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Non-circular or improper Gaussian signaling has proven beneficial in several interference-limited wireless networks. However, all implementable coding schemes are based on finite discrete constellations rather than Gaussian signals. In this paper, we propose a new family of improper constellations generated by widely linear processing of a square M-QAM (quadrature amplitude modulation) signal. This family of discrete constellations is parameterized by κ , the circularity coefficient and a phase ϕ . For uncoded communication systems, this phase should be optimized as ϕ∗(κ) to maximize the minimum Euclidean distance between points of the improper constellation, therefore minimizing the bit error rate (BER). For the more relevant case of coded communications, where the coded symbols are constrained to be in this family of improper constellations using ϕ∗(κ) , it is shown theoretically and further corroborated by simulations that, except for a shaping loss of 1.53 dB encountered at a high signal-to-noise ratio (snr), there is no rate loss with respect to the improper Gaussian capacity. In this sense, the proposed family of constellations can be viewed as the improper counterpart of the standard proper M-QAM constellations widely used in coded communication systems. [ABSTRACT FROM AUTHOR]

This paper studies the performance of improper Gaussian signaling (IGS) over a 2-user Rayleigh single-input single-output (SISO) interference channel, treating interference as noise. We assume that the receivers have perfect channel state information (CSI), while the transmitters have access to only statistical CSI. Under these assumptions, we consider a signaling scheme, which we refer to as proper/improper Gaussian signaling or PGS/IGS, where at most one user may employ IGS. For the Rayleigh fading channel model, we characterize the statistical distribution of the signal-to-interference-plus-noise ratio at each receiver and derive closed-form expressions for the ergodic rates. By adapting the powers, we characterize the Pareto boundary of the ergodic rate region for the 2-user fading IC. The ergodic transmission rates can be attained using fixed-rate codebooks and no optimization is involved. Our results show that, in the moderate and strong interference regimes, the proposed PGS/IGS scheme improves the performance with respect to the PGS scheme. Additionally, we numerically compute the ergodic rate region of the full IGS scheme when both users can employ IGS and their transmission parameters are optimized by an exhaustive search. Our results suggest that most of the Pareto optimal points for the 2-user fading IC channel are attained when either both users transmit PGS or when one transmits PGS and the other transmits maximally improper Gaussian signals and time sharing is allowed. [ABSTRACT FROM AUTHOR]