Array Weight Vector Research Articles

Are universal beamformers passive cognitive sonar systems?

Cognitive sonars dynamically tune system parameters to improve performance in pursuit of specific goals. Most research on cognitive sonar focuses on active sonar, varying the transmitted waveform and ping rate. Although passive sonar also faces the challenges of pursuing goals in varying and unknown environments, little research has been done exploring cognitive approaches to passive beamforming for sonar arrays. Universal beamformers provide one implementation of a cognitive approach to passive sonar. Practical adaptive beamformers generally regularize the sample covariance matrix before estimating the array weights. Universal beamformers blend the array weights across a family of beamformers competing on different choices for the regularization parameters. The blend of array weights is performance driven based, including the largest portion from the beamformers best suited for the current environment. Universal are “doubly adaptive” in that each competing beamformer is adapting its array weight vector in response to the data observed at the sensor array, the universal algorithm is then meta-adapting the blend of these array weight vectors used to process the data based on the performance of each competing beamformer. We will present examples of beamformers, which are universal over dominant subspace dimension and beam pattern notch width for moving interferers. [Work supported by ONR 321US.]

Fast Synthesis Method for Large Aperture Array Pattern in the Presence of Array Errors

In this paper, an improved array synthesis method with array errors is proposed for large aperture arrays. Because of the array errors such as amplitude-phase errors and positions errors, the performance of the array synthesis is reduced seriously. Firstly, the ideal fast low sidelobe synthesis method is obtained based on the discrete Fourier transform (DFT) method. Then, by using Taylor expansion to remove the coupling relationship between the position of the element and the scanning angle, the compensation matrix for the pattern function and the array weighted vector with amplitude phase and position errors are derived. At last, the conversion relationship between the array with errors and the array weight vector is corrected in the iterative process. The theoretical simulation experiments verify the effectiveness and robustness of the proposed method for the linear array and rectangular array pattern synthesis. Then, the influence of Taylor expansion order on the pattern synthesis results is analysed.

Cognitive FDA radar transmit power allocation for target tracking in spectrally dense scenario

In this paper, we propose a cognitive radar paradigm based on frequency diverse array (FDA), which allows flexible spectrum control via element-wise transmit power allocation. As an emerging array technique, FDA differs from conventional phased array (PA) in that it imposes an additional frequency increment across the array elements. The use of frequency increment provides the FDA radar with the ability of flexible spectrum adjustment. We propose the cognitive FDA radar for target tracking in spectrally dense scenarios. Two optimization criteria, i.e., signal-to-interference-plus-noise ratio (SINR) maximization and Cramér-Rao bound (CRB) minimization, are employed to adaptively update the array weight vector for power allocation at each transmission. Numerical results show that the proposed cognitive FDA radar can adjust the signal spectrum to avoid the interfered frequencies for better output SINR. The resulting tracking errors of FDA radar with adaptive power allocation are lower than that for fixed power allocation. Moreover, the CRB criterion further improves the tracking performance.

A unified sparse array design framework for beampattern synthesis

A smaller number of transmit antennas can reduce the array system cost, while sparse antenna design can provide additional degrees of freedom to beampattern synthesis. It is also known that the min-max beampattern matching design criterion can synthesize beampattern with small mainlobe ripple, low peak sidelobe level, and specified null/notch. Based on this design metric, we formulate a unified sparse array design framework for beampattern synthesis. Our framework includes the colocated multiple-input multiple-output (MIMO) radar transmit beampattern synthesis, phase-only beampattern synthesis, and phased-array beampattern synthesis as special cases. In the design formulation, the antenna positions and phase-only waveforms (for MIMO radar beampattern) or array weight vector (for phase-only and traditional phased-array beampattern) are jointly determined. The resultant problem is challenging because the nonconvex nonsmooth min-max objective function, and phase-only/unimodular requirements make it become typically NP-hard, and the antenna position selection results in a difficult Boolean constraint. Nevertheless, we are able to find a local optimal solution efficiently by applying the Lawson approximation and majorization-minimization. Numerical examples show that the devised approach can achieve the desired transmit beampattern by jointly optimizing the phase-only waveforms/weight vector and antenna locations.

Sparse Array Beampattern Synthesis via Alternating Direction Method of Multipliers

In this paper, we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers (ADMM). Unlike the usual weighted ${l} 1$ norm, we utilize the ${l} p$ norm of the array weight vector, where $0 , as the objective function to enhance its sparsity for arbitrary array configurations. To solve the resultant nonconvex and nonlinear optimization problem, we introduce auxiliary variables to decouple the array weight vector in the objective function from the complicated constraints on main lobes and sidelobes, and then, the array weight vector and auxiliary variables are updated alternately via ADMM. To determine the array weight vector with the ${l} p$ norm, we analyze the convexity or concavity of the subfunction related to each weight element using its derivatives. On the other hand, we divide the objective function of auxiliary variables into multiple nonlinear subfunctions, each of which is only dependent of the magnitude of the corresponding auxiliary variable and is calculated in parallel via analyzing simplified two-sided constraints. Furthermore, we extend our methodology to the symmetric excitation case with symmetric array configurations. Numerical examples show that the proposed methods can obtain satisfactory radiation pattern with fewer antennas than the existing techniques and are applicable for arbitrary or symmetric array configurations.

Equivalence between orbital angular momentum and multiple‐input multiple‐output in uniform circular arrays: Investigation by eigenvalues

AbstractIt had been shown that array weight vectors using uniform circular arrays (UCAs) in multiple‐input multiple‐output (MIMO) can generate helical phase distribution used in orbital angular momentum (OAM) communication system. In this letter, the MIMO channel, or OAM multiplexing characteristic, was investigated by means of eigenvalues. It was also found that the OAM is not effective as the distance between transmitting and receiving antennas increases because the radiation pattern along the direction of propagation is null with helical phase front. It was found that MIMO and/or OAM performance improve in near‐field region. It was also found that the performance improves when radius of UCAs becomes large.

Pattern Synthesis With Multipoint Accurate Array Response Control

In this paper, the problem of pattern synthesis with antenna arrays is addressed, and new approaches based on the recently developed accurate array response control ( $ {\textrm {A}}^{2}\textrm {RC} $ ) algorithm are presented. It is shown that the array weight vector obtained by the $ {\textrm {A}}^{2}\textrm {RC} $ algorithm to control the normalized response at a single direction in each step belongs to a specific set. Thus, an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses. This results in the so-called multipoint accurate array response control ( $ {\textrm {MA}}^{2}\textrm {RC} $ ) algorithm. Moreover, in order to avoid possible beam axis shift in pattern synthesis, a modified $ {\textrm {MA}}^{2}\textrm {RC} $ ( $ {\textrm {M}}^{2}{\textrm {A}}^{2}\textrm {RC} $ ) algorithm is proposed by imposing a derivative constraint on the direction of beam axis. Representative numerical examples are provided to demonstrate the effectiveness of the proposed $ {\textrm {MA}}^{2}\textrm {RC} $ and $ {\textrm {M}}^{2}{\textrm {A}}^{2}\textrm {RC} $ algorithms for multipoint responses control and pattern synthesis.

Robust adaptive beamforming against large DOA mismatch with linear phase and magnitude constraints for multiple‐input–multiple‐output radar

In this study, a robust adaptive beamformer against large direction-of-arrival (DOA) mismatch for multiple-input–multiple-output radar is proposed with linear phase and magnitude constraints on main lobe. First, the full-dimensional weight vector (WV) is expressed as the Kronecker product of the transmit and receive array WVs based on the WV separable principle. For the transmit array WV, the authors find an interesting property that the Fourier spectrum of its conjugate inverse arrangement is equal to its array response function within a phase factor. This property also exists in the receive array WV. Using this property, the phase response of the transmit and receive array, respectively, is set to be linear based on designing a finite impulse response filter. Then, a bi-quadratic cost function with respect to the transmit and receive WVs is established by only constraining the real magnitude response and it is effectively solved by the bi-iterative algorithm. The proposed beamformer has lower computational complexity and faster sample convergence rate, compared with the traditional magnitude response constraints beamformers with full degrees of freedom. Moreover, it can provide good robustness against large DOA mismatch. Numerical experiments are provided to demonstrate the effectiveness of the proposal.

The analysis of methods for determining direction of arrival of signals in problems of space-time access

The analysis of methods for estimation of the signals direction of arrival based on the analysis of the directional characteristics of the antenna array according to the criterion of maximum and minimum level of the incoming signal is conducted. It is shown that the minimum methods are more accurate in comparison to the maximum methods. Considering the direct functional connection of the amplitude-amplitude-phase distribution of signals over the array elements with the value of signals direction of arrival, the technique allowing estimation of the field distribution vector together with an estimate of the array weight vector, which showed the computational complexity of the procedure, is presented. A number of superresolution techniques have been analyzed. The results of methods modeling with numerical estimates of resolution have shown that the resolution of these methods allows their implementation in the problems of space-time access under strictly limited conditions. The analysis of the signal arrival estimation algorithm using the sum-differential directional pattern with the definition of the direction finding by means of the equisignal zone is conducted. It is shown that this method seems to be one of the most constructive and applicable to the problems of space-time access.

Robust and fast beamforming with magnitude response constraints for multiple‐input multiple‐output radar

In this study, a new robust and fast beamformer is developed for multiple-input multiple-output radar to improve the robustness against steering vector (SV) mismatches. A convex robust model with magnitude response constraints (MRC) is established by using the conjugate symmetry characteristic of the transmitted–received SV. To reduce the computational complexity and the number of samples required, the full-dimensional weight vector (WV) is expressed as the Kronecker product of the transmitted and received array WVs. Thus, the convex problem is converted into a bi-quadratic cost function and it is solved by combining the bi-iterative algorithm and convex quadratic program. The proposed beamformer can flexibly control the beamwidth of the robust region and achieve high output signal-to-interference-plus-noise ratio. Moreover, the proposed method has lower computational complexity and faster sample convergence rate as compared with the traditional MRC-iterative second-order cone programming and MRC-semi-definite programming beamformers. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed beamformer.

Digital Signal Processor-Based Broad Null Beamforming for Interference Reduction

Shaping the radiation pattern of an antenna array to null the reception (or radiation in the case of transmitting antenna) in the direction of undesired interferences has become essential in the environment of electromagnetic interferences. This paper proposes a digital signal processor-based method using space-selective digital filter with Blackman window to nullify the broad interferences of a linear array along with its implementation. Convolution between array weight vector and filter coefficients of digital filter is performed to obtain the desired beam pattern. The cutoff points of the filter and hence the array weight vector are updated adaptively so as to obtain the desired attenuation in the vicinity $$(\pm \Delta \varphi _{\mathrm{i}})$$(±Δ?i) of mean broad interfering direction $$(\varphi _{\mathrm{i}})$$(?i). The even symmetry of the modified weight vector about its center is utilized to minimize the computational burden. The proposed model offers advantages such as more than 80-dB attenuation to broad interferences and lesser computational time with respect to conventional processor. Numerical results are presented to justify the performance of the proposed method for nullifying the interferences that are arriving over a nulling range between $$[\varphi _{\mathrm{i}}-\Delta \varphi _{\mathrm{i}}]$$[?i-Δ?i] and $$[\varphi _{\mathrm{i}}+\Delta \varphi _{\mathrm{i}}]$$[?i+Δ?i]. The vicinity $$(\pm \Delta \varphi _{\mathrm{i}})$$(±Δ?i) considered in the proposed model varies between $$1^{\circ }$$1? and $$8^{\circ }$$8?. Exhaustive performance analysis is also provided with different directions of arrivals and desired attenuations for effective suppression of interference.

Robust Blind Algorithm based on Oblique Projection and Worst-Case Optimization

When adaptive arrays are applied to practical systems, the performance of the convention constant modulus algorithm degrades severely in the presence of array steering vector errors. The similar situation of performance degradation can occur even when the array steering vector is known exactly, but the training sample size is sm all. In this paper, we propose a novel doubly constrained robust constant modulus algorithm based on the worst case performance optimization and oblique projection technique. The proposed algorithm uses explicit modeling of uncertainties in the desired signal array response and in data snapshots, which provides sufficiently robustness to uncertainty in source DOA, and makes the mean output array SINR consistently close to the optimal one. The array weight vector is derived iteratively by the Lagrange multiplier approach and descent gradient technique, in which the factors can be precisely obtained at each step. A theoretical analysis for our propose d algorithm in terms of the optimal step size, convergence and array output SINR performance is presented in this paper. As compared with the linearly constrained constant modulus algorithm, our proposed robust constant modulus algorithm resolves the interference capture problem, has faster convergence speed, and enhances the array output performance under practical situations. Computer simulation results are presented to show the superiority of our proposed algorithm on output SINR enhancement and signal sampling resolution.

Striation-based beamforming for active sonar with a horizontal line array

A physics-based method for beamforming signals measured on a horizontal array is developed with an application to underwater active sonar systems. The proposed striation-based beamformer coherently combines the pressure from each element in the array at different frequencies, and these frequencies are selected based on a striation hypothesis. The linear frequency shift and corresponding phase term introduced in the array weight vector accounts for multipath-induced fading, producing beam output with increased signal gain. The method is demonstrated using data collected on an array towed in the North Atlantic. The combination of the striation-based beamformer with the waveguide invariant concept to improve tracker performance is discussed.

Robust Minimum Sidelobe Beamforming for Spherical Microphone Arrays

A robust minimum sidelobe beamforming approach based on the spherical harmonics framework for spherical microphone arrays is proposed. It minimizes the peaks of sidelobes while keeping the distortionless response in the look direction and maintaining the mainlobe width. A white noise gain constraint is also derived and employed to improve the robustness against array errors. The resulting beamformer can provide optimal tradeoff between the sidelobe level, the beamwidth and robustness, so it could be more practical than the existing spherical array Dolph-Chebyshev modal beamformer in the presence of array errors. The optimal modal beamforming problem is formulated as a tractable convex second-order cone programming program, which is more efficient than conventional element-space based approaches, since the dimension of array weight vectors can be significantly decreased by using the properties of spherical harmonics and Legendre polynomials. For the purpose of performance comparison, we also formulate current robust modal beamformers as equivalent optimization problems based on the proposed array model. Numerical results show the high flexibility and efficiency of the proposed beamforming approach.

A Novel Adaptive Beamformer Based on Semidefinite Programming (SDP) With Magnitude Response Constraints

A novel robust adaptive beamformer, formulated as a semidefinite programming (SDP) problem, is proposed in this paper. With new constraints on the magnitude response, the beamwidth and response ripple of the robust response region can be well controlled. Moreover, only a small part of these inequality constraints on the magnitude response are active during optimization so that few degrees of freedom (DOFs) of the adaptive beamformer are consumed. Consequently, the resultant beamformer has significant improvement on signal-to-interference-plus-noise ratio (SINR). An important problem in the proposed beamformer is how to generate the array weight vector from the optimal semidefinite matrix. In this paper, a method utilizing the extended spectral factorization method is proposed to solve this problem. Simple implementation, flexible performance control as well as significant SINR enhancement support the practicability of the proposed method.

A Study of Timing Control and Array Weight Error Effects in the Antenna Array Aided Uplink Synchronous DS-CDMA System

We investigate the effects of timing misalignment and imperfect array weight vector generation on the antenna array (AA)-aided uplink synchronous DS-CDMA system. Previous works have assumed perfect uplink synchronization among first path's receiving timing and perfect array weight vector calculation. Unfortunately, practical system will experience of timing control error (TCE) and array weight error (AWE). Accordingly, this letter undertakes an analysis of the impacts of TCE and AWE, evaluating a closed form BER performance considering the important factors such as the number of antennas, the variance of AWE and the misalignment factor as a measure of the TCE in dispersive Rayleigh multi-path fading channel. Additionally, the scenario of synchronous uplink with the cell-site AA is compared with asynchronous scheme. Numerical results show that the performance in the synchronous uplink can be further improved, even at high levels of AWE and TCE.

Joint transmitter receiver diversity for efficient space division multiaccess

The beamforming problem is studied in wireless networks where both the transmitters and receivers have linear adaptive antenna arrays. Algorithms are proposed that find the antenna array weight vectors at both the transmitters and receivers as well as the transmitter powers with one of the following two objectives: (1) to maximize the minimum signal-to-interference-and-noise ratio (SINR) over all receivers and (2) to minimize the sum of the total transmitted power satisfying the SINR requirements at all links. A numerical study is performed to compare the network capacity and the power consumption among systems having a different number of antenna array elements in a code division multiple access network.

Deep-water acoustic coherence at long ranges: theoretical prediction and effects on large-array signal processing

This paper presents results of combined consideration of sound coherence and array signal processing in long-range deep-water environments. Theoretical evaluation of the acoustic signal mutual coherence function (MCF) of space for a given sound-speed profile and particular scattering mechanism is provided. The predictions of the MCF are employed as input data to investigate the coherence-induced effects on the horizontal and vertical array gains associated with linear and quadratic beamformers with emphasis on the optimal ones. A method of the radiation transport equation is developed to calculate the MCF of the multimode signal under the assumption that internal waves or surface wind waves are the main source of long-range acoustic fluctuations in a deep-water channel. Basic formulations of the array weight vectors and small signal deflection are then exploited to examine optimal linear and quadratic processors in comparison with plane-wave beamformers. For vertical arrays, particular attention is paid also to evaluation of the ambient modal noise factor. The numerical simulations are carried out for range-independent environments from the Northwest Pacific for a sound frequency of 250 Hz and distances up to 1000 km. It was shown distinctly that both signal coherence degradation and modal noise affect large-array gain, and these effects are substantially dependent on the processing technique used. Rough surface sound scattering was determined to cause the most significant effects.

Recursive algorithm for adaptive arrays and systolic array implementation

In this paper, a new recursive algorithm of adaptive array weight vectors and its systolic array implementing structure is proposed, which is based on the QR decomposition algorithms and the idea of algorithmic engineering. The algorithm can realize fully parallel and pipeline processing.

Improvement of coupling corrected difference beams in small phased arrays

The corrupting effects of mutual coupling between radiating elements of small phased arrays means that conventional aperture weighting schemes (Taylor, Chebyshev etc.) cannot be applied to small phased array antennas to form low sidelobe sum and difference beams. The corrupting effects of mutual coupling can be removed by the determination of an inverted coupling matrix. This description of the couplings is not perfect. The imperfect coupling matrix description means the synthesised beams are degraded, particularly difference beams where a deep look direction null is an important characteristic of the beam. The results of applying an adaptive algorithm to the coupling corrected array weight vector in order to enhance difference beam nulls is presented.