Noncoherent minimum mean-squared error (MMSE)-based multiuser receivers are proposed for nonorthogonal multipulse modulation. The three proposed 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 ouptuts and the other two decision rules account for the second-order statistics of the residual multiple-access interference tha remains after MMSe filtering. An adaptive algorithm based on the stochastic approxiamtion method is then proposed for the distributed impelmentation of these receivers. The adaptation 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.
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