Signal Sequence Detection Given Noisy, Common Background Image Sets

The optimum processing (likelihood functional) is found for a set of M images {Zm = Sm + Y + Nm}, each the sum of a member Sm of a signal sequence {Sm}, due to an object to be detected and its parameters estimated, a sample function Nm of a noise field {Nm}, and a sample function Y of a common background field {Y}. The noise fields {{Nm}} are independent, zero mean, white Gaussian fields, all independent of the background field {Y}; the latter is assumed to be either 1} completely unknown or of known mean and covariance functions with 2) a certain fluctuation property or 3) Gaussian. Three equivalent forms of the optimum processing are found: 1) a summation of generalized matched filterings of the images, 2) a summation of matched filtering of certain generalized differences of the images, 3) a summation of ?estimator-correlator? type filterings. The detection performance and optimum signal/image selection under the Neyman-Pearson criterion is given and the singularity of the ({{Nm = O}} and M > 1) case noted. It is shown that optimum processor and signal design can completely eliminate any effect of the background on detectability (M > 1). The Cramer-Rao lower bound for the signal parameter estimates meansquare error is given along with an example; optimum signal/image selection in the single parameter case is discussed.     

Detection Performance of the Cell Averaging LOG/CFAR Receiver

The cell averaging LOG/CFAR receiver is a special implementation of a constant-false-alarm-rate (CFAR) receiver in which the noise level estimate is derived from a set of contiguous time samples of the output of a logarithmic (LOG) detector as obtained from a tapped delay line. This CFAR receiver is capable of operating over a larger dynamic range of noise levels than a conventional cell averaging CFAR receiver, but with somewhat poorer detectability. The performance in stationary Gaussian noise of the cell averaging LOG/CFAR receiver with no post-detection integration is determined in this paper. For a small number of reference noise samples, results were obtained by a Monte Carlo simulation using the technique of importance sampling. For a large number of reference noise samples, a second moment analysis gave the desired results. Both these results can be summarized in the following simple formula, NLOG = 1.65NLIN - 0.65, which relates the number of reference samples required by each of the two receivers for equivalent performance. Thus, for the cell averaging LOG/CFAR receiver to give the same detection performance as the conventional cell averaging CFAR receiver, the number of reference noise samples has to be increased by up to 65 percent.     

On Optimizing Array Reception of Multipath

This paper reviews system configuration requirements and analyzes detectability performance characteristics for maximum likelihood array reception of multipath. Performance is analyzed to determine the effects of channel multipath structure (multipath delay and signal power division among the paths), space-time correlation properties of the incident processes, and the array spacing. It is shown by a series of case studies, that for single element coupling, as well as array coupling, an increased multipath delay factor results in decreased system detectability for fixed signal and noise intensity levels. The performance capacity is degraded as the available signal power tends to distribute more uniformly between the paths. These effects are attributed to the loss of effective signal energy concentration, resulting in a lower effective pre-detection signal-to-noise ratio. An investigation of the effects upon system performance, due to array element spacing, shows that performance is enhanced by increasing the spacing relative to the multipath delay factor and the reciprocal signal bandwidth. The former is the result of a more directive detectability (beam) pattern arising from the increased spacing. In effect, with increased spacing, the main lobe of the pattern is narrowed, while the side lobes are optimally suppressed by the required noise related array element link, frequency filters (weights).     

Detection of a Distributed Target

The influence of increasing range resolution on the detectability of targets with dimensions greater than the resolution cell is studied. An N-cell target model is assumed, which contains k reflecting cells, each reflecting independently according to the same Rayleigh amplitude distribution. It will be referred to as the (N,k) target. Detection based on one transmitted pulse is performed against a background of white normal noise. Detection in stationary clutter is also considered. The optimum detector is obtained but, in view of its complexity, the performance of a simpler detector, the square-law envelope detector with linear integrator (SLEDLI), is analyzed, and a formula for the probability of detection is obtained. Graphs are presented which show the probability of detection as a function of signal-to-noise ratio (SNR) for various values of N k, and false alarm probability. For N/k not too large it is shown that the SLEDLI is near optimum.     

Detection of random signals via spectrum matching

Using a priori knowledge of the signal power spectral density (PSD), a spectrum matching approach which effectively utilizes the available signal spectral shape is developed for random signal detection. Two spectrum matching detector (SMD) structures, which are implemented by correlogram and periodogram, respectively, are examined. Theoretical calculation of their false alarm rates is derived and confirmed by simulations. It is also demonstrated that the proposed detectors outperform the standard periodogram, Bartlett method, and energy detector under constant false alarm rate (CFAR) condition for two different random signals.     

Analysis of Some Modified Cell-Averaging CFAR Processors in Multiple-Target Situations

A serious degradation of detection probability (Pd) in a cellaverging constant false alarm rate (CA-CFAR) detector is known to be caused by the presence of an interfering target in the set of reference cells. A technique which is often used to prevent excessive false alarms at clutter ?edges? is a ?greatest of? (GO) selection between the leading and lagging sets of cells (GO-CFAR). However, it is demonstrated for a Rayleigh target that the abovementioned suppression effect is more acute in the GO-CFAR. Practically, detection of closely separated targets is almost inhibited. Selection of the ?smallest of? (SO) the means for the adaptive threshold has been proposed to alleviate this problem. An analytic expression for Pd of this detector is also derived, and it is shown that though it does prevent the suppression effect, a large sensitivity loss is introduced unless the number of reference cells is sufficiently large. A modified CO-CFAR detector, combining a ?censoring? circuit, is proposed for automatic detection in a complex nonhomogeneous environment.     

Parametric Rao Test for Multichannel Adaptive Signal Detection

The parametric Rao test for a multichannel adaptive signal detection problem is derived by modeling the disturbance signal as a multichannel autoregressive (AR) process. Interestingly, the parametric Rao test takes a form identical to that of the recently introduced parametric adaptive matched filter (PAMF) detector for space-time adaptive processing (STAP) in airborne surveillance radar systems and other similar applications. The equivalence offers new insights into the performance and implementation of the PAMF detector. Specifically, the Rao/PAMF detector is asymptotically (for large samples) a parametric generalized likelihood ratio test (GLRT), due to an asymptotic equivalence between the Rao test and the GLRT. The asymptotic distribution of the Rao test statistic is obtained in closed form, which follows an exponential distribution under the null hypothesis H ₀ and, respectively, a noncentral Chi-squared distribution with two degrees of freedom under the alternative hypothesis H ₁. The noncentrality parameter of the noncentral Chi-squared distribution is determined by the output signal-to-interference-plus-noise ratio (SINR) of a temporal whitening filter. Since the asymptotic distribution under H ₀ is independent of the unknown parameters, the Rao/PAMF asymptotically achieves constant false alarm rate (CFAR). Numerical results show that these results are accurate in predicting the performance of the parametric Rao/PAMF detector even with moderate data support.     

Modified Savage and Modified Rank Squared Nonparametric Detectors

A modified form of the basic Savage statistic is considered and the performance of a modified Savage (MS) nonparametric detector using this modified statistic is derived. Also, a detector using a modified rank squared statistic (MRS) is introduced. The asymptotic relative efficiency (ARE) of the detectors is determined for chisquare, Rician, and log-normal signal fluctuations when the background noise is assumed Gaussian. The ARE performance of the generalized sign (GS) and Mann-Whitney (MW) detectors is also determined for these families of fluctuations. The ARE performance of the various detectors is then compared, and the results of a computer simulation are presented in which, for a finite number of samples, the performance of the modified detectors is compared with the performance of the GS and MW detectors. It is shown that when using a large number of reference noise samples, the ARE of the GS and MW detectors, the MRS and RS detectors, and the MS and Savage detectors are 0.75, 0.868, and 1, respectively. It is also shown that when using a finite number of reference noise samples the MS and MRS detectors can give a superior performance to that obtained with the MW detector, and that this is particularly true in the cases in which the degree of signal fluctuation is high.     

Linear FM Signal Formats for Beacon and Communication Systems

This paper examines the capabilities of the class of linear FM spread-spectrum signals within the context of potential communications systems usage in order to establish some performance criteria and bounds that permit comparison with other spread-spectrum formats. A systematic basis is provided for parameter selection for this class of signals by examining the interaction a mong the frequency-modulation indices, time-bandwidth product, and cross-talk criteria that determine the number of effective linear FM signals (or channels) that can be used within the constraints of a bounded time-frequency region. A general expression is derived relating N, the number of useful signals, R2, a cross-talk parameter, ToWo, the mean time-bandwidth product, and ?max and ?min, the maximum and minimum FM rates of the signal set. Canonic signal processor structures are described for ensembles of linear FM signals that have either constant duration or constant bandwidth. It is then shown that the signal modulation format can be modified in accordance with classical paired-echo theory to expand the utility of this class of signals in both synchronous and nonsynchronous operations to yield the equivalent of time-division and code multiplexing. Possible applications for this signal format are discussed.     

Hough transform for long chirp detection

The online detection of a very long and weak chirp signal is studied. The signal has an extremely slowly decreasing frequency, and is corrupted by white Gaussian noise and possibly also by powerful tones. By exploring and comparing candidate methods, it is found that the Hough transform (HT) detector appears to be most suitable given constraints on computational load and detectability. The analytical and the simulational performance of the HT detector are obtained and compared with the analytical performance of the generalized likelihood ratio test (GLRT), which is assumed to be optimal. Applying a suitable threshold for the HT can increase speed dramatically while preserving performance. We have found that both dithering (taking varied frequency shifts for fast Fourier transforms (FFTs)) and increasing the FFT length can reduce the minimum detectable frequency slope with nearly no additional computation     

New Autocorrelation and Prediction Techniques for the Demodulation of Binary Signals

The classic problem of detecting a narrowband signal received in a wideband noise is treated via new techniques, namely, autocorrelation computation and linear adaptive filtering. It is shown by analysis and simulation that the proposed techniques yield probility of bit errors cimparable to those provided by coding techniques. Expressions are derived for the detectability parameter of the new test statistics, and it is shown that these statistics are very close to the Gaussian approximation. The improvements obtained in the signal-to-noise ratio and the Gaussian nature of the new statistic implies an improvement in the capacity of the channel by the nonlinear and storage processes involved in the new techniques, something not achievable by linear filtering and/or memoryless detection techniques.     

An Upper Bound on Detection Probability for Fluctuating Signals

In the theory of signal detectability, the signal-to-noise ratio (SNR), defined as the quotient of the average received signal energy and the spectral density of the white Gaussian noise, is a fundamental parameter. For a signal which is exactly known, or known except for a random phase, this ratio uniquely defines the detection performance which can be achieved with a matched filter receiver. However, when the signal amplitude is a random parameter, the detection performance is changed and must be determined from the probability density function (pdf) of the amplitude. Relative to the case of a constant signal amplitude, such signal amplitude fluctuation usually degrades performance when a high probability of detection (Pd) is required, but improves performance at low values of Pd; the corresponding change in the required SNR is the so-called signal fluctuation loss Lf. Thus, since Lf in some cases represents an improvement in performance for low values of Pd, a question of at least theoretical interest is: how large might this improvement be, when the class of all signal amplitude pdf's is considered. The solution, presented here, results in a lower bound on the signal fluctuation loss Lf as a function of Pd, or equivalently an upper bound on Pd as a function of SNR. The corresponding most favorable pdf was determined using the Lagrange multiplier technique and results of a numerical maximization are included to provide insight into the general properties of the solution.     

Data Quantization for Narrowband Signal Detection

In automatic radar detection, digital integration of the envelope detector outputs is often used as a good approximation to the optimum. This requires quantizing the envelope detector outputs. In this paper, quantizer structures for narrowband signal detection are considered. Quantizer characteristics are derived to optimize performance as measured by the detector efficacy?an asymptotic performance measure. Asymptotic and finite sample performance results are presented. The results obtained are not limited in their application to Gaussian noise only, although this important case is given specific consideration.     

An adaptive array detector with mismatched signal rejection

An adaptive detection algorithm with a sensibility parameter for rejecting unwanted signals is presented. This algorithm is a simple modification of the generalized likelihood ratio (GLR) detector (or test) for detecting a signal in zero mean Gaussian noise with unknown correlation matrix. Specifically, the adaptive detection algorithm is obtained by introducing an arbitrary positive scalar, which is called the sensitivity parameter, into the GLR detector as a multiplier of an already existing quadratic term. The GLR detector then becomes a special case of this detector for the unity sensitivity parameter. It is shown that the sensitivity parameter controls the degree to which unwanted signals are rejected. From numerical examples, it is demonstrated how the sensitivity parameter can be chosen such that unwanted signals, can be rejected while maintaining acceptable detection loss for slightly mismatched signals. Further insight into previous work on adaptive detection is also given     

An Optimum Phase Reference Detector for Fully Modulated Phase-Shift Keyed Signals

Many modern telemetry systems which use phase-shift keying (PSK) have receivers which derive a coherent reference from the fully modulated PSK signal itself and thus conserve the energy which otherwise would be allocated to a discrete reference signal. In this paper, an optimum receiver structure for estimating a phase reference from the PSK signal itself is derived and its realization discussed. It is shown that at low signal-to-noise ratios, the optimum detector can be realized with a Costas loop. Since a Costas loop and squaring loop exhibit identical performance, it follows that either of these simple devices gives optimum performance for low-input signal-to-noise ratios.     

A Suboptimum Rank Test for Nonparametric Radar Detection

The optimum rank detector structure, in the Neyman-Pearson sense and under Gaussian noise conditions, is approximated by a suboptimum structure that depends on an adjustable parameter. This new rank detector, which operates on radar video signal, includes other well-known detectors as particular cases. The asymptotic relative efficiency (ARE) of the proposed rank detector is computed, with its maximum value the ARE of the locally optimum rank detector (LORD). The detection probability versus signal-to-noise ratio, and the effects of interfering targets are also calculated by Monte-Carlo simulations for different parameter values.     

M-ary CPSK Detection with Noisy Reference and Interferences

A general expression of the error probability on an M-ary coherent phase-shift-keyed (MCPSK) signal purturbed by a noisy reference carrier, multiple interferences, and additive Gaussian noise is presented taking into account the frequencey divider in the carrier recovery circuit. First, a new expression for the probability density function (pdf) of the phase of a composite wave of signal, multiple interferences, and additive Gaussian noise is derived. Then this result and a pdf of the phase error modified from the Tikhonov distribution are used to obtain the erro probability of an MCPSK detector. In addition, the comparison between the error probabilities with and without the frequency divider is given, and it is found that the estimation is more pessimistic when the frequency divider is included.     

基于IMF能量分布重构的目标检测技术

为提高海杂波中慢速目标的检测性能,提出了一种基于IMF能量分布重构的目标检测技术。该算法对原始信号尖峰区域经经验模态分解后得到的固有模态函数进行分段数据重构,计算前端IMF分量与后端IMF分量的能量比,并将其输入非参量检测器中进行目标检测。研究表明,相比于海杂波单元,目标单元尖峰区域有更小的前后端IMF分量能量比,适用于慢速目标的检测。     

Hard Limiter Performance as a Polarity Detector for Extremely Polluted Signals

A hard limiter is a simple, yet highly efficient, RF signal sensor for VLF and LF navigation receivers. The observation reliability is used as the single quality criterion for the hard limiter if applied as a singlebit analog-to-digital converter (ADC). The effects of noise (Gaussian and atmospheric), nonsynchronous and synchronous interference, and dc offset on the observation reliability are described extensively. The single parameter determination Pobs is adequate for characterizing the polarity detector. This facilitates rank ordering of influences disturbing the signal and is a useful tool in optimizing digital tracking loops. The ?built-in? noise-censoring properties of the hard limiter in the presence of atmospheric noise are excellent. Therefore, three different atmospheric noise models are used in the determination of the observation reliability Pobs. Some ways for coping with other disturbances that potentially threaten the good performance of the hard limiter are suggested.