Vandendorpe (see IEEE International Zurich Seminar, p.440-451, 1994) proposed the combination of multitone modulation with direct sequence spectrum spreading. The performance of a correlation receiver has been evaluated for a multipath channel. The analysis has been extended by Vandedorpe (see ICC'94, New Orleans, p.1638-1641, 1994) to the presence of a multiple access interference. We analyze the equalization problem of such a system for a single user scenario. In order to understand the potential of the system we first investigate the steady-state behavior of the MIMO equalizer for an MMSE design. The investigation is carried out for an equalizer following a receiver made of a bank of filters matched to both the symbol shape and the channel, which is a two-path channel. Assuming BPSK symbols an exact expression of the bit error probability before and after equalization is obtained in the form of an integral by means of the characteristic function method. Next adaptive LMS and RLS structures are proposed. The performance of the RLS algorithm is demonstrated.
Vandendorpe, L., & Van De Wiel, O. (1995). Performance analysis of linear MIMO equalizers for multitone DS/SS systems in multipath channels. Wireless Personal Communications : an international journal, 2(1-2), 145-165. https://doi.org/10.1007/BF01099535 (Original work published 1995)