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.

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.

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.

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.

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.