Benefits of Improper Gaussian Signaling in Interweave Cognitive Radio With Full and Partial CSI

Abstract

In this paper, we investigate the impact of using improper Gaussian signaling (IGS) scheme on the interweave cognitive radio (CR) paradigm when the cognitive user has access to full or partial channel-state-information (CSI). Throughout this work, we analyze the performance of both the primary user (PU) and secondary user (SU) in terms of instantaneous achievable rate and outage probability, for given sensing and detection capabilities. Then, we optimize the IGS scheme for full and partial CSI scenarios to maximize the achievable rate of the SU while maintaining a minimum quality-of-service (QoS) requirement for the PU. Meanwhile, we derive the corresponding feasibility conditions for the interweave cognitive radio system operation. IGS based systems are proven to provide notable gain over the conventional proper Gaussian signaling, which is considered our benchmark scheme. The IGS scheme is observed to be further beneficial at low SU detection capabilities, strong interference from the cognitive user to the licensed user, and low gain of the PU direct link. Index Terms-Interweave, cognitive radio, improper Gaussian signaling, asymmetric signaling, miss detection, interference channels. Rp (0, 0) > R min and subsequently is reduced to Rp 1 > R min , where Rp 1 is defined in 8. scenarios: Case II-a: P s,opt = p s,max , whenp s1 ≥ p s,max that is equivalent to I s ≤ I s,PGS. Case II-b: P s,opt =p s , whenp s1 < p s,max that is equivalent to I s > I s,PGS .

When Probabilistic Shaping Realizes Improper Signaling for Hardware Distortion Mitigation

“…Substituting the PEP derived in (18) to ( 9) along with the Gray coding assumption yields the following theoretical upper-bound on BER…”

“…IGS offers an additional degrees of freedom (DoF) in signaling design characterized by the circularity coefficient [14]. Several studies highlight the significance of IGS to improve the system performance under improper interference [15]- [18]. Recent studies quantified the impact of IGS in improving the ergodic rate and outage performance by effectively dampening the improper noise effects in multi-antenna or multi-nodal system settings [19]- [21], IGS benefits can also be reaped in various full-duplex/half-duplex relay settings by effectively compensating the residual self-interference, inter-relay interference and/or HWD [11], [20], [22].…”

A Journey From Improper Gaussian Signaling to Asymmetric Signaling

“…Initially, people argued the superiority of the proper complex signaling as it maximizes the entropy of a given system [1]. However, the reduced-entropy improper Gaussian signaling (IGS) can be beneficial in unlicensed spectrumsharing techniques with minimal interference to the legitimate users in underlay [49]- [53], overlay [54] and interweave [55] cognitive radio setups. Followed by the opinion of dominant improper/asymmetric signaling when the system is contaminated by the improper complex interference [56], [57], selfinterference [58]- [60], improper noise [8], [45], [61], [62], asymmetric noise/distortions [38], [63], [64] and non-circular hardware imperfections [9], [65]- [69].…”

“…A rate R is achievable if there exists a sequence of codes such that the maximal probability of error tends to 0 for sufficiently large block lengths. Recent contributions have highlighted a more general framework to quantify the achievable rate in order to accommodate the improper nature of the participating signals arising from IGS [9], [50], [52], [54], [55], [64], [82], [86], [88], [201]- [204], WL precoding of PGS [66], [71], [72], [79], [81], [84], [87], [95], [205], or complex beamforming resulting in dependent real and imaginary parts [90], [206].…”

“…computational complexity roughly by a factor of four when compared to the implementation of the augmented complex version in (55), owing to its inherent redundancy.…”