Space-Time Coding phần 10 doc

Performance of STTC in CDMA Systems 277Figure 8.18 Block diagram of the space-time matched filter receiver This is equivalent to maximizing 2Reˆx HAHHSH r− ˆxHAHHSH SHAˆx.. The receiver

Performance of STTC in CDMA Systems 277

Figure 8.18 Block diagram of the space-time matched filter receiver

This is equivalent to maximizing

2Re(ˆx HAHHSH r)− ˆxHAHHSH SHAˆx. (8.104)

As the maximum-likelihood detector is too complex, we consider a simple receiver ture as shown in Fig 8.18 [36] The receiver consists of a space-time matched filter detectorand a bank of STTC decoders, one for each user Assuming the knowledge of the channelmatrices, the matched filter detector generates decision statistics of the transmitted space-time symbols for all users and all transmit antennas at a given symbol period The matched

struc-filter is represented by an n T K × n R N c matrix HHSH The decision statistics at the output

of the detector can be represented by a complex n T K× 1 column vector, given by

where M = HHSHSH is the space-time correlation matrix and ny= HHSHn is the resulting

noise vector The (K(i − 1) + k)th element of the decision statistics vector y, denoted

by y k i , is simply the space-time matched filter output for the signal of the ith antenna and user k, obtained by correlating each of the n R received signals with its L p multipath

spreading sequences, (s k,1 , s k,2 , , s k,L p ), weighting them by the complex conjugate of the

corresponding channel coefficients (h k,1 j,i , h k,2 j,i , , h k,L j,i p , j = 1, 2, , n R ), and summing

over the multipath indices l and receive antenna j [33].

The decision statistics for user k, y1k , y k2, , y n T

k , are then passed to the user’s STTCdecoder, which estimates the transmitted binary information data ˆb k

Error Probability for The Space-Time Matched Filter Detector

The space-time matched filter detector in (8.105) demodulates the received signal using

the knowledge of the kth user’s spreading sequence, timing, and channel information for

each transmit antenna It does not take into account the structure of the multiple access

interference (MAI) The error probability for the signals of the ith antenna of the kth user

conditioned on the other users’ data and on the channel coefficients is

where the subscript (·) k denotes the kth element of the vector, and (·) k,k denotes the kth

diagonal element of the matrix

path with the minimum path metric as the decoded sequence

When the matched filter detection is considered as a multipath diversity reception nique for frequency-selective fading in a MIMO system, it introduces interference from

tech-multiple antennas and multipaths The output of the matched filter detector, y, does not only

have a diversity gain which is obtained from the diagonal element of the correlation matrix

(M) k,k, k = 1, 2, , n T K, but also has the multiple antenna and multipath interference

from the off-diagonal elements of (M) k,u, u = 1, 2, , n T K(u = k) Therefore, to

reduce the effect of the multiple antennas interference of the user, we reconstruct the trellisbranch labels as ˜x1

k (t ) is the matched filter output for the ith antenna of user k.

Space-Time MMSE Multiuser Detector

In order to reduce the effects of multipath, multiuser, and multiple antennas interference, weconsider a space-time MMSE detector [29] [33] as shown in Fig 8.19 Given the decision

statistics vector y in (8.105), the space-time MMSE detector applies a linear transformation

W to y so that the mean-squared error between the resulting vector and the data vector x is

minimized The space-time MMSE detection matrix W of size n T K × n T K should satisfy

Performance of STTC in CDMA Systems 279

Figure 8.19 Block diagram of the STTC MMSE receiver

which results in the standard Wiener solution

If all of the K users’ n T L p spreading sequences are linearly independent, then SHShas a

full rank Under this assumption, it can be shown that with probability one, Hj HSHSHj

has a full rank for any j It follows that matrix M = HHSHSH is of a full rank and invertible Then the space-time MMSE matrix W in (8.111) is simplified to

Error Probability of the Space-Time MMSE with STTC

We now consider the error probability conditioned on the interfering users’ data and onthe channel realization for the space-time MMSE receiver The space-time linear MMSEdetector takes into account both the interference and the background noise However, it

does not completely eliminate MAI The space-time MMSE detector output for antenna i

of user k in the synchronous system can be written as

(W H y) k = ([M + σ2

A−2]−1y)

k

= B i k

β u p= B

p u

The complexity of calculating the error probability from the above expression is exponential

in the number of users and the number of transmit antennas This computational burden ismainly due to the leakage coefficients calculation The error probability can be approximated

by replacing the multiple access interference with a Gaussian random variable with the samevariance [29] Thus, the error probability in (8.117) for the space-time MMSE detection can

eigen-Performance of STTC in CDMA Systems 281

An iterative MMSE receiver [34] is also considered in a multipath MIMO system The

interference estimate for the ith antenna of the kth user is formed by adding the regenerated signals of all users and all transmit antennas, except the one for the desired user k and antenna i After each decoding iteration, the soft decoder outputs are used to update the a

priori probabilities of the transmitted symbols These updated probabilities are applied inthe calculation of the MMSE filter feedforward and feedback coefficients Assuming that

z i k (t ) is the input to the kth user decoder corresponding to the ith transmit antenna at time

the feedback soft decisions for all users and all transmit antennas except the one for the

i th transmit antenna of user k Note that the feedback coefficients appear only through their

sum in (8.121) We can assume, without loss of generality, that

w i b,k (t ) = (w i

where w b,k i (t )is a single coefficient that represents the sum of the feedback terms

The coefficients wi f,k (t ) and w b,k i (t )are obtained by minimizing the mean square value

of the error  between the data symbols and its estimates, given by

c × (n T K − 1) matrix composed of the signature vectors of all users and antennas

except the ith antenna of the kth user, and x i k (t ) is the (n T K − 1) × 1 transmitted data vector from all users and antennas except the ith antenna of the kth user The optimum

feedforward and feedback coefficients wi f,k (t ) and w b,k i (t )can be represented by

wi f,k (t ) = (A + B + R n − F F H )−1hi

Figure 8.20 Block diagram of the space-time iterative MMSE receiver

R n = σ2

nIn R N c

(8.127)

where IN denotes the identity matrix of size N , x E i

k is the (n T K − 1) × 1 vector of the expected values of the transmitted symbols from the other n T K−1 users and their antennas.Figure 8.20 shows the space-time iterative MMSE receiver structure [36] In the firstdecoding iteration, we assume that the a priori probabilities for transmitting all symbols

are equal, and hence, xE i

k = 0 The feedforward filter coefficients vector wi

It is shown that the three different detectors provide similar performance regardless of the

Performance of STTC in CDMA Systems 283

Table 8.1 Parameters for system environmentsMultiple Access WCDMA / Forward link

Figure 8.21 Error performance of an STTC WCDMA system on a flat fading channel

number of users, since there is no MAI due to synchronous transmission and the orthogonalspreading sequences

Figure 8.22 depicts the FER performance of various receivers versus the number of users

on a two-multipath fading channel The performance curves show that the space-time MMSEmultiuser receiver improves the error performance significantly compared to the matchedfilter or the single-user receiver Figure 8.23 represents the BER performance versus thenumber of users on a two-multipath fading channel From the results, we can see that thespace-time MMSE multiuser receiver increases the number of users of the system about 3times than that of the single-user or the matched filter receiver at a BER of 10−3.

The performance of STTC WCDMA systems with iterative MMSE receivers is also

eval-uated by simulations We assume that the number of users is K= 4 and the spreading factor

is N c = 7 The spreading sequences assigned to different users were chosen randomly TheWCDMA chip rate is set to be 3.84 Mcps and each frame is composed of 130 symbols Thefading coefficients are constant within each frame and a 2×2 MIMO channel is considered.Figures 8.24 and 8.25 depict the FER performance of various receivers on flat fading and

Figure 8.22 FER performance of an STTC WCDMA system on frequency-selective fading channels

Figure 8.23 BER performance of an STTC WCDMA system on frequency-selective fading channels

Performance of STTC in CDMA Systems 285

Figure 8.24 FER performance of an STTC WCDMA system with the iterative MMSE receiver on

a flat fading channel

Figure 8.25 FER performance of an STTC WCDMA system with the iterative MMSE receiver on

a two-path Rayleigh fading channel

two-path Rayleigh fading channels, respectively The figures show that the iterative MMSEreceiver achieves a remarkable gain compared to the LMMSE receiver.

In this section we consider a synchronous DS-CDMA LST encoded system with both randomand orthogonal sequences over a multipath Rayleigh fading channel The transmitter blockdiagram is shown in Fig 8.26

There are K active users in the system The signal transmitted from each of the active users is encoded, interleaved and multiplexed into n T parallel streams All layers of thesame user are spread by the same random or orthogonal Walsh spreading sequence assigned

to that user Various layers of each user are transmitted simultaneously from n T antennas.The delay spread of the multipath Rayleigh fading channel is assumed to be uniformly

distributed between [0, N c T c /2] for random and [0, Nc T c /4] for orthogonal sequences,

where T c is the chip duration, N c is a spreading gain defined as a ratio of the symbol andthe chip durations andx denotes integer part of x The delay of the lth multipath, denoted

by τ k,l for user k, is an integer multiple of the chip interval.

Figure 8.26 Block diagram of a horizontal layered CDMA space-time coded transmitter

Performance of Layered STC in CDMA Systems 287

The receiver has n Rantennas and employs an IPIC-DSC or an IPIC-STD multiuser tor/decoder, described in Chapter 6 We assume that the receiver knows all user spreadingsequences and perfectly recovers the channel coefficients

detec-In the discrete time model, the spreading sequence and a vector with channel gains

on the paths from transmit antenna m to all receive antennas for the lth multipath are combined into a composite spreading sequence of length n R N c , where N c is the spreading

gain This composite spreading sequence for user k and transmit antenna m, shifted for the delay corresponding to the j th symbol and multipath l, can be expressed by a column

gain on the path from transmit antenna m to receive antenna n for user k and multipath l

and 0e is a row vector with e = (L − j)N c + τmax/T c  − τ k,l /T c zeros as elements,

where τmax= max{τ k,L p |k = 1, 2, , K} The composite spreading sequences h k,l

A block diagram of the CDMA iterative receiver is shown in Fig 8.27

The received chip matched signal sequence at antenna n is denoted by r n and can beexpressed as

where r j,q n denotes the received qth chip at discrete time j at receive antenna n.

The received signal sequences for n R receive antennas are arranged into a vector r as

r=( (r1) T , (r2) T , , (r n R ) T )T

(8.132)

Figure 8.27 Block diagram of a horizontal layered CDMA space-time coded iterative receiver

The transmitted symbols for user k at time j are arranged into a vector x k (j )as

xk (j )=& x j k,1 , x j k,2 , x k,n T

j

'T

(8.133)

where x j k,m is the symbol transmitted at discrete time j by user k and antenna m.

In order to incorporate the multipath effects in a system model with L p multipaths,

we introduce a vector xk P (j ) which is a column vector with L p replicas of vector xk (j ),given by

Performance of Layered STC in CDMA Systems 289

Let us denote the transmitted signals for a frame of L time intervals by x

x=( (x P ( 1)) T , (x P ( 2)) T , , (x P (L)) T )T

(8.136)

The chip sampled received signal for a frame of L symbols can now be expressed as

where r and H are given by Eqs (8.132) and (8.130), respectively, and n is a column vector

with AWGN samples

The output of the IPIC for user k, transmit antenna m and iteration i can be expressed as

whereˆxk,m,i−1 is a vector with transmitted symbol estimates in iteration i− 1 as elements,

except for the elements corresponding to the estimates of the kth user’s mth transmit antenna

symbols The latter are set to zero

In the IPIC-STD receiver the output of the PIC is approximated by a Gaussian random

variable with the mean µ k,m,i and the variance (σ k,m,i )2 and fed into the decoder for aparticular user and a transmit antenna

The mean of the decoder input is calculated as

Its variance is estimated as

(σ k,m,i )2= E[(y k,m,i (j )−

L p

l=1

(h k,l m (j )) Hhk,l m (j ) ˆx k,m,i−1(j ))2] (8.140)

whereˆx k,m,i−1(j ) is an LLR estimate in iteration i −1 for the kth user’s symbol transmitted

at time j by the mth transmit antenna.

The IPIC-DSC receiver performs soft parallel interference cancellation and decision tics combining for each user and each transmit antenna

statis-In the IPIC-DSC receiver the input to the decoder is formed as

y c k,m,i (j ) = p k,m,i

1 y k,m,i (j ) + p k,m,i

2 y k,m,i−1

where y k,m,i (j ) and y k,m,i−1

c (j ) are outputs of the PIC in the iteration i and the DSC in iteration i− 1, respectively

The DSC coefficients p k,m,i1 and p k,m,i2 are given by

p k,m,i1 = µ k,m,i (σ

k,m,i−1

c )2(µ k,m,i )2(σ k,m,i−1

where µ k,m,i and (σ k,m,i )2 are the mean and the variance of y k,m,i (j ) , and µ k,m,i c and

(σ k,m,i−1

c )2 are the mean and the variance of y k,m,i−1

c (j ) The performance of an HLSTC encoded down-link DS-CDMA system with PIC-DSC and

PIC-STD detectors is evaluated by simulation The HLST code employs n T = 4 transmit

and n R = 4 receive antennas and each layer’s signal is encoded by an R = 1/2 rate, 4-state

convolutional code The convolutional code is terminated to the all-zero state A frame for

each layer consists of L= 206 coded symbols Assuming that BPSK modulation is used,

the spectral efficiency of the system is η= 2 bits/s/Hz The spreading sequences are either

random with the spreading gain of N c = 7 or Walsh orthogonal sequences with the spreading gain of 16 and a long scrambling code The number of users in a system with random codes was variable and adjusted to achieve the FER close to the interference free performance while in the system with orthogonal sequences the multiple access interference is low and the maximum number of users equal to the spreading gain 16 was adopted The channel is

represented by a frequency-selective multipath Rayleigh fading model with L p = 2 equal power paths The signal transmissions are synchronous The channel is quasi-static, i.e the delay and the path attenuations are constant for a frame duration and change independently

from frame to frame It is assumed that E[*L p

l=1(h k,l m (j )) Hhk,l m (j )]= 1

Figures 8.28 and 8.29 show the bit error rate and frame error rate curves versus the number of the users for the multiuser system with PIC-STD and PIC-DSC receiver in a

10−5

10−4

10−3

10−2

10−1

100

number of users

PIC−DSC (LLR) PIC−STD (LLR)

I=1

I=2

I=3

I=4

I=5

I=8

Figure 8.28 BER performance of a DS-CDMA system with (4,4) HLSTC in a two-path Rayleigh

fading channel, E /N = 9 dB