Noncoherent MMSE Multiuser Receivers for Nonorthogonal Multipulse Modulation and Blind Adaptive Algorithms
A. Kapur, Deepak Kumar Das, Mahesh K. Varanasi · 2000
Noncoherent minimum mean-squared er- ror (MMSE)-based multiuser receivers are proposed for nonorthogonal multipulse modulation. The three pro- posed receivers have a common MMSE pre-filter and are followed by one of three distinct noncoherent decision rules. The simplest decision rule selects the maximum magnitude of the MMSE filter outputs and the other two decision rules account for the second-order statistics of the residual multiple-access interference that remains af- ter MMSE filtering. An adaptive algorithm based on the stochastic approximation method is then proposed for the distributed implementation of these receivers. The adapta- tion is shown to converge in the mean-squared error sense to the deterministic MMSE pre-filter. The convergence analysis yields insight on the trade-off between the rate of convergence and the residual mean-squared error. I. INTRODUCTION This paper investigates the problems of non-blind and blind noncoherent MMSE detection for Nonorthogonal Multipulse Modulation (NMM) in a multiuser environment. This prob- lem was first tackled in (1) using a decorrelative strategy that completely removes the Multiple Access Interference (MAI). We propose here an approach based on the MMSE criterion. In NMM, an -ary symbol is transmitted by sending one of possibly nonorthogonal and unequal-energy waveforms. The distinct energies and the correlations between the signals in NMM can be either viewed as design parameters or they can arise as a result of a distorting channel. The multiuser channel that we consider has several NMM based transmitters sending data simultaneously so that a superposition of several NMM waveforms plus additive white Gaussian noise is observed at the receiver. The multiple access technique employed is Cor- related Waveform Multiple Access (CWMA), where the sig- nature waveforms employed by the different users can be cor- related (and indeed even linearly dependent) as well. Following the idea introduced in (1), we represent NMM as a psuedo-linear modulation scheme and obtain a noncoherent MMSE pre-filter. Once the received signal is thus pre-filtered to obtain a suitable decision statistic for the user of interest, one of three noncoherent decision rules is applied to determine which of the possible signals was sent in any given time interval by that user. The first rule simply selects the signal corresponding to the output of the MMSE pre-filter that has maximum magnitude. The second and third rules addition- ally take into account the second-order characteristics of the residual MAI that remains after MMSE filtering. It is shown