Le-Nam Tran

Precoding for Full Duplex Multiuser MIMO Systems: Spectral and Energy Efficiency Maximization

We consider data transmissions in a full duplex (FD) multiuser multiple-input multiple-output (MU-MIMO) system, where a base station (BS) bidirectionally communicates with multiple users in the downlink (DL) and uplink (UL) channels on the same system resources. The system model of consideration has been thought to be impractical due to the self-interference (SI) between transmit and receive antennas at the BS. Interestingly, recent advanced techniques in hardware design have demonstrated that the SI can be suppressed to a degree that possibly allows for FD transmission. This paper goes one step further in exploring the potential gains in terms of the spectral efficiency (SE) and energy efficiency (EE) that can be brought by the FD MU-MIMO model. Toward this end, we propose low-complexity designs for maximizing the SE and EE, and evaluate their performance numerically. For the SE maximization problem, we present an iterative design that obtains a locally optimal solution based on a sequential convex approximation method. In this way, the nonconvex precoder design problem is approximated by a convex program at each iteration. Then, we propose a numerical algorithm to solve the resulting convex program based on the alternating and dual decomposition approaches, where analytical expressions for precoders are derived. For the EE maximization problem, using the same method, we first transform it into a concave-convex fractional program, which then can be reformulated as a convex program using the parametric approach. We will show that the resulting problem can be solved similarly to the SE maximization problem. Numerical results demonstrate that, compared to a half duplex system, the FD system of interest with the proposed designs achieves a better SE and a slightly smaller EE when the SI is small.

On the Spectral Efficiency of Full-Duplex Small Cell Wireless Systems

We investigate the spectral efficiency of full-duplex small cell wireless systems, in which a full-duplex capable base station (BS) is designed to send/receive data to/from multiple half-duplex users on the same system resources. The major hurdle for designing such systems is due to the self-interference at the BS and co-channel interference among users. Hence, we consider a joint beamformer design to maximize the spectral efficiency subject to certain power constraints. The design problem is first formulated as a rank-constrained optimization problem, and the rank relaxation method is then applied. However, the relaxed problem is still nonconvex, and thus, optimal solutions are hard to find. Herein, we propose two provably convergent algorithms to obtain suboptimal solutions. Based on the concept of the Frank-Wolfe algorithm, we approximate the design problem by a determinant maximization program in each iteration of the first algorithm. The second method is built upon the sequential parametric convex approximation method, which allows us to transform the relaxed problem into a semidefinite program in each iteration. Extensive numerical experiments under small cell setups illustrate that the full-duplex system with the proposed algorithms can achieve a large gain over the half-duplex system.

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.

On Transmission Efficiency for Wireless Broadcast Using Network Coding and Fountain Codes

This paper investigates the benefits of applying fountain codes (FCs) in improving the transmission efficiency in broadcasting systems. Particularly, an exact expression of the transmission efficiency for wireless broadcast using FCs is derived. This derivation allows us to compare the transmission efficiency of the fountain code approach (FCA) and network coding approach (NCA) in wireless broadcast. The numerical results demonstrate that FCA achieves better performance than NCA when the number of users is large and vice versa when the number of users is small.

A Conic Quadratic Programming Approach to Physical Layer Multicasting for Large-Scale Antenna Arrays

We investigate the problem of downlink physical layer multicasting that aims at minimizing the transmit power with a massive antenna array installed at the transmitter site. We take a solution based on semidefinite relaxation (SDR) as our benchmark. It is shown that instead of working on the semidefinite program (SDP) naturally produced by the SDR, the dual counterpart of the same problem may provide a more efficient numerical implementation. Later, by using a successive convex approximation strategy, we arrive at a provably convergent iterative second-order cone programming (SOCP) solution. Our thorough numerical investigations report that the newly proposed SOCP solution offers improved power efficiency and a massively reduced computational complexity. Therefore, the SOCP solution is seen as a suitable candidate for obtaining beamformers that minimize transmit power, especially, when a very large number of antennas is used at the transmitter.

Optimal Energy-Efficient Transmit Beamforming for Multi-User MISO Downlink

This paper studies beamforming techniques for energy efficiency maximization (EEmax) in multiuser multiple-input single-output (MISO) downlink system. For this challenging nonconvex problem, we first derive an optimal solution using branch-and-reduce-and-bound (BRB) approach. We also propose two low-complexity approximate designs. The first one uses the well-known zero-forcing beamforming (ZFBF) to eliminate inter-user interference so that the EEmax problem reduces to a concave-convex fractional program. Particularly, the problem is then efficiently solved by closed-form expressions in combination with the Dinkelbachs approach. In the second design, we aim at finding a stationary point using the sequential convex approximation (SCA) method. By proper transformations, we arrive at a fast converging iterative algorithm where a convex program is solved in each iteration. We further show that the problem in each iteration can also be approximated as a second-order cone program (SOCP), allowing for exploiting computationally efficient state-of-the-art SOCP solvers. Numerical experiments demonstrate that the second design converges quickly and achieves a near-optimal performance. To further increase the energy efficiency, we also consider the joint beamforming and antenna selection (JBAS) problem for which two designs are proposed. In the first approach, we capitalize on the perspective reformulation in combination with continuous relaxation to solve the JBAS problem. In the second one, sparsity-inducing regularization is introduced to approximate the JBAS problem, which is then solved by the SCA method. Numerical results show that joint beamforming and antenna selection offers significant energy efficiency improvement for large numbers of transmit antennas.

Weighted Sum Rate Maximization for MIMO Broadcast Channels Using Dirty Paper Coding and Zero-forcing Methods

We consider precoder design for maximizing the weighted sum rate (WSR) of successive zero-forcing dirty paper coding (SZF-DPC). For this problem, the existing precoder designs often assume a sum power constraint (SPC) and rely on the singular value decomposition (SVD). The SVD-based designs are known to be optimal but require high complexity. We first propose a low-complexity optimal precoder design for SZF-DPC under SPC, using the QR decomposition. Then, we propose an efficient numerical algorithm to find the optimal precoders subject to per-antenna power constraints (PAPCs). To this end, the precoder design for PAPCs is formulated as an optimization problem with a rank constraint on the covariance matrices. A well-known approach to solve this problem is to relax the rank constraints and solve the relaxed problem. Interestingly, for SZF-DPC, we are able to prove that the rank relaxation is tight. Consequently, the optimal precoder design for PAPCs is computed by solving the relaxed problem, for which we propose a customized interior-point method that exhibits a superlinear convergence rate. Two suboptimal precoder designs are also presented and compared to the optimal ones. We also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme.

Efficient Solutions for Weighted Sum Rate Maximization in Multicellular Networks With Channel Uncertainties

The important problem of weighted sum rate maximization (WSRM) in a multicellular environment is intrinsically sensitive to channel estimation errors. In this paper, we study ways to maximize the weighted sum rate in a linearly precoded multicellular downlink system where the receivers are equipped with a single antenna. With perfect channel information available at the base stations, we first present a novel fast converging algorithm that solves the WSRM problem. Then, the assumption is relaxed to the case where the error vectors in the channel estimates are assumed to lie in an uncertainty set formed by the intersection of finite ellipsoids. As our main contributions, we present two procedures to solve the intractable nonconvex robust designs based on the worst case principle. The proposed iterative algorithms solve semidefinite programs in each of their steps and provably converge to a locally optimal solution of the robust WSRM problem. The proposed solutions are numerically compared against each other and known approaches in the literature to ascertain their robustness towards channel estimation imperfections. The results clearly indicate the performance gain compared to the case when channel uncertainties are ignored in the design process. For certain scenarios, we also quantify the gap between the proposed approximations and exact solutions.

On Linear Precoding Strategies for Secrecy Rate Maximization in Multiuser Multiantenna Wireless Networks

Revived interest in physical layer security has led to a cascade of information theoretic results for various system topologies under different constraints. In the present paper, we provide practically oriented solutions to the problem of maximizing achievable secrecy rates in an environment consisting of multiple legitimate and eavesdropping radio nodes. By assuming “genie” aided perfect channel state information (CSI) feedback for both types of nodes, we first study two scenarios of interest. When independent messages are intended for all legitimate users (called “broadcast” mode), provably convergent second-order cone programming (SOCP)-based iterative procedure is used for designing secrecy rate maximizing beamformers. In the same manner, when a common message is intended only for legitimate nodes (dubbed “multicast” mode), SOCP-based design is proposed for obtaining linear precoders that maximize the achievable secrecy rate. Subsequently, we leverage the analysis to the more real-world scenario, where the CSI of the malicious nodes has to be somehow estimated and that of the legitimate users is corrupted with unavoidable errors. For this case, we devise provably convergent iterative semidefinite programming (SDP) procedures that maximize the achievable secrecy rates for both the beamforming-based broadcast and the linearly precoded multicast modes. Finally, numerical results are reported that evaluate the performance of the proposed solutions as a function of different system parameters. The results presented in the paper are demonstrated to outperform the ones based on interference alignment strategies. We also ascertain superior performance of the proposed schemes in the realms of real world.

Achieving Energy Efficiency Fairness in Multicell MISO Downlink

We investigate the fairness of achievable energy efficiency in a multicell multiuser multiple-input single-output (MISO) downlink system, where a beamforming scheme is designed to maximize the minimum energy efficiency among all base stations. The resulting optimization problem is a nonconvex max-min fractional program, which is generally difficult to solve optimally. We propose an iterative beamformer design based on an inner approximation algorithm which aims at locating a Karush-Kuhn-Tucker solution to the nonconvex program. By novel transformations, we arrive at a convex problem at each iteration of the proposed algorithm, which is amendable for being approximated by a second order cone program. The numerical results demonstrate that the proposed algorithm outperforms the existing schemes in terms of the convergence rate and processing time.