Turbo Multiuser Receiver in Turbo-Coded CDMA with Multipath Fading

Turbo Multiuser Receiver in Turbo-Coded CDMA with Multipath Fading

In this section we demonstrate the performance of the turbo multiuser receiver in a turbo-coded CDMA system with multipath fading. We consider a K-user CDMA system employing random aperiodic spreading waveforms and signaling through multipath fading channels. Each user's information data bits are encoded by a turbo encoder and then randomly interleaved. The interleaved code bits are then BPSK mapped and spread by a random signature waveform before being sent to the multipath fading channel. A block diagram of the system is illustrated in Fig. 6.15. The turbo multiuser receiver for this system iterates between the SISO multiuser detection stage (as discussed in Section 6.5.2) and the soft turbo decoding stage (as discussed in Section 6.6.1) by passing the extrinsic information of the code bits between the two stages.

To compare the performance of a turbo multiuser receiver with that of a conventional technique used in practical systems, a single-user RAKE receiver employing maximal-ratio combining followed by a turbo decoder for the turbo-coded CDMA system is described next. The received signal in this system is given by (6.133) and (6.134). In a single-user RAKE receiver, the decision statistic for the kth user's ith code bit, b_k[i], is given by y_k[i] defined in (6.138):

Equation 6.182

To obtain the LLR of the code bit b_k[i] based on y_k[i], a Gaussian assumption is made on the distribution of y_k[i]. Moreover, assume that the user spreading waveforms contain i.i.d. random chips and that the time delay t_l,k is distributed uniformly over a symbol interval. Assume also that the multipath fading gains are independent between different users and are normalized such that . It is shown in the Appendix (Section 6.9.2) that the LLR of b_k[i] based on the assumption above is given by

Equation 6.183

Note that the SISO multiuser detector discussed in Section 6.5.2 operates on the same decision statistic as the conventional RAKE receiver (i.e., the outputs of the maximum ratio combiners {y_k[i]}_k;i). The RAKE receiver demodulates the kth user's data bits based only on {y_k[i]}_i, whereas the SISO multiuser detector demodulates all users' data bits jointly using all decision statistics {y_k[i]}_i;k.

Next we demonstrate the performance of the proposed turbo multiuser receiver in multipath fading CDMA channels by some simulation examples. The multipath channel model is given by (6.132). The number of paths for each user is three (L = 3). The delays of all users' paths are randomly generated. The time-varying fading coefficients are randomly generated to simulate channels with different data rates and vehicle speeds. The parameters are chosen based on the prospective services of wideband CDMA systems [431].

We consider a reverse link of an asynchronous CDMA system with six users (K = 6). The spreading sequence of each different user's different coded bit is independently and randomly generated. The processing gain is N = 16. Each user uses a different random interleaver to permute its code bits. In all simulations, the same set of interleavers is used, and all users have equal signal amplitudes. The number of iterations within each soft turbo decoder is five.

The code we choose is a rate-1/3 binary turbo code, whose encoder is shown in Fig. 6.16. The two recursive convolutional constituent encoders have a generator polynomial,

with effective free distance 10 [30]. An S-random interleaver, p_j, shown in Fig. 6.14, is used and explained below. The interleaver size is I = 1000 and S = 22. (Hence the symbol frame length M = 3000.)

The S-random interleaver [103] is one type of semirandom interleaver. It is constructed as follows. To obtain a new interleaver index, a number is randomly selected from the numbers that have not previously been selected as interleaver indices. The number selected is accepted if and only if the absolute values of the differences between the number currently selected and the S numbers accepted previously are greater than S. If the number selected is rejected, a new number is selected randomly. This process is repeated until all I (interleaver size) indices are obtained. The searching time increases with S. Choosing S < usually produces a solution in reasonable time. Note that the minimum weight of the code words increases as S increases. This equivalently increases the effective free distance [30] of parallel concatenated codes, which improves the weight distribution and thus the performance of the code. In Example 1 we will see that S-random interleavers offer significant interleaver gains over random interleavers.

Example 1: Effect of the S-Interleaver The BER performance of the turbo code used in this study with random interleavers and an S-random interleaver in a single-user AWGN channel is plotted in Fig. 6.17. It is seen that the S-random interleaver offers a significant interleaver gain over random interleavers.

In the following three examples, the performance of a turbo multiuser receiver is compared with that of a conventional single-user RAKE receiver. The single-user RAKE receiver computes the code-bit LLRs of the Kth user using (6.183); these are then fed to a turbo decoder to decode the information bits. The BER averaged over all six users is plotted.

Example 2: Fast Vehicle Speed and Low Data Rate In this example we consider a Rayleigh fading channel with vehicle speed of 120 km/h, data rate of 9.6 kb/s, and carrier frequency of 2.0 GHz (the effective bandwidth–time product is BT = 0.0231). The results are plotted in Fig. 6.18.

Example 3: Medium Vehicle Speed and Medium Data Rate Next, we consider a multipath Rayleigh fading channel with vehicle speed 60 km/h, data rate 38.4 kb/s, and carrier frequency 2.0 GHz (BT = 0.00289). The results are plotted in Fig. 6.19.

Example 4: Very Slow Fading Finally, we consider a very slow fading channel (a time-invariant channel). The fading coefficients {a_l,k} of paths are randomly generated and kept fixed, and every user has equal received signal energy. The results are plotted in Fig. 6.20.

From Examples 2, 3, and 4 it is seen that significant performance gain is achieved by a turbo multiuser receiver compared with a conventional noniterative receiver (i.e., the RAKE receiver followed by a turbo decoder). The performance of a turbo multiuser receiver with two iterations is very close to that of a RAKE receiver in a single-user channel. Moreover, at high SNR, the detrimental effects of multiple-access and intersymbol interference in the channel can be eliminated almost completely. Furthermore, it is seen from the simulation results that a turbo multiuser receiver in a multiuser channel even outperforms a RAKE receiver in a single-user channel. This is because the RAKE receiver makes the assumption that the delayed signals from different paths for each user are orthogonal, which effectively neglects the intersymbol interference.