Frequency-invariant Pattern Research Articles

Synthesis of Wideband Frequency-Invariant Beam Patterns for Nonuniformly Spaced Arrays by Generalized Alternating Projection Approach

This work generalizes the alternating projection approach (APA) to synthesize wideband frequency-invariant (FI) beam patterns for linear nonuniformly spaced arrays (NUSAs). Different from the conventional APA where excitation weights are synthesized for a desired pattern at single frequency, the generalized APA intends to find appropriate finite-impulse response (FIR) filter coefficients for each antenna element to provide the required wideband frequency-dependent excitation for a desired wideband FI pattern, and two modification techniques called mainlobe FI modification and wideband sidelobe control are introduced in each iteration to successively update the FI pattern performance. Several examples for synthesizing wideband FI beam patterns for NUSAs in different applications are conducted to verify the effectiveness and advantages of the proposed generalized APA.

Efficient Synthesis of Filter-and-Sum Array With Scanned Wideband Frequency-Invariant Beam Pattern and Space-Frequency Notching

This work generalizes the Fourier transform (FT)-based frequency-invariant beamforming (FIB) method to the synthesis of scanned frequency-invariant (FI) beam pattern with space-frequency notching for an array with non-isotropic elements. Wideband FI pattern characteristics are described by using multiple reference sub-band FI patterns. By applying fast Fourier transform (FFT) on the combination of these multiple reference sub-band FI patterns, a wideband excitation distribution can be generated. Based on this excitation distribution, we construct a new wideband excitation distribution that is conjugate-symmetric about zero frequency, so that real-valued finite-impulse-response (FIR) filter coefficients can be obtained by applying FFT on the constructed distribution. Two numerical examples are introduced to show the effectiveness and efficiency of the proposed method.

Efficient and Accurate Frequency-Invariant Beam Pattern Synthesis Utilizing Iterative Spatiotemporal Fourier Transform

An iterative spatiotemporal Fourier transform (STFT) method is presented to efficiently design finite-impulse-response (FIR) filter coefficients for generating a desired frequency-invariant (FI) beam pattern of an antenna array. In this method, by introducing the concepts of normalized temporal angular frequency and spatial angular frequency, the broadband pattern is treated as a spatiotemporal spectral distribution. The relationship between the FIR coefficient distribution and the spatiotemporal spectral distribution can be built as an STFT, and consequently the 2-D fast Fourier transform (2D-FFT) and inverse 2D-FFT (2D-IFFT) can be utilized to efficiently accomplish the transformation between the FIR coefficient distribution and the spatiotemporal spectral distribution. Thus, the proposed synthesis method starts from an initial spatiotemporal spectral distribution and then adopt an iterative modification-and-transformation strategy to successively update the obtained spatiotemporal spectral distribution and the corresponding FIR coefficients. Two kinds of pattern modification techniques including the mainlobe FI modification and broadband sidelobe control are adopted in each iteration. Several examples for synthesizing different FI patterns are conducted. Synthesis results show that the proposed method can obtain much better FI pattern performance in terms of both mainlobe FI property and sidelobe control than the original FT method whilst costing less CPU time than the convex optimization method especially for the case of large FI arrays.

Reducing the Number of Elements in the Synthesis of a Broadband Linear Array With Multiple Simultaneous Frequency-Invariant Beam Patterns

The problem of reducing the number of elements in a broadband linear array with multiple simultaneous crossover frequency-invariant (FI) patterns is considered. Different from the single FI pattern array case, every element channel in the multiple FI pattern array is divided and followed by multiple finite-impulse-response (FIR) filters, and each of the multiple FIR filters has a set of coefficients. In this situation, a collective filter coefficient vector and its energy bound are introduced for each element, and then the problem of reducing the number of elements is transformed as minimizing the number of active collective filter coefficient vectors. In addition, the radiation characteristics including beam pointing direction, mainlobe FI property, sidelobe level, and space-frequency notching requirement for each of the multiple patterns can be formulated as multiple convex constraints. The whole synthesis method is implemented by performing an iterative second-order cone programming (SOCP). This method can be considered as a significant extension of the original SOCP for synthesizing broadband sparse array with single FI pattern. Numerical synthesis results show that the proposed method by synthesizing multiple discretized crossover FI patterns can save more elements than the original iterative SOCP by using a single continuously scannable FI pattern for covering the same space range. Moreover, even for multiple FI-patterns case with complicated space-frequency notching, the proposed method is still effective in the reduction of the number of elements.

Efficient unitary matrix pencil method for synthesising wideband frequency patterns of sparse linear arrays

A novel technique incorporating the unitary matrix pencil (UMP) method is extended to the case of sparse linear arrays with wideband frequency invariant (FI) patterns. Multiple pattern data at different frequencies are formulated with the same poles corresponding to the FI element positions by a new sampling strategy. The unitary transform converts the complex computations for block Hankel matrices into real ones, which contributes to the reduction of the computation complexity for the singular value decomposition and the eigenvalue decomposition procedures. Taking advantage of the equivalent matrix pencil obtained by the unitary transformation, a new relation between the element positions and generalised eigenvalues can be built by the UMP method, which contributes to the real solutions for all element positions win wideband. A new tactics is exploited to avoid small element spacing with the consideration of the size of array antennas. Multiple FI patterns are reconstructed with a higher matching accuracy by only varying the excitation distributions. A set of representative numerical examples demonstrate the efficiency and advantages of the proposed method.

Quantum Particle Swarm Optimization for Synthesis of Non-uniformly Spaced Linear Arrays with Broadband Frequency Invariant Pattern

This paper describes a method using Quantum Particle Swarm Optimization to obtain a broadband frequency invariant pattern for synthesis of nonuniformly spaced linear array of isotropic antennas. Two cases related to this work using QPSO have been studied, namely, in the first case, the generated frequency invariant far-field pattern is broadside in the vertical plane and in the second case, the far-field frequency invariant pattern is scanned in a particular direction. An effort is made such that the side lobe level and first null beam widths of the patterns are made similar to their related desired values. The two cases are presented in this paper to show the effectiveness of the proposed method in achieving the desired specifications. Even though, the developed method is utilized here for a linear array of isotropic antennas; it can be extended to other type of arrays.

Synthesis of Sparse Arrays With Frequency-Invariant-Focused Beam Patterns Under Accurate Sidelobe Control by Iterative Second-Order Cone Programming

It is shown in this communication that the problem of synthesizing a frequency-invariant (FI) beam pattern with as few elements as possible can be transformed into a sequence of weighted $\ell_1$ optimizations under multiple convex constraints. The objective of the weighted $\ell_1$ optimization is to minimize the number of radiating elements. For the filter-and-sum beamforming structure, this is equivalent to minimizing the number of filters, each with a set of optimized coefficients. The multiple constraints are adopted to individually control the mainlobe and sidelobe pattern characteristics, so as to preserve the FI property in the mainlobe region while satisfying a given upper bound in the sidelobe region. The WNG constraint can also be incorporated into the proposed method to enhance the synthesis robustness. This method can be easily implemented by iterative second-order cone programming (SOCP), and only few iterations are required to reach the convergence. A set of examples for the synthesis of FI patterns with uniform sidelobe level (SLL) or multiple nulls, scannable FI patterns, and the synthesis of FI pattern for an arc array with directive elements, is presented to validate the effectiveness and advantages of the proposed method. The element saving is about 23.3%–50% for the test cases.

Synthesis of Nonuniformly Spaced Linear Arrays With Frequency-Invariant Patterns by the Generalized Matrix Pencil Methods

This work extends the matrix pencil method (MPM)-based synthesis technique to the case of nonuniformly spaced linear arrays with wideband frequency-invariant (FI) patterns. A new sampling strategy is proposed to obtain multiple pattern data of different frequencies having the same poles that correspond to the FI element positions. The obtained multiple pattern sequences have the same shape for the FI pattern requirement, but with different lengths. The generalized MPM (GMPM) and its forward-backward version (GFBMPM) are developed to estimate the best common element positions for different frequencies, which can significantly reduce the number of elements required for the specified wideband pattern shape. The element excitations are solved by the regularized least-square (LS) method at each frequency. Then, an efficient method by utilizing the FFT is presented to obtain real-coefficient finite-impulse-response (FIR) filters for implementing the frequency-varying excitations. A set of numerical examples for the FI synthesis of pencil-beams, shaped patterns, scannable patterns, and Taylor patterns with low SLLs are presented to validate the effectiveness and advantages of the proposed methods. The element saving is about 11.2%-49.4% for usual cases.

Stochastic and Analytic Optimization of Sparse Aperiodic Arrays and Broadband Beamformers With Robust Superdirective Patterns

This paper addresses the spatial processing of signals collected by a linear array of sensors that feeds a filter-and-sum, data-independent beamformer. When the frequency band spanned by the signals to be processed is extremely wide, a given array can be shorter than the wavelength (at the lowest frequencies) and, at the same time, too scarcely populated for a correct sampling of the wavefield (at the highest frequencies). Superdirectivity and aperiodic sparse layouts are possible solutions to these two problems. However, these two solutions have never been considered jointly to achieve a broadband beam pattern with a desired profile. Through a mixed stochastic and analytic optimization, a method is proposed herein that synthesizes a sparse array layout and the tap coefficients of the beamformer filters to provide a broadband beam pattern that is superdirective and robust against the fluctuation of the sensors' characteristics, which is free from any grating lobes and possesses a controlled side-lobe level. Different types of beam patterns, from the frequency-invariant pattern to the maximum-directivity pattern, can be obtained and the synthesized solutions retain their validity for any steering direction inside a given interval. The functioning of the method is proven by considering a microphone array with four different design targets and by discussing the performance and the robustness of the synthesized solutions.

Frequency-invariant pattern synthesis of conformal array antenna with low cross-polarisation

Despite their potential and promising advantages over classical planar arrays, conformal arrays also present many challenges to the antenna designer, including varying element normal due to curvature, serious cross-polarisation effect, limited operational bandwidth and so on. A uniform method for the element polarised pattern transformation of arbitrary 3D conformal arrays is presented based on Euler rotation. A space–time-polarisation filter structure is proposed for the pattern synthesis of conformal array, in which the finite impulse response (FIR) filters assigned to every element are used to acquire the frequency-invariant array pattern and the element polarisation diversity in array global coordinates is used to depress the cross-polarisation level. The optimal weight vector is obtained by alternating projection method. The alternating projection method is a powerful and attractive method for the pattern synthesis in that it requires relatively smaller amount of computation burden and a wide variety of desirable constraints can be freely implemented in a ‘visible’ way, which is usually impossible for other optimisation method. The pattern synthesis method proposed has established a unified frame for the frequency-invariant and low cross-polarisation pattern synthesis of conformal array. Simulation results are provided to demonstrate the effectiveness and behaviour of the proposed method.

Optimal design of FIR beamformer with frequency invariant patterns

Two approaches to the optimal design of FIR beamformers with frequency invariant patterns using second-order cone programming (SOCP) are proposed. The first approach is a two-step method, which is implemented via separately optimal array pattern synthesis and optimal FIR filters design. The array weights for each frequency bin within the working frequency band are designed to insure that the array patterns approximate the reference ones. And the FIR filter corresponding to each sensor is designed to insure that the frequency responses approximate the array weights. The second approach is a direct method, in which the beam response is expressed as a linear function of FIR filter tap weights and the filters are designed by jointly optimizing the spatial and frequency responses to achieve the desired array patterns. All the optimal design problems (array pattern synthesis, FIR filter design and joint optimization) are formulated as the SOCP, which can be solved efficiently using the well-developed interior-point methods. Results of computer simulations and lake experiment for a twelve-element semicircular array confirm satisfactory performance of the two approaches proposed in this paper.

Response dynamics of goldfish saccular fibers: effects of stimulus frequency and intensity on fibers with different tuning, sensitivity, and spontaneous activity.

The effects of stimulus frequency and intensity on response patterns (PST histograms) to tone burst stimulation were examined in differently tuned saccular fibers of the goldfish. In addition, the sensitivity of these fibers to amplitude-modulated (AM) signals of different carrier frequencies was measured. The response patterns evoked by unmodulated signals were a complex function of tuning, spontaneous activity and sensitivity of the fiber, and the frequency and intensity of the signal. Frequency-dependent response patterns were found in low-frequency fibers with best frequencies (BF) below 200 Hz. Responses in these fibers ranged from tonic to phasic in nonspontaneous fibers and included more complex patterns in spontaneously active fibers, such as suppression of evoked activity below spontaneous levels. Midfrequency fibers (BF = 500-600 Hz) showed responses similar to those in low-frequency fibers, but with less dependence on frequency. In contrast, both high-frequency (BF = 800-1000 Hz) and wideband, untuned fibers showed frequency-invariant patterns of adaptation. High-frequency fibers were equally sensitive to AM signals at all frequencies tested. The sensitivity of low-frequency fibers to AM, however, increased as a function of carrier frequency and corresponded to the degree of adaptation in response to unmodulated tones. In general, the AM sensitivity of a fiber could be predicted more by its pattern of response to unmodulated signals than by its tuning characteristics.