An improved algorithm for optimal noncoherent QAM detection

Ryan et at. recently described two polynomial time algorithms for noncoherent detection of square QAM in block fading channels with additive white Gaussian noise (AWGN). The first algorithm is optimal with respect to the generalized likelihood ratio test (GLRT) and requires O(T³) arithmetic computations, where T is the block length of the noncoherent receiver. The second algorithm requires only O(T² logT) arithmetic computations but is statistically suboptimal. This paper derives a new algorithm that is optimal yet requires only O(T² logT) arithmetic computations. The new algorithm has the geometric interpretation of finding the nearest codeword to a plane (2 dimensional subspace). The nearest codeword is found by testing codewords that are near a finite number of lines formed by the intersection of the plane and the nearest neighbour boundaries of the codewords.