Henry Cox

A subarray approach to matched‐field processing

A simplified approach is presented for matched‐field processing of large vertical arrays in typical ocean environments. The large array is divided into subarrays such that a plane‐wave decomposition of the signal field is a good approximation over each subarray. A simple rule, based on the sound‐speed profile, is presented for subarray sizing. Plane‐wave beamforming is then performed to provide multiple beams from each subarray. For long‐range situations, only those beams need to be formed that are steered to receive rays that are not strongly bottom interacting. When elements are spaced at one‐half wavelength, the typical result of considering only these beams is a significant reduction in the size of the problem with far fewer beams required than elements. This first step is very robust and does not require a detailed knowledge of the signal field, or an assumption of signal coherence across the full array aperture. Beam outputs can then be combined to achieve full matched‐field processing. The relative...

Geometric comb waveforms for reverberation suppression

The major problem for sonar systems operating in shallow water is reverberation from the ocean bottom. A new class of waveforms is described which combines high range resolution with excellent Doppler properties for detecting moving targets in stationary reverberation. The waveforms consist of multiple simultaneously transmitted CW tone pulses. The tones are non-uniformly spaced in frequency to break up range ambiguities. A special subclass is the geometric comb in which the frequency spacing between the adjacent components follows a geometric progression. Analytic approximations can be used to obtain the important properties of this class, resulting in a practical design methodology. The resulting waveforms have excellent Doppler properties and an unambiguous high resolution range estimation capability. Techniques for reducing the peak-to-average power ratio are discussed.<<ETX>>

Effects of amplitude and phase errors on linear predictive array processors

The effects of amplitude and phase errors are determined for symmetric and asymmetric linear predictive array processors. The maximum entropy method (MEM) corresponds to linear prediction in the asymmetric case of a line array of equispaced elements with an end reference. A comparison to conventional beamforming and maximum-likelihood processing shows that they have the same peak location as the symmetric linear predictive array processor. >

Performance of Line Arrays of Vector and Higher Order Sensors

Arrays of vector and higher order directional sensors are of current interest in a number of applications. The performance of these arrays as a function of frequency and steering direction is examined. Results are presented for arrays of zero-th order (omni-directional), first order vector (omni + first spatial derivative) and second order combined (omni + first spatial directions derivatives + second spatial derivatives) sensors. The beampattern product theorem provides insight into to contribution of the individual components of the directional sensors. For endfire array steering, previous results are extended to higher order sensors. Only the axial components are important at endfire. Sensors with axial components up to order n can cancel up to n grating lobes providing extra gain up to (n+1) times the design frequency at which the sensors are spaced at one-half wavelength. Away from endfire only the cross-axial components are important. Simple techniques are presented for overcoming left/right ambiguity of horizontal line arrays using only the omni-directional and horizontal cross axial components. The results of simple deterministic processing approaches are found to be near optimum when compared with those achieved by optimum processing based on covariance matrix inversion.

Adaptive cardioid processing

Algorithms for adaptively steering the null of a cardioid to achieve interference rejection are developed. The algorithms are basically broadband, but by frequency filtering it is easy to steer independently in different frequency bands. Of particular interest is the nulling of highly directional reverberation when sonobuoys are considered as multistatic active receivers. Simple adaptive algorithms are shown to be effective in simulations.<<ETX>>

A Tactical Approach to Environmental Uncertainty and Sensitivity

The issues of acoustic sensitivity to environmental parameters and the uncertainty in performance prediction due to lack of accurate environmental inputs are addressed. Special emphasis is given to the current state of affairs and to the importance of communicating in a simple, robust means the uncertainty to the sonar operator. A multistaged approach to estimating sensitivity, computing acoustic propagation uncertainty due to environmental variability is presented. A heuristic approach to estimating the most sensitive environmental parameters is developed. A measurements-based statistical approach is applied to environmental data taken in the Mediterranean Sea to estimate performance uncertainty due to sound speed and geoacoustics uncertainty

An Adaptive Beamforming Algorithm With Simultaneous Mainlobe Response And Tolerance Sensitivity Constraints

Adaptive beamforming algorithms sometimes are very sensitive to slight errors in array characteristics. Errors which are uncorrelated from sensor to sensor pass through the beamformer like uncorrelated or spatially white noise. Hence, gain against white noise is a measure of robustness. A new algorithm is presented which includes a quadratic inequality constraint on the array gain against uncorrelated noise. while minimizing output power subject to multiple linear equality constraints. It is shown that a simple scaling of the projection of the weights in a subspace can be used to satisfy the quadratic inequality constraint. This leads to a simple effective robust adaptive beamforming algorithm.

DOA estimation using vector sensor arrays

We consider the problem of estimating the azimuth and elevation angle of sources using a vertical line array of vector sensors. Three alternative direction-of-arrival (DOA) estimators are considered. The first approach uses beam cross-correlation. The other two approaches are element-space and beamspace versions of an eigenvector-normalization scheme in which the eigenvector is normalized by its omni-directional component. The performance of these DOA estimators is evaluated for a vertical line array of 2D vector sensors (DIFARs) using simulation scenarios that involve mostly 3D isotropic noise and either no interferer or one loud interferer at various separation distances from a weak target.

Performance of vector sensors in noise

Vector sensors are super gain devices that can provide ‘‘array gain’’ against ocean noise with a point sensor. As supergain devices they have increased sensitivity to nonacoustic noise components. This paper reviews and summarizes the processing gain that is achievable in various noise fields. Comparisons are made with an omni‐directional sensor and with the correlation of a pair of closely spaced omni‐directional sensors. Total processing gain that consists of both spatial and temporal gain is considered so that a proper analysis and interpretation of multiplicative processing can be made. The performance of ‘‘intensity sensors’’ (pressure times velocity) that are obtained by multiplying the omnidirectional component with a co‐located dipole is also considered. A misinterpretation, that is common in the literature, concerning the performance of intensity sensors is discussed. The adaptive cardioid processing of vector sensors is also reviewed.

Reduced variance distortionless response (RVDR) performance with signal mismatch

Matched field processing of underwater acoustic fields frequently involves considerable mismatch between the actual received signal and the model of the complicated propagation from various possible source locations to the receiving array. This leads to significant signal suppression in the MVDR (minimum variance distortionless response) processor. The high sidelobes of the conventional processor make it unsatisfactory. The authors examine the effectiveness of modifying the diagonal of the spatial correlation matrix. Performance in the face of mismatch is quantified. A simple parametric relationship between MUSIC, MVDR, and conventional beamforming is developed. An important feature of the proposed GDR (generalized distortionless response) approach is that the weights may be used in beamformers to produce beam output time series and are not limited to direction estimation.<<ETX>>