Analysis of a reduced complexity generalized Minimum Mean Square Error detector

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. Using the circular approximation of the Toeplitz structured system matrix an approximate GMMSE detector can be derived, 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. The performance of this approximate GMMSE detector is analysed by investigating the noise enhancement due to the conditioning of the system matrix (Toeplitz) and its circular approximation. Simulation results for fading multipath channels are given and the computational complexity is briefly discussed.