θ-QAM: A parametric quadrature amplitude modulation family and its performance in AWGN and fading channels

We study a parametric quadrature amplitude modulation (QAM) family, called θ-QAM, which includes other known constellations, such as square QAM (SQAM) and triangular QAM (TQAM), as special cases. The versatile structure of the θ-QAM signal constellation, which occurs from the varying angle between the signal points, results in achieving the minimum symbol error rate (SER) or bit error rate (BER), under an average power constraint. The theoretical study aims at providing insight into the trade-off between error performance and complexity of this parametric modulation scheme. Exact analytical expressions are obtained for the SER in additive white Gaussian Noise (AWGN) and Nakagami-m fading channels, while highly accurate BER approximations are presented. Finally, we find the optimum angles, in a minimal SER or BER sense, for a specific signal-to-noise ratio (SNR) and modulation order, M. This serves as an indicator for the appropriate constellation with respect to channel conditions and SER or BER requirements. The presented theoretical analysis is validated via extensive computer simulations.