Polynomial-complexity maximum-likelihood block noncoherent MPSK detection

In wireless channels, maximum-likelihood (ML) block noncoherent detection offers significant gains over conventional symbol- by-symbol detection when the fading channel coefficients are not available and cannot be estimated at the receiver. Certainly, in general the complexity of the block detector grows exponentially with the symbol sequence length. However, it has been recently shown that for M-ary phase-shift keying (MPSK) modulation block noncoherent detection can be performed with polynomial complexity. In this work, we develop a new ML block noncoherent detector for MPSK transmission of arbitrary order and multiple-antenna reception. The proposed algorithm introduces auxiliary spherical variables and constructs with polynomial complexity a polynomial- size set which includes the ML data sequence. It is shown that the complexity of the proposed algorithm is polynomial in the sequence length and at least one order of magnitude lower than the complexity of computational-geometry based noncoherent detection algorithms that have been developed recently.