Hardware impairments (HWIs) impose a huge challenge on modern wireless commu- nication systems owing to the characteristics like compactness, least complexity, cost ef- fectiveness and high energy efficiency. Numerous techniques are implemented to minimize the detrimental effects of these HWIs ,however, the residual HWIs may still appear as an additive distortion, multiplicative interference, or an aggregate of both. Numerous studies have commenced efforts to model one or the other forms of hardware impairments in the ra- dio frequency (RF) transceivers. Many presented the widely linear model for in-phase and quadrature imbalance (IQI) but failed to recognize the impropriety induced in the system because of the self-interfering signals. Therefore, we have presented not only a rigorous ag- gregate impairment model along with its complete impropriety statistical characterization but also the appropriate performance analysis to quantify their degradation effects. Lat- est advances have endorsed the superiority of incorporating more generalized impropriety phenomenon as opposed to conventional propriety. In this backdrop, we propose the improper Gaussian signaling (IGS) to mitigate the drastic impact of HWIs and improve the system performance in terms of achievable rate and outage probability. Recent contributions have advocated the employment of IGS over traditional proper Gaussian signaling (PGS) in various interference limited scenarios even in the absence of any improper noise/interference. It is pertaining to the additional degree of freedom (DoF) offered by IGS, which can be optimized to reap maximum benefits. This reduced-entropy signaling is the preferred choice to pose minimal interference to a legitimate network yielding another mechanism to tackle undesired interference. Evidently, the incorporation of both inherent and induced impropriety characteristics is critical for effective utilization. Most of the recent research revolves around the theoretical analysis and advantages of improper signaling with minimal focus on its practical realization. We bridge this gap by adopting and optimizing asymmetric signaling (AS) which is the finite discrete implemen- tation of the improper signaling. We propose the design of both structural and stochastic shaping to realize AS. Structural shaping involves geometric shaping (GS) of the symbol constellation using some rotation and translation matrices. Whereas, stochastic shaping as- signs non-uniform prior probabilities to the symbols. Furthermore, hybrid shaping (HS) is also proposed to reap the gains of both geometric and probabilistic shaping. AS is proven superior to the conventional M-ary symmetric signaling in all of its forms. To this end, probabilistic shaping (PS) demonstrates the best trade-off between the performance en- hancement and added complexity. This research motivates further investigation for the utilization of impropriety concepts in the upcoming generations of wireless communications. It opens new paradigms in inter- ference management and another dimension in the signal space. Besides communications, the impropriety characterization has also revealed numerous applications in the fields of medicine, acoustics, geology, oceanography, economics, bioinformatics, forensics, image processing, computer vision, and power grids.

Next generation of wireless communication mostly relies on multiple-input multipleoutput (MIMO) configuration and full-duplex relaying to improve data-rates, spectrale efficiency, spatial-multiplexing, quality-of-service and energy-efficiency etc. However, multiple radio frequency (RF) transceivers in MIMO system and multi-hops in relay networks, accumulate transceiver impairments, rendering an unacceptable system performance. Majority of the technical contributions either assume ideal hardware or inappropriately model hardware impairments which often induce misleading results especially for high data-rate communication systems. We propose statistical mathematical modeling of various hardware impairment (HWI) to characterize their deteriorating effects on the information signal. In addition, we model the aggregate HWI as improper Gaussian signaling (IGS), to fully characterize their asymmetric properties and the self-interfering signal attribute under I/Q imbalance. The proposed model encourages to adopt asymmetric transmission scheme, as opposed to traditional symmetric signaling. First, we present statistical baseband equivalent mathematical models for general MIMO system and two special scenarios of receive and transmit diversity systems under HWI. Then, we express their achievable rate under PGS and IGS transmit schemes. Moreover, we tune the IGS statistical characteristics to maximize the achievable rate. We also present optimal beam-forming/pre-coding and receive combiner vector for multiple-input single-output (MISO) and single-input multiple output (SIMO) systems, which lead to SDNR maximization. Moreover, we propose an adaptive scheme to switch between maximal IGS (MIGS) and PGS transmission based on the described conditions to reduce computational overhead. Subsequently, two case studies are presented. 1) Outage analysis has been carried out for SIMO, under transceiver distortion noise, for two diversity combining schemes 2) The benefits of employing IGS is investigated in full duplex relaying (FDR) suffering from two types of interference, the residual self-interference (RSI) and I/Q distortions. We further optimize the pseudo-variance to compensate the interference impact and improve end-to-end achievable rate. Finally, we validate the analytic expressions through simulation results, to quantify the performance degradation in the absence of ideal transceivers and the gain reaped from adopting IGS scheme compared with PGS scheme.

In the last decade, wireless applications have witnessed a tremendous growth. This can be envisioned in the surge of smart devices which became almost in everyone's possession, demand for high speed connection and the internet of things (IoT) along with its enabling technologies. Hence, the multiuser interference became the main limiting factor in wireless communications. Moreover, just like diamonds and emeralds, the electromagnetic spectrum is limited and precious. Therefore, the high data rate application may not be satisfied by our current technologies. In order to solve this spectrum scarcity problem, researchers have steered their focus to develop new techniques such as cognitive radio (CR) and in-band full-duplex (FD). However, these systems suffer from the interference problem that can dramatically impede their quality-of-service (QoS). Therefore, investigating communication techniques/systems that can relieve the interference adverse signature becomes imperative. Improper Gaussian signaling (IGS) has been recently shown to outperform the traditional proper Gaussian signaling (PGS) in several interference-limited systems. In this thesis, we use IGS in order to mitigate the interference issue in three different communication settings. IGS has the ability to control the interference signal dimension, and hence, it can be considered as one form of interference alignment. In the first part, we investigate an underlay CR system with in-band FD primary users (PUs) and one-way communication for the secondary user (SU). IGS is employed to alleviate the interference introduced by the SU on the PUs. First, we derive a closed form expression and an upper bound for the SU and PUs outage probabilities, respectively. Second, we optimize the SU signal parameters, represented in its power and the circularity coefficient, to achieve the design objectives of the SU while satisfying certain QoS constraints for the PU under instantaneous, average and partial channel state information (CSI). Finally, we provide some numerical results that demonstrate the advantages that can be reaped by using IGS to access the spectrum of the FD PUs. Specifically, with the existence of week PU direct channels and/or strong SU interference channels, PGS tends to use less transmit power while IGS uses more power along with increasing the signal impropriety. Part 2 studies the potential employment of IGS in FD cooperative settings with non-negligible residual self-interference (RSI). In this part, IGS is used in an attempt to alleviate the RSI adverse effect in full-duplex relaying (FDR). To this end, we derive a tight upper bound expression for the end-to-end outage probability in terms of the relay signal parameters. We further show that the derived upper bound is either monotonic or unimodal in the relay's circularity coefficient. This result allows for easily locating the global optimal point using known numerical methods. Based on the analysis, IGS allows FDR systems to operate even with high RSI. It is shown that, while the communication totally fails with PGS as the RSI increases, the IGS outage probability approaches a fixed value that depends on the channel statistics and target rate. The obtained results show that IGS can leverage higher relay power budgets than PGS to improve the performance, meanwhile it relieves its RSI impact via tuning the signal impropriety. In part 3, we investigate the potential benefits of adopting IGS in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no CSI is available at the source. In this regard, we assume that the two relays use IGS and the source uses PGS. Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.