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”

Benefits of improper signaling for underlay cognitive radio

In this letter we study the potential benefits of improper signaling for a secondary user (SU) in underlay cognitive radio networks. We consider a basic yet illustrative scenario in which the primary user (PU) always transmit proper Gaussian signals and has a minimum rate constraint. After parameterizing the SU transmit signal in terms of its power and circularity coefficient (which measures the degree of impropriety), we prove that the SU improves its rate by transmitting improper signals only when the ratio of the squared modulus between the SU-PU interference link and the SU direct link exceeds a given threshold. As a by-product of this analysis, we obtain the optimal circularity coefficient that must be used by the SU depending on its power budget. Some simulation results show that the SU benefits from the transmission of improper signals especially when the PU is not highly loaded.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”. P. Schreier receives financial support from the Alfried Krupp von Bohlen und Halbach foundation, under its program ”Return of German scientists from abroad”

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)

Interference Alignment for Cognitive Radio Communications and Networks: A Survey

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Interference alignment (IA) is an innovative wireless transmission strategy that has shown to be a promising technique for achieving optimal capacity scaling of a multiuser interference channel at asymptotically high-signal-to-noise ratio (SNR). Transmitters exploit the availability of multiple signaling dimensions in order to align their mutual interference at the receivers. Most of the research has focused on developing algorithms for determining alignment solutions as well as proving interference alignment’s theoretical ability to achieve the maximum degrees of freedom in a wireless network. Cognitive radio, on the other hand, is a technique used to improve the utilization of the radio spectrum by opportunistically sensing and accessing unused licensed frequency spectrum, without causing harmful interference to the licensed users. With the increased deployment of wireless services, the possibility of detecting unused frequency spectrum becomes diminished. Thus, the concept of introducing interference alignment in cognitive radio has become a very attractive proposition. This paper provides a survey of the implementation of IA in cognitive radio under the main research paradigms, along with a summary and analysis of results under each system model.Peer reviewe

Robust improper signaling for two-user SISO interference channels

It has been shown that improper Gaussian signaling (IGS) can improve the performance of wireless interference-limited systems when perfect channel-state information (CSI) is available. In this paper, we investigate the robustness of IGS against imperfect CSI on the transmitter side in a two-user single-input single-output (SISO) interference channel (IC) as well as in a SISO Z-IC, when interference is treated as noise. We assume that the true channel coefficients belong to a known region around the channel estimates, which we call the uncertainty region. Following a worst-case robustness approach, we study the rate-region boundary of the IC for the worst channel in the uncertainty region. For the two-user IC, we derive a robust design in closed form, which is independent of the phase of the channels by allowing only one of the users to transmit IGS. For the Z-IC, we provide a closed-form design for the transmission parameters by considering an enlarged uncertainty region and allowing both users to employ IGS. In both cases, the IGS-based designs are ensured to perform no worse than proper Gaussian signaling. Furthermore, we show, through numerical examples, that the proposed robust designs significantly outperform non-robust solutions.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 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)