Blind adaptive noncoherent multiuser detection for nonlinear modulation

Noncoherent multiuser detection for nonlinear modulation was recently studi ed and the idea of phase-independent noncoherent decorrelation was introduc ed and three post-decorrelative detectors were obtained and analyzed. Howev er, their implementation requires the knowledge of the signature waveforms of all the users, which may be available only for centralized implementatio n, In this paper, we obtain a blind adaptive noncoherent decorrelative dete ctor for nonlinear modulation that is suitable for distributed implementati on with the knowledge of only the normalized signals of the desired user an d the additive noise variance. This detector is based on the stochastic app roximation method and does not require the overhead of any kind of "trainin g." Two adaptive algorithms are developed, one guided by every signal in th e desired user's signal set individually, and the other by the user's entir e signal space. While this paper focuses on the particular problem of blind adaptive noncoherent decorrelative detection, it addresses a more general adaptation issue, namely, that of improving convergence properties of an ad aptive scheme by effectively using all the information that is known, and a dapting only to the part of the desired solution that is truly unknown. Con vergence is shown in the mean squared error sense for both the fixed step-s ize and time-varying step-size versions of the two algorithms.