Abstract—In the traditional transmitting beamforming radar system, the transmitting antennas send coherent waveforms which form a highly focused beam. In the multiple-input multiple-output (MIMO) radar system, the transmitter sends noncoherent (possibly orthogonal) broad (possibly omnidirectional) waveforms. These waveforms can be extracted at the receiver by a matched filterbank. The extracted signals can be used to obtain more diversity or to improve the spatial resolution for clutter. This paper focuses on space–time adaptive processing (STAP) for MIMO radar systems which improves the spatial resolution for clutter. With a slight modification, STAP methods developed originally for the single-input multiple-output (SIMO) radar (conventional radar) can also be used in MIMO radar. However, in the MIMO radar, the rank of the jammer-and-clutter subspace becomes very large, especially the jammer subspace. It affects both the complexity and the convergence of the STAP algorithm. In this paper, the clutter space and its rank in the MIMO radar are explored. By using the geometry of the problem rather than data, the clutter subspace can be represented using prolate spheroidal wave functions (PSWF). A new STAP algorithm is also proposed. It computes the clutter space using the PSWF and utilizes the block-diagonal property of the jammer covariance matrix. Because of fully utilizing the geometry and the structure of the covariance matrix, the method has very good SINR performance and low computational complexity. Index Terms—Clutter subspaces, multiple-input multiple-output (MIMO) radar, prolate spheroidal wave function, space–time adaptive processing (STAP). I.

In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most prominent theoretical results of RO over the past decade, we will also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we will highlight successful applications of RO across a wide spectrum of domains, including, but not limited to, finance, statistics, learning, and engineering.

Abstract—In this letter, we show that worst-case robust beamforming, with uncertain weights subject to multiplicative variations, can be cast as a convex optimization problem. We interpret this problem as a weighted complex I-regularization of the nominal beamforming problem, and show that it can be solved with the same computational complexity as nominal beamforming, ignoring the variations. We derive a simple lower bound on how much worse the robust beamformer will be compared to the nominal beamformer solution with no weight uncertainty. We demonstrate the robust approach with a simple narrowband beamformer. Index Terms—Regularization, robust beamforming, robust optimization, robust sensor array signal processing. I. BEAMFORMING WE consider an array of sensor elements. Let be the array response to a wave of unit amplitude

We consider the design of linear precoders (beamformers) for broadcast channels with Quality of Service (QoS) constraints for each user, in scenarios with uncertain channel state information (CSI) at the transmitter. We consider a deterministically-bounded model for the channel uncertainty of each user, and our goal is to design a robust precoder that minimizes the total transmission power required to satisfy the users ’ QoS constraints for all channels within a specified uncertainty region around the transmitter’s estimate of each user’s channel. Since this problem is not known to be computationally tractable, we will derive three conservative design approaches that yield convex and computationally-efficient restrictions of the original design problem. The three approaches yield semidefinite program (SDP) formulations that offer different trade-offs between the degree of conservatism and the size of the SDP. We will also show how these conservative approaches can be used to derive efficiently-solvable quasi-convex restrictions of some related design problems, including the robust counterpart to the problem of maximizing the minimum signal-to-interference-plus-noise-ratio (SINR) subject to a given power constraint. Our simulation results indicate that in the presence of uncertain CSI the proposed approaches can satisfy the users ’ QoS requirements for a significantly larger set of uncertainties than existing methods, and require less transmission power to do so.

It is well known that the performance of the minimum variance distortionless response (MVDR) beamformer is very sensitive to steering vector mismatch. Such mismatches can occur as a result of direction-of-arrival (DOA) errors, local scattering, near-far spatial signature mismatch, waveform distortion, source spreading, imperfectly calibrated arrays and distorted antenna shape. In this paper, an adaptive beamformer that is robust against the DOA mismatch is proposed. This method imposes two quadratic constraints such that the magnitude responses of two steering vectors exceed unity. Then, a diagonal loading method is used to force the magnitude responses at the arrival angles between these two steering vectors to exceed unity. Therefore, this method can always force the gains at a desired range of angles to exceed a constant level while suppressing the interferences and noise. A closed-form solution to the proposed minimization problem is introduced, and the diagonal loading factor can be computed systematically by a proposed algorithm. Numerical examples show that this method has excellent signal-to-interference-plus-noise ratio performance and a complexity comparable to the standard MVDR beamformer.

Multiantenna MIMO channels have recently become a popular means to increase the spectral efficiency and quality of wireless communications by the use of spatial diversity at both sides of the link [1–4]. In fact, the MIMO concept is much more general and embraces many other scenarios such as wireline digital subscriber line (DSL) systems [5] and singleantenna

We consider the array signal processing problem of choosing the weight vector to minimize noise power, subject to a unit array gain for the desired wave, and subject to rejection constraints on interferences. We model the variations in the array response with ellipsoidal uncertainty, and take the worst-case robust optimization approach, i.e., we require the constraints to hold for all possible data in the uncertainty ellipsoid. We show that this robust array signal processing problem can be formulated as a second-order cone program, which interior-point algorithms can solve efficiently. The robust solution is demonstrated with an example.

An order recursive algorithm for minimum mean square error (MMSE) estimation of signals under a Bayesian model defined on the steering vector is introduced. The MMSE estimate can be viewed as a mixture of conditional MMSE estimates weighted by the posterior probability density function (PDF) of the random steering vector given the observed data. This paper derives an adaptive closed form Kalman-filter implementation that updates the weight vector by successive incorporations of data collected from additional array elements in the steering vector. The performance of the Bayesian beamformer is compared against several robust beamformers in terms of mean square error (MSE) and output signal-to-interference-plus-noise ratio (SINR). 1. BACKGROUND The received data vector of an N-element sensor array at sample time k has the form x(k) =a s ∗ (k)+i(k)+n(k), (1) where s(k) is the desired signal with known power σ 2 s, a ∈ C N is the steering vector, i(k) is the interence and n(k) is the noise. Let Ri+n � E[(i(k) +n(k))(i(k) +n(k)) H] be the interference-plus-noise covariance. Let (·) ∗ , (·) T and (·) H be the complex conjugate, transpose and Hermitian transpose, respectively. Assume that s(k), i(k) and n(k) are zero mean, temporally white, complex Gaussian processes that are mutually independent to each other. In practice, the true steering vector often deviates from its presumed value for various reasons such as improper array modeling, asynchronous sampling, pointing error, miscalibration, or source motion. It is often reasonable to model these

Abstract—A Bayesian approach to adaptive narrowband beamforming for uncertain source direction-of-arrival (DOA) is presented. The DOA is modeled as a random variable with prior statistics that describe its level of uncertainty. The Bayesian beamformer is the corresponding minimum mean-square error (MMSE) estimator, which can be viewed as a mixture of directional beamformers combined according to the posterior distribution of the DOA given the data. Under a deterministic DOA, the mean-square error (MSE) of the Bayesian beamformer becomes as low as that of the directional beamformer equipped with the DOA candidate in the prior set that is the closest to the true DOA at exponential rate, where closeness is defined in the Kullback–Leibler sense. Two efficient algorithms using a uniform linear array (ULA) are presented. The first method utilizes the efficiency of the fast Fourier transform (FFT) to compute the posterior distribution on a large number of DOA candidates. The second method approximates the posterior distribution by a Gaussian distribution, which leads to a directional beamformer incorporated with a particular spreading matrix and an adjusted DOA. Numerical simulations show that the proposed beamformer outperforms other related blind or robust beamforming algorithms over a wide range of signal-to-noise ratios (SNRs). Index Terms—Adaptive beamforming, Bayesian model, direction-of-arrival (DOA) uncertainty, minimum mean-square error (MMSE) estimation. I.

Abstract not found