$M$-QAM Precoder Design for MIMO Directional Modulation Transceivers

Abstract: Spectrally efficient multi-antenna wireless communication systems are a key challenge as service demands continue to increase. At the same time, powering up radio access networks is facing environmental and regulation limitations. In order to achieve more power efficiency, we design a directional modulation precoder by considering an $M$-QAM constellation, particularly with $M=4,8,16,32$. First, extended detection regions are defined for desired constellations using analytical geometry. Then, constellation points are placed in the optimal positions of these regions while the minimum Euclidean distance to adjacent constellation points and detection region boundaries is kept as in the conventional $M$-QAM modulation. For further power efficiency and symbol error rate similar to that of fixed design in high SNR, relaxed detection regions are modeled for inner points of $M=16,32$ constellations. The modeled extended and relaxed detection regions as well as the modulation characteristics are utilized to formulate symbol-level precoder design problems for directional modulation to minimize the transmission power while preserving the minimum required SNR at the destination. In addition, the extended and relaxed detection regions are used for precoder design to minimize the output of each power amplifier. We transform the design problems into convex ones and devise an interior point path-following iterative algorithm to solve the mentioned problems and provide details on finding the initial values of the parameters and the starting point. Results show that compared to the benchmark schemes, the proposed method performs better in terms of power and peak power reduction as well as symbol error rate reduction for a wide range of SNRs.