Performance analysis of maximally improper signaling for multiple-antenna systems

The transmission of improper Gaussian signals, instead of the conventional proper ones, has been shown to improve the performance in interference-limited networks. In this work we analyze the performance of a multiple-antenna user that transmits maximally improper signals and whose transmit covariance matrix satisfies a set of constraints that limit the harmfulness of the interference caused by this user. As opposed to the single-antenna case, there are different possible improper spatial signatures, which provide different performance. We first obtain new results for maximally improper random vectors based on majorization theory. We then apply these results to derive the improper spatial signatures that either maximize or minimize the performance. Numerical examples show that the performance difference between these two extreme cases can be surprisingly large.The work of C. Lameiro and P. J. Schreier was supported by the German Research Foundation (DFG) under grants SCHR 1384/6-1 and LA 4107/1-1. The work of I. Santamaría was supported by the Ministerio de Economía y Competitividad (MINECO) and AEI/FEDER funds of the UE, Spain, under projects RACHEL (TEC2013-47141-C4-3-R) and CARMEN (TEC2016-75067-C4-4-R)

Analysis of maximally improper signaling schemes for underlay cognitive radio networks

In this paper, the impact of improper Gaussian signaling is studied for an underlay cognitive radio (CR) scenario comprised of a primary user (PU), which has a rate constraint, and a secondary user (SU), both single-antenna. We first derive expressions for the achievable rate of the SU when it transmits proper and maximally improper Gaussian signals (assuming that the SU is solely limited by the CR constraint). These expressions depend on the channel gains to and from the SU through a single variable. Thereby, we observe that improper signaling is beneficial whenever the SU rate is below a threshold, which depends on the signal-to-noise ratio (SNR) and rate requirement of the PU. Furthermore, we provide bounds on the achievable gain that also depend only on the PU parameters. Then, the achievable rate is studied from a statistical viewpoint by deriving its cumulative distribution function considering a constant received SNR at the PU. In addition, we specialize this expression for the Z interference channel, for which the expected achievable rate is also derived. Numerical examples illustrate our claims and show that the SU may significantly benefit from using improper signaling.C. Lameiro and I. Santamaría have received funding from the Spanish Government (MICINN) under projects CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS), TEC2013-47141-C4-3-R (RACHEL) and FPU Grant AP2010-2189; and also from the Deutscher Akademischer Austauschdienst (DAAD) under its programm “Research grants for doctoral candidates and young academics and scientists”. Peter Schreier receives financial support from the Alfried Krupp von Bohlen und Halbach foundation, under its program “Return of German scientists from abroad”

Ergodic rate for fading interference channels with proper and improper Gaussian signaling

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.The work of M. Soleymani, C. Lameiro and P. J. Schreier was supported by the German Research Foundation (DFG) under grants LA 4107/1-1, SCHR 1384/7-1 and SCHR 1384/8-1. The work of I. Santamaria was supported by MINECO of Spain and AEI/FEDER funds of the E.U., under grant TEC2016-75067-C4-4-R (CARMEN)

Rate region boundary of the SISO Z-interference channel with improper signaling

This paper provides a complete characterization of the boundary of an achievable rate region, called the Pareto boundary, of the single-antenna Z interference channel (Z-IC), when interference is treated as noise and users transmit complex Gaussian signals that are allowed to be improper. By considering the augmented complex formulation, we derive a necessary and sufficient condition for improper signaling to be optimal. This condition is stated as a threshold on the interference channel coefficient, which is a function of the interfered user rate and which allows insightful interpretations into the behavior of the achievable rates in terms of the circularity coefficient (i.e., degree of impropriety). Furthermore, the optimal circularity coefficient is provided in closed form. The simplicity of the obtained characterization permits interesting insights into when and how improper signaling outperforms proper signaling in the single-antenna Z-IC. We also provide an in-depth discussion on the optimal strategies and the properties of the Pareto boundary.The work of C. Lameiro and P. J. Schreier was supported by the German Research Foundation (DFG) under grant SCHR 1384/6-1. The work of I. Santamaría was supported by the Ministerio de Economía y Competitividad (MINECO), Spain, under projects RACHEL (TEC2013-47141-C4-3-R) and CARMEN (TEC2016-75067-C4-4-R)

Improper Gaussian signaling for multiple-access channels in underlay cognitive radio

This paper considers an unlicensed multiple-access channel (MAC) that coexists with a licensed point-to-point user, following the underlay cognitive radio paradigm. We assume that every transceiver except the secondary base station has one antenna and that the primary user (PU) is protected by a minimum rate constraint. In contrast to the conventional assumption of proper Gaussian signaling, we allow the secondary users to transmit improper Gaussian signals, which are correlated with their complex conjugate. When the secondary base station performs zero-forcing, we show that improper signaling is optimal if the sum of the interference channel gains (in an equivalent canonical model) is above a certain threshold. Additionally, we derive an efficient algorithm to compute the transmission parameters that attain the rate region boundary for this scenario. The proposed algorithm exploits a single-user representation of the secondary MAC along with new results on the optimality of improper signaling in the single-user case when the PU is corrupted by an improper noise.The work of C. Lameiro and P. J. Schreier was supported by the German Research Foundation (DFG) under grants SCHR 1384/6-1 and LA 4107/1-1. The work of I. Santamaría was supported by the Ministerio de Economía y Competitividad (MINECO) and AEI/FEDER funds of the UE, Spain, under projects RACHEL (TEC2013-47141-C4-3-R) and CARMEN (TEC2016-75067-C4-4-R)

Information-theoretic analysis of a family of improper discrete constellations

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.The work of Pedro M. Crespo and Ignacio Santamaria has been partially supported by the Ministerio de Economía y Competitividad (MINECO) of Spain and Agencia Estatal de Investigación (AEI)/(European Fund for Economic and Regional Development) FEDER funds of the E.U., under Grants TEC2013-47141-C4-R (RACHEL), TEC2016-75067-C4-4-R (CARMEN). The work of Christian Lameiro and Peter J. Schreier was supported by the German Research Foundation (DFG) under Grants LA 4107/1-1 and SCHR 1384/6-1