Using hidden convexity in structured communication problems

Generalized minimum mean squared error (GMMSE) detector has a bit error rate (BER) performance that is almost the same as minimum mean squared error (MMSE) detector and it has the advantage that it does not require the knowledge of the noise power. However, the computational complexity of GMMSE detector is higher than that of MMSE detector. In this paper, the computational complexity of the GMMSE detector is reduced by using the hidden convexity combined with the idea of using the circular approximation of the banded Toeplitz channel matrix. In this case, the solutions are obtained by computing the EVD of the circular matrix using FFT/IFFT such that, the required EVD implies no additional effort.