Computational Precision Requirements for Optimal Weights in Adaptive Processing

The required accuracy for computing the estimated optimum weights of an adaptive processor has been analyzed by investigating the effects of errors in computing the inverse matrix. It is shown that the required precision depends upon the matrix. An equation for the general case is derived. Several special cases are considered in detail. It is shown that the case of a single interference source requires the highest precision. The least stressing case is identifi'ed and compared to the worst case. The requirements for a "typical" case are also considered. A comparison of the requirements for the covariance matrix estimation technique and for adaptive weight implementation using gradient descent techniques is given. It is shown that there is a dichotomy in that cases that do not stress one technique tend to stress the other.     

Constant-False-Alarm-Rate Processors for Locally Nonstationary Clutter

A technique for designing normalizing processors for locally non-stationary clutter is discussed. The design procedure assumes the logarithm of the clutter power varies as a polynomial with range. When the actual environment matches the design environment, the false-alarm rate is a constant that is independent of the polynomial coefficients. A measure of the relative target detection capability as a function of the number of normalization cells and the degree of the design-environment polynomial is given. The applicability of the processors to non-Rayleigh clutter is discussed.     

An effect of range-heterogeneous clutter on adaptive Dopplerfilters

The practical implementation of adaptive Doppler filters requires estimates of clutter parameters to determine the adaptive weights. A method of deriving the estimate via the sample matrix inversion (SMI) algorithm using multiple data snapshots from adjacent range cells is presented. For homogeneous clutter environments, the results of this technique asymptotically approach the optimum (a priori known covariance matrix) as the number of snapshots approaches infinity; this asymptotic behavior does not occur for heterogeneous clutter environments. An equation for the decrease in improvement factor is derived. To promote understanding, the simplified special case of narrowband clutter is considered in detail. In almost all cases, the loss is small     

Performance of Digital Implementations of an Adaptive Processor

The performance of a digital implementation of an Applebaum-Howells type adaptive processor is analyzed for both a limiter and nonlimiter configuration. The performance is evaluated in terms of steady-state residue power, using either a single-pole filter or a perfect integrator to smooth the output of the correlation mixer. The latter filter is the more commonly used for digital implementations. It is shown that when using the perfect integrator filter for both the limiter and linear digital implementations, the steady-state average weight vector equals the optimum weight vector. Thus, for this filter, the steady-state residue power is the minimum possible for either implementation. When using the single-pole filter, neither implementation achieves the minimum possible steady-state residue power. The relative performance of the two implementations depends upon the relative gain settings. When the gains are adjusted to give comparable servo stability for the design maximum jammer power, a reasonable criterion for digital implementations because of analog to digital saturation, the limiter configuration always has smaller steady-state residue power.     

Clutter Map CFAR Analysis

An analysis of the probability of target detection for a clutter map CFAR using digital exponential filtering has been performed. General performance equations are derived. The probability of detection versus signal-to-noise ratio is plotted for a false alarm probability of 1.E-06 for several weight values. The CFAR loss is plotted for a detection probability of 0.9 and false alarm probabilities of 1.E-06 and 1.E-08.     

Detection Loss of the Sample Matrix Inversion Technique

The sample matrix inversion (SMI) technique is used for Doppler and/or array processing. Previous analysis of the technique has been in terms of signal-to-interference plus noise ratio (SINR). For Gaussian statistics, this performance measure gives the same loss values as does a probability of detection analysis for linear-time invariant systems. It is often somewhat less valid for nonlinear or time variant systems. As SMI is a nonlinear technique, a probability of detection analysis has been performed. It is shown that the detection loss is larger than that computed by the SINR measure. It is also shown that though the loss predicted by the SINR measure only depends upon the number of measurements used to estimate the covariance matrix, the detection loss depends upon the false alarm probability and the number of adaptable elements in addition to the number of measurements.     

Normalized LMS Algorithm Degradation Due to Estimation Noise

The steady-state weight vector derived by either the least mean square (LMS) or normalized least mean square (NLMS) algorithms has random deviations from the optimum values. These deviations increase the steady-state residue power. A previous paper derived the LMS weight noise effects for a multiple sidelobe canceller (MSLC) application. This paper describes the NLMS weight noise effects. It is shown that for a thermal noise environment, the weight noise effect for the LMS algorithm is insignificant but is quite significant for the NLMS algorithm. Calculations for example noise plus interference environments imply that the NLMS weight noise effects are always larger than that for LMS.     

Effect of Particular Gain Changes upon LFM Sidelobes

The envelope variation of an LFM waveform due to transmitter droop or receiver STC tends to cause range sidelobes. A parametric analysis of the magnitude of the sidelobes has been performed. It is shown that the sidelobes can be quite high at the matched filter output, but are low at the output of the sidelobe reduction filter. 40-dB sidelobes can be achieved even with a 4-dB envelope droop. It is shown that these results are consistent with conventional paired-echo theory. Similar results are shown to hold for droop variations of the filter transfer function.     

Effect of a Few Dominant Specular Reflectors Target Model Upon Target Detection

Some data indicate that aircraft targets viewed from certain aspects are well modeled as consisting of a few specular reflectors. The effect of a simplified form of this target model upon radar detection performance for two different waveforms has been analyzed. The signal-to-noise ratio (SNR) required for detection as a function of waveform bandwidth for a conventional-single-channel waveform and for a four-channel frequency diversity waveform is evaluated. It is shown that for either waveform there is an optimum bandwidth to minimize the SNR required for detection. In addition, the single-channel minimum is less than the four-channel minimum. The best performance occurs for the single-channel waveform when the waveform bandwidth just resolves the individual reflectors. For typical targets, this bandwidth is of the order of 35 to 75 MHz. It is also shown that only a 0.8-dB loss relative to this minimum is incurred when using a four-channel narrow bandwidth waveform.