Turbo Multiuser Detection in Space-Time Block-Coded Systems

Turbo Multiuser Detection in Space-Time Block-Coded Systems

The recently developed space-time coding (STC) techniques [350] integrate the methods of transmitter diversity and channel coding and provide significant capacity gains over traditional communication systems in fading wireless channels. STC has been developed along two major directions: space-time block coding (STBC) and space-time trellis coding (STTC). The common features of STBC and STTC lie in their realizations of spatial diversity (i.e., both methods transmit a vector of complex code symbols simultaneously from multiple transmitter antennas). Their differences, on the other hand, lie in their realizations of temporal diversity: In STBC, the temporal constraint is represented in matrix form; whereas in STTC, the temporal constraint is represented in the form of a trellis tree, which is akin to the trellis-coded modulation (TCM) code.

From the coding perspective, the single-user performance of STBC and STTC has been studied in [476, 477], and some code design criteria have been developed. However, in wireless communication systems, sharing the limited radio resources among multiple users is inevitable. Indeed, the emerging wireless systems with multiple transmitter and receiver antennas enable a new dimension for multiple accessing: space-division multiple access (SDMA) [492], which when employed with the more conventional TDMA or CDMA techniques, can substantially increase system capacity. However, if not properly ameliorated, the presence of multiuser interference can significantly degrade receiver performance as well as system capacity. Therefore, the development of efficient detection and decoding techniques for multiuser STC systems (illustrated in Fig. 6.21) is the key to bringing STC techniques into the practical arena of wireless communications. Research results along this direction first appeared in [349, 476], where some techniques for combined array processing, interference cancellation, and space-time decoding for multiuser STC systems were proposed.

Figure 6.21. Multiuser wireless communication system employing multiple transmitter and receiver antennas. There are K users in the system, each user employing N transmitter antennas. At the receiver side, there are M receiver antennas.

In this and the following sections we discuss turbo receiver structures for joint detection and decoding in multiuser STC systems, based on the techniques developed in previous sections. Such iterative receivers and their variants, which were first developed in [288], are described for both STBC and STTC systems. During iterations, extrinsic information is computed and exchanged between a soft multiuser demodulator and a bank of MAP decoders to achieve successively refined estimates of the users' signals. Further developments of low-complexity turbo structures for multiuser STTC systems are given in [217].

6.7.1 Multiuser STBC System

The transmitter end of a multiuser STBC system is shown in Fig. 6.22. The information bit stream for the kth user, {d_k[n]}_n, is encoded by a convolutional encoder; the resulting convolutional code-bit stream {b_k[i]}_i is then interleaved by a code-bit interleaver. After interleaving, the interleaved code-bit stream is then fed to an M-PSK modulator, which maps the binary bits into complex symbols {c_k[l]}_l, where , and W_C is the M-PSK symbol constellation set (M = |W_C|). The symbol stream {c_k[l]}_l, is partitioned into blocks, with each block consisting of N symbols. Due to the existence of the interleaver, we can ignore the temporal constraint induced by the outer convolutional encoder and assume that the set {c_k[l]}_l contains independent symbols. Hence, from the STBC decoder's perspective, we need only consider one block of symbols in the code symbol stream: the code vector .

Figure 6.22. Transmitter structure for a multiuser STBC system.

STBC was first proposed in [12] and was later generalized systematically in [476]. Following [476], the kth user's STBC is defined by a P x N code matrix , where N denotes the number of transmitter antennas or the spatial transmitter diversity order, and P denotes the number of time slots for transmitting an STBC code word or the temporal transmitter diversity order. Each row of is a permuted and transformed (i.e., negated and/or conjugated) form of the code vector c_k. An STBC encoder takes as input the code vector c_k and transmits each row of symbols in at P consecutive time slots. At each time slot, the symbols contained in an N-dimensional row vector of are transmitted through N transmitter antennas simultaneously.

As a simple example, we consider a particular user employing a 2 x 2 STBC (i.e., P = 2, N = 2). Its code matrix is defined by

Equation 6.184

The input to this STBC is the code vector c = [c[1] c[2]]^t. During the first time slot, the two symbols in the first row of (i.e., c[1] and c[2]) are transmitted simultaneously at the two transmitter antennas; during the second time slot, the symbols in the second row of (i.e., –c[2]^* and c[1]*) are transmitted.

We assume a flat-fading channel between each transmitter–receiver pair. Specifically, denote a_m,n as the complex fading gain from the nth transmitter antenna to the mth receiver antenna, where a_m,n ~ N_c(0, 1) is assumed to be a zero-mean circularly symmetric complex Gaussian random variable with unit variance. It is also assumed that the fading gains remain constant over an entire signal frame, but they may vary from one frame to another.

In general, we consider an STBC system with K users, each employing N transmitter antennas. At the receiver side, there are M receiver antennas. In this case, the received signal can be written as

Equation 6.185

In (6.185), m = 1,2, ..., M, consists of the received signal from time slots 1 to P, at the mth receiver antenna; H_k, k = 1, 2, ..., K, is the channel response matrix for the kth user, as explained below; is the code vector for the kth user; and contains the additive Gaussian noise samples from time slots 1 to P at the mth receiver antenna.

As a simple example, consider a single-user (K = 1) STBC system with two (N = 2) transmitter antennas and M receiver antennas, employing the code matrix g₁ in (6.184), the received signal at the mth receiver antenna for this single user can be written as

Equation 6.186

For notational convenience, we write (6.186) in an alternative form by conjugating r^m [1]:

Equation 6.187

We can see that contains information not only of the channel response related to the mth receiver antenna, but also the code constraint of the STBC . Finally, by stacking all the r^m in (6.187), we obtain

Equation 6.188

The signal model in (6.188) can easily be extended to the general model (6.185) of a K-user P x N STBC system, in which each user employs the code defined in [476]. The analogy between this multiuser STBC signal model and the synchronous CDMA signal model (6.74) is evident. Note that to effectively suppress the interfering signals in model (6.185), the size of the receiver signal r should be larger than the number of symbol to be decoded (i.e., MP NK).