Robust Beamforming Under Channel Prediction Errors for Time-Varying MIMO System

The accuracy of acquired channel state information(CSI)for beamforming design is essential for achievable performance in multiple-input multiple-output(MIMO)systems.However,in a high-speed moving scene with time-division duplex(TDD)mode,the acquired CSI depending on the channel reciprocity is inevitably outdated,leading to outdated beamforming design and then performance degradation.In this paper,a robust beamforming design under channel prediction errors is proposed for a time-varying MIMO system to combat the degradation further,based on the channel prediction technique.Specifically,the statistical characteristics of historical channel prediction errors are exploited and modeled.Moreover,to deal with random error terms,deterministic equivalents are adopted to further explore potential beamforming gain through the statistical information and ultimately derive the robust design aiming at maximizing weighted sum-rate performance.Simulation results show that the proposed beamforming design can maintain outperformance during the downlink transmission time even when channels vary fast,compared with the traditional beamforming design.

Robust beamforming for IRS-aided SWIPT in cognitive radio networks

Intelligent reflecting surface(IRS)is widely recognized as a promising technique to enhance the system perfor-mance,and thus is a hot research topic in future wireless communications.In this context,this paper proposes a robust BF scheme to improve the spectrum and energy harvesting efficiencies for the IRS-aided simultaneous wireless information and power transfer(SWIPT)in a cognitive radio network(CRN).Here,the base station(BS)utilizes spectrum assigned to the primary users(PUs)to simultaneously serve multiple energy receivers(ERs)and information receivers(IRs)through IRS-aided multicast technology.In particular,by assuming that only the imperfect channel state information(CSI)is available,we first formulate a constrained problem to maximize the minimal achievable rate of IRs,while satisfying the harvesting energy threshold of ERs,the quality-of-service requirement of IRs,the interference threshold of PUs and transmit power budget of BS.To address the non-convex problem,we then adopt triangle inequality to deal with the channel uncertainty,and propose a low-complexity algorithm combining alternating direction method of multipliers(ADMM)with alternating optimi-zation(AO)to jointly optimize the active and passive beamformers for the BS and IRS,respectively.Finally,our simulation results confirm the effectiveness of the proposed BF scheme and also provide useful insights into the importance of introducing IRS into the CRN with SWIPT.

Fast and accurate covariance matrix reconstruction for adaptive beamforming using Gauss-Legendre quadrature

Most of the reconstruction-based robust adaptive beamforming(RAB)algorithms require the covariance matrix reconstruction(CMR)by high-complexity integral computation.A Gauss-Legendre quadrature(GLQ)method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity.The interference angular sector in RAB is regarded as the GLQ integral range,and the zeros of the threeorder Legendre orthogonal polynomial is selected as the GLQ nodes.Consequently,the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral.The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques,and it is able to provide the similar performance close to the optimal.These advantages are verified by numerical simulations.

Joint Antenna Selection and Robust Beamforming Design in Multi-cell Distributed Antenna System

Most of studies on Distributed Antenna System(DAS) focus on maximizing the sum capacity and perfect channel state information at transmitter(CSIT).However,CSI is inevitable imperfect in practical wireless networks.Based on the sources of error,there are two models.One assumes error lies in a bounded region,the other assumes random error.Accordingly,we propose two joint antenna selection(AS) and robustbeamforming schemes aiming to minimize the total transmit power at antenna nodes subject to quality of service(QoS) guarantee for all the mobile users(MUs) in multicell DAS.This problem is mathematically intractable.For the bounded error model,we cast it into a semidefinite program(SDP) using semidefinite relaxation(SDR) and S-procedure.For the second,we first design outage constrained robust beamforming and then formulate it as an SDP based on the Bernstein-type inequality,which we generalize it to the multi-cell DAS.Simulation results verify the effectiveness of the proposed methods.

Multi-objective robust secure beamforming for cognitive satellite and UAV networks

A multi-objective optimization based robust beamforming(BF)scheme is proposed to realize secure transmission in a cognitive satellite and unmanned aerial vehicle(UAV)network.Since the satellite network coexists with the UAV network,we first consider both achievable secrecy rate maximization and total transmit power minimization,and formulate a multi-objective optimization problem(MOOP)using the weighted Tchebycheff approach.Then,by supposing that only imperfect channel state information based on the angular information is available,we propose a method combining angular discretization with Taylor approximation to transform the non-convex objective function and constraints to the convex ones.Next,we adopt semi-definite programming together with randomization technology to solve the original MOOP and obtain the BF weight vector.Finally,simulation results illustrate that the Pareto optimal trade-off can be achieved,and the superiority of our proposed scheme is confirmed by comparing with the existing BF schemes.

A double constrained robust capon beamforming based imaging method for early breast cancer detection

Ultra-wideband （UWB） microwave images are proposed for detecting small malignant breast tumors based on the large contrast of electric parameters between a malignant tumor and normal breast tissue. In this study, an antenna array composed of 9 antennas is applied to the detection. The double constrained robust capon beamforming （DCRCB） algorithm is used for reconstructing the breast image due to its better stability and high signal-to-interference-plus-noise ratio （SINR）. The successful detection of a tumor of 2 mm in diameter shown in the reconstruction demonstrates the robustness of the DCRCB beamforming algorithm. This study verifies the feasibility of detecting small breast tumors by using the DCRCB imaging algorithm.

Robust adaptive beamforming for constant modulus signal of interest

It is required in the diagonally loaded robust adaptive beamforming the automatic determination of the loading level which is practically a challenging problem.A constant modulus restoral method is herein presented to choose the diagonal loading level adaptively for the extraction of a desired signal with constant modulus(a common feature of the phase modulation signals).By introducing the temporal smoothing technique,the proposed constant modulus restoral diagonally loaded robust adaptive beamformer provides increased capability compared with some existing robust adaptive beamformers in rejecting interferences and noise while protecting the signal-of-interest.Simulation results are included to illustrate the performance of the proposed beamformer.

Diagonally loaded SMI algorithm based on inverse matrix recursion

The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.

Frequency-invariant robust adaptive beamforming based on interference covariance matrix reconstruction

Consider the problems of frequency-invariant beampattern optimization and robustness in broadband beamforming.Firstly,a global optimization algorithm,which is based on phase compensation of the array manifolds,is used to construct the frequency-invariant beampattern.Compared with some methods presented recently,the proposed algorithm is not only available to get the global optimal solution,but also simple for physical realization.Meanwhile,a robust adaptive broadband beamforming algorithm is also derived by reconstructing the covariance matrix.The essence of the proposed algorithm is to estimate the space-frequency spectrum using Capon estimator firstly,then integrate over a region separated from the desired signal direction to reconstruct the interference-plus-noise covariance matrix,and finally caleulate the adaptive beamformer weights with the reconstructed matrix.The design of beamformer is formulated as a convex optimization problem to be solved.Simulation results show that the performance of the proposed algorithm is almost always close to the optimal value across a wide range of signal to noise ratios.

Robust adaptive beamforming algorithm based on Bayesian approach

The performance of adaptive array beamform-ing algorithms substantially degrades in practice because of a slight mismatch between actual and presumed array res-ponses to the desired signal.A novel robust adaptive beam-forming algorithm based on Bayesian approach is therefore proposed.The algorithm responds to the current envi-ronment by estimating the direction of arrival(DOA)of the actual signal from observations.Computational com-plexity of the proposed algorithm can thus be reduced com-pared with other algorithms since the recursive method is used to obtain inverse matrix.In addition,it has strong robustness to the uncertainty of actual signal DOA and makes the mean output array signal-to-interference-plus-noise ratio(SINR)consistently approach the optimum.Simulation results show that the proposed algorithm is bet-ter in performance than conventional adaptive beamform-ing algorithms.

Constrained minimum power combination for broadband beamformer design in the STFT domain

Beamforming using sensor array is widely used in spatial signal processing since it offers better spatial focusing capability than single sensor. However, in practical appli- cations for broadband signal, there always exists a trade-off issue between the directivity capability of an array and its robustness on system errors. In this paper, in order to combine merits of different beamformers instead of trade-off their per- formances, we propose a constrained minimum-power com- bination method. We firstly analyze two optimal beamform- ers that maximize Directivity Factor （DF） and White Noise Gain （WNG） respectively. Then we propose a non-linear combination method, which automatically selects the best beamformer that has the minimum output power, so as to control the unwanted white noise amplification and keep the maximum DF if possible. Two solutions to the proposed com- bination strategy are given. They do not need to determine the correct trade-off factor used in linear combination method, and avoid challenge ~stimations on noise and target statistics required in adaptive beamforming. The performance of the proposed beamformer is evaluated in ideal noise fields and complicated noise fields respectively. It is shown that the proposed beamformer integrates merits of different beamform- ers. It always achieves the best speech quality and biggest noise reduction compared to other popular beamformers.

Adaptive robust beamformer for multi-pair two-way relay networks with imperfect channel state information

In wideband multi-pair two-way relay networks, the performance of beamforming at a relay station(RS) is intimately related to the accuracy of the channel state information(CSI) available. The accuracy of CSI is determined by Doppler spread, delay between beamforming and channel estimation, and density of pilot symbols,including transmit power of pilot symbols. The coefficient of the Gaussian-Markov CSI error model is modeled as a function of CSI delay, Doppler spread, and signal-to-noise ratio, and can be estimated in real time. In accordance with the real-time estimated coefficients of the error model, an adaptive robust maximum signal-to-interferenceand-noise ratio(Max-SINR) plus maximum signal-to-leakage-and-noise ratio(Max-SLNR) beamformer at an RS is proposed to track the variation of the CSI error. From simulation results and analysis, it is shown that: compared to existing non-adaptive beamformers, the proposed adaptive beamformer is more robust and performs much better in the sense of bit error rate(BER); with increase in the density of transmit pilot symbols, its BER and sum-rate performances tend to those of the beamformer of Max-SINR plus Max-SLNR with ideal CSI.