Frequency invariant MVDR beamforming without filters and implementation using MIMO radar

Frequency invariant beamforming with sensor arrays is generally achieved using filters in the form of tapped delay-lines following each sensor. However it has been recently shown that with the help of the rectangular smart antenna array, it is possible to generate frequency invariant beampattern without using filters. In this paper, this frequency invariant beamforming technique is utilized to perform MVDR beamforming in the beamspace by designing frequency invariant beams spanning the desired range of azimuthal angles and optimally combining them. However, the performance of the frequency invariant beamformer depends on the number of sensors which could be large for a rectangular array of size M × N. Making use of the virtual array concept used in MIMO radar, a novel method of producing the same frequency invariant beam, using only M transmitting and N receiving antennas, is proposed and a design example is provided to demonstrate the idea

Adaptive beamforming using frequency invariant uniform concentric circular arrays

This paper proposes new adaptive beamforming algorithms for a class of uniform concentric circular arrays (UCCAs) having near-frequency invariant characteristics. The basic principle of the UCCA frequency invariant beamformer (FIB) is to transform the received signals to the phase mode representation and remove the frequency dependence of individual phase modes through the use of a digital beamforming or compensation network. As a result, the far field pattern of the array is electronic steerable and is approximately invariant over a wider range of frequencies than the uniform circular arrays (UCAs). The beampattern is governed by a small set of variable beamformer weights. Based on the minimum variance distortionless response (MVDR) and generalized sidelobe canceller (GSC) methods, new recursive adaptive beamforming algorithms for UCCA-FIB are proposed. In addition, robust versions of these adaptive beamforming algorithms for mitigating direction-of-arrival (DOA) and sensor position errors are developed. Simulation results show that the proposed adaptive UCCA-FIBs converge much faster and reach a considerable lower steady-state error than conventional broadband UCCA beamformers without using the compensation network. Since fewer variable multipliers are required in the proposed algorithms, it also leads to lower arithmetic complexity and faster tracking performance than conventional methods. © 2007 IEEE.published_or_final_versio

Efficient frequency invariant beamforming using virtual arrays

In wideband array processing, frequency invariant beamforming provides a popular means to make the beampattern allpass with respect to frequency. Traditionally, such beampatterns are realized as a two dimensional filter, using tapped delay-line (TDL) filters following each spatial sensor. However it has been recently shown that with the help of a rectangular antenna array, it is possible to generate fixed frequency invariant beampatterns without using filters. In this paper, this concept is generalized to the case of two dimensional arrays with elements on a (possibly nonseparable) lattice. Since performance of the frequency invariant beamformer depends on the number of sensors which could be large for a 2D array of size M × N, a novel approach to beamforming based on the difference co-array of a physical array is also proposed, which avoids use of additional physical sensors. The realization of the frequency invariant beams using second order statistics of the impinging signal with only M + N physical sensors, instead of the two dimensional array of size M×N, is demonstrated. The usefulness of the proposed method is verified through computer simulation

Adaptive beamforming using uniform concentric circular arrays with frequency invariant characteristics

This paper proposes a new method for adaptive beamforming using uniform concentric circular array (UCCA) that has nearly frequency invariant (FI) characteristics. The basic principle of FI UCCA is to transform the received signals to the phase mode and compensate for the frequency dependency of the individual phase mode through the use of a digital beamforming network. The far field pattern of the array is then determined by a set of weights and it is approximately invariant over a wide range of frequencies. Therefore, the minimum variance beamforming (MVB) approach can be used to adapt the small set of weights, as if it is a narrowband array, Design examples and simulation are given to demonstrate the usefulness of the proposed FI UCCA in broadband DOA estimation and beamforming. © 2005 IEEE.published_or_final_versio

Wideband data-independent beamforming for subarrays

The desire to operate large antenna arrays for e.g. RADAR applications over a wider frequency range is currently limited by the hardware, which due to weight, cost and size only permits complex multipliers behind each element. In contrast, wideband processing would have to rely on tap delay lines enabling digital filters for every element.As an intermediate step, in this thesis we consider a design where elements are grouped into subarrays, within which elements are still individually controlled by narrowband complex weights, but where each subarray output is given a tap delay line or finite impulse response digital filter for further wideband processing. Firstly, this thesis explores how a tap delay line attached to every subarray can be designed as a delay-and-sum beamformer. This filter is set to realised a fractional delay design based on a windowed sinc function. At the element level, we show that designing a narrowband beam w.r.t. a centre frequency of wideband operation is suboptimal,and suggest an optimisation technique that can yield sufficiently accurate gain over a frequency band of interest for an arbitrary look direction, which however comes at the cost of reduced aperture efficiency, as well as significantly increased sidelobes. We also suggest an adaptive method to enhance the frequency characteristic of a partial wideband array design, by utilising subarrays pointing in different directions in different frequency bands - resolved by means of a filter bank - to adaptively suppress undesired components in the beam patterns of the subarrays. Finally, the thesis proposes a novel array design approach obtained by rotational tiling of subarrays such that the overall array aperture is densely constructed from the same geometric subarray by rotation and translation only. Since the grating lobes of differently oriented subarrays do not necessarily align, an effective grating lobe attenuation w.r.t. the main beam is achieved. Based on a review of findings from geometry,a number of designs are highlight and transformed into numerical examples, and the theoretically expected grating lobe suppression is compared to uniformly spaced arrays.Supported by a number of models and simulations, the thesis thus suggests various numerical and hardware design techniques, mainly the addition of tap-delay-line per subarray and some added processing overhead, that can help to construct a large partial wideband array close in wideband performance to currently existing hardware.The desire to operate large antenna arrays for e.g. RADAR applications over a wider frequency range is currently limited by the hardware, which due to weight, cost and size only permits complex multipliers behind each element. In contrast, wideband processing would have to rely on tap delay lines enabling digital filters for every element.As an intermediate step, in this thesis we consider a design where elements are grouped into subarrays, within which elements are still individually controlled by narrowband complex weights, but where each subarray output is given a tap delay line or finite impulse response digital filter for further wideband processing. Firstly, this thesis explores how a tap delay line attached to every subarray can be designed as a delay-and-sum beamformer. This filter is set to realised a fractional delay design based on a windowed sinc function. At the element level, we show that designing a narrowband beam w.r.t. a centre frequency of wideband operation is suboptimal,and suggest an optimisation technique that can yield sufficiently accurate gain over a frequency band of interest for an arbitrary look direction, which however comes at the cost of reduced aperture efficiency, as well as significantly increased sidelobes. We also suggest an adaptive method to enhance the frequency characteristic of a partial wideband array design, by utilising subarrays pointing in different directions in different frequency bands - resolved by means of a filter bank - to adaptively suppress undesired components in the beam patterns of the subarrays. Finally, the thesis proposes a novel array design approach obtained by rotational tiling of subarrays such that the overall array aperture is densely constructed from the same geometric subarray by rotation and translation only. Since the grating lobes of differently oriented subarrays do not necessarily align, an effective grating lobe attenuation w.r.t. the main beam is achieved. Based on a review of findings from geometry,a number of designs are highlight and transformed into numerical examples, and the theoretically expected grating lobe suppression is compared to uniformly spaced arrays.Supported by a number of models and simulations, the thesis thus suggests various numerical and hardware design techniques, mainly the addition of tap-delay-line per subarray and some added processing overhead, that can help to construct a large partial wideband array close in wideband performance to currently existing hardware

Theory and design of uniform concentric spherical arrays with frequency invariant characteristics

IEEE International Conference on Acoustics, Speech and Signal Processing, Toulouse, France, 14-19 May 2006This paper proposes a new digital beamformer for uniform concentric spherical array (UCSA) having nearly frequency invariant (FI) characteristics. The basic principle is to transform the received signals to the phase mode and remove the frequency dependency of the individual phase mode through the use of a digital beamforming network. It is shown that the far field pattern of the array is determined by a set of weights and it is approximately invariant over a wide range of frequencies. FI UCSAs are electronic steerable in both the azimuth angle and elevation angle, unlike their concentric circular array counterpart. A design example is given to demonstrate the design and performance of the proposed FI UCSA. © 2006 IEEE.published_or_final_versio

Theory and design of uniform concentric circular arrays with frequency invariant characteristics

This paper proposes a new digital beamformer for uniform concentric circular array (UCCA) having nearly frequency invariant (FI) characteristics. The basic principle is to transform the received signals to the phase mode and remove the frequency dependency of the individual phase mode through the use of a digital beamforming network. The far field pattern of the array is determined by a set of weights and it is approximately invariant over a wide range of frequencies. Compared with FI uniform circular array (UCA), FI UCCAs are able to achieve a wider bandwidth. Design examples are given to demonstrate the principle of the proposed UCCA-FIB and its application to broadband DOA estimation of coherent sources. © 2005 IEEE.published_or_final_versio

Sparse Array Design for Wideband Beamforming with Reduced Complexity in Tapped Delay-lines

Sparse wideband array design for sensor location optimization is highly nonlinear and it is traditionally solved by genetic algorithms (GAs) or other similar optimization methods. This is an extremely time-consuming process and an optimum solution is not always guaranteed. In this work, this problem is studied from the viewpoint of compressive sensing (CS). Although there have been CS-based methods proposed for the design of sparse narrowband arrays, its extension to the wideband case is not straightforward, as there are multiple coefficients associated with each sensor and they have to be simultaneously minimized in order to discard the corresponding sensor locations. At first, sensor location optimization for both general wideband beamforming and frequency invariant beamforming is considered. Then, sparsity in the tapped delay-line (TDL) coefficients associated with each sensor is considered in order to reduce the implementation complexity of each TDL. Finally, design of robust wideband arrays against norm-bounded steering vector errors is addressed. Design examples are provided to verify the effectiveness of the proposed methods, with comparisons drawn with a GA-based design method

Frequency invariant uniform concentric circular arrays with directional elements

A new approach for designing frequency invariant (FI) uniform concentric circular arrays (UCCAs) with directional elements is proposed, and their applications to direction-of-arrival (DOA) estimation and adaptive beamforming are studied. By treating the sensors along the radial direction of the UCCA as linear subarrays and using appropriately designed beamformers, each subarray is transformed to a virtual element with appropriate directivity. Consequently, the whole UCCA can be viewed as a virtual uniform circular array (UCA) with desired element directivity for broadband processing. By extending the approach for designing FI-UCAs, the frequency dependency of the phase modes of the virtual UCA is compensated to facilitate broadband DOA and adaptive beamforming. Both the linear array beamformers (LABFs) and compensation filters can be designed separately using second- order cone programming (SOCP). Moreover, a new method to tackle the possible noise amplification problem in such large arrays by imposing additional norm constraints on the design of the compensation filters is proposed. The advantages of this decoupled approach are 1) the complicated design problem of large UCCAs can be decoupled into simpler problems of designing the LABFs and compensation filters, and 2) directional elements, which are frequently encountered, can be treated readily under the proposed framework. Numerical examples are provided to demonstrate the effectiveness and improvement of the proposed methods in DOA estimation, adaptive beamforming, and elevation control over the conventional FI-UCCA design method.published_or_final_versio

Wideband 2-Dimensional scanning planar subarray

Achieving frequency invariance in antenna array requires linear-phase system to maintain frequency independent time lag. For example True Time Delay or tapped delay line. In this paper, the array elements are divided into subarrays. Then all subarrays are steered towards the desired azimuth direction, while the wideband property is preserved by exploiting the subarray two-dimensional structure as a sensor delay line. Each subarray pattern is then individually rotated around the desired elevation direction. Eventually superposition of subarrays is maximally constructive towards the desired direction and partially constructive or destructive everywhere else. Two frequency invariant beamformers are used. These are inverse DFT and Least squares. Results are compared with wideband wideband one-dimensional pattern syntheses of the same design methods in power concentration