Optimal OSTBC sequence detection over unknown correlated fading channels

We prove that maximum-likelihood (ML) noncoherent sequence detection of orthogonal space-time block coded (OSTBC) signals can be performed in polynomial time with respect to the sequence length for time-varying Rayleigh or Ricean distributed, correlated (in general) channel coefficients, if the mean channel vector belongs to the range of the channel co-variance matrix. We develop a novel algorithm that, provided the above condition, performs ML noncoherent sequence detection with polynomial complexity the order of which equals twice the rank of the channel covariance matrix. Therefore, for Rayleigh fading, polynomial ML noncoherent detection complexity is always guaranteed; the lower the channel covariance rank the lower the receiver complexity. Instead, for Ricean fading, full-rank channel correlation is desired to guarantee polynomial ML noncoherent detection complexity.