Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch

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

Efficient Covariance Matrix Reconstruction with Iterative Spatial Spectrum Sampling

This work presents a cost-effective technique for designing robust adaptive beamforming algorithms based on efficient covariance matrix reconstruction with iterative spatial power spectrum (CMR-ISPS). The proposed CMR-ISPS approach reconstructs the interference-plus-noise covariance (INC) matrix based on a simplified maximum entropy power spectral density function that can be used to shape the directional response of the beamformer. Firstly, we estimate the directions of arrival (DoAs) of the interfering sources with the available snapshots. We then develop an algorithm to reconstruct the INC matrix using a weighted sum of outer products of steering vectors whose coefficients can be estimated in the vicinity of the DoAs of the interferences which lie in a small angular sector. We also devise a cost-effective adaptive algorithm based on conjugate gradient techniques to update the beamforming weights and a method to obtain estimates of the signal of interest (SOI) steering vector from the spatial power spectrum. The proposed CMR-ISPS beamformer can suppress interferers close to the direction of the SOI by producing notches in the directional response of the array with sufficient depths. Simulation results are provided to confirm the validity of the proposed method and make a comparison to existing approachesComment: 14 pages, 8 figure

MIMO radar space–time adaptive processing using prolate spheroidal wave functions

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

Robust Adaptive Beamforming Using k-means Clustering: A Solution to High Complexity of the Reconstruction-Based Algorithm

Recently, a new robust adaptive beamforming (RAB) algorithm has been proposed to reconstruct the interference-plus-noise covariance matrix (IPNCM) based on narrowing the interference angular domain and using an annular uncertainty set (NIAD-AUS). The method is robust against unknown arbitrary-type mismatches. However, its computational complexity will increase exponentially with the number of array sensors. In this paper, a novel method is proposed to solve this problem. First, k-means clustering (KMC) algorithm is utilized to estimate the annulus uncertainty set with fewer clustering weight points rather than whole sampling. Second, the KMC Capon spectrum is used to reconstruct the IPNCM. Compared with the previous reconstruction-based algorithms, the proposed approach can retain the high performance of the state-of-the-art NIAD-AUS algorithm. More importantly, it can also obtain the IPNCM more quickly. Lastly, simulation results demonstrate the effectiveness and robustness of the proposed algorithm

High Performance Robust Adaptive Beamforming in the Presence of Array Imperfections

A high performance robust beamforming scheme is proposed to combat model mismatch. Our method lies in the novel construction of interference-plus-noise (IPN) covariance matrix. The IPN covariance matrix consists of two parts. The first part is obtained by utilizing the Capon spectrum estimator integrated over a region separated from the direction of the desired signal and the second part is acquired by removing the desired signal component from the sample covariance matrix. Then a weighted summation of these two parts is utilized to reconstruct the IPN matrix. Moreover, a steering vector estimation method based on orthogonal constraint is also proposed. In this method, the presumed steering vector is corrected via orthogonal constraint under the condition where the estimation does not converge to any of the interference steering vectors. To further improve the proposed method in low signal-to-noise ratio (SNR), a hybrid method is proposed by incorporating the diagonal loading method into the IPN matrix reconstruction. Finally, various simulations are performed to demonstrate that the proposed beamformer provides strong robustness against a variety of array mismatches. The output signal-to-interference-plus-noise ratio (SINR) improvement of the beamformer due to the proposed method is significant

Overcoming DoF Limitation in Robust Beamforming: A Penalized Inequality-Constrained Approach

A well-known challenge in beamforming is how to optimally utilize the degrees of freedom (DoF) of the array to design a robust beamformer, especially when the array DoF is smaller than the number of sources in the environment. In this paper, we leverage the tool of constrained convex optimization and propose a penalized inequality-constrained minimum variance (P-ICMV) beamformer to address this challenge. Specifically, we propose a beamformer with a well-targeted objective function and inequality constraints to achieve the design goals. The constraints on interferences penalize the maximum gain of the beamformer at any interfering directions. This can efficiently mitigate the total interference power regardless of whether the number of interfering sources is less than the array DoF or not. Multiple robust constraints on the target protection and interference suppression can be introduced to increase the robustness of the beamformer against steering vector mismatch. By integrating the noise reduction, interference suppression, and target protection, the proposed formulation can efficiently obtain a robust beamformer design while optimally trade off various design goals. When the array DoF is fewer than the number of interferences, the proposed formulation can effectively align the limited DoF to all of the sources to obtain the best overall interference suppression. $\$To numerically solve this problem, we formulate the P-ICMV beamformer design as a convex second-order cone program (SOCP) and propose a low complexity iterative algorithm based on the alternating direction method of multipliers (ADMM). Three applications are simulated to demonstrate the effectiveness of the proposed beamformer.Comment: submitted to IEEE Transactions on Signal Processin

Interference-plus-Noise Covariance Matrix Reconstruction via Spatial Power Spectrum Sampling for Robust Adaptive Beamforming

Recently, a robust adaptive beamforming (RAB) technique based on interference-plus-noise covariance (INC) matrix reconstruction has been proposed, which utilizes the Capon spectrum estimator integrated over a region separated from the direction of the desired signal. Inspired by the sampling and reconstruction idea, in this paper, a novel method named spatial power spectrum sampling (SPSS) is proposed to reconstruct the INC matrix more efficiently, with the corresponding beamforming algorithm developed, where the covariance matrix taper (CMT) technique is employed to further improve its performance. Simulation results are provided to demonstrate the effectiveness of the proposed method

MIMO Radar Waveform Optimization With Prior Information of the Extended Target and Clutter

The concept of multiple-input multiple-output (MIMO) radar allows each transmitting antenna element to transmit an arbitrary waveform. This provides extra degrees of freedom compared to the traditional transmit beamforming approach. It has been shown in the recent literature that MIMO radar systems have many advantages. In this paper, we consider the joint optimization of waveforms and receiving filters in the MIMO radar for the case of extended target in clutter. A novel iterative algorithm is proposed to optimize the waveforms and receiving filters such that the detection performance can be maximized. The corresponding iterative algorithms are also developed for the case where only the statistics or the uncertainty set of the target impulse response is available. These algorithms guarantee that the SINR performance improves in each iteration step. Numerical results show that the proposed methods have better SINR performance than existing design methods