Reducing complexity of generalized minimum mean square error detection

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 idea of using the structure of the system matrix (Toeplitz) is combined with a convex relaxation of the detection problem to reduce the computational complexity of GMMSE detector. Furthermore, by using circular approximation of this structure 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 required additionally.