Robust design of block diagonalization using perturbation analysis

Block diagonalization (BD) is a low-complexity linear precoding technique for multi-user MIMO (MU-MIMO) downlink systems, which can provide a performance that is close to theMU-MIMO capacity. However, imperfect channel state information (CSI) will result in a degraded performance of the BD scheme. Thus, studying the performance of BD under imperfect CSI is crucial for a practical system design since the robustness of BD to real-world imperfections should be verified. In this paper we apply a first-order perturbation analysis of the SVD to derive analytic expressions of the signal to interference plus noise ratio (SINR) for each subchannel of each UT using BD in presence of imperfect CSI. To demonstrate the usefulness of these expressions, a robust BD technique via worst SINR maximization is developed. Numerical simulations show the accuracy and the usefulness of the derived analytical results.