Coordinated Multicell Beamforming Research Articles

Coordinated Multicell Beamforming Based on Power Minimization in an Uplink–Downlink Configured Massive MIMO Network

Coordinated Multicell Beamforming Based on Power Minimization in an Uplink–Downlink Configured Massive MIMO Network

Quantized Massive MIMO Systems With Multicell Coordinated Beamforming and Power Control

In this paper, we investigate a coordinated multipoint (CoMP) beamforming and power control problem for base stations (BSs) with a massive number of antenna arrays under coarse quantization at low-resolution analog-to-digital converters (ADCs) and digital-to-analog converter (DACs). Unlike high-resolution ADC and DAC systems, non-negligible quantization noise that needs to be considered in CoMP design makes the problem more challenging. We first formulate total power minimization problems of both uplink (UL) and downlink (DL) systems subject to signal-to-interference-and-noise ratio (SINR) constraints. We then derive strong duality for the UL and DL problems under coarse quantization systems. Leveraging the duality, we propose a framework that is directed toward a twofold aim: to discover the optimal transmit powers in UL by developing iterative algorithm in a distributed manner and to obtain the optimal precoder in DL as a scaled instance of UL combiner. Under homogeneous transmit power and SINR constraints per cell, we further derive a deterministic solution for the UL CoMP problem by analyzing the lower bound of the SINR. Lastly, we extend the derived result to wideband orthogonal frequency-division multiplexing systems to optimize transmit power and beamformer for all subcarriers. Simulation results validate the theoretical results and proposed algorithms.

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.

A Stochastic ADMM Approach to Distributed Coordinated Multicell Beamforming for Renewables Powered Wireless Cellular Networks

The availability of renewable energy sources (RES) has facilitated efficient and sustainable resource allocation for wireless communication systems. In this paper, a novel framework is proposed to implement coordinated multicell beamforming (CMBF) scheme for cellular networks powered by a smart microgrid, where the BSs are equipped with RES harvesting devices and can buy/sell energy from/to the main grid. New models are developed to capture the stochastic energy harvesting, dynamic electricity prices, and energy transaction cost gauged by the conditional value-at-risk (CVaR) function. Based upon these models, a distributed CMBF scheme is put forth to minimize the grid-wide transaction cost under user quality-of-service (QoS) constraints. Specifically, it is shown that the relevant task can be cast into a convex program to be tackled in a distributed fashion, leveraging the state of the art optimization tools. To deal with the unpredictable nature of the renewable energy, the stochastic alternating direction method of multipliers is then employed to develop a novel distributed CMBF scheme. It is established that the proposed scheme can guarantee optimality of the obtained CMBF solution, using only local channel state information at each BS and limited information exchange among the BSs. Merits of the proposed scheme are corroborated by extensive numerical results.

Coordinated Beamforming With Artificial Noise for Secure SWIPT Under Non-Linear EH Model: Centralized and Distributed Designs

This paper investigates the artificial noise (AN)-aided multi-cell coordinated beamforming (MCBF) for secure simultaneous wireless information and power transfer in both centralized and distributed manners. The proposed transmit design is formulated into a power-minimization problem to guarantee the authorized users’ information and energy harvesting (EH) requirements while avoiding the information interception by unauthorized users. Power splitting receiver architecture and the non-linear EH model are employed. Both perfect and imperfect channel state information (CSI) cases are considered. For the perfect CSI case, the non-robust design is presented by applying semi-definition relaxation (SDR). When no user harvests energy, the global optimum is guaranteed, and when some users harvest energy, approximate global optimum is achieved. For the imperfect CSI case, the worst-case robust design under the deterministic uncertainty channel model is studied, where a solving approach based on SDR and S-procedure is proposed, and the statistically robust design under the stochastic uncertainty channel model is also studied, where an upper bound to the global optimum is obtained by using SDR and Bernstein-type inequality. We further propose a distributed AN-aided MCBF design framework by using an alternating direction method of multipliers for the non-robust, worst-case robust, and statistically robust designs, with which each BS is able to optimize its own transmit design with the local CSI. Simulation results demonstrate our theoretical analysis, which show that our proposed distributed algorithm converges to the optimal results obtained by the centralized one. It also shows that employing the non-linear EH model is able to avoid false output power and save power consumption at the BSs.

Optimal coordinated beamforming with artificial noise for secure SWIPT in multi-cell networks

This paper investigates the multi-cell coordinated beamforming (MCBF) design for secure simultaneous wireless information and power transfer (SWIPT) in both centralized and distributed manners. In each cell, one transmitter serves multiple information receivers (IRs) and energy receivers (ERs) with the non-linear energy harvesting (EH) model. Meanwhile, several eavesdroppers (Eves) intend to intercept the confidential information transmitted for IRs. To achieve a secure transmission, the artificial noise (AN) is embedded in the transmit signals of each transmitter. The proposed design is formulated into a power-minimization problem to guarantee the IRs’ information and ERs’ energy requirements while avoiding the information being intercepted by Eves. Since the problem is non-convex and not easy to solve, a solution method based on semi-definition relaxation (SDR) is proposed and the global optimum is proved to be guaranteed with full channel state information (CSI). We further present a distributed AN-aided MCBF for the system by using alternating direction method of multipliers (ADMM), with which each transmitter is able to calculate its own beamforming vectors and AN covariance matrix based on its local CSI. Simulation results show that our proposed distributed design converges to the global optimum obtained by the centralized one. It is also shown that by employing AN, the total required power of the system is reduced and the effect of AN on the system performance decreases with increment of transmit antennas. Compared with traditional linear EH model, optimizing the system under the non-linear EH one avoids false output power at the ERs and saves power at the transmitter.

Secrecy Energy Efficiency in Wireless Powered Heterogeneous Networks: A Distributed ADMM Approach

This paper investigates the physical layer security in heterogeneous networks (HetNets) supported by simultaneous wireless information and power transfer (SWIPT). We first consider a two-tier HetNet composed of a macrocell and several femtocells, where the macrocell base station (BS) serves multiple users in the presence of a malicious eavesdropper, while each femtocell BS serves a couple of Internet-of-Things (IoT) users. With regard to the energy constraint of IoT users, SWIPT is performed at the femtocell BSs, and IoT users accomplish the reception of information and energy in a time-switching manner, where information secrecy is to be protected. To enhance the secrecy performance, we inject artificial noise (AN) into the transmit beam at both macrocell and femtocell BSs, and for the sake of achieving green communications, we formulate the problem of maximizing secrecy energy efficiency while considering the fairness in a cross-tier multi-cell coordinated beamforming (MCBF) design. To handle this resulting nonconvex max–min fractional program problem, we propose an iterative algorithm by applying successive convex approximation method. Then, we further develop a decentralized solution based on alternative direction multiplier method (ADMM), which reduces the overhead of information exchange among coordinated BSs and achieves good approximation performance. Finally, simulation results demonstrate the performance of the proposed AN-aided cross-tier MCBF design and verify the validity of distributed ADMM-based approach.

Optimal Multicell Coordinated Beamforming for Downlink High-Speed Railway Communications

This paper investigates the multicell coordinated beamforming (MCBF) design for high-speed railway communications, where a high-mobility train goes through a multicell multiuser system in urban areas. All passengers in the train are aggregated to be a high-mobility “big user.” In order to explore the downlink system performance limit, we formulate an optimization problem to maximize the information rate from the serving base station to the high-mobility train while guaranteeing the minimal required achievable information rates of all low-mobility users outside the train by optimizing MCBF vectors. The interchannel interference (caused by Doppler effect to the train), the intercell interference and the interuser interference are jointly considered. Since the problem is nonconvex and cannot be solved directly, we first introduce an auxiliary variable (AV), and for a given AV, we find the optimal MCBF vectors via solving a second-order cone programming. Then, by updating the AV with the bisection method, the corresponding global optimal MCBF vectors are numerically obtained. Simulation results show that our proposed MCBF design greatly enhances the information throughput of the high-mobility train without degrading the required data rates of low-mobility users.

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.

Coordinated beamforming design for multicell systems with transceiver impairments: from perspective of spectral efficiency to energy efficiency

Physical transceiver implementations for wireless communication systems usually suffer from transmit-radio frequency (Tx-RF) and receiver-RF (Rx-RF) impairments. In this paper, we aim to design efficient coordinated beamforming for multicell multiuser multi-antenna systems by fully taking into account the residual transceiver impairments. Our design objectives include both spectral efficiency and energy efficiency. In particular, we first derive the closed-form expression of the mean square error (MSE) which includes the impact of transceiver impairments. Based on that, we propose an alternating optimization algorithm to solve the coordinated multicell beamforming problems with the goal of minimizing the worst user MSE, and the sum MSE. Then, by exploiting the relationship between the minimum mean square error (MMSE) and the achievable rate, we develop a new algorithm to address the sum rate maximization problem. This approach is further generalized to solve the more intractable energy efficiency optimization problem. We prove that all the proposed iterative algorithms guarantee to converge to a stationary point. Numerical results show that our proposed schemes achieve a better performance than conventional coordinated beamforming algorithms that were designed ignoring the transceiver impairments.

Multicell Coordinated Beamforming With Rate Outage Constraint—Part I: Complexity Analysis

This paper studies the coordinated beamforming (CoBF) design in the multiple-input single-output interference channel, assuming only channel distribution information given a priori at the transmitters. The CoBF design is formulated as an optimization problem that maximizes a predefined system utility, e.g., the weighted sum rate or the weighted max-min-fairness (MMF) rate, subject to constraints on the individual probability of rate outage and power budget. While the problem is non-convex and appears difficult to handle due to the intricate outage probability constraints, so far it is still unknown if this outage constrained problem is computationally tractable. To answer this, we conduct a computational complexity analysis of the outage constrained CoBF problem. Specifically, we show that the outage constrained CoBF problem with the weighted sum rate utility is intrinsically difficult, i.e., NP-hard. Moreover, the outage constrained CoBF problem with the weighted MMF rate utility is also NP-hard except the case when all the transmitters are equipped with single antenna. The presented analysis results confirm that efficient approximation methods are indispensable to the outage constrained CoBF problem.

Multicell Coordinated Beamforming With Rate Outage Constraint—Part II: Efficient Approximation Algorithms

This paper studies the coordinated beamforming (CoBF) design for the multiple-input single-output interference channel, provided that only channel distribution information is known to the transmitters. The problem under consideration is a probabilistically constrained optimization problem which maximizes a predefined system utility subject to constraints on rate outage probability and power budget of each transmitter. Our recent analysis has shown that the outage-constrained CoBF problem is intricately difficult, e.g., NP-hard. Therefore, the focus of this paper is on suboptimal but computationally efficient algorithms. Specifically, by leveraging on the block successive upper bound minimization (BSUM) method in optimization, we propose a Gauss-Seidel type algorithm, called distributed BSUM algorithm, which can handle differentiable, monotone and concave system utilities. By exploiting a weighted minimum mean-square error (WMMSE) reformulation, we further propose a Jocobi-type algorithm, called distributed WMMSE algorithm, which can optimize the weighted sum rate utility in a fully parallel manner. Both algorithms are shown to converge to the stationary points of the original NP-hard problems. To further provide a performance benchmark, a relaxed approximation method based on polyblock outer approximation is also proposed. Simulation results show that the proposed algorithms are significantly superior to the existing successive convex approximation method in both performance and computational efficiency, and can yield promising approximation performance by comparing with the performance benchmark.

Coordinated Multicell Beamforming for Massive MIMO: A Random Matrix Approach

We consider the problem of coordinated multicell downlink beamforming in massive multiple input multiple output (MIMO) systems consisting of $N$ cells, $N_{t}$ antennas per base station (BS) and $K$ user terminals (UTs) per cell. In particular, we formulate a multicell beamforming algorithm for massive MIMO systems that requires limited amount of information exchange between the BSs. The design objective is to minimize the aggregate transmit power across all the BSs subject to satisfying the user signal-to-interference-noise ratio (SINR) constraints. The algorithm requires the BSs to exchange parameters which can be computed solely based on the channel statistics rather than the instantaneous channel state information (CSI). We make use of tools from random matrix theory to formulate the decentralized algorithm. We also characterize a lower bound on the set of target SINR values for which the decentralized multicell beamforming algorithm is feasible. We further show that the performance of our algorithm asymptotically matches the performance of the centralized algorithm with full CSI sharing. While the original result focuses on minimizing the aggregate transmit power across all the BSs, we formulate a heuristic extension of this algorithm to incorporate a practical constraint in multicell systems, namely the individual BS transmit power constraints. Finally, we investigate the impact of imperfect CSI and pilot contamination effect on the performance of the decentralized algorithm, and propose a heuristic extension of the algorithm to accommodate these issues. Simulation results illustrate that our algorithm closely satisfies the target SINR constraints and achieves minimum power in the regime of massive MIMO systems. In addition, it also provides substantial power savings as compared with zero-forcing beamforming when the number of antennas per BS is of the same orders of magnitude as the number of UTs per cell.

Interference Pricing Mechanism for Downlink Multicell Coordinated Beamforming

We consider the downlink coordinated beamforming problem in a cellular network in which the base stations (BSs) are equipped with multiple antennas and each user is equipped with a single antenna. The BSs cooperate in sharing their local interference information, and they aim to maximize the sum-rate of the users in the network. A decentralized interference pricing beamforming (IPBF) algorithm is proposed to identify the coordinated beamformer, where a BS is penalized according to the interference it creates to its peers. We show that the decentralized pricing mechanism converges to an interference equilibrium, which is a KKT point of the sum-rate maximization problem. The proofs rely on the identification of rank-1 solutions of each BSs' interference-penalized rate maximization problem. Numerical results show that the proposed iterative mechanism reduces significantly the exchanged information with respect to other state-of-the-art beamforming algorithms with very little sum-rate loss. The version of the algorithm that limits the coordination to a cluster of base stations (IPBF-L) is shown to have very small sum-rate loss with respect to the full coordinated algorithm with much less backhaul information exchange.

Distributed Robust Multicell Coordinated Beamforming With Imperfect CSI: An ADMM Approach

Multicell coordinated beamforming (MCBF), where multiple base stations (BSs) collaborate with each other in the beamforming design for mitigating the intercell interference (ICI), has been a subject drawing great attention recently. Most MCBF designs assume perfect channel state information (CSI) of mobile stations (MSs); however CSI errors are inevitable at the BSs in practice. Assuming elliptically bounded CSI errors, this paper studies the robust MCBF design problem that minimizes the weighted sum power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the MSs. Our goal is to devise a distributed optimization method to obtain the worst-case robust beamforming solutions in a decentralized fashion with only local CSI used at each BS and limited backhaul information exchange between BSs. However, the considered problem is difficult to handle even in the centralized form. We first propose an efficient approximation method for solving the nonconvex centralized problem, using semidefinite relaxation (SDR), an approximation technique based on convex optimization. Then a distributed robust MCBF algorithm is further proposed, using a distributed convex optimization technique known as alternating direction method of multipliers (ADMM). We analytically show the convergence of the proposed distributed robust MCBF algorithm to the optimal centralized solution. We also extend the worst-case robust beamforming design as well as its decentralized implementation method to a fully coordinated scenario. Simulation results are presented to examine the effectiveness of the proposed SDR method and the distributed robust MCBF algorithm.