Reduced Complexity Spatial Modulation Transmit Precoding for PSK Constellation

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 MPSK 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.