, zero-mean, complex-valued Gaussian

random variables, with variances |c k|2 with independent quadrature components Thetime-varying nature of the channel is described via the spaced-time correlation function

13.5.1 Multiuser maximum likelihood sequence detection

By using analogy from the previous section, the likelihood function in this case can berepresented as

MULTIUSER DETECTION IN FREQUENCY NONSELECTIVE RAYLEIGH FADING CHANNEL 473

with normalized signature waveform vector

Since there is no intersymbol interference (ISI), R( ) = 0, ∀| | > 1 and R(−1) = R H ( 1).

Because of the ordering of the user, RH(1) is an upper triangular matrix with zero elements

on the diagonal The decorrelating detector front end consists of K filters matched to the

normalized signature waveforms of the users The output of this filter bank, sampled at

the th bit epoch is

y( )=

 +∞

The vector of sufficient statistics can also be represented as

y( ) = R(−1)EC( + 1)b( + 1) + R(0)EC( )b( )

As in equation (13.25), the decorrelator is a K-input K-output linear time-invariant (LTI)

filter with transfer function matrix

G(z) = [R(−1)z + R(0) + R(1)z−1]−1 = S−1(z) ( 13.46)

The z-transform of the decorrelator output vector is

Np(z) is the z-transform of the output noise vector sequence having power spectral density

Matched filter User 2

Matched filter User K

Decorrelating filter

Decision for User 1

Decision for User K Decorrelating filter

r (t )

Matched filter User 1

Matched filter User 2

MULTIUSER DETECTION IN FREQUENCY-SELECTIVE RAYLEIGH FADING CHANNEL 475

Conventional detector Decorrelator detector MLS detector upper bound Isolated transmission

(1993) Multiuser Detection for Rayleigh Fading Channel Ph.D Thesis, Department of Electrical

and Computer Engineering, Northeastern University, Boston, MA, by permission of IEEE.

SNR (dB)

(1993) Multiuser Detection for Rayleigh Fading Channel Ph.D Thesis, Department of Electrical

and Computer Engineering, Northeastern University, Boston, MA, by permission of IEEE.

In equation (13.49), h k (t) is the equivalent received symbol waveform of finite duration

[0, T k ] [convolution of equivalent low-pass signature waveform u k (t) and the channel

impulse response c k (t) ] We define the memory of this channel as v, the smallest integer such that h k (t) = 0 for t > (v + 1)T, and all k = 1, , K The impulse response of the

kth user channel is given by

When the signaling interval T is much smaller than the coherence time of the channel,

the channel is characterized as slow fading, implying that the channel characteristics can

be measured accurately Since the channel is assumed to be Rayleigh fading, the

coef-ficients c k, (t)are modeled as independent zero-mean complex-valued Gaussian randomprocesses In the sequel we use the following notation

MULTIUSER DETECTION IN FREQUENCY-SELECTIVE RAYLEIGH FADING CHANNEL 477

where E k is the energy, s k (t) is the real-valued, unit-energy signature waveform with

period T and φ k is the carrier phase In this case the received signal given byequation (13.49) becomes

r(t) = S(t, b) + n(t) = bTht + n(t) ( 13.55)

The equivalent data sequence is as in equation (13.31)

b= [b1( −M) · · · b K ( −M) · · · b1(M) · · · b K (M)]T ( 13.56) The equivalent waveform vector of NK elements is

is the equivalent signature vector of KL elements.

13.6.1 Multiuser maximum likelihood sequence detection

Log likelihood function in this case becomes

is the output of the bank of matched filters sampled at the bit epoch of the users

Matrix H is an N × N block-Toeplitz cross-correlation waveform matrix with K × K

13.6.2 Viterbi algorithm

Since every waveform h k (t) is time-limited to [0, T k ], T k < (v + 1)T , it follows that

H(l) = 0, ∀|l| > v + 1 and H(j) = H H (j ) for j = 1, , v + 1.

Because of the ordering of the users, HH (v + 1) is an upper triangular matrix with zero

elements on the diagonal Provided that knowledge of a channel is available, the MLSdetector may be implemented as a dynamic programming algorithm of the Viterbi type

The vector Viterbi algorithm is the modification of the one introduced for input

M-output linear channels where the dimensionality of the state space is 2(v +1)K As in the case

of the additive white Gaussian noise (AWGN) channel, a more efficient decomposition ofthe likelihood function results in an algorithm with a state space of dimension 2(v +1)K−1.Frequency-selective fading is described by the wide-sense stationary uncorrelated-

scattering model The bandwidth of each signature waveform is much larger than the

coherence bandwidth of the channel, Bw c The time-varying frequency-selective

channel for each user can be represented as a tapped delay line with tap spacing 1/Bw,

so that equation (13.51) becomes

So, the received signal from Figure 13.22 can be represented as

In addition, if we use notation

b(i) = [b1(i)b2(i) · · · b K (i)]T, i = −M, , M