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.     

Design of Truncated Sequential Tests for Rapidly Fading Radar Targets

Curves and equations are presented from which the exact performance of truncated sequential tests can be determined for one important case: the biased square-law detector for the detection of rapidly fading targets. The method of generating functions is used to derive probability distributions for sample size. It is shown how these probability distributions can be used to determine truncation errors and the effects of multiple-resolution elements. Sample calculations are performed to determine the effects of a particular truncation procedure.     

Adaptive polarimetric target detection with coherent radar. I.Detection against Gaussian background

The derivation of a completely adaptive polarimetric coherent scheme to detect a radar target against a Gaussian background is presented. A previously proposed Generalized Likelihood Ratio Test (GLRT) polarimetric detector is extended to the case of a general number of channels; this exploits the polarimetric characteristics of the received radar echoes to improve the detection performance. Together with the fully adaptive scheme, a model-based detector is derived that has a lower estimation loss. A complete theoretical expression is derived for the detection performance of both proposed polarimetric detectors. They are shown to have Constant False Alarm Rate (CFAR) when operating against Gaussian clutter, but to be sensitive to deviations from the Gaussian statistic. The application to recorded radar data demonstrates the performance improvement achievable in practice     

Multisensor distributed sequential detection

A conceptual generalization of the Wald's sequential probability ratio test (SPRT) to a decentralized environment is presented. The local tests are chosen to be SPRT's, which quantize the temporally independent identically distributed (IID) observations into three levels for transmission to the fusion detector. Spatial independence among the local observations is assumed. The fusion test is also an SPRT. An analysis for the decentralized scheme is developed. Performance comparisons with the centralized and other decentralized schemes are presented     

Modeling and analysis for the GPS pseudo-range observable

In this paper, a digital system for the Global Positioning System (GPS) pseudo-range observable is modeled and analyzed theoretically. The observable is measured in a GPS receiver by accurately tracking the pseudorandom noise (PRN) code phase of the input GPS signal using a digital energy detector and a digital delay lock loop (DDLL). The following issues are presented: (1) mathematical modeling of the digital PRN code acquisition and tracking system, (2) the closed-form expression derivation for the detection and false-alarm probabilities of the acquisition process and for the variance of code phase tracking error, and (3) the linear and nonlinear performance analysis of the DDLL for optimizing the receiver structures and parameters with tradeoff between the tracking errors due to receiver dynamics and due to input noise     

A Sequential Detector

The PRSD detector improves radar performance by controlling the distribution of energy in space, thus making a radar adaptive to its environment. An increase in performance over classical detectors may be realized in any of several ways: 1) greater maximum range; 2) smaller minimum detectable targets; 3) higher data rates; 4) lower average transmitted power, which allows smaller size and weight of equipment. The model of the PRSD detector described herein was tested with a semi-agile beam radar, and gave measured field performance improvement (for this particular radar) equivalent to an S/N increase ranging from 5 to 22 dB with a mean of 9.5 dB. This increase is greater than the 5-dB improvement predicted for the system in a white noise environment because many of the field tests were at locations subjected to heavy interference. The PRSD detector was extremely effective reducing the interference. In this paper, we will briefly review the theory of operation, describe the equipment and the method of test, and present experimental data. The data presented here are essential to a complete understanding of sequential detection since a rigorous theory encompassing multiple range bin radar has not been developed at this time. Finally, an extensive bibliography is appended.     

Performance of the Analog Moving Window Detector

A type of analog integrating moving window detector for use with a scanning pulse radar is examined. A performance analysis is carried out, which takes into account both the radiation pattern of the antenna and the dynamic character of the detection process due to the angular scanning of the antenna. An expression for the false alarm rate of the detector is first derived and evaluated numerically. The detection performance and angular accuracy are next determined in a direct Monte Carlo simulation of the detector on a digital computer for both no fading and pulse-to-pulse Rayleigh fading. Finally the influence on detection performance of the width used for the moving window is investigated.     

Hard Limiting and Sequential Detection Applied to Loran-C

The combination of an antenna, a 100 kHz bandpass filter, a hard limiter, and a sequential detector can supply highly accurate Loran-C data to a digital processor, even under low signal-to-noise-ratio conditions. For such a simple, low-cost receiver, calculations are given for the accuracy of the envelope and phase tracking of the Loran-C signal as a function of the signal-to-noise (Gaussian and atmospheric) ratio, averaging time, and radian speed of the observer with respect to the transmitter. Mentioned are the quasi-noise censoring effects of the hard limiter. Besides the Loran-C application, the hard limiter-sequential detector system can in general be applied for low-cost, synchronous signal detection under poor signal-to-noise ratio.     

A variably trimmed mean CFAR radar detector

A variably trimmed mean (VTM) constant false alarm rate (CFAR) detector in which the threshold is determined by processing a linear combination of a group of ordered samples in each window is introduced. Unlike the trimmed mean detector, the number of ordered samples that require further processing is allowed to vary according to a data-dependent rule. It is demonstrated that the VTM detector exhibits performance characteristics that are independent of the total (stationary) noise power. Simulated performance results are presented for regions of clutter power transitions and for multiple target environments to illustrate the possible improvement over the order-statistic detector that can be obtained by using a VTM detector     

Multiband coherent radar detection against compound-Gaussianclutter

A Multiband GLRT-LQ (Generalized Likelihood Ratio Test-Linear Quadratic), MBGLRT-LQ, detector is derived for the coherent radar target detection against a compound-Gaussian clutter background. This scheme is an extension to the multiband case of the Asymptotically Optimum Detector (AOD), also derived under the name of GLRT-LQ in. The proposed multiband version of the algorithm shows two main advantages with respect to the original single-band algorithm. 1) For the adaptive implementation, it requires a much smaller area of homogeneous clutter echoes to estimate the covariance matrix of the interference; 2) it provides an optimum processing of the radar echoes when the radar operates in frequency agility, as electronic counter-countermeasure (ECCM) strategy. A closed form performance analysis is provided for the MBGLRT-LQ detector, which is used to compare it with the single-band version. An application to live recorded data is also presented to validate the obtained results     

Difference beam aided target detection in monopulse radar

The classical detection step in a monopulse radar system is based on the sum beam only,the performance of which is not optimal when target is not at the beam center. Target detection aided by the difference beam can improve the performance at this case. However, the existing difference beam aided target detectors have the problem of performance deterioration at the beam center, which has limited their application in real systems. To solve this problem, two detectors are proposed in this paper. Assuming the monopulse ratio is known, a generalized likelihood ratio test(GLRT) detector is derived, which can be used when targeting information on target direction is available. A practical dual-stage detector is proposed for the case that the monopulse ratio is unknown. Simulation results show that performances of the proposed detectors are superior to that of the classical detector.     

Performance Analysis of the Censored Mean-Level Detector

The censored mean-level detector (CMLD) is an alternative to the mean-level detector that achieves robust detection performance in a multiple-target environment by censoring several of the largest samples of the maximum likelihood estimate of the background noise level. Here we derive exact expressions for the probability of detection of the CMLD in a multiple-target environment when a fixed number of Swerling II targets are present. The primary target is modeled by Swerling case II, and only single-pulse processing is analyzed. Optimization of the CMLD parameters is considered, and a comparison to other detectors is presented.     

Performance of max-mean level detector with and without censoring

The maximum-mean-level detector (MX-MLD) is a constant false-alarm rate (CFAR) detector designed to eliminate the excessively high false-alarm rate seen with the MLD at the edges of contiguous clutter regions. The concomitant high target suppression effect led M. Weiss (1982) to suggest a censored modification. The authors analyze the detection performance of the maximum-censored-mean-level detector (MX-CMLD). A homogeneous Swerling II target and clutter environment are assumed, and only single-pulse detection is considered. Analytic results apply equally to the MX-MLD and extend previous analysis. Simulation results are presented that demonstrate the qualitative effects of various CFAR detectors in nonhomogeneous clutter environments     

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.     

Data quantization effects in CFAR signal detection

In this paper, we investigate data quantization effects in constant false alarm rate (CFAR) signal detection. Exponential distribution for the input data and uniform quantization are assumed for the CFAR detector analysis. Such assumptions are valid in the case of radar for a Swerling I target in Gaussian clutter plus noise and a receiver with analog square-law detection followed by analog-to-digital (A/D) conversion. False alarm and detection probabilities of the cell averaging (CA) and order statistic (OS) CFAR detectors operating on quantized observations are analytically determined. In homogeneous backgrounds with 15 dB clutter power fluctuations, we show analytically that a 12-bit uniform quantizer is sufficient to achieve false alarm rate invariance. Detector performance characteristics in nonhomogeneous backgrounds, due to regions of clutter power transitions and multiple interfering targets, are also presented and detailed comparisons are given     

Nonparametric Radar Extraction Using a Generalized Sign Test

A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described. The detector is based on a generalization of the well-known two-sample sign test and thus requires a set of reference noise observations in addition to the set of observations being tested for signal presence. The detection performance against Gaussian noise is determined for a finite number of observations and asymptotically, for both nonfluctuating and pulse-to-pulse Rayleigh fluctuating target statistics. It is noted that the performance loss, as compared to the optimum parametric detector, depends critically on the number of reference noise observations available when the number of hits per target is not large. In the same case a much larger loss is also found for a pulse-to-pulse fluctuating target even though the asymptotic loss is the same as for a nonfluctuating target. A comparison is finally made with a detector based on the Mann-Whitney test, which usually is considered to be one of the better nonparametric procedures for the two-sample case.     

On the performance of polarimetric target detection algorithms

The performance of six polarimetric target detection algorithms is analyzed. The detection performance of the optimal polarimetric detector (OPD), the identity-likelihood-ratio-test (ILRT), the polarimetric whitening filter (PWF), the single-polarimetric channel detector, the span detector, and the power maximization synthesis (PMS) detector is compared. Results are presented for both probabilistic and deterministic targets in the presence of complex Gaussian clutter. The results indicate that the PWF and the ILRT typically achieve near optimal performance. The remaining detection algorithms typically yield performance that is degraded compared to the performance of the OPD, the PWF, and the ILRT     

A Postdetection Method of Measuring Predetection RF Signal-to-Noise Ratio

A method of determining the predetection signal-to-noise power ratio in a radio receiving system by measurement of average postdetection signal-plus-noise and noise-only voltages (dc output of the detector) is described. The principle has actually been known for many years, but does not seem to be well known or widely used, possibly because of some associated computational difficulties. Some digital computer tabulated results are presented which remove these difficulties, and measurement techniques are discussed. The calculation of expected signal-to-noise ratio for radio and radar systems is briefly reviewed.     

A sequential detection approach to target tracking

Sequential hypothesis testing is investigated for multiframe detection and tracking of low-observable maneuvering point-source targets in a digital image sequence. The proposed multiple multistage hypothesis test tracking (MMHTT) algorithm extends tracks formed from sequentially detected target trajectory segments using a multiple hypothesis tracking strategy. The MMHTT algorithm does not require a probabilistic larger maneuver model. Computational efficiency is achieved by using a truncated sequential probability ratio test (SPRT) to prune a dense tree of candidate target trajectories and score the detected trajectory segments. An analytical performance evaluation is presented and confirmed by experimental results from an optical satellite tracking application     

Analysis of the linear amplifier/analog-digital converter interfacein a digital microwave receiver

An analysis of the relationship between a linear amplifier chain and an analog-to-digital converter (ADC) in a digital microwave receiver, with respect to sensitivity and dynamic range issues, is presented. The effects of gain, third-order intermodulation products and ADC characteristics on the performance of the receiver are illustrated and design criteria for the linear amplifier chain (given a specified ADC) are developed. A computer program is included which calculates theoretical receiver performance based on gain and third-order intermodulation product selections. Experimental results are also presented and compared with theoretical values