Achievable rates of SVD-based codebooks for zero-forcing and Tomlinson-Harashima precoding schemes with limited feedback MU-MIMO system

In this manuscript, we developed a new SVD-based codebook design criterion for linear zero-forcing (ZF) precoding and Tomlinson-Harashima (TH) precoding with limited feedback. In limited feedback systems where only quantized channel state information is available, precoding on transmitter causes sum-rate degradation because of quantization errors. Thus, we propose more efficient codebooks that reduce the quantization error with lower feedback overheads. We also develop a closed-form expression for sum-rate of the proposed codebooks in case of TH and ZF precoding schemes in a multiuser MIMO system with limited feedback. The numerical consequences prove that TH precoding can achieve sum-rate gain of 0.5–2.5 bps/Hz at 25 dB signal-to-noise ratio as compared with linear ZF precoding with 10 and 20 feedback bits per user, respectively. Moreover, the numerical results also prove that the performance of nonlinear TH precoding is better than linear ZF precoding for low signal-to-noise ratio value or for the large number of feedback bits.