S.U. Pillai

Optimal transmit-receiver design in the presence of signal-dependent interference and channel noise

Optimal detection of a target return contaminated by signal-dependent interference, as well as additive channel noise, requires the design of a transmit pulse f(t) and a receiver impulse response h(t) jointly maximizing the output signal to interference plus noise ratio, SINR. Despite the highly nonlinear nature of this problem, it has been possible to show that f(t) may always be chosen minimum-phase. A full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs (f,h) that appears to converge satisfactorily for most values of input SINR. Extensive simulation reveals that the shape of f(t) can be a critical factor. In particular the performance of a chirp-like pulse is often unacceptable, especially when the clutter and channel noise are low-pass dominant and comparable.

A new approach to array geometry for improved spatial spectrum estimation

In this letter, we address the problem of element placement in a linear aperiodic array for use in spatial spectrum estimation. By making use of a theorem by Caratheodory, it is shown that, for a given number of elements, there exists a distribution of element positions which, for uncorrelated sources, results in superior spatial spectrum estimators than are otherwise achievable. The improvement is obtained by constructing an augmented covariance matrix, made possible by the choice of element positions, with dimension greater than the number of array elements. The augmented matrix is then used in any of the known spectrum estimation methods in conjunction with a correspondingly augmented search pointing vector. Examples are given to show the superior detection capability, the larger dynamic range for spectral peak to background level, the lower sidelobes, and the relatively low bias values, when one of the known spectrum estimation techniques based on eigenstructure is used.

Performance analysis of MUSIC-type high resolution estimators for direction finding in correlated and coherent scenes

An asymptotic analysis is presented of a class of high-resolution estimators for resolving correlated and coherent plane waves in noise. These estimators are in turn constructed from certain eigenvectors associated with spatially smoothed (or unsmoothed) covariance matrices generated from a uniform array. The analysis is first carried out for the smoothed case, and from this the conventional (i.e., unsmoothed) multiple signal classification (MUSIC) scheme follows as a special case. Independent of the total number of sources present in the scene, the variance of the conventional MUSIC estimator along the true arrival angles is shown to be zero within a first-order approximation. The bias expressions in the smoothed case are used to obtain a resolution threshold for two coherent, equipowered plane waves in white noise, and the result is compared to the one derived by Kaveh et al. (1986) for two uncorrelated, equipowered plane waves. >

Theory and application of optimum transmit-receive radar

Recent advances in linear amplifier and arbitrary waveform generation technology have spawned interest in adaptive transmitter systems as a means for both optimizing target signal gain and enhancing ID. In this paper rigorous theoretical performance bounds are constructively established for the joint transmitter-target-channel-receiver optimization problem in the presence of additive colored noise (ACN), (e.g., interference multipath). For the ACN case, an analytical solution is obtained as an eigenvector (with associated maximum eigenvalue) of a homogeneous Fredholm integral equation of the second type. The kernel function is Hermitian and is obtained from the cascade of the target impulse response with the ACN whitening filter. The theoretical performance gains achievable over conventional transmitter strategies (e.g., chirp) are presented for various simulation scenarios including interference multipath mitigation. Also discussed is the potential effectiveness of an optimal discriminating pulse solution for the N-target ID problem that arises naturally from the theory.

Statistical analysis of a high resolution spatial spectrum estimator utilizing an augmented covariance matrix

In the context of multiple source location with multiple sensors, it was shown [1] that by using an M element array with elements arranged in a minimum redundancy fashion and by augmenting the array output covariance matrix to create a covariance-type matrix of larger dimensions, it is possible to estimate the directions of arrival of as many as M(M - 1)/2 uncorrelated sources. The earlier work assumed perfectly estimated covariances. This paper addresses the statistical properties and related issues of the augmented covariance matrix in the case when the array output sample covariances are estimated from finite data using the maximum likelihood method. Using a matrix factorization technique, the distribution of the sample Bartlett spatial spectrum estimator based on the augmented covariance matrix is shown to be a sum of weighted and dependent χ2-distributed random variables. The degradation in performance in making use of the augmented matrix is here found in terms of the variance of the Bartlett estimator. This is shown to be in the order of twice the variance obtained with a uniform array of actual elements, the latter being equal in number to the dimension of the augmented array. To match the performance of the uniform array of actual elements using the augmented array would then require about twice the number of data samples.

An algorithm for near-optimal placement of sensor elements

An important question in array design is that of where to place the elements of a sparse array for optimal performance in terms of its ability to detect and resolve a greater number of sources than conventionally possible. In particular, it has been shown that when sensor elements are arranged in the minimum redundancy fashion, by performing an augmentation technique on the covariances obtained from the array outputs, an M element array can be made to estimate the directions of arrival of as many as M(M-1)/2 uncorrelated sources unambiguously. Constructive procedures are developed to evaluate integer locations for an array of given sensors that span a prescribed distance, such that any missing integer is expressible as the difference of two sensor locations. New upper bounds for the ratio of the square of the minimum number of elements to the spanning distance are also established. >

Full-polarization matched-illumination for target detection and identification

This paper investigates the optimization of the full-polarization radar transmission waveform and the receiver response to maximize either target detection or identification performance. Application of such full-polarization matched-illumination techniques to simulated VHF-band frequency response data of mobile surface targets yields a significant performance improvement over that corresponding to chirped full-polarization transmission waveforms.

Generalized forward/backward subaperture smoothing techniques for sample starved STAP

A major issue in space-time adaptive processing (STAP) for moving target indicator (MTI) radar is the so-called sample support problem. Often, the available sample support for estimating the requisite interference covariance matrix is inadequate, thereby precluding STAP beamforming utilizing many adaptive degrees-of-freedom (DOFs). Although deterministic rank-reduction methods can reduce sample support requirements, they are invariably suboptimal from a signal-to-interference-plus-noise-ratio (SINR) standpoint. A new generalized subspatial and subtemporal aperture smoothing method employing forward and backward data vectors is introduced to overcome the data deficiency problem. It is shown that multiplicative improvement in data samples can be obtained at the expense of negligible loss in space-time aperture of the steering vector.

Dispersive modes in the time domain: analysis and time-frequency representation

Four algorithms for time-frequency (TF) distributions are considered for the processing and interpretation of dispersive time-domain (TD) data: the short-time Fourier transform, frequency and time-domain wavelets, and a new ARMA-based representation. The TF resolutions of the various distributions are discussed and compared with reference to results for the scattered fields from a chirped finite grating excited by a pulsed plane wave. The processing in the TF phase space extracts TD phenomenology, in particular the instantaneous dispersion relation /spl minus/ with its associated time-dependent frequencies-descriptive of the local TD Floquet modes on the chirped truncated grating.<<ETX>>

A new technique for ARMA-system identification and rational approximation

The fundamental problem of identifying a linear time-invariant system from measured samples of its output response to a known input is addressed, utilizing a new and simple deterministic theory founded on well-established passive network concepts. The analysis, together with documented numerical results, demonstrates that the proposed method achieves two goals: stable rational minimum-phase transfer functions can be identified with a priori knowledge of either numerator or denominator degrees; and stable rational minimum-phase Pade-like approximations appear to be generated automatically in the nonrational case. To substantiate these claims, a detailed theoretical exposition of the basic ideas, an extensive discussion of numerical results, and a summary of related results are given. >