Abstract-This work presents the optimum detector for detection of two non-orthogonal n-PAM signals with spectral overlapping through an AWGN band-limited channel based on joint maximum-likelihood criterion. The performance of signal detection in terms of symbol error rate for the new detector is evaluated using Monte Carlo simulations. The obtained results from this strategy represent a benchmark to this sort of communication system and comparative simulations are carried out in order to evaluate the performance faced to existing detection techniques for the discussed system showing the obtained lower bound.