Ching-Yih Tseng

A simple algorithm to achieve desired patterns for arbitrary arrays

A simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented. The method can be applied to nonuniform array geometries in which the individual elements have arbitrary (and differing) radiation patterns. The method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification. Computation of each successive pattern is based on the solution of a linearly constrained least-squares problem. The constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values. Phase values for the sidelobes do not change during this process, and problems associated with choosing a specific phase value are therefore avoided. Experimental evidence suggests that the procedure terminates in remarkably few iterations, even for arrays with significant numbers of elements. >

A unified approach to the design of linear constraints in minimum variance adaptive beamformers

A simple, systematic procedure for designing linear constraints in minimum-variance beamformers which allows an arbitrary specification of the quiescent response (the beamformer response when only white noise is present) is described. In this approach, the first constraint is dedicated to the imposition of a desired quiescent response, and additional constraints are included to assure proper reception of the desired signal. These additional constraints make the overall beamformer response equal to the quiescent response in the desired signal region so that the signal is not cancelled when it is present. Optionally, the response can be fixed in other regions of interest by adding more constraints. This design procedure demonstrates that the key to designing efficient constraints is finding the weighting coefficients which specify the desired quiescent response, a problem identical to the synthesis of desired beam patterns for nonadaptive arrays. The effectiveness of the procedure is illustrated by examples in both narrowband and broadband arrays. >

Minimum variance beamforming with phase-independent derivative constraints

A set of first- and second-order derivative constraints that can be used in minimum variance beamformers to achieve flat main beam response is presented. Efficient algorithms are derived for the implementation of these constraints. In contrast to conventional derivative constraint methods which constrain both the magnitude (power) and phase responses of the beamformer, the method only constrains the magnitude response. The unnecessary constraint on the phase is a major drawback to the conventional methods since it causes the beamformer performance to vary with the particular spatial reference point used to define the array element positions. This phenomenon is clearly undesirable because the choice of a reference point is generally made for notational convenience. As a direct sequence of the phase constraint, an inappropriately chosen reference point can easily result in a beamformer response which has undesirably high sidelobes. The problem is avoided through the use of phase-independent derivative constraints. >

Steering vector estimation in uncalibrated arrays

This paper presents an iterative algorithm for estimating the signal steering vectors and associated power levels received by an array of uncalibrated isotropic sensors. The inputs are assumed to consist of narrowband, uncorrelated directional signals in the presence of additive white noise. An iterative algorithm is employed to successively search for estimates that simultaneously satisfy a signal subspace and an orthogonality condition. These conditions are shown to be both necessary and sufficient for identification of the underlying steering vectors in the case when the data covariance matrix is known exactly, i.e. for the case of infinite data observation. The iterative method employs minimum distance criterion (projections) to successively map the solution between three constraint sets until a stable point is determined. Two examples are presented which illustrate the application of the algorithm in direction finding and beamforming. >

A Systematic Procedure For Implementing The Blocking Matrix In Decomposed Form

The Generalized Sidelobe Canceller (GSC) is an important beam- forming structure for implementing adaptive linearly constrained beamformers. A significant feature of the GSC is that it effi- ciently eliminates the constraints such that the weights can be updated unconstrainedly in a reduce-dimensional space. The elimination of constraints is achieved by specifying a blocking matrix whose columns form a basis orthogonal to the constraints. For a given linearly-constrained minimization problem, the specification of the blocking matrix is not unique. However, the com- putational complexity of GSC depends entirely on the detailed composition of the blocking matrix. This paper presents a systematic procedure to construct the blocking matrix with effective implementation structure.

Are equiripple digital FIR filters always optimal with minimax error criterion

For exact linear phase digital finite impulse response (FIR) filters, it is well known that a filter with equiripple error function must be optimal with the minimax (Chebyshev) error criterion. The present letter points out that such analogy is not true for FIR filters which approximate arbitrarily specified magnitude and phase responses.<<ETX>>

Estimation of signal steering vectors in uncalibrated arrays

This paper considers the problem of extracting the signal powers and steering vectors from the signal covariance matrix without the knowledge of array manifold. Under the assumption of narrowband and uncorrelated signals, it is shown that it is necessary and sufficient for the signal powers and steering vectors to satisfy two conditions, termed the signal subspace and orthogonality conditions, in order for them to match the signal covariance matrix asymptotically. Based upon these two conditions, an algorithm is derived to iteratively search for the signal powers and steering vectors which closely match the signal covariance matrix estimated from the observed data. A real-data example is presented to illustrate the robustness of the proposed algorithm.<<ETX>>

A Novel Approach for Designing Linear Constraints in Adaptive Arrays

This paper describes an approach for designing linear constraints in adaptive arrays which allows arbitrary specification of the quiescent response (the array response when only white noise is present). The first step of this approach is to use available pattern synthesis techniques for determining weights which result in a desired quiescent pattern. A set of linear constraints is then derived which, when the array operates in the adaptive mode, produces this quiescent response and also prevents signals of interest from being cancelled. This design method also suggests that the key to designing linear constraints in adaptive arrays lies in developing efficient algorithms to achieve well-behaved array responses for nonadaptive arrays.

A note on the derivative constraints for minimum variance beamforming

A novel set of first and second order derivative constraints is presented which can be used in minimum variance beamformers to achieve flat main beam responses. In contrast to other derivative constraint methods which constrain both the magnitude and phase responses of the beamformer, the method only constrains the magnitude response. The constraint on the phase is shown to be the reason that the conventional magnitude-phase derivative constraint methods are sensitive to the location of the spatial reference point used to define the array element positions. This problem, which is a major drawback of the conventional methods, is eliminated in the new approach. A simulation example which illustrates the superiority of the approach is given.<<ETX>>

A Unification and Comparison of Several Adaptive Linearly-Constrained Beamformer Structures

In this paper, a unified implementation model for adaptive linearly-constrained beamformers is presented and several implementation structures which employ this model are compared. It is shown that adaptive linearly-constrained beamformers can be implemented efficiently using matrix decompoition methods.