Discrete‐rate adaptive modulation with optimum switching thresholds for space‐time coded multiple‐input multiple‐output system with imperfect channel state information

Abstract

The performance analysis of a space-time coded multiple-input multiple-output (MIMO) system with variable-rate adaptive modulation over flat Rayleigh fading channels for both perfect and imperfect channel state information (CSI) is presented. In this study, the optimum fading gain switching thresholds for attaining maximum spectrum efficiency (SE) subject to an average bit error rate (BER) constraint are derived. The existence and uniqueness of the Lagrange multiplier in the constrained SE optimisation is studied. It is shown that the Lagrange multiplier does exist and is unique for imperfect CSI. On the other hand, the Lagrange multiplier will be unique if the existence condition for MIMO under perfect CSI is satisfied. A practical iterative algorithm based on Newton's method for finding the Lagrange multiplier is proposed. By the switching thresholds, closed-form expressions of the SE and average BER are obtained. Simulation results for SE and BER are in good agreement with the theoretical analysis. The results show that the space-time block coded MIMO system using adaptive modulation (AM-STBC-MIMO) with average BER constraint provides SE better than AM-STBC-MIMO with fixed thresholds, and AM-STBC-MIMO using a BER upper bound, but it has performance degradation in SE for imperfect CSI.