Convex programming for detection in structured communication problems

The generalized Minimum Mean Squared Error (GMMSE) detector has a bit error rate performance, which is similar to the MMSE detector. The advantage of the GMMSE detector is that it does not require the knowledge of the noise power. However, the computational complexity of the GMMSE detector is significantly higher than the computational complexity of the MMSE detector. In this paper, the complexity of the GMMSE detector is reduced by taking into account the structure of the system matrix (Toeplitz). Furthermore, by using circular approximation of the structured system matrix an approximate GMMSE detector is presented, whose computational complexity is only slightly higher than MMSE, i.e.~only an iterative gradient descent algorithm based on the inversion of diagonal matrices is additionally required.