Reducing the average complexity of ML detection using semidefinite relaxation

Maximum likelihood (ML) detection of symbols transmitted over a MIMO channel is generally a difficult problem due to its NP-hard nature. However, not every instance of the detection problem is equally hard. Thus, the average complexity of an ML detector may be significantly smaller than its worst-case counterpart. This is typically true in the high SNR regime where the received signals are closer to the noise free transmitted signals. Herein, a method which may be used to lower the average complexity of any ML detector is proposed. The method is based on the ability to verify if a symbol estimate is ML, using an optimality condition provided by the near-ML semidefinite relaxation technique. The average complexity reduction advantage of the proposed method is confirmed by numerical results.