Power and Modulo Loss Tradeoff for Tomlinson-Harashima Precoding Applied to Geometric Mean Decomposition based MIMO Systems

Tomlinson-Harashima precoding (THP) can be combined with geometric mean decomposition (GMD) to decouple a multiple- input multiple-output (MIMO) channel into multiple single-input single-output (SISO) subchannels with identical signal-to-noise ratios (SNRs). The combined system is called GMD-THP MIMO system. In this system, there is an increase in the transmission power caused by the interferences cancellation at the transmitter. To bind the transmission power, a modulo operation is used at the transmitter. However, there is still an overall increase in transmission power and this loss is referred to as power loss. A corresponding modulo operation at the receiver to demap the signals will create modulo errors. Performance loss due to the modulo errors is referred to as modulo loss. In this paper, we do a tradeoff between the power loss and the modulo loss to obtain the minimum combined loss. This tradeoff is achieved by adjusting the modulo size of the modulo operation. Detailed theoretical analysis of the power loss and modulo loss are done and from the analysis, the optimum modulo size for the tradeoff is found. Simulations are carried out to confirm the theoretical analysis and to prove that tradeoff improves the BER performance of the GMD-THP MIMO systems.