Efficient maximum-likelihood noncoherent orthogonal STBC detection

Orthogonal space-time block coding (STBC) offers linear-complexity one-shot maximum-likelihood (ML) reception when the channel coefficients are known to the receiver. However, when the channel coefficients are unknown, the optimal receiver takes the form of sequence detection. In this work, we prove that ML noncoherent sequence detection can always be performed in polynomial time with respect to the block length for orthogonal STBC and Rayleigh distributed channel coefficients. Using recent results on efficient maximization of reduced-rank quadratic forms over finite alphabets, we develop a novel algorithm that performs ML noncoherent orthogonal STBC detection with polynomial complexity in the block length. The order of the polynomial complexity of the proposed receiver is determined by the number of transmit and receive antennas.