Projection-Based Turbo Multiuser Detection

Projection-Based Turbo Multiuser Detection

In Section 6.7.2 we considered the problem of decoding the information of all users in the system. In some cases, however, we are interested in decoding the information of specific users only and are not willing to pay extra receiver complexity for decoding the information of undesired users. One approach to addressing this problem is to null out the signals of the K_u undesired users at the front end and then to apply the iterative soft multiuser demodulation algorithm on the rest of K_d = K – K_u users' signals [439]. In [476], a projection-based technique was proposed for interference cancellation in STC multiuser systems. Here, we discuss applying soft multiuser demodulation and iterative processing on the projected signal to further enhance the receiver performance.

Consider again the signal model (6.185). Divide the users into two groups, desired users and undesired users. Rewrite (6.185) as

Equation 6.205

where the subscript d denotes desired users and u denotes undesired users. Define , , and (where is the Moore–Penrose generalized inverse of H_u [189]). It is assumed that the matrix H_u is "tall" (i.e., MP > NK_u) and has full column rank. It is easily seen that

Equation 6.206

(i.e., the undesired users' signals are nulled out by this projection operation). Moreover, before projection, the number of linearly independent rows of H is MP, whereas after projection, the number of linearly independent rows of becomes MP – NK_u, which implies that in the projected system the effective number of receiver antennas (the effective receiver diversity order) is reduced to M' (MP – NK_u)/P. Hence, the projection operation incurs a diversity loss. Following the same derivations as in Section 6.7.2, we can apply the soft multiuser demodulator and MAP decoder on the projected signal in (6.206) to iteratively detect and decode the information bits of the desired users.

Since we assume that the fading channel remains static within an entire signal frame, which normally contains hundreds of code blocks (of N symbols), we need only compute the projection matrix once per signal frame. Therefore, the dominant computation of the projection-based soft multiuser demodulator is the same as before. However, the overall computational complexity of the multiuser receiver is reduced, since now we need only decode K_d users' information [i.e., only K_d (instead of K) MAP decoders are needed].

Next we provide computer simulation results to illustrate the performance of the turbo receivers in multiuser STBC systems. It is assumed that the fading processes are uncorrelated among all transmitter–receiver antenna pairs of all users; and for each user, the fading processes are uncorrelated from frame to frame but remain static within each frame. It is also assumed that the channel response matrix H in (6.185) is known perfectly. All users employ the same STBC code, but each user uses a different random interleaver. Furthermore, all users transmit M-PSK symbols with equal powers, a scenario in space-division multiple-access (SDMA) systems. Such an equal-power setup is also the worst-case scenario from the interference mitigation point of view.

We consider a four-user (K = 4) STBC system, as shown in Fig. 6.22. Each user employs the STBC defined in (6.184) and two transmitter antennas (N = 2). An 8-PSK signal constellation is used in the modulator. The outer convolutional code, which is the same for all users, is a four-state, rate-½ code with generator (5,7) in octal notation. The encoder is forced to the all-zero state at the end of every signal frame. Each signal frame contains 128 8-PSK symbols. At the receiver side, four antennas (M = 4) are used.

Assume that all K users' signals are to be decoded (K = 4). We first demonstrate the performance of the iterative receiver discussed in Section 6.7.2. The frame-error rate (FER) and the bit-error rate (BER) are shown in Fig. 6.24. For the purpose of comparison, we also include the performance of the single-user STBC system with iterative decoding. The dotted lines (denoted as SU1-1) in Fig. 6.24 represent the performance of the single-user system with two transmitter antennas (N = 2) and four receiver antennas (M = 4) after its first iteration [i.e., the conventional (noniterative) single-user performance]. The dash-dotted lines (denoted as SU1-6) in Figs. 6.24 and 6.25 represent the single-user performance after six iterations using the same iterative structure discussed in Section 6.7.2.

Since a single user transmits different STC code symbols from its N transmitter antennas, it could be viewed as a virtual N-user system as discussed in Section 6.7.2. Then the iterative receiver structure for the multiuser STC systems can also be applied to single-user STC systems. Note that the optimal receiver of the proposed multiuser STBC system involves joint decoding of the multiuser STBC and outer convolutional codes, which has a prohibitive complexity [|W_c|^NK2ⁿ]. However, the STBC signal model in (6.188), either single-user or multiuser, is analogous to the synchronous CDMA multiuser system model. As seen from previous sections, at high SNR, the iterative technique for interference suppression and decoding in a multiuser system can approach the performance of a single-user system (which is a lower bound for optimal performance). Hence it is reasonable to view the performance of the iterative single-user STBC system as an approximate lower bound on optimal joint decoding performance. It is seen from Fig. 6.24 that after six iterations the performance, in terms of both FER and BER, of both the single-user and multiuser STBC systems is significantly improved compared with that of the noniterative receivers (i.e., the performance after the first iteration). More impressively, the performance of the iterative receiver in a multiuser system approaches that of the iterative single-user receiver at high SNR.

We next demonstrate the performance of the projection-based turbo receiver. Assume that K_d out of all K users' signals are to be decoded (K = 4, K_d = 2). In this scenario, two users are first nulled out by a projection operation, and the other two users are iteratively detected and decoded, as discussed in Section 6.7.3. The performance is shown in Fig. 6.25. It is shown in [476] that due to the projection operation, the equivalent receiver antenna number (the receiver diversity) is reduced from MP to MP – NK_u. So, for a fair comparison, in Fig. 6.25 we also present the iterative decoding performance after the first iteration (denoted by SU2-1) and after the sixth iteration (denoted by SU2-6) of the single-user system with two transmitter antennas (N = 2) and two receiver antennas (M' = 2), where M' denotes the effective number of receiver antennas for the projected system, with M' (MP – NK_u)/P. It is seen that the projection-based turbo receiver still significantly outperforms the projection-based noniterative receiver. However, compared with the turbo receiver discussed above, the projection operation incurs a substantial performance loss. The reason for such a performance loss is twofold. First, the projection operation causes a diversity loss by suppressing the interference from other K_u users; second, the projection operation enhances the background ambient noise. It is therefore preferable to use turbo receiver operating on all users' signals in STBC systems.