Generalized Detector under Nonorthogonal Multipulse Modulation in Remote Sensing Systems

We develop the minimum mean-squared-error (MMSE) multiuser generalized detector for nonorthogonal multipulse modulation in wireless sensor networks employed by remote sensing systems over the noncoherent additive white Gaussian noise channel. The generalized detector (GD) is constructed based on the generalized approach to signal processing in the presence of noise. We analyze the asymptotic performance of the generalized detector and show that, unlike the case of linear modulation, the MMSE generalized detector does not generally approach the generalized detector discussed previously but outperforms the detector based on the generalized maximum-likelihood detection rule. However, it does approach a detector, which nulls out the multi-access interference. This detector is termed the multipulse generalized detector due to its similarity to the decorrelating detector. The probability of error for this generalized detector is derived and used to find the asymptotic multiuser efficiencies of both the multipulse generalized detector and the MMSE generalized detector. It is shown that for noncoherent binary signaling, in which the multipulse modulation is two-dimensional, the multipulse generalized detector is superior to the generalized maximum-likelihood detector. This result does not generalize to larger dimensionality signal set. Key-Words: Minimum mean-squared-error detection, multipulse modulation, multiuser detection, generalized detector, noncoherent detection.