Adaptive Modeling and Identification of Nonlinear MIMO Channels Using Neural Networks - Adaptive Signal Processing in Wireless Communications - page 145

unusual” happened to the unknown system (or to the backpropagation algorithm) at
iteration 12,500, without any further indication of what exactly happened during the
learning process.

5.3.3 Tracking of Slowly Time-Varying Propagation Channels
This section deals with another application in which matrix H is slowly time varying.
In this application, we consider a multiple antenna transmitter/receiver system
( Figure 5.1 ), with M = L = 2. The propagation channel H coefficients are modeled as
slowly time-varying Ricean fading gains with a Ricean factor K = 5, and a normalized
Doppler frequency of 0.0001.
Figure 5.12 shows the learning curves of the block structure and MLP. It can be
noticed that the MSE errors here are higher than those of the static case studied in sec-
tion 5.3.1 ( Figure 5.6 ). This is because of the fact that gradient descent algorithms do not
provide excellent tracking capabilities in time-varying environments.
As shown in Figure 5.12, our approach is faster and yields lower MSE than the MLP.
Moreover, the proposed structure allows good identification of the unknown non-
linearities ( Figures 5.13 and 5.14 ) . The time-varying coefficients were correctly tracked
by matrix W . An illustration is made for w 11 ( n ) versus h 11 ( n ) ( Figure 5.15 ).

5.3.4 Nonlinear MIMO Channel Receiver Design
This section applies the NN identification scheme to MIMO receiver design [17, 18].
A V-BLAST (Vertical Bell Laboratories Layered Space-Time) receiver is proposed. It

10 -1

10 -2

MLP

Proposed NN

10 -3

0 20 40 60 80 100

× 5,000 Iterations

FIgure 5.12 Learning curves: time-varying case.