7.7 Adaptive Linear MMSE NBI Suppression

In Section 7.6, we saw that the linear MMSE detector is an excellent technique for suppressing NBI from spread-spectrum systems. A further advantage of the MMSE detector is that it is easily adapted to unknown NBI statistics. As discussed in Chapter 2, a number of adaptive algorithms for the linear MMSE detector as an MAI suppressor have been explored, including both those using a sequence of known training symbols and blind algorithms, which do not require such sequences [183, 237, 267, 325, 369, 403] (see [184] for a survey). Many of these studies have employed the LMS algorithm for adaptation because of its simplicity and overall good performance characteristics against wideband MAI. However, unlike the case of adaptive prediction-based NBI suppression discussed in Sections 7.2 and 7.3 (in which LMS features prominently), adaptation of the linear MMSE detector takes place at the symbol rate rather than at the chip rate. This does not cause difficulties with the LMS algorithm for wideband interference such as MAI. But for NBI, some problems may arise in using LMS at the symbol rate, due to resulting large eigenvalue spreads of the covariance matrix of the observations (cf. [603] for a review of the properties of LMS). These problems can be corrected by using instead the recursive-least-squares (RLS) algorithm, which may have better properties in such situations [389].

The use of the RLS algorithm for blind adaptation of the linear MMSE detector for MAI suppression is discussed in Section 2.3.2 of this book (cf. Algorithm 2.3). Exactly the same algorithm can be employed for adaptive suppression of both MAI and NBI. It is shown in the Appendix to this chapter (Section 7.9.5) that the steady-state SINR of the blind RLS linear MMSE detector is given by

Equation 7.140

where SINR ^* is the optimum SINR value given in (7.77) and where (recall that l is the forgetting factor)

Equation 7.141

Usually, the RLS algorithm operates in the range such that d << 1. From (7.140) it can be seen that the performance of the blind adaptive algorithm in terms of the steady-state SINR can be severely degraded from the optimum value SINR ^* , especially when SINR ^* >> 1. In fact, it is seen that the SINR in the steady state is upper bounded by 1/ d . This problem can be overcome by switching to the conventional RLS algorithm that uses decision feedback, after the initial blind adaptation converges. The steady-state SINR of this scheme can be estimated via that of trained RLS, which is given in this case by [cf. the Appendix (Section 7.9.6)]

Equation 7.142

It is seen from (7.142) that in contrast to the blind adaptive algorithm, when the adaptive algorithm has access to the transmitted symbols b ₁ [ i ], the steady-state output SINR is close to its optimum possible value. Therefore, it is best to switch to a decision-directed adaptation mode as soon as the blind adaptation converges. However, decision-directed adaptation is subject to catastrophic error propagation in case of a sudden change in the environment. Whenever such a situation happens, the receiver should immediately switch back to the blind adaptation mode and stay in the blind mode until it converges, before it switches to the decision-directed mode again.

A difficulty with RLS relative to LMS is that RLS is more complex computationally . The complexity per update of RLS in this application is compared with for LMS, where we recall that N denotes the spreading gain. This complexity can be mitigated by using a parallel implementation on a systolic array first proposed in [316], as discussed in Section 2.3.3.

Simulation Examples

The first example illustrates the tracking capability of the RLS blind adaptive algorithm in a dynamic environment. Figure 7.17 shows a plot of time-averaged output SINR versus time of the RLS blind adaptive algorithm, in a synchronous CDMA system with processing gain N = 31 when the number and types of interferers in the system vary with time. The signal power to background noise power is 20 dB (after despreading). The simulation starts with one desired user's signal and six MAI signals, each at 10 dB above the desired user 's signal. At time n = 500, a strong NBI signal of 20 dB above the desired user is added in the system. At time n = 1000, another strong MAI signal of 20 dB above the desired user is added. At time n = 1500, three of the original 10 dB MAI signals are removed from the system. The desired user's signature sequence is an m -sequence; and the signature sequences of the MAIs are generated randomly . The NBI signal is a second-order AR signal with both poles at 0.99. The forgetting factor is l = 0.995. The data shown in the plot are values averaged over 100 simulations. It is seen that the RLS blind adaptive algorithm can adapt rapidly to the changing environment, which makes it suitable for practical use in a mobile environment.

Figure 7.17. Tracking behavior of the RLS blind adaptive algorithm in a dynamic environment

The second example illustrates the difference between the steady-state SINRs of the blind adaptation rule and the decision-directed adaptation rule. Figure 7.18 shows a plot of time-averaged output SINR versus time for the RLS adaptive algorithms in a strong near “far environment. This example assumes a synchronous CDMA system with processing gain N = 31. There are three 10-dB MAIs, each with a randomly chosen signature sequence. In addition, there is a 20-dB NBI which is a second-order AR signal with both poles at 0.99. The signal power to background noise power is 20 dB. The blind adaptation rule is used for the first 500 iterations, and the conventional RLS algorithm using decision feedback is used thereafter. The forgetting factor is l = 0.995. Again the data shown in the plot are values averaged over 100 simulations. It is seen from Fig. 7.18 that there is a significant gap between the steady-state SINR of the blind RLS algorithm and that of the conventional RLS algorithm, which can readily be explained by (7.140) and (7.142). Moreover, the steady-state SINR of the conventional RLS algorithm using decision feedback is very close to the optimal value of the MMSE detector, which is also plotted in Fig. 7.18 as the dashed line.

Figure 7.18. Time-averaged SINR for the blind adaptation and decision-directed adaptation rules.