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Both the single user and multi user MIMO system design with individual transmit power constraint and improper constellation

This work address the problem of designing joint optimum transceiver for both single-user (SU) and multi-user (MU) MIMO system. Most of the previous works on both SU and MU-MIMO system, the joint precoder and decoder designs are based on the total transmit power constraint (TTPC) with proper modulation techniques. On the other hand, in practice, individual transmit power constraint (ITPC) is more realistic as the power at each antenna at the transmitter is restricted independently by the linearity of the power amplifier. In this work, a minimum total mean squared error (TMSE) design is formulated as a non-convex optimisation problem. This formulation is under equal power allocation (EPA) and the power constraint that jointly meets both EPA and TTPC (i.e., ITPC). The closed-form optimum linear precoder and decoder for SU-MIMO systems with an improper modulation are determined by solving this non-convex optimisation problem. It considers both the perfect and imperfect channel state information (CSI) is available at both the transmitter and receiver. The simulation results show the performance improvement of the proposed work over conventional work in terms of bit error rate (BER).