Max-min SINR Research Articles

Max-Min SINR Analysis of STAR-RIS Assisted Massive MIMO Systems With Hardware Impairments

Max-Min SINR Analysis of STAR-RIS Assisted Massive MIMO Systems With Hardware Impairments

Achievable Rate Analysis and Max-Min SINR Optimization in Intelligent Reflecting Surface Assisted Cell-Free MIMO Uplink

In this paper, we study the uplink transmission in an intelligent reflecting surface (IRS) assisted cell-free multiple-input multiple-output (MIMO) system where the central processing unit (CPU) only has statistical channel state information (CSI) to detect symbols, and to design the receiver filter coefficients, the power allocations, and the IRS phase shifts. The access points (APs) estimate only their local end-to-end channels with the users using minimum mean squared error (MMSE) estimation to implement matched filtering, thereby avoiding the large overhead associated with estimating individual IRS-assisted channels. Under this framework, we derive a closed-form expression for the achievable uplink net rate that only depends on the channel statistics. Using this expression, we formulate the problem of maximizing the minimum (max-min) signal-to-interference plus noise ratio (SINR) to design the receiver filter coefficients at the CPU, the power allocations at the users, and the phase shifts at the IRS, subject to per user power constraints as well as IRS phase shift resolution constraints. The resulting problem is jointly non-convex in the three design variables and is solved using an alternating optimization algorithm. In particular, the receiver filter design is formulated as a generalized eigenvalue problem leading to a closed-form solution, the power allocation problem is solved using a geometric programming (GP) approach, and the IRS phase shifts are designed using an alternating maximization algorithm. For comparison, we also formulate and solve the max-min SINR problem for the scenario where the instantaneous imperfect CSI of all individual direct and IRS-assisted channels is available at the CPU. Numerical results show that the scheme designed using statistical CSI has the potential to outperform the scheme based on instantaneous CSI for moderate to large number of IRS elements, due to savings in the channel estimation overhead.

Beamforming Optimization for Intelligent Reflecting Surface-Aided SWIPT IoT Networks Relying on Discrete Phase Shifts

Intelligent reflecting surface (IRS) is capable of constructing the favorable wireless propagation environment by leveraging massive low-cost reconfigurable reflect array elements. In this article, we investigate the IRS-aided multiple-input-multiple-output (MIMO) simultaneous wireless information and power transfer (SWIPT) for Internet-of-Things (IoT) networks, where the active base station (BS) transmits beamforming and the passive IRS reflection coefficients are jointly optimized for maximizing the minimum signal-to-interference-plus-noise ratio (SINR) among all information decoders (IDs), while maintaining the minimum total harvested energy at all energy receivers (ERs). Moreover, the IRS with practical discrete phase shifts is considered, and thereby the max-min SINR problem becomes an NP-hard combinatorial optimization problem with a strong coupling among optimization variables. To explore the insights and generality of this max-min design, both the single-ID single-ER (SISE) scenario and the multiple-IDs multiple-ERs (MIME) scenario are studied. In the SISE scenario, the classical combinatorial optimization techniques, namely, the special ordered set of type 1 (SOS1) and the reformulation-linearization (RL) technique, are applied to overcome the difficulty of this max-min design imposed by discrete optimization variables. Then, the optimal branch-and-bound algorithm and suboptimal alternating optimization algorithm are, respectively, proposed. We further extend the idea of alternating optimization to the MIME scenario. Moreover, to reduce the iteration complexity, a two-stage scheme is considered aiming to separately optimize the BS transmit beamforming and the IRS reflection coefficients. Finally, numerical simulations demonstrate the superior performance of the proposed algorithms over the benchmarks in both the two scenarios.

Performance analysis and SINR‐based power allocation strategies for downlink NOMA networks

This study analyses the performance of downlink non-orthogonal multiple-access (NOMA) networks over independent but not necessarily identically distributed Rayleigh fading channels by deriving closed-form expressions for the average signal-to-interference-plus-noise ratio (SINR), average achievable rate, and outage probability of all network users. Moreover, SINR-based power allocation strategies are studied. Specifically, the optimisation problems of max–min SINR, multi-objective SINR, sum-SINR and proportional-fairness-SINR maximisation under minimum SINR constraints are formulated and shown to be non-convex. Additionally, the problems of total power and sum-SINR minimisation are also formulated. Particularly, the formulated problems take the form of linear-fractional programming problems. By applying intelligent reformulation techniques, these problems have been reformulated into convex optimisation problems, and thus efficiently solved. Numerical evaluations are presented to validate the derived closed-form expressions for the different performance metrics, which are found to be in agreement with the network simulation results. More importantly, it has been demonstrated that the user with the best channel conditions achieves full diversity order, whereas all the other users achieve diversity orders equivalent to their ordered channel conditions. Finally, the reformulated power allocation strategies are evaluated, and shown to coincide with the original problem formulations.

Min-SINR Maximization for mmWave Massive MISO-NOMA System With Randomly Directional Beamforming

Based on the high-direction characteristic of millimeter wave (mmWave) transmission, randomly directional beamforming (RDB) can be used for the mmWave massive multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) system to reduce the number of radio frequency (RF) chains. However, the impact of RDB on the signal-to-interference-plus-noise ratio (SINR) of each user is related to the corresponding beamforming gain and interference from other users. Thus, in this paper, we investigate the max-min SINR among all users to evaluate user fairness. In particular, we focus on the single-cell downlink mmWave MISO-NOMA system with RDB, where single-antenna users are divided into multiple NOMA clusters according to their azimuth angles. We formulate the minimum achievable SINR maximization problem associated with power allocation and propose the sum of power allocation coefficients based iterative algorithm (SPACIA) to find the max-min SINR. We also prove that the max-min SINR monotonically decreases as the number of paired users in an NOMA cluster increases as well as the number of beams in the cell with large-scale base station (BS) antenna array increases. Moreover, we derive the upper bound of the max-min SINR. Simulation results verify our theoretical analyses and demonstrate that the proposed algorithm guarantees user fairness, thus outperforming existing schemes.

Coordinated multicell beamforming and power allocation for massive MIMO: A large system analysis

This paper is concerned with coordinated multicell beamforming and power allocation for downlink massive multiple input and multiple output (MIMO) system. The design objective is to minimize the total transmit power under users’ signal to interference plus noise ratio (SINR) constraints. Another closely related optimization problem is to maximize the minimum of all users’ SINR values under a total power limitation, and we employ the relationship between the two problems to solve the former one. In particular, the power minimization problem can be transformed to a max-min SINR problem with an appropriate power limitation. This power limitation value is found by using the bisection method. Then, the max-min SINR problem is settled by solving a conditional eigenvalue problem. Note that the whole calculation process is done in the asymptotic regime where base station (BS) antenna number and user number both tend to infinity. Simulation results demonstrate that this algorithm is effective, and can achieve the near optimal performance with low complexity.

Symbol-Level Precoding Design Based on Distance Preserving Constructive Interference Regions

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.

Robust Designs of Beamforming and Power Splitting for Distributed Antenna Systems With Wireless Energy Harvesting

In this paper, we investigate a multiuser distributed antenna system with simultaneous wireless information and power transmission under the assumption of imperfect channel state information (CSI). In this system, a distributed antenna port with multiple antennas supports a set of mobile stations who can decode information and harvest energy simultaneously via a power splitter. To design robust transmit beamforming vectors and the power splitting (PS) factors in the presence of CSI errors, we maximize the average worst-case signal-to-interference-plus- noise ratio (SINR) while achieving individual energy harvesting constraint for each mobile station. First, we develop an efficient algorithm to convert the max-min SINR problem to a set of "dual" min-max power balancing problems. Then, motivated by the penalty function method, an iterative algorithm based on semi-definite programming (SDP) is proposed to achieve a local optimal rank-one solution. Also, to reduce the computational complexity, we present another iterative scheme based on the Lagrangian method and the successive convex approximation (SCA) technique to yield a suboptimal solution. Simulation results are shown to validate the robustness and effectiveness of the proposed algorithms.

Enhanced Max-Min SINR for Uplink Cell-Free Massive MIMO Systems

In this paper, we consider the max-min signal-to-interference plus noise ratio (SINR) problem for the uplink transmission of a cell-free Massive multiple-input multiple-output (MIMO) system. Assuming that the central processing unit (CPU) and the users exploit only the knowledge of the channel statistics, we first derive a closed-form expression for uplink rate. In particular, we enhance (or maximize) user fairness by solving the max-min optimization problem for user rate, by power allocation and choice of receiver coefficients, where the minimum uplink rate of the users is maximized with available transmit power at the particular user. Based on the derived closed-form expression for the uplink rate, we formulate the original user max-min problem to design the optimal receiver coefficients and user power allocations. However, this max-min SINR problem is not jointly convex in terms of design variables and therefore we decompose this original problem into two sub-problems, namely, receiver coefficient design and user power allocation. By iteratively solving these sub-problems, we develop an iterative algorithm to obtain the optimal receiver coefficient and user power allocations. In particular, the receiver coefficients design for a fixed user power allocation is formulated as generalized eigenvalue problem whereas a geometric programming (GP) approach is utilized to solve the power allocation problem for a given set of receiver coefficients. Numerical results confirm a three-fold increase in system rate over existing schemes in the literature.

Max–Min SINR in Large-Scale Single-Cell MU-MIMO: Asymptotic Analysis and Low-Complexity Transceivers

This work focuses on the downlink and uplink of large-scale single-cell MU-MIMO systems in which the base station (BS) endowed with $M$ antennas communicates with $K$ single-antenna user equipments (UEs). Particularly, we aim at reducing the complexity of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio subject to a given power constraint. To this end, we consider the asymptotic regime in which $M$ and $K$ grow large with a given ratio. Tools from random matrix theory (RMT) are then used to compute, in closed form, accurate approximations for the parameters of the optimal precoder and receiver, when imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BS. The asymptotic analysis allows us to derive the asymptotically optimal linear precoder and receiver that are characterized by a lower complexity (due to the dependence on the large scale components of the channel) and, possibly, by a better resilience to imperfect channel state information. However, the implementation of both is still challenging as it requires fast inversions of large matrices in every coherence period. To overcome this issue, we apply the truncated polynomial expansion (TPE) technique to the precoding and receiving vector of each UE and make use of RMT to determine the optimal weighting coefficients on a per-UE basis that asymptotically solve the max-min SINR problem. Numerical results are used to validate the asymptotic analysis in the finite system regime and to show that the proposed TPE transceivers efficiently mimic the optimal ones, while requiring much lower computational complexity.

Robust Transceivers Design for Multi-Stream Multi-User MIMO Visible Light Communication

Visible light communication (VLC) is an emerging technique that uses light-emitting diodes to combine communication and illumination. It is considered as a promising scheme for indoor wireless communication that can be deployed at reduced costs, while offering high data rate performance. This paper focuses on the design of precoding and receiving schemes for downlink multi-user multiple-input multiple-output VLC systems using angle diversity receivers. Two major concerns need to be considered while solving such a problem. The first one is related to the inter-user interference, basically inherent to our consideration of a multi-user system, while the second results from the users’ mobility, causing imperfect channel estimates. To address both concerns, we propose robust precoding and receiver that solve the max-min SINR problem. The performance of the proposed VLC design is studied under different working conditions, where a significant gain of the proposed robust transceivers over their non-robust counterparts has been observed.

Coordinated multicell beamforming for massive multiple‐input multiple‐output systems based on uplink–downlink duality

This paper studies joint beamforming and power allocation for multicell multiuser multi-antenna systems with the objective of maximising the minimum signal-to-interference-plus-noise ratio (max-min SINR). The authors first consider developing an iterative algorithm to achieve the optimal performance by extending the uplink-downlink duality for finite-scale wireless communication systems. The solution is then generalised to achieve the asymptotically optimal multicell beamforming with the aim to reduce the overhead of signalling exchange between coordinated base stations based on large dimension random matrix theory. Based on that, an efficient multicell beamforming algorithm is proposed to asymptotically achieve the max-min SINR. To further solve the complexity issue of large dimensional matrix inversion involved in the calculation of beamforming vectors, they propose a low-complexity beamforming calculator based on truncated polynomial expansion approach. Numerical results validate the effectiveness of the authors' proposed algorithms and show that they can achieve the optimal or asymptotically optimal performance in a massive multi-input multi-output system with low complexity and small backhaul overhead.

Optimized Power Allocation for Interference Channel With SWIPT

This letter studies a $K$ -link interference channel (IFC) with simultaneous wireless information and power transfer (SWIPT). Our objective is to maximize the minimum signal to interference plus noise ratio (SINR) of the $K$ links by jointly designing the power allocations at all transmitters and the power splitting (PS) ratios at their receivers under both the individual minimum energy harvesting (EH) constraints and maximum transmit power constraints. We propose a centralized algorithm to optimally solve the nonconvex problem. A distributed algorithm is further designed where each link updates its transmit power and PS ratio through an iterative process. Numerical results show that the proposed algorithms provide improved tradeoffs in the achievable max–min SINR versus harvested energy compared against other existing algorithms.

Robust beamforming designs for multiuser MISO downlink with per-antenna power constraints

This paper studies the robust beamforming designs for a multiuser multiple-input single-output (MISO) downlink system. Different from the conventional sum-power constraint across all transmit antennas, we consider individual power constraints per antenna at the base station. Assuming that the channel uncertainty is bounded by a spherical region, we develop the optimal robust designs to maximize the minimum worst-case signal-to-interference-plus-noise ratio (SINR) among all users. Specifically, we show that the optimal max-min SINR beamformers can be obtained by solving a sequence of “dual” min-max power problems. Relying on the S-procedure and the linear matrix inequality representation for the cone of Lorentz-positive maps (LPMs), respectively, two designs, which are referred to as Robust-SP and Robust-LPM, are proposed to efficiently solve such min-max power problems. Building on either Robust-SP or Robust LPM, a bisection search algorithm is then developed to find the robust max-min SINR beamformers with guaranteed global optimality and geometrically fast convergence speed. Using the max-min SINR solutions as a cornerstone, we further put forth the optimal robust design for the worst-case weighted sum-rate (WSR) maximization. By formulating the worst-case WSR maximization problem into a monotonic program (MP), we develop a polyblock outer approximation algorithm to obtain the globally optimal solution. Numerical results are presented to demonstrate the merits of the proposed robust beamforming designs.

Reduced-Complexity Coordinated Beamforming for Multicell Downlink Max–Min SINR Problem

This letter presents a reduced-complexity algorithm for coordinated beamforming aimed at solving the multicell downlink max-min signal-to- interference-plus-noise problem under per-base-station power constraints. It is shown that the proposed algorithm can achieve close performance to the optimum algorithm with faster convergence and lower complexity. © 2014 IEEE.

Coordinated Multicast Beamforming in Multicell Networks

We study physical layer multicasting in multicell networks where each base station, equipped with multiple antennas, transmits a common message using a single beamformer to multiple users in the same cell. We investigate two coordinated beamforming designs: the quality-of-service (QoS) beamforming and the max-min SINR (signal-to-interference-plus-noise ratio) beamforming. The goal of the QoS beamforming is to minimize the total power consumption while guaranteeing that received SINR at each user is above a predetermined threshold. We present a necessary condition for the optimization problem to be feasible. Then, based on the decomposition theory, we propose a novel decentralized algorithm to implement the coordinated beamforming with limited information sharing among different base stations. The algorithm is guaranteed to converge and in most cases it converges to the optimal solution. The max-min SINR (MMS) beamforming is to maximize the minimum received SINR among all users under per-base station power constraints. We show that the MMS problem and a weighted peak-power minimization (WPPM) problem are inverse problems. Based on this inversion relationship, we then propose an efficient algorithm to solve the MMS problem in an approximate manner. Simulation results demonstrate significant advantages of the proposed multicast beamforming algorithms over conventional multicasting schemes.

Max-Min SINR Coordinated Multipoint Downlink Transmission—Duality and Algorithms

This paper considers the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem subject to multiple weighted-sum power constraints, where the weights can represent relative power costs of serving different users. First, we study the power control problem. We apply nonlinear Perron-Frobenius theory to derive closed-form expressions for the optimal value and solution and an iterative algorithm which converges geometrically fast to the optimal solution. Then, we use the structure of the closed-form solution to show that the problem can be decoupled into subproblems each involving only one power constraint. Next, we study the multiple-input-single-output (MISO) transmit beamforming and power control problem. We use uplink-downlink duality to show that this problem can be decoupled into subproblems each involving only one power constraint. We apply this decoupling result to derive an iterative subgradient projection algorithm for the problem.

A Multi-Cell Beamforming Design by Uplink-Downlink Max-Min SINR Duality

In this paper, we address the problem of the coordinated beamforming design for multi-cell multiple input single output (MISO) downlink system subject to per-BS power constraints. The objective is taken as the maximization of the minimum signal-to-interference plus noise ratio (SINR), while a complete analysis of the duality between the multi-cell downlink and the virtual uplink optimization problems is provided. A hierarchical iterative scheme is proposed to solve the virtual uplink optimization problem, whose solution is then converted to derive the one of the multi-cell downlink beamforming problem. The proposed algorithm is proved to converge to a stable point. Additional, the complexity of the proposed algorithm is analyzed. Simulation results show that, in contrast to existing multi-cell beamforming schemes, the proposed algorithm achieves better performance in terms of both rate per energy (RPE) and the worst-user rate.

Interference Alignment: A Building Block of Coordinated Beamforming Transceiver Designs

Interference alignment (IA) has recently been used for the transceiver design of the K-user constant MIMO interference channel. Since this system is a coordinated beamforming system and there are other design criteria, it is important to evaluate IA transceiver designs in light of other designs. In this paper, relationships between IA and the MMSE, Max Min SINR, Max Sum Capacity, and Min BER transceiver designs are rigorously established for all SNR’s and power constraints. A MMSE based transceiver design approach, applicable for general linear equality power constraints, is also proposed—the first such design for this system. It is used, along with some IA transceiver designs, to demonstrate numerically the derived relationships and to perform a comparison of the designs. One of the main conclusions is that IA is a building block of the traditional transceiver designs considered (MMSE, Max Min SINR, etc.) and generally should not be pursued alone.

Joint Power Optimization for Multi-Source Multi-Destination Relay Networks

In this paper, low-complexity joint power assignment algorithms are developed for multi-source multi-destination relay networks where multiple sources share a common relay that forwards all received signals simultaneously to destinations. In particular, we consider the following power optimization strategies: (i) Minimization of the total transmission power of the sources and the relay under the constraint that the signal-to-interference-plus-noise ratio (SINR) requirement of each source-destination pair is satisfied, and (ii) Maximization of the minimum SINR among all source-destination pairs subject to any given total power budget. Both optimization problems involve K power variables, where K is the number of source-destination pairs in the network, and an exhaustive search is prohibitive for large K. In this work, we develop a methodology that allows us to obtain an asymptotically tight approximation of the SINR and reformulate the original optimization problems to single-variable optimization problems, which can be easily solved by numerical search of the single variable. Then, the corresponding optimal transmission power at each source and relay can be calculated directly. The proposed optimization schemes are scalable and lead to power assignment algorithms that exhibit the same optimization complexity for any number (K) of source-destination pairs in the network. Moreover, we apply the methodology that we developed to solve a related max-min SINR based optimization problem in which we determine power assignment for the sources and the relay to maximize the minimum SINR among all source-destination pairs subject to any given total power budget. Extensive numerical studies illustrate and validate our theoretical developments.