Deterministically Weighted Square-Law Combining in Correlated Fading

We consider a wireless system with a multi-branch diversity receiver employing noncoherent reception. The receiver has information on the channel statistics instead of the instantaneous channel state information, and the average branch signal-to-noise ratios (SNRs) are all distinct. In such a scenario, a deterministically weighted square-law combining scheme can be used to improve the error performance over conventional square-law combining. We focus on such a scheme for a system with orthogonal signaling in uniformly correlated Rayleigh fading. We obtain suboptimal weights, by least squares fit of the matrix elements of the characteristic functions of the decision variables of the weighted square-law combining and the optimum quadratic combining receivers, in closed form that are computed easily using an iterative algorithm. For the case of a dual-diversity system, an implicit expression for the optimal weights, chosen to minimize the symbol error probability, is obtained; for binary signaling, we derive closed form expressions for the weights. It is found that weighted square-law combining offers significant performance improvement over conventional square-law combining at a cost of increased complexity, and the performance gap increases with increasing branch SNR imbalance and number of branches.