  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.
