MIMO DFE equalization for multitone DS/SS systems over multipath channels

The combination of multitone modulation with direct sequence spectrum spreading (DS/SS) has been introduced in the past. The performance of a correlation receiver has been evaluated for a multipath channel and in the presence of an additional multiple access interference. We analyze the problem of decision feedback equalization (DFE) for such a system. In order to understand the potential of the system with equalization, we first study the steady-state behavior of the equalizer for a minimum mean square error (MMSE) criterion. The investigation is carried out for a receiver made of a bank of filters matched to both the symbol shape and the channel, and for a two path channel. Assuming transmission of binary phase shift keying (BPSK) symbols, an exact expression of the bit error probability is obtained in the form of an integral. Then adaptive least mean square (LMS) and recursive least square (RLS) structures are derived. The performance of the adaptive RLS algorithm is demonstrated by means of computer simulations.