Spatial modulation (SM) conveys extra data by selecting the transmit
antenna. This makes SM prone to channel irregularities like multipath Raleigh
fading. Hence, employing and optimizing a transmit precoder (TPC) that matches
the channel can enhance the SM bit error rate performance by increasing the
Euclidean distance (ED) among all possible received vectors. However, it is
common that optimization algorithms endure high complexity. Focusing on M-
PSK constellation, and by reducing the number of Euclidean Distance constraints,
we cut the complexity by nearly a factor of M. This is a significant reduction for
high order constellations with a large value of M. This concept is shown to benefit
any TPC optimization algorithm for SM and its variants. To further shrink the
complexity, we introduce an optimization algorithm that minimizes the sum of the
exponentials of negative EDs. The paper shows that the complexity can be reduced
significantly without loss in performance.
