A soft output low complexity maximum likelihood sequence estimation (MLSE) equalizer is proposed to equalizeM-QAM signals
in systems with extremely long memory. The computational complexity of the proposed equalizer is quadratic in the data block
length and approximately independent of the channel memory length, due to high parallelism of its underlying Hopfield neural
network structure. The superior complexity of the proposed equalizer allows it to equalize signals with hundreds of memory
elements at a fraction of the computational cost of conventional optimal equalizer, which has complexity linear in the data block
length but exponential in die channel memory length. The proposed equalizer is evaluated in extremely long sparse and dense
Rayleigh fading channels for uncoded BPSK and 16-QAM-modulated systems and remarkable performance gains are achieved.