Discrete-Rate Adaptive Modulation Schemes for Uplink Massive MIMO Systems With Imperfect CSI

In this paper, under the instantaneous and average bit error rate (BER) constraints, discrete-rate adaptive modulation (AM) schemes of uplink massive multiple-input-multiple-output (MIMO) system with imperfect channel state information (CSI) over composite Rayleigh fading channels are presented. The average spectrum efficiency (ASE) and average BER (ABER) of the AM schemes are analyzed for theoretical performance evaluation. Closed-form SE and BER are developed to facilitate the designs of switching thresholds of the AM schemes. For the AM scheme with the instantaneous BER (IBER) constraint (referred to as AM-IBER), the lower switching threshold of each fading region is obtained by setting the corresponding IBER equal to the target BER. The resulting ABER of the AM-IBER is lower than the target BER by a large margin resulting in the loss of SE. Considering this reason, the AM schemes with the ABER constraint (referred to as AM-ABER) and the corresponding switching thresholds optimization are studied. The optimization problem for maximizing the SE under the ABER constraint is formulated. The Lagrange multiplier method is employed to solve the problem yielding a procedure to design the optimal thresholds, and the corresponding existence condition is developed. Due to a two-layer iteration in the optimal design procedure, a lower-complexity suboptimal threshold design is introduced, which requires only a single-layer iteration and has small performance loss. Simulation results show that the derived theoretical performance expressions for all the proposed schemes are all effective, and the system with the AM schemes can achieve high SE while meeting the target BER. Moreover, using the obtained optimal and suboptimal thresholds, the system with AM-ABER has a higher SE than that with the AM-IBER.