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Non-terrestrial networks (NTNs) traditionally have certain limited applications. However, the recent technological advancements and manufacturing cost reduction opened up myriad applications of NTNs for 5G and beyond networks, especially when integrated into terrestrial networks (TNs). This article comprehensively surveys the evolution of NTNs highlighting their relevance to 5G networks and essentially, how it will play a pivotal role in the development of 6G ecosystem. We discuss important features of NTNs integration into TNs and the synergies by delving into the new range of services and use cases, various architectures, technological enablers, and higher layer aspects pertinent to NTNs integration. Moreover, we review the corresponding challenges arising from the technical peculiarities and the new approaches being adopted to develop efficient integrated ground-air-space (GAS) networks. Our survey further includes the major progress and outcomes from academic research as well as industrial efforts representing the main industrial trends, field trials, and prototyping towards the 6G networks., Comment: Accepted for publication in IEEE Communications Surveys & Tutorials

This paper addresses the optimization problem of symbol-level precoding (SLP) in the downlink of a multiuser multiple-input multiple-output (MU-MIMO) wireless system while the precoder's output is subject to partially-known distortions. In particular, we assume a linear distortion model with bounded additive noise. The original signal-to-interference-plus-noise ratio (SINR) -constrained SLP problem minimizing the total transmit power is first reformulated as a penalized unconstrained problem, which is referred to as the relaxed robust formulation. We then adopt a worst-case design approach to protect the users' intended symbols and the targeted constructive interference with a desired level of confidence. Due to the non-convexity of the relaxed robust formulation, we propose an iterative algorithm based on the block coordinate ascent-descent method. We show through simulation results that the proposed robust design is flexible in the sense that the CI constraints can be relaxed so as to keep a desirable balance between achievable rate and power consumption. Remarkably, the new formulation yields more energy-efficient solutions for appropriate choices of the penalty parameter, compared to the original problem., Comment: 10 pages, 2 figures, IEEE GlobalSIP 2019 (Accepted)

In this paper, we propose a low-complexity method to approximately solve the SINR-constrained optimization problem of symbol-level precoding (SLP). First, assuming a generic modulation scheme, the precoding optimization problem is recast as a standard non-negative least squares (NNLS). Then, we improve an existing closed-form SLP (CF-SLP) scheme using the conditions for nearly perfect recovery of the optimal solution support, followed by solving a reduced system of linear equations. We show through simulation results that in comparison with the CF-SLP method, the improved approximate solution of this paper, referred to as ICF-SLP, significantly enhances the performance with a negligible increase in complexity. We also provide comparisons with a fast-converging iterative NNLS algorithm, where it is shown that the ICF-SLP method is comparable in performance to the iterative algorithm with a limited maximum number of iterations. Analytic discussions on the complexities of different methods are provided, verifying the computational efficiency of the proposed method. Our results further indicate that the ICF-SLP scheme performs quite close to the optimal SLP, particularly in the large system regime., Comment: 7 pages, 2 figures, Submitted to IEEE SPAWC 2019

In this paper, we address robust design of symbol-level precoding for the downlink of multiuser multiple-input multiple-output wireless channels, in the presence of imperfect channel state information (CSI) at the transmitter. In particular, we consider two common uncertainty models for the CSI imperfection, namely, spherical (bounded) and stochastic (Gaussian). Our design objective is to minimize the total (per-symbol) transmission power subject to constructive interference (CI) constraints as well as users' quality-of-service requirements in terms of signal-to-interference-plus-noise ratio. Assuming bounded channel uncertainties, we obtain a convex CI constraint based on the worst-case robust analysis, whereas in the case of Gaussian uncertainties, we define probabilistic CI constraints in order to achieve robustness to statistically-known CSI errors. Since the probabilistic constraints of actual interest are difficult to handle, we resort to their convex approximations, yielding tractable (deterministic) robust constraints. Three convex approximations are developed based on different robust conservatism approaches, among which one is introduced as a benchmark for comparison. We show that each of our proposed approximations is tighter than the other under specific robustness conditions, while both always outperform the benchmark. Using the developed CI constraints, we formulate the robust precoding optimization as a convex conic quadratic program. Extensive simulation results are provided to validate our analytic discussions and to make comparisons with existing robust precoding schemes. We also show that the robust design increases the computational complexity by an order of the number of users in the large system limit, compared to its non-robust counterpart., Comment: 19 pages, 9 figures, Submitted to IEEE Transactions in Signal Processing

In this paper, we investigate the downlink transmission of a multiuser multiple-input single-output (MISO) channel under a symbol-level precoding (SLP) scheme, having imperfect channel knowledge at the transmitter. In defining the SLP problem, a general category of constructive interference regions (CIR) called distance preserving CIR (DPCIR) is adopted. In particular, we are interested in the robust SLP design minimizing the total transmit power while satisfying the users' quality-of-service (QoS) requirements. We consider two common models for the channel uncertainty region, namely, norm-bounded spherical and stochastic. For the spherical uncertainty model, a worst-case robust precoder is proposed, while for the stochastic uncertainties, we define a convex optimization problem with probabilistic constraints. We simulate the performance of the proposed robust approaches, and compare them with the existing methods. Through the simulation results, we also show that there is an essential trade-off between the two robust approaches., Comment: 9 pages, 3 figures, submitted to GLOBECOM 2018

In this paper, we investigate the symbol-level precoding (SLP) design problem in the downlink of a multiuser multiple-input single-output (MISO) channel. We consider generic constellations with any arbitrary shape and size, and confine ourselves to one of the main categories of constructive interference regions (CIR), namely, distance preserving CIR (DPCIR). We provide a comprehensive study of DPCIRs and derive some properties for these regions. Using these properties, we first show that any signal in a given DPCIR has a norm greater than or equal to the norm of the corresponding constellation point if and only if the convex hull of the constellation contains the origin. It is followed by proving that the power of the noiseless received signal lying on a DPCIR is a monotonic strictly increasing function of two parameters relating to the infinite Voronoi edges. Using the convex description of DPCIRs and their properties, we formulate two design problems, namely, the SLP power minimization with signal-to-interference-plus-noise ratio (SINR) constraints, and the SLP SINR balancing problem under max-min fairness criterion. The SLP power minimization based on DPCIRs can straightforwardly be written as a quadratic program (QP). We provide a simplified reformulation of this problem which is less computationally complex. The SLP max-min SINR, however, is non-convex in its original form, and hence difficult to tackle. We propose several alternative optimization approaches, including semidefinite program (SDP) formulation and block coordinate descent (BCD) optimization. We discuss and evaluate the loss due to the proposed alternative methods through extensive simulation results., Comment: 19 pages, 12 figures, Submitted to IEEE Transactions in Signal Processing