Capacity analysis of lattice reduction aided equalizers for MIMO systems

Lattice reduction (LR)-aided equalizers have been well studied for multi-input multi-output (MIMO) systems due to their great bit-error-rate (BER) improvement over linear equalizers (LEs) and relatively low complexity. In this paper, we present results on the maximum information rate (denoted as “capacity” hereafter) of MIMO transmission with LR-aided equalizers employed at the receiver. First, we derive the main steps for calculating the capacity with different equalizers. Then, we illustrate the capacity when LR-aided equalizers are adopted. We show that the capacity gap between maximum likelihood equalizer (MLE) and LR-aided LEs is linked to the orthogonality deficiency (od) of the dual of the lattice-reduced channel matrix. Although LR-aided LEs do not guarantee to improve capacity every channel realization, we give the conditions when the ergodic capacity of LR-aided LEs is greater than that of LEs, as well as when their outage diversity is the same as that of MLE. Lastly, we show numerical examples with several state-of-the-art LR algorithms to corroborate the theoretical analysis.