Sergiy A. Vorobyov

Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem

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.

Spectrum Sharing in Wireless Networks via QoS-Aware Secondary Multicast Beamforming

Secondary spectrum usage has the potential to considerably increase spectrum utilization. In this paper, quality-of-service (QoS)-aware spectrum underlay of a secondary multicast network is considered. A multiantenna secondary access point (AP) is used for multicast (common information) transmission to a number of secondary single-antenna receivers. The idea is that beamforming can be used to steer power towards the secondary receivers while limiting sidelobes that cause interference to primary receivers. Various optimal formulations of beamforming are proposed, motivated by different ldquocohabitationrdquo scenarios, including robust designs that are applicable with inaccurate or limited channel state information at the secondary AP. These formulations are NP-hard computational problems; yet it is shown how convex approximation-based multicast beamforming tools (originally developed without regard to primary interference constraints) can be adapted to work in a spectrum underlay context. Extensive simulation results demonstrate the effectiveness of the proposed approaches and provide insights on the tradeoffs between different design criteria.

Phased-MIMO Radar: A Tradeoff Between Phased-Array and MIMO Radars

We propose a new technique for multiple-input multiple-output (MIMO) radar with colocated antennas which we call phased-MIMO radar. The new technique enjoys the advantages of the MIMO radar without sacrificing the main advantage of the phased-array radar which is the coherent processing gain at the transmitting side. The essence of the proposed technique is to partition the transmit array into a number of subarrays that are allowed to overlap. Then, each subarray is used to coherently transmit a waveform which is orthogonal to the waveforms transmitted by other subarrays. Coherent processing gain can be achieved by designing a weight vector for each subarray to form a beam towards a certain direction in space. Moreover, the subarrays are combined jointly to form a MIMO radar resulting in higher angular resolution capabilities. Substantial improvements offered by the proposed phased-MIMO radar technique as compared to the phased-array and MIMO radar techniques are demonstrated analytically and by simulations through analyzing the corresponding beam patterns and the achievable output signal-to-noise-plus-interference ratios. Both analytical and simulation results validate the effectiveness of the proposed phased-MIMO radar.

Collaborative beamforming for wireless sensor networks with Gaussian distributed sensor nodes

Collaborative beamforming has been recently introduced in the context of wireless sensor networks (WSNs) to increase the transmission range of individual sensor nodes. The challenge in using collaborative beamforming in WSNs is the uncertainty regarding the sensor node locations. However, the actual sensor node spatial distribution can be modeled by a properly selected probability density function (pdf). In this paper, we model the spatial distribution of sensor nodes in a cluster of WSN using Gaussian pdf. Gaussian pdf is more suitable in many WSN applications than, for example, uniform pdf which is commonly used for flat ad hoc networks. The average beampattern and its characteristics, the distribution of the beampattern level in the sidelobe region, and the distribution of the maximum sidelobe peak are derived using the theory of random arrays. We show that both the uniform and Gaussian sensor node deployments behave qualitatively in a similar way with respect to the beamwidths and sidelobe levels, while the Gaussian deployment gives wider mainlobe and has lower chance of large sidelobes.

Power allocation in wireless multi-user relay networks

In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.

Transmit Energy Focusing for DOA Estimation in MIMO Radar With Colocated Antennas

In this paper, we propose a transmit beamspace energy focusing technique for multiple-input multiple-output (MIMO) radar with application to direction finding for multiple targets. The general angular directions of the targets are assumed to be located within a certain spatial sector. We focus the energy of multiple (two or more) transmitted orthogonal waveforms within that spatial sector using transmit beamformers which are designed to improve the signal-to-noise ratio (SNR) gain at each receive antenna. The subspace decomposition-based techniques such as MUSIC can then be used for direction finding for multiple targets. Moreover, the transmit beamformers can be designed so that matched-filtering the received data to the waveforms yields multiple (two or more) data sets with rotational invariance property that allows applying search-free direction finding techniques such as ESPRIT or parallel factor analysis (PARAFAC). Unlike previously reported MIMO radar ESPRIT/PARAFAC-based direction finding techniques, our method achieves the rotational invariance property in a different manner combined also with the transmit energy focusing. As a result, it achieves better estimation performance at lower computational cost. The corresponding Cramer-Rao bound is derived and its dependence on the number of waveforms used is discussed. Simulation results also show the superiority of the proposed technique over the existing techniques.

Blind noise reduction for multisensory signals using ICA and subspace filtering, with application to EEG analysis

Abstract. In many applications of signal processing, especially in communications and biomedicine, preprocessing is necessary to remove noise from data recorded by multiple sensors. Typically, each sensor or electrode measures the noisy mixture of original source signals. In this paper a noise reduction technique using independent component analysis (ICA) and subspace filtering is presented. In this approach we apply subspace filtering not to the observed raw data but to a demixed version of these data obtained by ICA. Finite impulse response filters are employed whose vectors are parameters estimated based on signal subspace extraction. ICA allows us to filter independent components. After the noise is removed we reconstruct the enhanced independent components to obtain clean original signals; i.e., we project the data to sensor level. Simulations as well as real application results for EEG-signal noise elimination are included to show the validity and effectiveness of the proposed approach.

Robust Adaptive Beamforming Based on Steering Vector Estimation With as Little as Possible Prior Information

A general notion of robustness for robust adaptive beamforming (RAB) problem and a unified principle for minimum variance distortionless response (MVDR) RAB techniques design are formulated. This principle is to use standard MVDR beamformer in tandem with an estimate of the desired signal steering vector found based on some imprecise prior information. Differences between various MVDR RAB techniques occur only because of the differences in the assumed prior information and the corresponding signal steering vector estimation techniques. A new MVDR RAB technique, which uses as little as possible and easy to obtain imprecise prior information, is developed. The objective for estimating the steering vector is the maximization of the beamformer output power, while the constraints are the normalization condition and the requirement that the estimate does not converge to any of the interference steering vectors and their linear combinations. The prior information used is only the imprecise knowledge of the antenna array geometry and angular sector in which the actual steering vector lies. Mathematically, the proposed MVDR RAB is expressed as the well known non-convex quadratically constrained quadratic programming problem with two constraints, which can be efficiently and exactly solved. Some new results for the corresponding optimization problem such as a new algebraic way of finding the rank-one solution from the general-rank solution of the relaxed problem and the condition under which the solution of the relaxed problem is guaranteed to be rank-one are derived. Our simulation results demonstrate the superiority of the proposed method over other previously developed RAB techniques.

Adaptive beamforming with joint robustness against mismatched signal steering vector and interference nonstationarity

Adaptive beamforming methods degrade in the presence of both signal steering vector errors and interference nonstationarity. We develop a new approach to adaptive beamforming that is jointly robust against these two phenomena. Our beamformer is based on the optimization of the worst case performance. A computationally efficient convex optimization-based algorithm is proposed to compute the beamformer weights. Computer simulations demonstrate that our beamformer has an improved robustness as compared to other popular robust beamforming algorithms.

Robust Adaptive Beamforming Using Sequential Quadratic Programming: An Iterative Solution to the Mismatch Problem

A new approach to the design of robust adaptive beamforming is introduced. The essence of the new approach is to estimate the difference between the actual and presumed steering vectors and to use this difference to correct the erroneous presumed steering vector. The estimation process is performed iteratively where a quadratic convex optimization problem is solved at each iteration. Contrary to the worst-case performance-based and the probability-constrained-based approaches, our approach does not make any assumptions on either the norm of the mismatch vector or its probability distribution. Hence, it avoids the need for estimating their values.