Cascaded detector for multiple high-PRF pulse Doppler radars

A postdetection design methodology for a multiple high-pulse-repetition frequency (PRF) pulse Doppler radar has been developed. The postdetection processor consists of an M out of N detector where range and target ambiguities are resolved, followed by a square-law detector which enhances the minimum signal-to-noise (S/N) power-ratio per pulse burst performance. For given probabilities of false alarm and detection, formulas are derived from which the three thresholds associated with the cascaded detector can be found. Fundamental tradeoffs between the minimum S/N required, number of ghosts, and the number of operations (NOPs) that the cascaded detector must perform are identified. It is shown that the NOPs and the number of ghosts increase and the minimum S/N required decreases as the binary M out of N detector passes more detections to the square-law detector     

Implementation and convergence considerations of a linearlyconstrained adaptive array

O.L. Frost (1972) introduced a linearly constrained optimization algorithm that allows certain main beam properties to be preserved while good cancellation is attained. An open-loop implementation of this algorithm is developed. This implementation is shown to be equivalent to the technique developed by C.W. Jim (1977), L.J. Griffiths and C.W. Jin (1982), and K.M. Buckley and L.J. Griffiths (1982) whereby the constrained problem is reduced to an unconstrained problem. Analytical results are presented for the convergence rate when the sampled matrix inversion (SMI) or Gram-Schmidt (GS) algorithm are employed. It has been previously shown that the steady-state solution for the optimal weights is identical for both constrained and reduced unconstrained problems. It is shown that if the SMI or GS algorithm is employed, then the transient weighting vector solution for the constrained problem is identical to the equivalent transient weight vector solution for the reduced unconstrained implementation     

Fast converging adaptive processor or a structured covariance matrix

The use of adaptive linear techniques to solve signal processing problems is needed particularly when the interference environment external to the signal processor (such as for a radar or communication system) is not known a priori. Due to this lack of knowledge of an external environment, adaptive techniques require a certain amount of data to cancel the external interference. The number of statistically independent samples per input sensor required so that the performance of the adaptive processor is close (nominally within 3 dB) to the optimum is called the convergence measure of effectiveness (MOE) of the processor. The minimization of the convergence MOE is important since in many environments the external interference changes rapidly with time. Although there are heuristic techniques in the literature that provide fast convergence for particular problems, there is currently not a general solution for arbitrary interference that is derived via classical theory. A maximum likelihood (ML) solution (under the assumption that the input interference is Gaussian) is derived here for a structured covariance matrix that has the form of the identity matrix plus an unknown positive semi-definite Hermitian (PSDH) matrix. This covariance matrix form is often valid in realistic interference scenarios for radar and communication systems. Using this ML estimate, simulation results are given that show that the convergence is much faster than the often-used sample matrix inversion method. In addition, the ML solution for a structured covariance matrix that has the aforementioned form where the scale factor on the identity matrix is arbitrarily lower-bounded, is derived. Finally, an efficient implementation is presented.     

Adaptive pulse compression via MMSE estimation

Radar pulse compression involves the extraction of an estimate of the range profile illuminated by a radar in the presence of noise. A problem inherent to pulse compression is the masking of small targets by large nearby targets due to the range sidelobes that result from standard matched filtering. This paper presents a new approach based upon a minimum mean-square error (MMSE) formulation in which the pulse compression filter for each individual range cell is adaptively estimated from the received signal in order to mitigate the masking interference resulting from matched filtering in the vicinity of large targets. The proposed method is compared with the standard matched filter and least-squares (LS) estimation and is shown to be superior over a variety of stressing scenarios.     

The effect of I,Q mismatch errors on adaptive cancellation

The effects of in-phase (I) and quadrature-phase (Q) amplitude errors and low-pass-filter (LPF) errors on adaptive cancellers are investigated. I,Q errors occur because of errors in the synthesis process of the mixers and LPFs designed to be identical for each input channel. These I,Q errors among the channels result in cancellation degradation. Tapped delay line transversal filters have been proposed as a way to compensate for these errors and thus improve cancellation performance. However, it is shown that if there is any LPF mismatch, then transversal filtering has a small effect on improving canceler performance. The use of individual I,Q adaptive transversal filter weighting is suggested as a means of completely eliminating the phase amplitude errors, and making the canceler performance responsive to transversal filter compensation     

Doppler Compensation & Single Pulse Imaging using Adaptive Pulse Compression

The effects of target Doppler are addressed in relation to adaptive receive processing for radar pulse compression. To correct for Doppler-induced filter mismatch over a single pulse, the Doppler-compensated adaptive pulse compression (DC-APC) algorithm is presented whereby the respective Doppler shifts for large target returns are jointly estimated with the illuminated range profile and subsequently incorporated into the original APC adaptive receive filter formulation. As a result, the Doppler-mismatch-induced range sidelobes can be suppressed thereby regaining a significant portion of the sensitivity improvement that is possible when applying adaptive pulse compression (APC) without the existence of significant Doppler mismatch. In contrast, instead of compensating for Doppler mismatch, the single pulse imaging (SPI) algorithm generalizes the APC formulation for a bank of Doppler-shifted matched filters thereby producing a sidelobe-suppressed range-Doppler image from the return signal of a single radar pulse which is applicable for targets with substantial variation in Doppler. Both techniques are based on the recently proposed APC algorithm and its generalization, the multistatic adaptive pulse compression (MAPC) algorithm, which have been shown to be effective for the suppression of pulse compression range sidelobes thus dramatically increasing the sensitivity of pulse compression radar.     

New results in importance sampling [of false alarm statistics]

Importance sampling is a technique which can significantly reduce the number of Monte Carlos necessary to accurately estimate the probability of low-probability of occurrence events (e.g., the probability of false alarm P_F associated with a given detection scheme). A new technique called the Chernoff Importance Sampling Method is introduced. It is shown that the number of required Monte Carlos can be reduced by a factor of a Chernoff-like bound on P _F. In addition, techniques for choosing the multiplying factor of the distorted variance method (the most common method used in importance sampling) are presented     

Reciprocal radar waveforms

Digitally coded radar waveforms can be used to obtain large time-bandwidth products (pulse compression ratios). It is demonstrated that periodic radar waveforms with zero sidelobes or almost zero sidelobes can be defined. A perfect periodic code is a periodic code whose autocorrelation function has zero sidelobes and whose amplitude is uniform (maximum power efficiency=1). An asymptotically perfect periodic code has the property that as the number of elements in the code goes to infinity the autocorrelation function of the code has zero sidelobes and its power efficiency is one. The authors introduce a class of radar waveforms that are either perfect or asymptotically perfect codes. These are called reciprocal codes because they can be derived through a linear transformation of known codes. The aperiodic performance of the reciprocal code is examined     

A mean level adaptive detector using nonconcurrent data

Convergence results for a mean level adaptive detector (MLAD) are presented. The MLAD consists of an adaptive matched filter (for spatially correlated inputs) followed by a mean level detector (MLD). The optimal weights of the adaptive matched filter are estimated from one batch of data and applied to a statistically independent batch of nonconcurrent data. The threshold of the MLD is determined from the resultant data. Thereafter a candidate cell is compared against this threshold. Probabilities of false alarm and detection are derived as a function of the threshold factor, the order of the matched filter, the number of independent samples per channel used to calculate the adaptive matched filter weights, the number of samples used to set the MLD threshold, and the output signal-to-noise power ratio of the optimal matched filter. A number of performance curves are shown and discussed     

Spatially distributed target detection in non-Gaussian clutter

Two detection schemes for the detection of a spatially distributed, Doppler-shifted target in non-Gaussian clutter are developed. The non-Gaussian clutter is modeled as a spherically invariant random vector (SIRV) distribution. For the first detector, called the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT), the detector takes the form of a sum of logarithms of identical functions of data from each individual range cell. It is shown under the clutter only hypothesis, that the detection statistic has the chi-square distribution so that the detector threshold is easily calculated for a given probability of false alarm P_F. The detection probability P_D is shown to be only a function of the signal-to-clutter power ratio (S/C)_opt of the matched filter, the number of pulses N, the number of target range resolution cells J, the spikiness of the clutter determined by a parameter of an assumed underlying mixing distribution, and P_F. For representative examples, it is shown that as N, J, or the clutter spikiness increases, detection performance improves. A second detector is developed which incorporates a priori knowledge of the spatial scatterer density. This detector is called the scatterer density dependent GLRT (SDD-GLRT) and is shown for a representative case to improve significantly the detection performance of a sparsely distributed target relative to the performance of the NSDD-GLRT and to be robust for a moderate mismatch of the expected number of scatterers. For both the NSDD-GLRT and SDD-GLRT, the detectors have the constant false-alarm rate (CFAR) property that P_F is independent of the underlying mixing distribution of the clutter, the clutter covariance matrix, and the steering vector of the desired signal