Constructive Interference for Generic Constellations

In this letter, we investigate optimal and relaxed constructive interference regions (CIR) for the symbol-level precoding (SLP) problem in the downlink of a multiuser multiple-input single-output (MISO) channel. We define two types of CIRs, namely, distance preserving CIR (DPCIR) and union bound CIR (UBCIR) for any given constellation shape and size. We then provide a systematic way to describe these regions as convex sets. Using the definitions of DPCIR and UBCIR, we show that the SLP power minimization problem, minimizing either sum or peak (per-antenna) transmit power, can always be formulated as a convex optimization problem. Our results indicate that these regions allow further reduction of the transmit power compared to the current state of the art without increasing the computational complexity at the transmitter or receiver.