Maximum Likelihood Detection With a Closed-Form Solution for the Square QAM Constellation

A low complexity maximum likelihood (ML) detection method is proposed for the square quadrature amplitude modulation (QAM) constellation. In order to reduce the implementation complexity of ML detection, set-partition, subset-selection, and subset-shift are recursively applied to the square QAM constellation. The estimated square QAM symbol is finally given in a closed form as a function of the received signal and the estimated channel. Complexity analysis and numerical simulation confirm that the proposed detection method reduces the implementation complexity substantially and achieves exactly the same performance as the conventional ML detection irrespective of the channel estimation error.