Ha Hoang Kha

Fast Global Optimal Power Allocation in Wireless Networks by Local D.C. Programming

Power allocations in an interference-limited wireless network for global maximization of the weighted sum throughput or global optimization of the minimum weighted rate among network links are not only important but also very hard optimization problems due to their nonconvexity nature. Recently developed methods are either unable to locate the global optimal solutions or prohibitively complex for practical applications. This paper exploits the d.c. (difference of two convex functions/sets) structure of either the objective function or constraints of these global optimization problems to develop efficient iterative algorithms with very low complexity. Numerical results demonstrate that the developed algorithms are able to locate the global optimal solutions by only a few iterations and they are superior to the previously-proposed methods in both performance and computation complexity.

Nonsmooth Optimization for Efficient Beamforming in Cognitive Radio Multicast Transmission

It is known that the design of optimal transmit beamforming vectors for cognitive radio multicast transmission can be formulated as indefinite quadratic optimization programs. Given the challenges of such nonconvex problems, the conventional approach in literature is to recast them as convex semidefinite programs (SDPs) together with rank-one constraints. Then, these nonconvex and discontinuous constraints are dropped allowing for the realization of a pool of relaxed candidate solutions, from which various randomization techniques are utilized with the hope to recover the optimal solutions. However, it has been shown that such approach fails to deliver satisfactory outcomes in many practical settings, wherein the determined solutions are found to be unacceptably far from the actual optimality. On the contrary, we in this contribution tackle the aforementioned optimal beamforming problems differently by representing them as SDPs with additional reverse convex (but continuous) constraints. Nonsmooth optimization algorithms are then proposed to locate the optimal solutions of such design problems in an efficient manner. Our thorough numerical examples verify that the proposed algorithms offer almost global optimality whilst requiring relatively low computational load.

Joint Optimization of Source Precoding and Relay Beamforming in Wireless MIMO Relay Networks

This paper considers joint linear processing at multi-antenna sources and one multiple-input multiple-output (MIMO) relay station for both one-way and two-way relay-assisted wireless communications. The one-way relaying is applicable in the scenario of downlink transmission by a multi-antenna base station to multiple single-antenna users with the help of one MIMO relay. In such a scenario, the objective of join linear processing is to maximize the information throughput to users. The design problem is equivalently formulated as the maximization of the worst signal-to-interference-plus-noise ratio (SINR) among all users subject to various transmission power constraints. Such a program of nonconvex objective minimization under nonconvex constraints is transformed to a canonical d.c. (difference of convex functions/sets) program of d.c. function optimization under convex constraints through nonconvex duality with zero duality gap. An efficient iterative algorithm is then applied to solve this canonical d.c program. For the scenario of using one MIMO relay to assist two sources exchanging their information in two-way relying manner, the joint linear processing aims at either minimizing the maximum mean square error (MSE) or maximizing the total information throughput of the two sources. By applying tractable optimization for the linear minimum MSE estimator and d.c. programming, an iterative algorithm is developed to solve these two optimization problems. Extensive simulation results demonstrate that the proposed methods substantially outperform previously-known joint optimization methods.

Efficient Design of Cosine-Modulated Filter Banks via Convex Optimization

This paper presents efficient approaches for designing cosine-modulated filter banks with linear phase prototype filter. First, we show that the design problem of the prototype filter being a spectral factor of 2M th-band filter is a nonconvex optimization problem with low degree of nonconvexity. As a result, the nonconvex optimization problem can be cast into a semi-definite programming (SDP) problem by a convex relaxation technique. Then the reconstruction error is further minimized by an efficient iterative algorithm in which the closed-form expression is given in each iteration. Several examples are given to illustrate the effectiveness of the proposed method over the existing ones.

Beamforming Optimization in Multi-User Amplify-and-Forward Wireless Relay Networks

Optimization problems of beamforming in multi-user amplify-and-forward (AF) wireless relay networks are indefinite (nonconvex) quadratic programs, which require effective computational solutions. Solutions to these problems have often been obtained by relaxing the original problems to semi-definite programs (SDPs) of convex optimization. Most existing works have claimed that these relaxed SDPs actually provide the optimal beamforming solutions. This paper, however, shows that this is not the case in many practical scenarios where SDPs fail to provide even a feasible beamforming solution. To fill this gap, we develop in this paper a nonsmooth optimization algorithm, which provides the optimal solution at low computational complexity.

Optimization of Cooperative Beamforming for SC-FDMA Multi-User Multi-Relay Networks by Tractable D.C. Programming

This paper addresses the optimal cooperative beamforming design for multi-user multi-relay wireless networks in which the single-carrier frequency division multiple access (SC-FDMA) technique is employed at the terminals. The problem of interest is to find the beamforming weights across relays to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among source users subject to individual power constraints at each relay. Such a beamforming design is shown to be a hard nonconvex optimization problem and therefore it is mathematically challenging to find the optimal solution. By exploring its partial convex structures, we recast the design problem as minimization of a d.c. (difference of two convex) objective function subject to convex constraints and develop an effective iterative algorithm of low complexity to solve it. Simulation results show that our optimal cooperative beamforming scheme realizes the inherent diversity order of the relay network and it performs significantly better than the equal-power beamforming weights.

Optimized Training Sequences for Spatially Correlated MIMO-OFDM

In this paper, the training sequence design for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems under the minimum mean square error (MMSE) criterion is addressed. The optimal training sequence for channel estimation in spatially correlated MIMO-OFDM systems was not known for an arbitrary signal-to-noise ratio (SNR). Only one class of training sequences was proposed in the literature in which the power allocation is given only for the extreme conditions of low and high SNRs. The current paper presents a necessary and sufficient condition for the optimal training sequence, and reformulates the training design problem as a convex optimization problem whose optimal solution is efficiently solved. In addition, tight upper bounds for MMSE and resulting low complexity iterative algorithms with the closed-form expression in iterations to find the optimum training sequence are derived. Simulation results confirm the superiority of the proposed design over the existing one in terms of both MSE estimation and BER performance. The proposed methods are also shown to be robust with respect to the spatial correlation mismatch at the transmitter.

Joint Optimization of Source Power Allocation and Cooperative Beamforming for SC-FDMA Multi-User Multi-Relay Networks

This paper is concerned with design problems of joint source power allocation and relay beamforming in multi-user multi-relay networks that use single-carrier frequency division multiple access (SC-FDMA) and amplify-and-forward relaying. Examined are the joint programs of (i) maximizing the minimum signal-to-interference-plus-noise ratio (SINR) under various transmitted power constraints, and (ii) minimizing the total transmitted power subject to prescribed SINR thresholds of users. Although these optimization problems are highly nonconvex and have large dimensions, by exploiting their partial convexities and making elegant nonlinear variable changes, they are recast as d.c. (difference of two convex) programs. Efficient d.c. iterative procedures are then developed to find the solutions. Simplified joint programs under the two cases of equal source power and equal relay beamforming weights, respectively, are also considered. Branch-and-bound algorithms of deterministic global optimization are then proposed for solving the simplified joint programs. Simulation results confirm the excellent performance and computational efficiency of all the proposed solutions.

Nonsmooth Optimization for Beamforming in Cognitive Multicast Transmission

It is well-known that the optimal beamforming problems for cognitive multicast transmission are indefinite quadratic (nonconvex) optimization programs. The conventional approach is to reformulate them as convex semi-definite programs (SDPs) with additional rank-one (nonconvex and discontinuous) constraints. The rank-one constraints are then dropped for relaxed solutions, and randomization techniques are employed for solution search. In many practical cases, this approach fails to deliver satisfactory solutions, i.e., its found solutions are very far from the optimal ones. In contrast, in this paper we cast the optimal beamforming problems as SDPs with the additional reverse convex (but continuous) constraints. An efficient algorithm of nonsmooth optimization is then proposed for seeking the optimal solution. Our simulation results show that the proposed approach yields almost global optimal solutions with much less computational load than the mentioned conventional one.

Globally Optimized Power Allocation in Multiple Sensor Fusion for Linear and Nonlinear Networks

The present paper is concerned with a sensor network, where each sensor is modeled by either a linear or nonlinear sensing system. These sensors team up in observing either static or dynamic random targets and transmit their observations through noisy communication channels to a fusion center (FC) for locating/tracking the targets. Physically, the network is limited by energy resource. According to the available sum power budget, we develop a novel technique for power allocation to the sensor nodes that enables the FC produce the best linear estimate in terms of the mean square error (MSE). Regardless of whether the sensor measurements are linear or nonlinear, the targets are scalar or vectors, static or dynamic, the corresponding optimization problems are shown to be semidefinite programs (SDPs) of tractable optimization and thus are globally and efficiently solved by any existing SDP solver. In other words, new tractably computational algorithms of distributed Bayes filtering are derived with full multisensor diversity achieved. Intensive simulation shows that these algorithms clearly outperform previously known algorithms.