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Spectrally efficient multi-antenna wireless communication systems are a keychallenge as service demands continue to increase. At the same time, poweringup radio access networks is facing environmental and regulation limitations. Inorder to achieve more power efficiency, we design a directional modulationprecoder by considering an $M$-QAM constellation, particularly with$M=4,8,16,32$. First, extended detection regions are defined for desiredconstellations using analytical geometry. Then, constellation points are placedin the optimal positions of these regions while the minimum Euclidean distanceto adjacent constellation points and detection region boundaries is kept as inthe conventional $M$-QAM modulation. For further power efficiency and symbolerror rate similar to that of fixed design in high SNR, relaxed detectionregions are modeled for inner points of $M=16,32$ constellations. The modeledextended and relaxed detection regions as well as the modulationcharacteristics are utilized to formulate symbol-level precoder design problemsfor directional modulation to minimize the transmission power while preservingthe minimum required SNR at the destination. In addition, the extended andrelaxed detection regions are used for precoder design to minimize the outputof each power amplifier. We transform the design problems into convex ones anddevise an interior point path-following iterative algorithm to solve thementioned problems and provide details on finding the initial values of theparameters and the starting point. Results show that compared to the benchmarkschemes, the proposed method performs better in terms of power and peak powerreduction as well as symbol error rate reduction for a wide range of SNRs.

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