Hopfield neural network implementation of the optimal CDMA multiuser detector

We investigate the application of Hopfield mural networks (HNN's) to the problem of multiuser detection in spread spectrum/CDMA (code division multiple access) communication systems, It is shown that the NP-complete problem of minimizing the objective function of the optimal multiuser detector (OMD) can be translated into minimizing an HNN ''energy'' function, thus allowing to take advantage of the ability of HNN's to perform very fast gradient descent algorithms in analog: hardware and produce in real-time suboptimal solutions to hard combinatorial optimization problems. The performance of the proposed HNN receiver is evaluated via computer simulations and compared to that of other suboptimal schemes as well as to that of the OMD for both the synchronous and the asynchronous CDMA transmission cases. It is shown that the HNN detector exhibits a number of attractive properties and that it provides in fact a powerful generalization of a well-known and extensively studied suboptimal scheme, namely the multistage detector (MSD).