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Journal ArticleDOI

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

01 Aug 2016-IEEE Transactions on Signal Processing (IEEE)-Vol. 64, Iss: 15, pp 3919-3932
TL;DR: This paper presents cost-effective low-rank techniques for designing robust adaptive beamforming algorithms based on the exploitation of the cross-correlation between the array observation data and the output of the beamformer, resulting in the proposed orthogonal Krylov subspace projection mismatch estimation (OKSPME) method.
Abstract: This paper 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. First, 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.

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Citations
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Journal ArticleDOI
TL;DR: This paper derives a diagonal loading CGLS algorithm (CG applied to normal equations) and proposes a simple method to choose the loading level based on a coarse estimation of the desired signal power, which can effectively reduce the signal self-cancellation at high signal-to-noise ratio.
Abstract: The mismatches of signal and array geometry will seriously degrade the performance of adaptive beamformer. In this paper, we propose two methods for robust adaptive beamforming based on the conjugate gradient (CG) algorithm. The proposed beamformers offer a significant improvement in the computational complexity while providing the same performance of the best robust beamformers at present. The first method belongs to the diagonal loading technique. We derive a diagonal loading CGLS algorithm (CG applied to normal equations) and propose a simple method to choose the loading level based on a coarse estimation of the desired signal power. This parameter-free method can effectively reduce the signal self-cancellation at high signal-to-noise ratio. The second method belongs to the regularization technique. Since the CG algorithm has a regularizing effect with iteration number being the regularization parameter, the stopping criterion plays an important role on the robustness. We develop three fast stopping criteria for CG iteration, which reduce the stopping complexity from $O(N)$ or $O(N^2)$ to $O(1)$ . The former two are the fast versions of existing methods and the later one is new. Moreover, the new criterion based on fast Ritz value estimation has better performance than others.

60 citations


Cites background from "Robust Adaptive Beamforming Based o..."

  • ...Digital Object Identifier 10.1109/TSP.2016.2605075 [8], uncertainty set constraint (USC) [9], [10], covariance matrix reconstruction (CMR) [11], [12], steering vector estimation (SVE) [13], [14] and others [15]–[20]....

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Journal ArticleDOI
TL;DR: Simulation results demonstrate that the overestimation of interference powers hardly degrades the performance of adaptive beamforming, and the proposed algorithm achieves nearly optimal performance across a wide range of signal-to-noise ratios.
Abstract: Adaptive beamformer is very sensitive to model mismatch, especially when the signal-of-interest is present in the training data. In this paper, we focus on the topic of robust adaptive beamforming (RAB) based on interference-plus-noise covariance matrix (INCM) reconstruction. First, we analyze the effectiveness of several INCM reconstruction schemes, and particularly analyze the impacts of interference power estimation on RAB. Second, according to the analysis results, we develop a simplified algorithm to estimate the interference powers, and a RAB algorithm based on INCM reconstruction is then presented. Compared with some existing methods, the proposed algorithm simplifies the interference power estimation of INCM reconstruction. Aligned with our analysis, simulation results demonstrate that the overestimation of interference powers hardly degrades the performance of adaptive beamforming, and our proposed algorithm achieves nearly optimal performance across a wide range of signal-to-noise ratios.

52 citations

Journal ArticleDOI
TL;DR: In this paper, the robust adaptive beamforming design problem based on estimation of the signal-of-interest (SOI) steering vector is considered, and a beamformer output power maximization problem is formulated and solved subject to a double-sided norm perturbation constraint, a similarity constraint, and an inhomogeneous constraint that guarantees that the direction of arrival (DOA) of the SOI is away from the DOA region of all linear combinations of the interference steering vectors.
Abstract: The robust adaptive beamforming design problem based on estimation of the signal-of-interest (SOI) steering vector is considered in the paper. The common criteria to find the best estimate of the steering vector are the beamformer output signal-to-noise-plus-interference ratio (SINR) and output power, while the constraints assume as little as possible prior inaccurate knowledge about the SOI, the propagation media, and the antenna array. Herein, in order to find the optimal steering vector, a beamformer output power maximization problem is formulated and solved subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint that guarantees that the direction-of-arrival (DOA) of the SOI is away from the DOA region of all linear combinations of the interference steering vectors. The prior knowledge required is some allowable error norm bounds and approximate knowledge of the antenna array geometry and angular sector of the SOI. It turns out that the array output power maximization problem is a non-convex quadratically constrained quadratic programming problem with inhomogeneous constraints. However, we show that the problem is still solvable, and develop efficient algorithms for finding globally optimal estimate of the SOI steering vector. The results are generalized to the case when an ellipsoidal constraint is considered instead of the similarity constraint, and sufficient conditions for the global optimality are derived. In addition, a new quadratic constraint on the actual signal steering vector is proposed in order to improve the array performance. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformers in terms of the output SINR as well as the output power.

40 citations

Journal ArticleDOI
TL;DR: A new low-complexity RAB approach based on interference-plus-noise covariance matrix (IPNC) reconstruction and steering vector (SV) estimation is proposed, which can provide superior performance to several previously proposed beamformers.
Abstract: To ensure signal receiving quality, robust adaptive beamforming (RAB) is of vital importance in modern communications. In this letter, we propose a new low-complexity RAB approach based on interference-plus-noise covariance matrix (IPNC) reconstruction and steering vector (SV) estimation. In this method, the IPNC and desired signal covariance matrices are reconstructed by estimating all interference powers as well as the desired signal power using the principle of maximum entropy power spectrum (MEPS). Numerical simulations demonstrate that the proposed method can provide superior performance to several previously proposed beamformers.

38 citations


Cites methods from "Robust Adaptive Beamforming Based o..."

  • ...In [14], a computationally efficient algorithm via low complexity shrinkage-based mismatch estimation (LOCSME) is proposed followed by the introduction of the orthogonal Krylov subspace projection mismatch estimation (OKSPME) technique [20]....

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Journal ArticleDOI
TL;DR: The proposed RDB approach mitigates the effects of channel errors in wireless networks equipped with relays based on the exploitation of the cross-correlation between the received data from the relays at the destination and the system output and low-rank techniques.
Abstract: In this work, we present a novel robust distributed beamforming (RDB) approach based on low-rank and cross-correlation techniques. The proposed RDB approach mitigates the effects of channel errors in wireless networks equipped with relays based on the exploitation of the cross-correlation between the received data from the relays at the destination and the system output and low-rank techniques. The relay nodes are equipped with an amplify-and-forward (AF) protocol and the channel errors are modeled using an additive matrix perturbation, which results in degradation of the system performance. The proposed method, denoted low-rank and cross-correlation RDB (LRCC-RDB), considers a total relay transmit power constraint in the system and the goal of maximizing the output signal-to-interference-plus-noise ratio (SINR). We carry out a performance analysis of the proposed LRCC-RDB technique along with a computational complexity study. The proposed LRCC-RDB does not require any costly online optimization procedure and simulations show an excellent performance as compared to previously reported algorithms.

38 citations

References
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Journal ArticleDOI
Max Costa1
TL;DR: It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it, which is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N.
Abstract: A channel with output Y = X + S + Z is examined, The state S \sim N(0, QI) and the noise Z \sim N(0, NI) are multivariate Gaussian random variables ( I is the identity matrix.). The input X \in R^{n} satisfies the power constraint (l/n) \sum_{i=1}^{n}X_{i}^{2} \leq P . If S is unknown to both transmitter and receiver then the capacity is \frac{1}{2} \ln (1 + P/( N + Q)) nats per channel use. However, if the state S is known to the encoder, the capacity is shown to be C^{\ast} =\frac{1}{2} \ln (1 + P/N) , independent of Q . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N . Therefore, the state S does not affect the capacity of the channel, even though S is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it.

4,130 citations


"Robust Adaptive Beamforming Based o..." refers background in this paper

  • ...…derived from the proposed optimization problems to reduce the cost for computing the beamforming weights for large sensor arrays [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109], [110], [111], [112], [114], [115],…...

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Journal ArticleDOI
TL;DR: A new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch is developed based on the optimization of worst-case performance.
Abstract: Adaptive beamforming methods are known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated. In particular, if the desired signal is present in training snapshots, the adaptive array performance may be quite sensitive even to slight mismatches between the presumed and actual signal steering vectors (spatial signatures). Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration, distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance. It turns out that the natural formulation of this adaptive beamforming problem involves minimization of a quadratic function subject to infinitely many nonconvex quadratic constraints. We show that this (originally intractable) problem can be reformulated in a convex form as the so-called second-order cone (SOC) program and solved efficiently (in polynomial time) using the well-established interior point method. It is also shown that the proposed technique can be interpreted in terms of diagonal loading where the optimal value of the diagonal loading factor is computed based on the known level of uncertainty of the signal steering vector. Computer simulations with several frequently encountered types of signal steering vector mismatches show better performance of our robust beamformer as compared with existing adaptive beamforming algorithms.

1,347 citations


"Robust Adaptive Beamforming Based o..." refers background or methods in this paper

  • ...Popular approaches include worst-case optimization [2], [9], diagonal loading [4], and eigen-subspace decomposition and projection techniques [6], [8], [11]....

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  • ...However, the SMI beamformer requires a large number of snapshots to converge and is sensitive to steering vector mismatches [2], [3]....

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Journal ArticleDOI
TL;DR: It is shown that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonalloading can be precisely calculated based on the uncertainty set of the steering vector.
Abstract: The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.

1,113 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that modulo arithmetic may be used in the inverse filter to eliminate completely the possibility of instability, and a very simple automatic or adaptive equalisation system is presented.
Abstract: The limitations of present automatic and adaptive equalisers stem from the use of feedforward transversal filters. These drawbacks may be obviated by using a feedback transversal filter, the inverse filter, but this is only suitable for limited use since it can be an unstable circuit. It is shown that modulo arithmetic may be used in the inverse filter to eliminate completely the possibility of instability, and a very simple automatic or adaptive equalisation system is presented. Some interesting properties of the modulo inverse filter are included.

1,035 citations


Additional excerpts

  • ...problems to reduce the cost for computing the beamforming weights for large sensor arrays [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109], [110], [111], [112], [114], [115], [116], [117], [118], [119],[120], [121], [122], [123], [124], [125], [126], [131], [128], [129], [130], [131], [132], [133], [134], [135], [136]. , resultin...

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Journal ArticleDOI
TL;DR: A simple encoding algorithm is introduced that achieves near-capacity at sum-rates of tens of bits/channel use and a certain perturbation of the data using a "sphere encoder" can be chosen to further reduce the energy of the transmitted signal.
Abstract: Recent theoretical results describing the sum-capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves near-capacity at sum-rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a "sphere encoder" to perturb the data to reduce the energy of the transmitted signal. The paper is comprised of two parts. In this second part, we show that, after the regularization of the channel inverse introduced in the first part, a certain perturbation of the data using a "sphere encoder" can be chosen to further reduce the energy of the transmitted signal. The performance difference with and without this perturbation is shown to be dramatic. With the perturbation, we achieve excellent performance at all signal-to-noise ratios. The results of both uncoded and turbo-coded simulations are presented.

972 citations


Additional excerpts

  • ...ts for large sensor arrays [91], [92], [93], [94], [95], [96], [97], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109], [110], [111], [112], [114], [115], [116], [117], [118], [119],[120], [121], [122], [123], [124], [125], [126], [131], [128], [129], [130], [131], [132], [133], [134], [135], [136]. , resulting in the proposed OKSPMESG, OKSPME-CCG and OKSPME-MCG RAB algor...

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