Robust Adaptive Beamforming Algorithms Based on the Constrained Constant Modulus Criterion

We present a robust adaptive beamforming algorithm based on the worst-case criterion and the constrained constant modulus approach, which exploits the constant modulus property of the desired signal. Similarly to the existing worst-case beamformer with the minimum variance design, the problem can be reformulated as a second-order cone (SOC) program and solved with interior point methods. An analysis of the optimization problem is carried out and conditions are obtained for enforcing its convexity and for adjusting its parameters. Furthermore, low-complexity robust adaptive beamforming algorithms based on the modified conjugate gradient (MCG) and an alternating optimization strategy are proposed. The proposed low-complexity algorithms can compute the existing worst-case constrained minimum variance (WC-CMV) and the proposed worst-case constrained constant modulus (WC-CCM) designs with a quadratic cost in the number of parameters. Simulations show that the proposed WC-CCM algorithm performs better than existing robust beamforming algorithms. Moreover, the numerical results also show that the performances of the proposed low-complexity algorithms are equivalent or better than that of existing robust algorithms, whereas the complexity is more than an order of magnitude lower.Comment: 11 pages, 8 figures and 4 tables. IET Signal Processing, 201

Blind Adaptive Beamforming Based on Constrained Constant Modulus RLS Algorithm for Smart Antennas

In this paper, we study the performance of blind adaptive beamforming algorithms for smart antennas in realistic environments. A constrained constant modulus (CCM) design criterion is described and used for deriving a recursive least squares (RLS) type optimization algorithm. Furthermore, two kinds of scenarios are considered in the paper for analyzing its performance. Simulations are performed to compare the performance of the proposed method to other well-known methods for blind adaptive beamforming. Results indicate that the proposed method has a significant faster convergence rate, better robustness to changeable environments and better tracking capability.Comment: 3 figure

Low-Complexity Constrained Constant Modulus SG-based Beamforming Algorithms with Variable Step Size

In this paper, two low-complexity adaptive step size algorithms are investigated for blind adaptive beamforming. Both of them are used in a stochastic gradient (SG) algorithm, which employs the constrained constant modulus (CCM) criterion as the design approach. A brief analysis is given for illustrating their properties. Simulations are performed to compare the performances of the novel algorithms with other well-known methods. Results indicate that the proposed algorithms achieve superior performance, better convergence behavior and lower computational complexity in both stationary and non-stationary environments.Comment: 3 figures, 1 table ICASSP 2008. arXiv admin note: substantial text overlap with arXiv:1303.184

Reduced-rank Adaptive Constrained Constant Modulus Beamforming Algorithms based on Joint Iterative Optimization of Filters

This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant modulus (CM) criterion with different constraints. The first devised algorithm is formulated as a constrained joint iterative optimization of a projection matrix and a reduced-rank filter with respect to the CM criterion subject to a constraint on the array response. The constrained constant modulus (CCM) expressions for the projection matrix and the reduced-rank weight vector are derived, and a low-complexity adaptive algorithm is presented to jointly estimate them for implementation. The second proposed algorithm is extended from the first one and implemented according to the CM criterion subject to a constraint on the array response and an orthogonal constraint on the projection matrix. The Gram-Schmidt (GS) technique is employed to achieve this orthogonal constraint and improve the performance. Simulation results are given to show superior performance of the proposed algorithms in comparison with existing methods.Comment: 4 figure

Design of Robust Adaptive Beamforming Algorithms Based on Low-Rank and Cross-Correlation Techniques

This work presents cost-effective low-rank techniques for designing robust adaptive beamforming (RAB) algorithms. The proposed algorithms are based on the exploitation of the cross-correlation between the array observation data and the output of the beamformer. Firstly, we construct a general linear equation considered in large dimensions whose solution yields the steering vector mismatch. Then, we employ the idea of the full orthogonalization method (FOM), an orthogonal Krylov subspace based method, to iteratively estimate the steering vector mismatch in a reduced-dimensional subspace, resulting in the proposed orthogonal Krylov subspace projection mismatch estimation (OKSPME) method. We also devise adaptive algorithms based on stochastic gradient (SG) and conjugate gradient (CG) techniques to update the beamforming weights with low complexity and avoid any costly matrix inversion. The main advantages of the proposed low-rank and mismatch estimation techniques are their cost-effectiveness when dealing with high dimension subspaces or large sensor arrays. Simulations results show excellent performance in terms of the output signal-to-interference-plus-noise ratio (SINR) of the beamformer among all the compared RAB methods.Comment: 11 figures, 12 page

Adaptive Reduced-Rank Constrained Constant Modulus Beamforming Algorithms Based on Joint Iterative Optimization of Filters

This paper proposes a robust reduced-rank scheme for adaptive beamforming based on joint iterative optimization (JIO) of adaptive filters. The novel scheme is designed according to the constant modulus (CM) criterion subject to different constraints, and consists of a bank of full-rank adaptive filters that forms the transformation matrix, and an adaptive reduced-rank filter that operates at the output of the bank of filters to estimate the desired signal. We describe the proposed scheme for both the direct-form processor (DFP) and the generalized sidelobe canceller (GSC) structures. For each structure, we derive stochastic gradient (SG) and recursive least squares (RLS) algorithms for its adaptive implementation. The Gram-Schmidt (GS) technique is applied to the adaptive algorithms for reformulating the transformation matrix and improving performance. An automatic rank selection technique is developed and employed to determine the most adequate rank for the derived algorithms. The complexity and convexity analyses are carried out. Simulation results show that the proposed algorithms outperform the existing full-rank and reduced-rank methods in convergence and tracking performance.Comment: 10 figures; IEEE Transactions on Signal Processing, 201

Study of Efficient Robust Adaptive Beamforming Algorithms Based on Shrinkage Techniques

This paper proposes low-complexity robust adaptive beamforming (RAB) techniques based on shrinkage methods. We firstly briefly review a Low-Complexity Shrinkage-Based Mismatch Estimation (LOCSME) batch algorithm to estimate the desired signal steering vector mismatch, in which the interference-plus-noise covariance (INC) matrix is also estimated with a recursive matrix shrinkage method. Then we develop low complexity adaptive robust version of the conjugate gradient (CG) algorithm to both estimate the steering vector mismatch and update the beamforming weights. A computational complexity study of the proposed and existing algorithms is carried out. Simulations are conducted in local scattering scenarios and comparisons to existing RAB techniques are provided.Comment: 9 pages, 2 figures. arXiv admin note: text overlap with arXiv:1505.0678

Adaptive Low-rank Constrained Constant Modulus Beamforming Algorithms using Joint Iterative Optimization of Parameters

This paper proposes a robust reduced-rank scheme for adaptive beamforming based on joint iterative optimization (JIO) of adaptive filters. The scheme provides an efficient way to deal with filters with large number of elements. It consists of a bank of full-rank adaptive filters that forms a transformation matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. The transformation matrix projects the received vector onto a low-dimension vector, which is processed by the reduced-rank filter to estimate the desired signal. The expressions of the transformation matrix and the reduced-rank weight vector are derived according to the constrained constant modulus (CCM) criterion. Two novel low-complexity adaptive algorithms are devised for the implementation of the proposed scheme with respect to different constrained conditions. Simulations are performed to show superior performance of the proposed algorithms in comparison with the existing methods.Comment: 4 figures, 4 pages. arXiv admin note: substantial text overlap with arXiv:1303.157

Study of Joint MSINR and Relay Selection Algorithms for Distributed Beamforming

This paper presents joint maximum signal-to-interference-plus-noise ratio (MSINR) and relay selection algorithms for distributed beamforming. We propose a joint MSINR and restricted greedy search relay selection (RGSRS) algorithm with a total relay transmit power constraint that iteratively optimizes both the beamforming weights at the relays nodes, maximizing the SINR at the destination. Specifically, we devise a relay selection scheme that based on greedy search and compare it to other schemes like restricted random relay selection (RRRS) and restricted exhaustive search relay selection (RESRS). A complexity analysis is provided and simulation results show that the proposed joint MSINR and RGSRS algorithm achieves excellent bit error rate (BER) and SINR performances.Comment: 7 pages, 2 figures. arXiv admin note: text overlap with arXiv:1707.0095

Robust Low-Rank LCMV Beamforming Algorithms Based on Joint Iterative Optimization Strategies

This chapter presents reduced-rank linearly constrained minimum variance (LCMV) algorithms based on the concept of joint iterative optimization of parameters. The proposed reduced-rank scheme is based on a constrained robust joint iterative optimization (RJIO) of parameters according to the minimum variance criterion. The robust optimization procedure adjusts the parameters of a rank-reduction matrix, a reduced-rank beamformer and the diagonal loading in an alternating manner. LCMV expressions are developed for the design of the rank-reduction matrix and the reduced-rank beamformer. Stochastic gradient and recursive least-squares adaptive algorithms are then devised for an efficient implementation of the RJIO robust beamforming technique. Simulations for a application in the presence of uncertainties show that the RJIO scheme and algorithms outperform in convergence and tracking performances existing algorithms while requiring a comparable complexity.Comment: 7 figures. arXiv admin note: substantial text overlap with arXiv:1205.439