Design and analytical error performance of MMSE-DFE receiver with spatial diversity

We consider the design and theoretical error performance analysis of an MMSE-DFE receiver with spatial diversity reception modeled as SIMO channel. At the base station of cellular mobile systems, such a structure is highly effective by using spatial diversity as the anti-fading technique, and decision feedback equalization for tackling the temporal delay spread. First, we derive the optimum SIMO-MMSE-DFE receiver in vector-matrix form by assuming a known SIMO channel. Next, to obviate the need of time-consuming Monte-Carlo (MC) simulations, we derive the signal-to-noise ratio at the slicer's input and then the theoretical BER performance by using the technique of Gaussian approximation (GA). Alternatively, we also provide a second way, namely, the quasi-analytical (QA) method, for BER estimation.