Asymptotic analysis of the MMSE multiuser detector for nonorthogonal multipulse modulation

We develop the minimum mean-squared-error (MMSE) multiuser detector for nonorthogonal multipulse modulation over the noncoherent additive white Gaussian noise channel. We analyze the asymptotic performance of the detector and show that, unlike the case of linear modulation, the MMSE detector does not generally approach the generalized maximum-likelihood (GML) detection rule as the noise power vanishes. It does, however, approach a detector which nulls out the multiaccess interference. This detector is termed the multipulse decorrelating detector due to its similarity to the linear decorrelating detector. The probability of error for this detector is derived and used to find the asymptotic multiuser efficiencies of both the multipulse decorrelating detector and the MMSE detector. It is shown that for noncoherent binary signaling, in which the multipulse modulation is two-dimensional, the multipulse decorrelating detector is superior to the GML detector asymptotically. This result does not generalize to larger dimensionality signal sets