Multicell MISO Research Articles

Analysis and Optimization of Spectral and Energy Efficiency in Underlaid D2D Multi-Cell Massive MISO Over Rician Fading

This paper investigates the uplink spectral efficiency (SE) characterization and energy efficiency (EE) optimization of device-to-device (D2D) communications underlying a multi-cell massive multiple-input single-output (m-MISO) network, assuming that the channels are modeled with Rician fading. First, an analytical expression for the lower-bound of the ergodic capacity of a typical cellular user (CU) is derived with imperfect channel state information in the presence of D2D links’ interference. Then, a closed-form approximate achievable SE expression for a typical D2D pair is derived considering Rician fading between D2D pairs. The asymptotic SE behavior is analyzed in strong line-of-sight (LOS) conditions for CU and D2D pairs. Also, simplified expressions are obtained for the special case of Rayleigh fading. Next, to optimize the total EE, a transmit data power allocation based on the derived rate expressions is formulated. Since the optimization problem has a non-linear and non-convex objective function, it is intractable to be solved straightforwardly. Therefore, we resort to utilizing an iterative algorithm relying on fractional programming. The numerical results show that a stronger LOS component (i.e., larger Rician K-factor) between a typical CU and its serving BS leads to a significant improvement in the system performance, while it has less effect on the D2D network.

Joint User Scheduling and Phase Shift Design for RIS Assisted Multi-Cell MISO Systems

This letter investigates the joint user scheduling and phase shift design for reconfigurable intelligent surface (RIS) assisted multi-cell downlink systems. A closed-form ergodic sum spectral efficiency (SE) approximation is utilized as the optimization metric. Based on this approximation, we schedule the users, whose cascaded channels are mostly correlated with each other’s, to maximize each user’s effective signal. Moreover, the RIS phase shift is designed to be the mean of the scheduled users’ cascaded channel phases. With the proposed transmission design, we find the optimal RIS deployment to achieve the highest maximum throughput which depends only on the relative locations of the BSs and RIS. In addition, we consider a more practical discrete RIS phase shift design based on a discrete Fourier transform (DFT) codebook. Simulation results show that the proposed low-complexity scheduling algorithm performs well.

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.

SINR Balancing via Base Station Association, Beamforming, and Power Control in Downlink Multicell MISO Systems

This paper considers the downlink channel of multicell multiuser multiple-input single-output systems with arbitrary architecture. We aim to maximize the minimum weighted signal-to-interference-plus-noise ratio (SINR) through user-base station (BS) association, coordinated beamforming among BSs, and power control subject to per BS power constraints. The problem is known to be NP-hard. In the high-SNR regime, where the performance is interference-limited, we globally optimize the upper bound, which is achieved asymptotically, of the balanced SINR. In the low-SNR regime, where the performance is restricted by the tightest per BS power constraint, we balance the transmit power using relaxed integer programming and group sparse optimization techniques. The two goals can be integrated to achieve a universally better performance. From the perspective of optimization methods, the corresponding algorithms are based on Lagrangian relaxation and are guaranteed to converge. Simulation results show that the proposed algorithms outperform the existing algorithms designed for the downlink single-input single-output systems.

Admission Control Algorithms for QoS-Constrained Multicell MISO Downlink Systems

The problem of admission control in a multicell downlink multiple-input single-output system is considered. The objective is to maximize the number of admitted users subject to the signal-to-interference-plus-noise ratio constraint for each admitted user and a transmit power constraint at each base station. We cast the admission control problem as an $\ell _{0}$ minimization problem. This problem is known to be combinatorial NP-hard. Hence, we have to rely on suboptimal algorithms to solve it. We first approximate the $\ell _{0}$ minimization problem via a non-combinatorial one. Then, we propose centralized and distributed algorithms to solve the non-combinatorial problem. To develop the centralized algorithm, we use the sequential convex programming method. The distributed algorithm is derived by using the alternating direction method of multipliers in conjunction with sequential convex programming. We show numerically that the proposed admission control algorithms achieve a near-to-optimal performance. Next, we extend the admission control problem to provide fairness, where a long term fairness among the users is guaranteed. We focus on proportional and max–min fairness and propose dynamic control algorithms via Lyapunov optimization. It is shown numerically that the proposed fair admission control algorithms guarantee fairness among the users.

Distributed Solutions for Energy Efficiency Fairness in Multicell MISO Downlink

This paper aims at guaranteeing the achievable energy efficiency (EE) fairness in a multicell multiuser multiple-input single-output downlink system. The design objective is to maximize the minimum EE among all base stations (BSs) subject to per-BS power constraints. This results in a max-min fractional program and as such is difficult to solve in general. Our goal is to develop decentralized algorithms for the max-min EE problem based on combining the successive convex approximation (SCA) framework and the alternating direction method of multipliers (ADMMs). Specifically, leveraging the SCA principle, we iteratively approximate the nonconvex design problem by a sequence of convex programs for which two decentralized algorithms are then proposed. In the first approach, the convex program obtained at each step of the SCA procedure is solved optimally by allowing the BSs to exchange the required information until the ADMM converges. The convergence of the first method is analytically guaranteed but the amount of backhaul signaling can be noticeable in some realistic settings. To reduce the backhaul overhead, the second method performs an abstract version of the ADMM where only one variables update is carried out. Numerical results are provided to demonstrate the effectiveness of the two proposed decentralized algorithms.

Coordinated Regularized Zero-Forcing Precoding for Multicell MISO Systems with Limited Feedback

We investigate coordinated regularized zero-forcing precoding for limited feedback multicell multiuser multiple-input single-output systems. We begin by deriving an approximation to the expected signal-to-interference-plus-noise ratio for the proposed scheme with perfect channel direction information (CDI) at the base station (BS). We also derive an expected SINR approximation for limited feedback systems with random vector quantization (RVQ) based codebook CDI at the BS. Using the expected interference result for the RVQ based limited feedback CDI, we propose an adaptive feedback bit allocation strategy to minimize the expected interference by partitioning the total number of bits between the serving and out-of-cell interfering channels. Numerical results show that the proposed adaptive feedback bit allocation method offers a spectral efficiency gain over the existing coordinated zero-forcing scheme.

Physical Layer Security in Multi-Cell MISO Downlinks With Incomplete CSI—A Unified Secrecy Performance Analysis

In this paper, we consider a multi-cell MISO downlink, where a multi-antenna base station (BS) sends messages to its intended user, while a passive eavesdropper tries to intercept the information in each cell. Physical layer security is employed in order to guarantee information security. Due to incomplete channel state information (CSI) at BSs, residue inter-cell interference exists even with coordinated beamforming, which exerts a great impact on the secrecy performance. In this paper, we conduct a unified performance analysis for physical layer security with incomplete CSI, and derives closed-form expressions of ergodic secrecy rate, secrecy outage probability, and interception probability, considering CSI estimation accuracy, transmit signal to noise ratio (SNR), and channel condition. We reveal some insights on the secrecy performance through asymptotic analysis. Furthermore, based on the derived theoretical results, we propose a CSI exchange amount allocation scheme. Finally, the simulations validate our theoretical claims.

An Online Distributed Transceiver Design for Multicell MISO Systems with Low Complexity

This paper studies the jointly distributed transceiver design for time-division-duplex multicell multiple-input single-output downlink systems where there is no information exchange between the base stations (BSs). With an aim to minimize the sum MSE under per-BS power constraint, we give a hierarchical iterative algorithm which can be implemented in a distributed manner with low complexity. The algorithm is described as follows. First, with given precoders, the equalizers are updated by MMSE method. Second, by keeping the equalizers fixed, the original problem is convex in precoders and the precoders can be solved with the aid of KKT conditions. Finally, repeat the above steps until the algorithm converges. The proof of the convergence and the analysis of the complexity are given as well. Simulation results show that the proposed algorithm converge within few iterations and outperforms the existing distributed algorithms.

Decentralized Robust Beamforming for Coordinated Multi-Cell MISO Networks

In this letter, we consider a multi-cell multiuser MISO network. We aim to minimize the sum power over base stations (BSs) while guaranteeing the worst case SINR for each user. We propose a decentralized robust beamforming design which relies only on local imperfect channel state information and limited backhaul signaling. First, the non-convex problem is approximated by a convex one via the semidefinite relaxation and S-Procedure methods. Then, we propose a primal decomposition method to equivalently turn the approximated problem into a network-level master problem and BS-level subproblems, which can be optimally solved using an iterative projected subgradient method and a convex optimization solver, respectively. The proposed algorithm is applicable when it yields a rank-one solution providing an optimal solution also for the original problem. Computational and backhaul signaling loads per iteration are reduced as compared with the existing algorithm.

Multi-Cell Beamforming With Decentralized Coordination in Cognitive and Cellular Networks

This paper considers a downlink beamforming problem in a cognitive radio network where multiple primary and secondary cells coexist. Each multiantenna primary and secondary transmitter serves its own set of single antenna users. The optimization objective is to minimize the sum transmission power over secondary transmitters while guaranteeing the minimum SINR for each secondary user and satisfying the maximum aggregate interference power constraint for each primary user. We propose a decentralized beamforming algorithm where the original centralized problem is decomposed via primal decomposition method into two levels, i.e., transmitter-level subproblems managed by a network-level master problem. The master problem is solved independently at each secondary transmitter using a projected subgradient method requiring limited backhaul signaling among secondary transmitters. To solve the independent transmitter-level subproblems, we propose three alternative approaches which are based on second order cone programming, semidefinite programming and uplink-downlink duality. Special emphasis is put on the last approach, which is also considered in a multi-cell MISO cellular network. Numerical results show that the proposed algorithm achieves close to optimal solution even after a few iterations in quasi-static channel conditions. Moreover, near centralized performance is demonstrated in time-correlated channels.

Guard Zone Protected Capacity in Multi-Cell MISO Networks under Fading and Shadowing

The exact power distribution of the inter-cell interference is obtained explicitly for cell edge users who are surrounded by circular guard zones. Compared with recent works, the underlying channel model is generalized from Rayleigh fading to a combination of Nakagami fading and Gamma shadowing. In addtion, asymptotic analysis shows that the mean power of intercell interference changes from infinite to finite with a guard zone. Based on this interference distribution, the average capacity at the cell edge is further obtained. Special case approximation indicates that the capacity scales proportionally to the exponential of the guard zone size. Analytical capacities are validated by Monte Carlo simulations.

Multicell MISO Downlink Weighted Sum-Rate Maximization: A Distributed Approach

We develop an easy to implement distributed method for weighted sum-rate maximization (WSRMax) problem in a multicell multiple antenna downlink system. Unlike the recently proposed minimum weighted mean-squared error based algorithms, where at each iteration all mobile terminals needs to estimate the covariance matrices of their received signals, compute and feedback over the air certain parameters to the base stations (BS), our algorithm operates without any user terminal assistance. It requires only BS to BS signalling via reliable backhaul links (e.g., fiber, microwave links) and all required computation is performed at the BSs. The algorithm is based on primal decomposition and subgradient methods, where the original nonconvex problem is split into a master problem and a number of subproblems (one for each BS). A novel sequential convex approximation strategy is proposed to address the nonconvex master problem. In the case of subproblems, we adopt an existing iterative approach based on second-order cone programming and geometric programming. The subproblems are coordinated to find a (possibly suboptimal) solution to the master problem. Subproblems can be solved by BSs in a fully asynchronous manner, though the coordination between subproblems should be synchronous. Numerical results are provided to see the behavior of the algorithm under different degrees of BS coordination. They show that the proposed algorithm yields a good tradeoff between the implementation-level simplicity and the performance.

Fast Converging Algorithm for Weighted Sum Rate Maximization in Multicell MISO Downlink

The problem of maximizing weighted sum rates in the downlink of a multicell environment is of considerable interest. Unfortunately, this problem is known to be NP-hard. For the case of multi-antenna base stations and single antenna mobile terminals, we devise a low complexity, fast and provably convergent algorithm that locally optimizes the weighted sum rate in the downlink of the system. In particular, we derive an iterative second-order cone program formulation of the weighted sum rate maximization problem. The algorithm converges to a local optimum within a few iterations. Superior performance of the proposed approach is established by numerically comparing it to other known solutions.

Distributed Multicell-MISO Precoding Using the Layered Virtual SINR Framework

In this letter, we address the problem of distributed multi-antenna cooperative transmission in a cellular system. Most research in this area has so far assumed that base stations not only have the data dedicated to all the users but also share the full channel state information (CSI). In what follows, we assume that each base station (BS) only has local CSI knowledge. We propose a suboptimal, yet efficient, way in which the multicell MISO precoders may be designed at each BS in a distributed manner, as a superposition of so-called virtual SINR maximizations: a virtual SINR maximizing transmission scheme yields Pareto optimal rates for the MISO Interference Channel (IC); its extension to the multicell MISO channel is shown to provide a distributed precoding scheme achieving a certain fairness optimality for the two link case. We illustrate the performance of our algorithm through Monte Carlo simulations.