Hung Lai

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>>

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.

Cramer-Rao Lower Bound for DOA Estimation Using Vector and Higher-Order Sensor Arrays

The Cramer-Rao lower bound for estimating the azimuth and elevation angles of multiple planewave sources using a line array of general nth-order sensors is derived, generalizing the results of Nehorai and Paldi (1994) [1] for vector (first order) sensors. An analytical framework using spherical harmonics is used to derive the bound and the MVDR estimator for the higher order sensor array. Theoretical and simulation results for both a single higher-order sensor and a vertical line array are presented.

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.

Spatial correlation for directional sensors in arbitrary noise fields

Spatial correlation provides the basis for determining the covariance matrix used in calculating the optimum gain performance and Direction-of-Arrival (DOA) Cramer-Rao Lower Bound (CRLB) for arrays of directional sensors. A general formulation for the spatial correlation between two pressure sensors in a noise field of arbitrary directional distribution F was presented in [1]. The approach involves the expansion of the directional noise density F(θ, φ, ω) in cylindrical or spherical surface harmonics. This approach has been extended to the case of two directional sensor components l and k whose directional amplitude responses are g<inf>l</inf>(θ, φ, ω) and g<inf>k</inf>(θ, φ, ω). The spatial correlation between the directional sensors can be obtained using a similar harmonic expansion procedure by replacing F(θ, φ, ω) with H(θ, φ, ω) = g<inf>l</inf>(θ, φ, ω)g<inf>k</inf>(θ, φ, ω)F(θ, φ, ω).

Simultaneous grating lobe and backlobe rejection with a line array of vector sensors

Horizontal line arrays in underwater acoustics have a so-called “left / right” ambiguity due to the conical shape of the beampattern. When operated above the design frequency at which the inter-element spacing is one-half wavelength, a conical grating lobe further complicates array response. It is shown how vector sensors can be used to simultaneously discriminate against grating lobe and backlobe arrivals by using both the axial and cross-axial dipole components. Results with adaptive algorithms of varying complexity and new deterministic algorithms are compared.

Endfire Supergain with a Uniform Line Array of Pressure and Velocity Sensors

Endfire steered arrays of collocated omni-directional pressure and dipole velocity sensors can achieve supergain even when the sensors are spaced at one-half wavelength. The explanation of this phenomenon lies in the ability of a collocated pair to steer a null to cancel a grating lobe. Sensitivity to uncorrelated noise can render this idealized optimum solution impractical, but by using a white noise gain constraint, significant, practically realizable gain over CBF can be achieved. A simple new deterministic approach combining shading, oversteering and grating cancellation can achieve similar performance to the constrained optimum.

Response pattern control in spite of failed array elements

Large arrays of many elements usually are shaded to achieve low sidelobes. However, in practice these arrays typically operate with some element failures that significantly degrade sidelobe performance. First, the effects of different numbers of failed elements on sidelobe levels are analyzed and illustrated with simulations. Statistics and bounds for sidelobe levels with failed elements are presented. The inability and limitations of conventional shading modifications to compensate for failed elements is discussed and illustrated. Missing elements give rise to large inter‐element spacings that in turn result in grating effects that cannot be compensated for using modified shading weights. An adaptive compensation approach for failed elements is then presented. This involves narrowband interpolation from nearby elements to estimate the missing data prior to applying the original shading weights. Failures of both isolated and neighboring elements are considered. When there is a strong source present it is relatively easy to estimate its value on missing elements. But this is exactly the case of interest, when sidelobe levels are important. The adaptive interpolation approach provides good bearing response patterns so that strong signals are well isolated in bearing. Results are illustrated with large array simulations with different failure patterns and multiple strong sources.

Effects of failed elements on sidelobes of array beampatterns

It is common for arrays to degrade as elements fail, resulting in high sidelobes. The sensitivity of sidelobe levels to element failures is examined for an arbitrarily shaded array. Using the difference of complex beampatterns, it is found that the beampattern, which can be associated with just the failed elements, controls the degraded array response in the deep sidelobe region. Using results for addition of weighted random phasers, expressions are presented for an upper bound, the mean and standard deviation of the power sidelobes of the degraded array in terms of the number and shading weights of the failed elements. The upper bound depends on the percent of elements that fail and is independent of array size. The average sidelobe level depends on both the failed-to-good ratio and the number of remaining good elements, making large arrays more robust for the same percentage of failed elements. The standard deviation of sidelobe levels is approximately equal to the mean. The ratio of failed to remaining good elements is analogous to the combined amplitude and phase variance for uncorrelated tolerance errors. Combined effects of element failures and random amplitude and phase errors are then presented.

Adaptive factored beamforming for vector sensor arrays

We consider a new beamspace adaptive beamformer for vector sensor arrays. The sample support and computational requirement for this beamformer is roughly the same as that of a comparable beamspace MVDR beamformer for only the omnidirectional component of the same array. We refer to the new beamformer as ldquoAdaptive Factored Beamformerrdquo or AFBF since it assumes that the weight vector can be written as a Kronecker product of two weight vectors. The performance of this algorithm is evaluated against other adaptive beamformers using simulated data.