Time domain and frequency domain concepts which aid in the design and efficient implementation of a digital beamformer have been described at various times in the literature. The numerous beam-former structures that result are discussed with an emphasis on hardware requirements and spectral areas of application. Time domain procedures which include delay-sum, partial-sum, interpolation and shifted-sideband beamforming, and frequency domain techniques which include the application of discrete Fourier transforms and phase shift beam-forming are considered. Hardware considerations are primarily in the areas of analog-to-digital conversion, data storage, and computational throughput requirements.

A comparison of efficient beamforming algorithms

Digital time-domain beamforming requires that samples of the sensor signals be available at a sufficient rate to realize accurate time delays for beam steering. For many applications, this input rate, which may be significantly higher than the Nyquist rate required for waveform reconstruction, places stringent requirements on A/D converter hardware and transmission cable bandwidth. Recently, a technique referred to as digital interpolation beamfonning was introduced which greatly relaxes the sampling requirement and provides substantial hardware savings through more flexible design options. In this approach, the sensor channels need only be sampled at a rate which satisfies aliasing requirements. The vernier beam-delay increments are then synthesized using digital interpolation which can be implemented at the beamformer input or output to minimize digital processing complexity. Previously, this concept was presented for the case of "low-pass" signals. This paper extends this work by examining the relationship between interpolation and beamforming for the important class of "bandpass" signals. Specifically, sampling methods are discussed whereby the original waveform can be reconstructed from samples taken at a rate consistent with the bandwidth of the bandpass signal. Beamformer implementations are presented which utilize these bandwidth-sampling techniques in conjunction with interpolation and which compute beam output points at the generally low rate dictated by the signal bandwidth. The interpolation beamformer achieves time-delay quantization (beam-steering accuracy) independent of both the input and output sampling rates. This approach generally requires less hardware than conventional procedures. Interpolation falter characteristics dictated by the bandwidth-sampling procedure are described and efficient methods of implementation employing nonrecursive digital bandpass and low-pass filters are presented.

Digital interpolation beamforming for low-pass and bandpass signals

This is a collection of articles written by members of the Underwater Acoustic Signal Processing (UASP) Technical Committee. The first article, by D. W. Tufts, deals with the history of UASP prior to 1980. In this period, initial mathematical models were developed and the first experimental investigations of underwater acoustic propagation were performed. It was also recognized during this time that there are many similarities between radar and sonar signal processing. The article by J.P. Ianniello deals with research in passive and active sonar from 1980 to the present. Work in this period included experimental verification of algorithms that had been developed in the 1960s and 1970s (e.g. for adaptive beamforming), as well as the development of new approaches, which include acoustic propagation modeling in the design of signal processing algorithms. Such processing is referred to as matched field processing. A common task in passive sonar systems is to estimate the difference in times at which different sensors receive the same signal. Time-delay estimation is a first stage that feeds into subsequent processing blocks. I. Lourtie provides a concise review of work in this field. The article by J.C. Preisig deals with underwater acoustic communications. The underwater channel has several features that make reliable communication a challenging problem. Nevertheless, progress is being made by combining results from ocean acoustic modeling, communication theory, and signal processing. The final article, by J.M.F. Moura, deals with the future of signal processing in the ocean. In addition to considering advances in detection and localization, he deals with new applications such as acoustic tomography, physical oceanography, and synthetic aperture sonar.

The past, present, and the future of underwater acoustic signal processing

It is proposed to specify a filter only in terms of upper and lower limits on the response, find the shortest filter length which allows these constraints to be met, and then find a filter of that order which is farthest from the upper and lower constraint boundaries in a minimax sense. The simplex algorithm for linear programming is used to find a best linear-phase FIR filter of minimum length, as well as to find the minimum feasible length itself. The simplex algorithm, while much slower than exchange algorithms, also allows the incorporation of more general kinds of constraints, such as concavity constraints (which can be used to achieve very flat magnitude characteristics). Examples are given to illustrate how the proposed and common approaches differ, and how the proposed approach can be used to design filters with flat passbands, filters which meet point constraints, minimum phase filters, and bandpass filters with controlled transition band behavior. >

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METEOR: a constraint-based FIR filter design program

The problem of designing a finite duration impulse response (FIR) digital filter to approximate a desired spectral response is treated in this paper. The philosophy adopted is that for a given FIR filter structure, the filter coefficients can be designed to provide a minimum mean-squared error (MMSE) estimate of a random signal sequence (the design-signal) imbedded in a random noise sequence. By treating the signal and noise covariance functions as design parameters, one can design FIR filters with spectral responses that approximate the power spectral density of the design-signal. For signal processing applications that require some attention to signal fidelity, as well as noise rejection, the MMSE philosophy seems appropriate (as opposed to a maximum signal-to-noise ratio philosophy, for example). Several practical designs are presented that emphasize the simplicity of the design technique and illustrate the selection of design parameters. The designs show quite dramatically that the MMSE design technique can be competitive with existing low-pass and bandpass design techniques. Finally, considerable attention is given to an efficient Toeplitz matrix inversion algorithm that permits rapid inversion of the covariance matrices that arise in the MMSE design. The resulting computation times for the design of high-order filters (N = 128, e.g.) appear to be shorter than computation times for competing algorithms.

Statistical design of nonrecursive digital filters

The general Remes exchange algorithm and its implementation are discussed briefly An analog of the exchange algorithm is applied to the problem in which upper and lower constraints are imposed on the frequency response of a nonrecursive digital filter with linear phase. A typical design example is presented with rather tight constraints in the passband

J. Lewis

Papers

Interactive minimax design of linear-phase nonrecursive digital filters subject to upper and lower function constraints