Gaussian Signaling Research Articles

Critical Points in the Noiseberg Achievable Region of the Gaussian Z-Interference Channel

The Gaussian signaling strategy with power control for the Gaussian Z-interference channel with weak interference is reviewed in this paper. In particular, we study the various communication strategies that may arise at various points of the capacity region and identify the locations of the phase transitions between the various strategies. The Gaussian Z-interference channel with weak interference is known to have two critical points in its capacity region, where the slope of the region shows a sudden change. They occur at the points of the unconditional maximum rate for one of the users and the maximum rate that can be accommodated by the other user. In this paper, we discuss additional critical points (locations of phase transitions) in the achievable region of this channel. These turn out to be second-order phase transitions, i.e., we do not observe a discontinuous slope in the achievable rate region, but there is a discontinuity in the second derivative of the rate contour of the achievable region. This review paper is mainly based on some of our ITA (Information Theory and Applications Workshop, UCSD, San Diego, CA, USA) papers since 2011.

On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling

On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling

A Two-Layer Iterative Algorithm for Max-Min Rate Optimization in IRS Assisted Multiuser Systems With Improper Gaussian Signaling

A Two-Layer Iterative Algorithm for Max-Min Rate Optimization in IRS Assisted Multiuser Systems With Improper Gaussian Signaling

Improper Gaussian Signaling for IRS Assisted Multiuser SWIPT Systems With Hardware Impairments

In this paper, we focus on intelligent reflecting surface (IRS) assisted multiuser simultaneous wireless information and power transfer (SWIPT) systems with hardware impairments (HWIs), which result from the aggregate effect of in-phase and quadrature-phase imbalance (IQI), power amplifier non-linearity, quantization distortion, phase noise, etc. Improper Gaussian signaling (IGS) is employed to combat the signal distortion incurred by HWIs and the interference from other users. We aim to maximize the minimum achievable information rate among all users by jointly optimizing the active beamforming vectors, passive reflecting coefficients, and power splitting coefficients, subject to the minimum harvested energy requirements of these users and the total power budget at the transmitter. Due to the intricate coupling between the reflecting coefficients and beamforming vectors, we propose a two-level iterative optimization algorithm to solve this non-convex problem. Based on the above, we also study the weighted rate-energy region maximization problem. Numerical results show that the use of IGS significantly outperforms traditional proper Gaussian signaling (PGS) in the considered systems and also affirm the effectiveness of the proposed optimization algorithm.

Outage Performance Analysis of Improper Gaussian Signaling for Two-User Downlink NOMA Systems with Imperfect Successive Interference Cancellation.

The improper Gaussian signaling (IGS) technique can improve the achievable rate of an interference-limited network by fully exploiting the second-order statistics of complex signaling. This paper addresses the outage performance analysis of a two-user downlink non-orthogonal multiple access (NOMA) system using the IGS technique in the presence of imperfect successive interference cancellation (SIC). The strong channel user (SU) adopts the IGS, while the weak channel user (WU) adopts the traditional proper Gaussian signaling (PGS). Considering a practical scenario where the transmitter has obtained the statistics of the channel coefficients instead of the instantaneous channel state information (CSI), the expressions of the achievable rates of both users under residual interference due to imperfect SIC are derived, together with their outage probabilities, subject to predetermined target rates and channel statistics. Given a fixed transmit power of the WU, both the transmit power and the degree of impropriety of the SU are optimized to minimize the outage probability subject to the outage constraint of the WU. Numerical results are provided to assess the benefits of the proposed IGS-based downlink NOMA system, which are consistent with the analysis.

Downlink Transmission With Heterogeneous URLLC Services: Discrete Signaling With Single-User Decoding

The problem of designing downlink transmission schemes for supporting heterogeneous ultra-reliable low-latency communications (URLLC) and/or with other types of services is investigated. We consider the broadcast channel, where the base station sends superimposed signals to multiple users. Under heterogeneous blocklength constraints, strong users who are URLLC users cannot wait to receive the entire transmission frame and perform successive interference cancellation (SIC) due to stringent latency requirements, in contrast to the conventional infinite blocklength cases. Even if SIC is feasible, SIC may be imperfect under finite blocklength constraints. To cope with the heterogeneity in latency and reliability requirements, we propose a practical downlink transmission scheme with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">discrete signaling</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">single-user decoding (SUD), i.e., without SIC</i> . We carefully design the discrete input distributions to enable efficient SUD by exploiting the structural interference. Furthermore, we derive the second-order achievable rate under heterogenous blocklength and error probability constraints and use it to guide the design of channel coding and modulations. It is shown that in terms of achievable rate under short blocklength, the proposed scheme with regular quadrature amplitude modulations and SUD can operate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">extremely close</i> to the benchmark schemes that assume perfect SIC with Gaussian signaling.

Low-Complexity Pareto-Optimal 3D Beamforming for the Full-Dimensional Multi-User Massive MIMO Downlink

Full-dimensional (FD) multi-user massive multiple-input multiple output (m-MIMO) systems employ large two-dimensional (2D) rectangular antenna arrays to control both the azimuth and elevation angles of signal transmission. We introduce the sum of two outer products of the azimuth and elevation beamforming vectors having moderate dimensions as a new class of FD beamforming. We show that this low-complexity class is capable of outperforming 2D beamforming relying on the single outer product of the azimuth and elevation beamforming vectors. It is also capable of performing close to its FD counterpart of massive dimensions in terms of either the users' minimum rate or their geometric mean rate (GM-rate), or sum rate (SR). Furthermore, we also show that even FD beamforming may be outperformed by our outer product-based improper Gaussian signaling solution. Explicitly, our design is based on low-complexity algorithms relying on convex problems of moderate dimensions for max-min rate optimization or on closed-form expressions for GM-rate and SR maximization.

Unsuspicious User Enabled Proactive Eavesdropping in Interference Networks Using Improper Gaussian Signaling

Proactive eavesdropping is an effective approach to improve the performance of wireless information surveillance, where suspicious users are legitimately eavesdropped by authorized monitors. For the situation when no monitor is available, we propose to authorize unsuspicious users to surveil suspicious users provided that the quality-of-service (QoS) of unsuspicious users is guaranteed. This paper considers an interference network consisting of a suspicious-transmitter (STx)/suspicious-receiver (SRx) pair and an unsuspicious-transmitter (UTx)/unsuspicious-receiver (URx) pair. We assume that URx acts as a monitor to eavesdrop the suspicious communication, and UTx adopts improper Gaussian signaling (IGS) for flexibly managing the interference to SRx. The QoS of the unsuspicious communication is guaranteed by enforcing its outage performance to be higher than a desirable level. The problem of optimizing the transmit power and the IGS circularity coefficient of UTx to maximize the average eavesdropping rate is optimally solved by the Lagrange duality method. Theoretical results show that IGS is effective when the eavesdropping is successful and the unsuspicious communication is in non-outage status. Simulation results confirm that the proposed design works well even when no additional outage of the unsuspicious communication is allowed, and show that IGS can greatly outperform proper Gaussian signaling in most cases.

Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling

In this paper, we propose an optimization framework for rate splitting (RS) techniques in multiple-input multiple-output (MIMO) reconfigurable intelligent surface (RIS)-assisted systems, possibly with I/Q imbalance (IQI). This framework can be applied to any optimization problem in which the objective and/or constraints are linear functions of the rates and/or transmit covariance matrices. Such problems include minimum-weighted and weighted-sum rate maximization, total power minimization for a target rate, minimum-weighted energy efficiency (EE) and global EE maximization. The framework may be applied to any interference-limited system with hardware impairments. For the sake of illustration, we consider a multicell MIMO RIS-assisted broadcast channel (BC) in which the base stations (BSs) and/or the users may suffer from IQI. Since IQI generates improper noise, we consider improper Gaussian signaling (IGS) as an interference-management technique that can additionally compensate for IQI. We show that RS when combined with IGS can substantially improve the spectral and energy efficiency of overloaded networks (i.e., when the number of users per cell is larger than the number of transmit/receive antennas).

A New Noncoherent Gaussian Signaling Scheme for Low Probability of Detection Communications

We propose a novel, Gaussian signaling mechanism for low probability of detection (LPD) communication systems with either single or multiple antennas. The new scheme is designed to allow the noncoherent detection of Gaussian-distributed signals, enabling LPD communications using signals that follow the complex Gaussian distribution in the time and frequency domains. It is demonstrated via simulations that the proposed scheme achieves better performance than a comparable conventional scheme over the entire SNR region, with the advantage becoming more significant in scenarios with lower overhead.

Quadratic Signaling With Prior Mismatch at an Encoder and Decoder: Equilibria, Continuity, and Robustness Properties

We consider communications through a Gaussian noise channel between an encoder and a decoder which have subjective probabilistic models on the source distribution. Although they consider the same cost function, the induced expected costs are misaligned due to their prior mismatch, which requires a game-theoretic approach. We consider two approaches: a Nash setup, with no prior commitment, and a Stackelberg solution concept, where the encoder is committed to a given announced policy <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> . We show that the Stackelberg equilibrium cost of the encoder is upper semicontinuous, under the Wasserstein metric, as encoder’s prior approaches the decoder’s prior, and it is also lower semicontinuous with Gaussian priors. For the Stackelberg setup, the optimality of affine policies for Gaussian signaling no longer holds under prior mismatch, and thus, team-theoretic optimality of linear/affine policies are not robust to perturbations. We provide conditions under which there exist informative Nash and Stackelberg equilibria with affine policies. Finally, we show existence of fully informative Nash and Stackelberg equilibria for the cheap talk problem under an absolute continuity condition.

NOMA-Based Improper Signaling for Multicell MISO RIS-Assisted Broadcast Channels

In this paper, we study the performance of reconfigurable intelligent surfaces (RISs) in a multicell broadcast channel (BC) that employs improper Gaussian signaling (IGS) jointly with non-orthogonal multiple access (NOMA) to optimize either the minimum-weighted rate or the energy efficiency (EE) of the network. We show that although the RIS can significantly improve the system performance, it cannot mitigate interference completely, so we have to employ other interference-management techniques to further improve performance. We show that the proposed NOMA-based IGS scheme can substantially outperform proper Gaussian signaling (PGS) and IGS schemes that treat interference as noise (TIN) in particular when the number of users per cell is larger than the number of base station (BS) antennas (referred to as overloaded networks). In other words, IGS and NOMA complement to each other as interference management techniques in multicell RIS-assisted BCs. Furthermore, we consider three different feasibility sets for the RIS components showing that even a RIS with a small number of elements provides considerable gains for all the feasibility sets.

Improper Gaussian Signaling for Two-User MISO-NOMA Systems Considering Hardware Impairments and Imperfect SIC

Improper Gaussian Signaling for Two-User MISO-NOMA Systems Considering Hardware Impairments and Imperfect SIC

Constrained Capacity Optimal Generalized Multi-User MIMO: A Theoretical and Practical Framework

Conventional multi-user multiple-input multiple-output (MU-MIMO) mainly focused on Gaussian signaling, independent and identically distributed (IID) channels, and a limited number of users. It will be laborious to cope with the heterogeneous requirements in next-generation wireless communications, such as various transmission data, complicated communication scenarios, and unprecedented massive user access. Therefore, this paper studies a generalized MU-MIMO (GMU-MIMO) system with more generalized and practical constraints, i.e., practical channel coding, non-Gaussian signaling, right-unitarily-invariant channels (covering Rayleigh fading channel matrices, certain ill-conditioned and correlated channel matrices, etc.), and massive users and antennas. These generalized assumptions bring new challenges in theory and practice. For example, there is no accurate constrained capacity region analysis for GMU-MIMO. In addition, it is unclear how to achieve constrained-capacity-optimal performance with practical complexity. To address these challenges, a unified framework is proposed to derive the constrained capacity region of GMU-MIMO and design a constrained-capacity-optimal transceiver, which jointly considers encoding, modulation, detection, and decoding. Group asymmetry is developed to group users according to their rates, which makes a tradeoff between user rate allocation and implementation complexity. Specifically, the constrained capacity region of group-asymmetric GMU-MIMO is characterized by using the minimum mean-square error (MMSE) optimality of orthogonal/vector approximate message passing (OAMP/VAMP) and the relationship between mutual information and MMSE. Furthermore, a theoretically optimal multi-user OAMP/VAMP receiver and practical multi-user low-density parity-check (MU-LDPC) codes are proposed to achieve the constrained capacity region of group-asymmetric GMU-MIMO. Numerical results demonstrate that the proposed MU-LDPC coded GMU-MIMO systems achieve asymptotic performance within 0.2 dB from the theoretical sum capacity. Moreover, their finite-length performances are about 1~2 dB away from the associated sum capacity of GMU-MIMO.

Placement Optimization of UAV Relaying for Covert Communication

Covert communication has attracted growing interests as a new security technique, which focuses on concealing the signal transmission. Owing to the high flexibility, unmanned aerial vehicles (UAVs) can be utilized to realize long-distance covert transmission. In this correspondence, we propose a UAV relaying scheme to assist the covert communication between two terrestrial nodes. Due to the high risk of eavesdropping in line-of-sight (LoS) channels, we assume that the UAV adopts the Gaussian signalling to confuse the warden's detection. First, we divide the transmission into two phases. Then, in both phases, the requirement of covertness is derived to optimize the transmit power and blocklength. With different distance between the transmitter and warden, the location of UAV is optimized to maximize the effective throughput under the constraint of transmit power and blocklength. Simulation results show the effectiveness of the proposed UAV relaying scheme to guarantee the covert transmission.

Improper Gaussian Signaling for Downlink NOMA Systems With Imperfect Successive Interference Cancellation

Non-orthogonal multiple access (NOMA) exhibits superiority in spectrum efficiency which is particularly essential in the Internet of Things (IoT) system involving massive number of device connections. This paper addresses the achievable rate improvement for the downlink NOMA system, in the context of imperfect successive interference cancellation (SIC), by means of the improper Gaussian signaling (IGS) technique. We investigate a basic scenario where the strong user transmits the conventional proper data, while the weak user adopts an improper signaling scheme. The users’ data rates are first formulated in terms of the impropriety degree of the IGS, under residual interference introduced by the imperfect SIC. In this way, analytical expressions for the best improper transmission can be characterized by jointly optimizing the user’s power and the impropriety degree, where their sufficient and necessary conditions are provided. When the strong user transmits with its maximum power, the IGS scheme always increases the achievable rate of the strong user while the weak user may also benefit. When the weak user transmits with its maximum power, such a scheme enables us optimize the achievable rate of the strong user under various levels of channel-to-noise ratios (CNR) and imperfect SIC. Finally, when both the users are imposed by quality of service (QoS) constraints, a Q-learning based solution is proposed to maximize their sum rate. Simulations on the downlink NOMA system support the analysis.

Energy Efficiency Maximization of Full-Duplex NOMA Systems With Improper Gaussian Signaling Under Imperfect Self-Interference Cancellation

This work addresses the energy efficiency maximization for a downlink cooperative full-duplex non-orthogonal multiple access (FD-NOMA) system in the presence of imperfect self-interference cancellation. We consider the case where users adopt improper Gaussian signaling (IGS) for their transmission and consequently derive the achievable rate of each link in the cooperative system. We jointly optimize the power allocation at the base-station and the IGS circularity coefficients of the cooperative IGS-based FD-NOMA system to maximize its energy efficiency subject to quality-of-service (QoS) requirements. Furthermore, improper constellation diagrams are designed using the predefined optimized IGS coefficients to study the impact of IGS on bit error rate performance. Simulation results demonstrate considerable energy efficiency performance gain of IGS-based FD-NOMA system over its proper Gaussian signaling (PGS)-based FD-NOMA counterpart under residual interference from imperfect self interference cancellation.

On the Kurtosis of Modulation Formats for Characterizing the Nonlinear Fiber Propagation

Knowing only two high-order statistical moments of modulation symbols, often represented by the fourth moment called “kurtosis”, the overestimation of nonlinear interference (NLI) in a Gaussian noise (GN) model due to Gaussian signaling assumption can be corrected through an enhanced GN (EGN) model. However, in some modern optical communication systems where the transmitted modulation symbols are statistically correlated, such as in systems that use probabilistic constellation shaping (PCS) with finite-length sphere shaping, the kurtosis-based EGN model produces significant inaccuracies in analytical prediction of NLI. In this paper, we show that for correlated modulation symbols, the NLI can be more accurately estimated by substituting a statistical measure called windowed kurtosis into the EGN model, instead of the conventional kurtosis. Remarkably, the optimal window length for windowed kurtosis is found to be consistent with the self-phase modulation (SPM) and cross-phase modulation (XPM) characteristic times in various system configurations. The findings can be used in practice to analytically evaluate and design NLI-tolerant modulation formats.

Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance

This paper studies the performance of improper Gaussian signaling (IGS) in a multicell broadcast multiple-input, multiple-output (MIMO) reconfigurable-intelligent-surface (RIS)-assisted channel. The transceivers are non-ideal devices with I/Q imbalance, which further motivates the use of IGS. We propose IGS schemes to improve the spectral and energy efficiency (EE) of the system by solving different optimization problems such as minimum-weighted-rate, weighted-sum-rate, minimum-weighted-EE and global-EE maximization. Two different RIS implementations are considered: in the first one, the phase and amplitude of the RIS components can be optimized independently, which provides an upper-bound for RIS performance. In the second implementation, the amplitude of each RIS component is fixed, and only its phase can be optimized, which is referred to as reflecting surfaces. We show that RIS can significantly increase the spectral and energy efficiency of the system, while the reflecting surfaces perform very close to the upper-bound performance of RISs. Moreover, distributed RIS implementations that use spatially separated RIS with fewer components, can outperform centralized implementations consisting of a single RIS with co-located reflecting elements. Additionally, our results indicate that IGS can provide considerable gains from both spectral and energy-efficiency perspectives, and the benefits of IGS can be even higher in RIS-assisted systems.

Non-Orthogonal Multiple Access: The Case of Improper Gaussian Signaling and Imperfect Successive Interference Cancellation

This paper studies a two-user downlink non-orthogonal multiple access (NOMA) system that adopts an improper Gaussian signaling (IGS) strategy to compensate for the performance loss due to imperfect successive interference cancellation (SIC). Joint optimization problems are formulated to maximize the overall spectral efficiency and energy efficiency of a two-user NOMA system under minimum user-rate requirements and total power constraints. Sub-optimal solutions of IGS circularity coefficients and power allocation are obtained for the formulated problems. Furthermore, improper constellation diagrams are designed using widely linear transformation with predefined optimized IGS coefficients to study the impact of IGS on throughput and error performance. Simulation results show that the performance of IGS-based NOMA systems, where the IGS strategy is adopted by both users, outperforms that of the proper Gaussian signal (PGS)-based NOMA system under imperfect SIC.