The present paper investigates the trade‐offs between the energy efficiency (EE) and spectral efficiency (SE) in the full‐duplex (FD) multiuser multi‐input multioutput (MU‐MIMO) cloud radio access networks (CRANs) with simultaneous wireless information and power transfer (SWIPT). In the considered network, the central unit (CU) intends to concurrently not only transfer both energy and information toward downlink (DL) users using power splitting structures but also receive signals from uplink (UL) users. This communication is executed via FD radio units (RUs) which are distributed nearby users and connected to the CU through limited capacity fronthaul (FH) links. In order to unveil interesting trade‐offs between the EE and SE metrics, we first introduce three conventional single‐objective optimization problems (SOOPs) including (i) system sum rate maximization, (ii) total power minimization, and (iii) fractional energy efficiency maximization. Then, by making use of the multiobjective optimization (MOO) framework, the MOO problem (MOOP) with the objective vector of the achievable rate and power consumption is addressed. All considered problems are nonconvex with respect to designing variables comprising precoding matrices, compression matrices, and DL power splitting factors; thus, it is extremely intractable to solve these problems directly. To overcome these issues, we develop iterative algorithms by utilizing the sequential convex approximation (SCA) approach for the first two SOO problems and the SCA‐based Dinkelbach method for the fractional EE problem. Regarding the MOOP, we first rewrite it as an SOOP by applying the modified weighted Tchebycheff method and, then, propose the iterative algorithm‐based SCA to find its optimal Pareto set. Various numerical simulations are conducted to study the system performance and appealing EE‐SE trade‐offs in the considered system.

Brain-computer interfaces (BCIs) are used to assist people, especially those with verbal or physical disabilities, communicate with the computer to indicate their selections, control a device or answer questions only by their mere thoughts. Due to the noisy nature of brain signals, the required time for each experimental session must be lengthened to reach satisfactory accuracy. This is the trade-off between the speed and the precision of a BCI system. In this paper, we propose a unified method which is the integration of ensemble classifier, dynamic stopping, and adaptive learning. We are able to both increase the accuracy, as well as to reduce the spelling time of the P300-Speller. Another merit of our study is that it does not require the training phase for any new subject, hence eliminates the extensively time-consuming process for learning purposes. Experimental results show that we achieve the averaged bit rate boost up of 182% on 15 subjects. Our best achieved accuracy is 95.95% by using 7.49 flashing iterations and our best achieved bit rate is 40.87 bits/min with 83.99% accuracy and 3.64 iterations. To the best of our knowledge, these results outperformed most of the related P300-based BCI studies.

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.

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.

Optimizations of precoding matrices in precode-and-forward (PF) MIMO relaying are nonconvex programs in precoding matrix variables. The semidefinite relaxation (SDR) technique, which relaxes the concerned nonconvex quadratic constraints by (convex) semi-definite ones, can locate the optimal solutions, provided that the numbers of relaying antennas and users are very small. The computational complexity of the SDR grows explosively even with a very moderate increase in the numbers of relaying antennas and/or users, making the existing semidefinite programming (SDP) solvers incapable. In this paper, much more efficient problem formulations of precoding matrix design that exploit the spectral matrix optimization are developed. Such formulations have a low dimensionality and are computationally-tractable nonconvex matrix programs. Furthermore, by exploiting their partial convex structures in the d.c. (difference of two convex functions) framework, new effective iterative solutions are obtained. Extensive simulation results are presented to support the computational advantage of the proposed approach and show that the proposed approach can effectively handle all three considered optimization problems of precoding matrices in MIMO PF relaying, while the SDR approach either is computationally impractical or fails.

We are concerned with a 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 users subject to individual power constraints at each relay. Such a beamforming design is shown to be a hard nonconvex program 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.

Sensor selection is to pick out an appropriate subset of active sensors for reliable collaborative sensing. Naturally, the selected sensors should be as uncorrelated as possible to have more independent sensing outputs for information fusion. In this paper, various uncorrelation metrics are unified by the concept of Bregman divergence. The sensor selections are then systematically formulated as NP-hard integer programs. Unlike commonly used exhaustive enumeration, heuristic searches or simple relaxation of discrete constraints with inherent drawbacks, this paper recasts them into a continuous d.c. (difference of two convex functions) program under convex constraints. Accordingly, an efficient iterative optimization procedure is tailored for locating the optimal solution. Simulation results show its superior performances in comparison with other existing sensor selections.

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.

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.

Power allocations in an interference-limited wireless network for global maximization of the weighted sum throughput or global maximization of the minimum 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 constraint of the 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.

Beamforming problems in amplify-forward (AF) wireless relay network can be formulated as nonconvex quadratically constrained quadratic programming (QCQP) problems which is very difficult to solve directly. Generally, by transforming a QCQP problem into a semi-definite program (SDP) and by relaxing rank-one constraints, the problem can be tackled essentially. If resulting matrices found after solving SDP problems are of rank-one then the task can be terminated. However, in some scenarios such as minimizing individual power constraints on relays, most of the rank-one dropped SDP solutions have rank higher than one. In this case, a nonsmooth reverse convex optimization technique is employed to solve the problem iteratively then rank-one solutions can be optimized numerically.

The paper is concerned with a multiuser communication network, which is assisted by multiple relays. It has been observed through our previous related works that the conventional simultaneous beamforming at parallel amply-and-forward (AF) relays is not quite effective and often infeasible to target practically desirable signal-to-interference-and-noise ratio (SINR) at the destinations. To overcome this shortage, we propose the time-division for multiple-user transmission to the relays so the later can perform beamforming on signals received from the individuals and then parallelly forward its combinations at once to the destinations. The optimal beamforming problem is a nonconvex quadratically constrained optimization, which is globally solved by our tailored algorithm of nonsmooth optimization. Its found global optimal solutions are shown very effective and over-perform other possible multi-user relay beamformings.

This paper discusses dynamic state estimation for nonlinear measurement model through distributed multisensor network under power constraints. For this scenario, we propose an optimized power allocation strategy based on semidefinite programming, that achieves minimum mean-squared error for the estimate subject to constraints on total transmit power. System nonlinearity is handled effectively with the help of distributed unscented Kalman filtering and linear fractional transformation. Furthermore, advantage of using multiple sensors over a single independent sensor is established through simulation results for tracking a maneuvering target.

This paper deals with optimized training sequences to estimate multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) channel states in the presence of spatial fading correlations. The optimization criterion is the entropy minimization of the error between the high multi-dimensional and correlated channel state and its estimator. The globally optimized training sequences are exactly solved by a semi-definite programming (SDP) of tractable computational complexity O((Mt(Mt+ 1)/2)2.5), where Mtis the transmit antenna number. With new tight two-sided bounds for the objective function, the optimal value of the generic SDP can be approximately solved by the standard water-filling algorithm. Intensive simulation results are provided to illustrate the performance of our methods.

The paper proposes a new approach for the design of linear phase finite impulse response (FIR) filters with discrete co-efficient values. This problem is a very hard combinatoric discrete optimization, which results in the prohibitive computational complexity for solution. In this paper, we first explicitly express the discrete coefficients of filters as indefinite quadratic but continuous constraints. We then develop an efficient iterative algorithm to tackle the nonconvex optimization problem to locate optimal discrete filter coefficients. By numerical simulation results, we show that our proposed method significantly outperform the methods using quantized coefficients of filters. We also provide an image sampling application to illustrate the performance of our designed filters.

This correspondence proposes an efficient semidefinite programming (SDP) method for the design of a class of linear phase finite impulse response triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. The design problem is formulated as the minimization of the least square error subject to peak error constraints and regularity constraints. By using the linear matrix inequality characterization of the trigonometric semi-infinite constraints, it can then be exactly cast as a SDP problem with a small number of variables and, hence, can be solved efficiently. Several design examples of the triplet halfband filter bank are provided for illustration and comparison with previous works. Finally, the image coding performance of the filter bank is presented.

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.

A design method of a linear-phased, two-dimensional (2-D), two-fold symmetric circular shaped filter is presented in this paper. Although the proposed method designs a non-separable filter, its implementation has linear complexity. The shape of the passband and the stopband is expressed in terms of level sets of second order trigonometric polynomials. This enables the transformation of the filter specifications to a Semi-Definite Program (SDP) of moderate dimension. The proposed filter outperforms currently available filter design methods. We present a performance comparison, as well as a homomorphic processing image enhancement example to illustrate the effectiveness of this method.

The optimal beamforming for cognitive multicast transmission is nonconvex rank-one constrained optimization problem. For a solution, a popular method is the combination of relaxed convex semi-definite programming, where the rank-one constraint is dropped, and randomization. We show that in many cases, this method cannot give satisfactory solutions. As an initial step, we develop a simple alternative method, which gives much better solutions. Our simulation confirms this fact.

This paper presents an efficient technique for power allocation to the sensor nodes in a nonlinear sensor network (NSN). We minimize mean square error of the estimation of a random scalar parameter subject to a constraint on total amount of power consumed by the sensor nodes. This estimation is carried out at fusion center (FC) which receives the local observations from the sensors located at different positions. We convert the optimization problem into a convex one, and then use semidefinite programming to find the global optimal solution. The simulation results show that our approach outperforms the previous work both for the channel with white noise and the one with colored noise. The proposed strategy also gives better results in case of nonlinear model when compared to the strategy of assigning equal power to sensor nodes.

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.

The paper presents an efficient semidefinite programming (SDP) based design for prototype filters of cosine-modulated filter banks (CMFBs). We consider a class of near-perfect reconstruction CMFBs with the linear phase prototype filter, which structurally eliminates the amplitude overall distortion. The prototype filter design problem is then formulated into a convex semi-infinite programming problem. Furthermore, to handle the semi-infinite constraints, we use the linear matrix inequality (LMI) characterization of positive trigonometric polynomials to cast the semi-infinite programming problem into SDP one. Finally, convex duality is applied to transform the SDP into another SDP with the minimal number of additional variables, which is efficiently solved. An additional advantage of the proposed method is that we can precisely control the filter specifications.

The paper proposes a new approach for the design of M-channel pseudo-quadrature mirror filter (QMF) banks. First, the convex hull of 2Mth band linear phase filters admitting linear phase spectral factors is analytically described by semidefinite programming (SDP). Then, the prototype filter design is cast into an SDP problem, which is efficiently solved. Design examples are presented to illustrate the effectiveness of the proposed method and to evaluate the design performance in comparison with the existing designs.

A new design method for complex-valued two-channel FIR filter banks with both orthogonality and symmetry properties is developed. Based on a novel linear matrix inequality (LMI) characterization of trigonometric curves, the optimal design of the perfect reconstruction filter bank is reformulated as a semi-definite programme. The dimension of the resulting semi-definite programme is further reduced by exploiting the strong convex duality. Consequently, the globally optimal solution can be effectively found for any practical filter length and desired regularity order