Multiple-Tone Signals and Detection Probabillities

An analysis technique is presented for multiple-tone signals insystems employing noncoherent integration of a square-law detectoroutput. It is shown how the characteristic function for the teststatistic can be found from the easily determined "coherent"characteristic function defined in the two-dimensional signal space.This result is applied to two detection problems, the detection of multiple-tone signals in Gaussian noise and the detection of a Gaussian signal in multiple-tone plus Gaussian noise interference.The detection curves are compared to an approximation that is often used in practice to estimate performance. It is found that detection performance in the presence of multiple-tone interferences can be significantly different from that in the presence of Gaussian noise alone.     

Noncoherent approach to through-the-wall radar localization

A noncoherent through-the-wall radar system approach, based on stepped-frequency signal synthesis and trilateration technique, is presented. This approach involves multiple independent monostatic radar units and as such, provides flexibility in positioning the units with various standoff distances and inter-element spacing. The performance of the proposed noncoherent localization system was demonstrated using simulated and real data. The results show that the radar is able to detect and locate multiple targets behind walls     

Coherent Doppler tomography-a technique for narrow band SAR

Some concerns regarding a technique of narrowband synthetic aperture radar (N-SAR) imaging called coherent Doppler tomography (CDT), which may be a good candidate for spaceborne applications, are addressed. Using a single-frequency signal, are addressed. Using a single-frequency signal, resolution of two tenths of a wavelength can be achieved in the point spread function if the radar platform circles the ground path to be imaged. However, the high sidelobe level of -8-dB in the point spread function results in an unacceptable dynamic range. To reduce the sidelobe level, two approaches are presented: coherent processing using multiple discrete frequencies and noncoherent subaperture processing. Simulation results demonstrate that the sidelobe level is substantially reduced by both methods. However, the resolution is degraded and the computational overhead is greatly increased for noncoherent subaperture processing. Also presented is a possible satellite geometry configuration that could utilize N-SAR processing to provide high-resolution global mapping capability     

A Comparison of Noncoherent and Coherent MTI Improvement Factors

An analysis based on statistical considerations and Monte Carlo simulations indicates that a noncoherent moving target indicator (MTI) using a linear envelope detector differs from one using a square law envelope detector. The square law envelope detector is usually described in the literature because of ease of analysis, and it is commonly stated or implied that the results are the same for the two cases because of the similar spectral characteristics of the detectors. A comparison is made between the two noncoherent MTIs and the coherent MTI in terms of clutter attenuation and MTI improvement factors.     

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     

Direct position determination using single moving rotating linear array: Noncoherent and coherent processing

To improve the resolution and accuracy of Direct Position Determination (DPD), this paper investigates the problem of positioning multiple emitters directly with a single moving Rotating Linear Array (RLA). Firstly, the geometry of the RLA is formulated and analysed. According to its geometry, the intercepted noncoherent signals in multiple interception intervals are modeled. Correspondingly, the MUltiple SIgnal Classification (MUSIC) based noncoherent DPD approach is proposed. Secondly, the synchronous coherent pulse signals are individually considered and formulated. And the coherent DPD approach which aims for localizing this special type of signal is presented by stacking all array responses at different interception intervals. Besides, we also derive the constrained Cramér-Rao Lower Bound (CRLB) expression for both noncoherent and coherent DPD with RLA under the constraint that the altitudes of the emitters are known. At last, computer simulations are included to examine the performance of the proposed approach. The results demonstrate that the localization accuracy and resolution of DPD with single moving linear array can be significantly improved by the array rotation. In addition, coherent DPD with RLA further improves the resolution and increases the maximum emitter number that can be localized compared with the noncoherent DPD with RLA.     

Variance Analysis of the Angle Output Voltage for an Amplitude Monopulse Receiver

The amplitude-comparison monopulse receiver utilizes two overlapping antenna patterns to determine the angle of arrival of an incoming RF signal for use in a direction-finding application. The thermal noise introduced by the receiver distorts the signal, causing an error in determining the exact angle of arrival of the signal. The analysis derives an expression for the deviation of the angle output voltage, or the angular error, due to receiver noise as a function of 1) the angle of arrival and 2) the signal-to-noise ratios of the two channels of the receiver. A receiver using a square-law detector and one using a linear detector are analyzed.     

Detectability of signals in Laplace noise

Closed-form expressions for the false-alarm and detection probabilities attained by the optimum and the linear detectors of a positive signal in n independent samples of noise having a bilateral exponential or Laplace distribution require lengthy computation when n is large, and those for the optimum detector suffer from round-off error because their terms alternate in sign. It is shown how the method of saddlepoint integration can be conveniently applied to compute these probabilities, and numerical comparisons of the accuracies of the methods are presented. The relative efficiency of the two detectors is calculated as a function of n and found to approach the asymptotic value of 2 very slowly     

Moments of Estimated Input Power for Finite Sample Averages of Radar Receiver Outputs

Closed-form solutions for all the estimated power moments as a function of the number of independent samples were found for the linear and logarithmic receiver. Incoming signal envelope distribution is assumed to be Rayleigh. The estimates' expected value and standard deviations are plotted and compared with those of a square-law receiver. It is shown that the bias in the expected value for both receivers depends on the number of samples. Only when the number of samples is large does the bias become constant, and the standard deviation around the unbiased mean becomes inversely proportional to the square root of the number of samples. The logarithmic receiver produces the largest standard deviation. When the input samples are dependent, an expansion of the method is suggested to obtain approximate moments.     

Analysis and Design Considerations of Hard Limiters for LF and VLF Navaid Receivers

Hard limiters, followed by a D-type flip-flop as a digital-signal-polarity detector, are very effective receiver/phase detectors for low frequency (LF) and very low frequency (VLF) navigation receivers. However the performance not only depends on the signal quality, but also on the specifications of the hard limiter and the flip-flop. Analysis of the tracking accuracy is given as a function of the dc offsets of the limiter and the flip-flop, the linear gain of the limiter, the signal-to-noise ratios of one or more input signals, and the power consumption of the limiter. The results are presented in formulas and graphs for application by circuit designers. A design example of a low-power, high-gain limiter is given.     

Simple Expressions for Determining Radar Detection Thresholds

The threshold value required to obtain a specified false-alarm probability, when postdetection integration follows a square-law or an envelope detector, is frequently needed in theoretical and practical studies of radar signal processor performance. The determination of such threshold values requires a substantial numerical computational effort. In this correspondence, simple expressions are presented with which these thresholds can be determined with excellent accuracy using only a scientific calculator.     

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.     

Nonparametric rank detectors under K-distributed clutter in radar applications

This correspondence deals with a comparative analysis of parametric detectors versus rank ones for radar applications, under K-distributed clutter and nonfluctuating and Swerling II target models. We show that the locally optimum detectors (LODs) (optimum for very low signal-to-clutter ratio (SCR)) under K-distributed clutter are not practical detectors; on the contrary, asymptotically optimum detectors (optimum for high SCR) are the practical ones. The performance analysis of the parametric log-detector and the nonparametric (linear rank) detector is carried out for independent and identically distributed (IID) clutter samples, correlated clutter samples, and nonhomogeneous clutter samples. Some results of Monte Carlo simulations for detection probability (P/sub d/) versus SCR are presented in curves for different detector parameter values.     

Cancellation of Unwanted Spectral Components in an FM Multivibrator System

The performance of FM multivibrator systems for high quality communications applications is limited by the presence of unwanted spectral components. A theory is presented for an improved system in which unwanted spectral components are cancelled, achieved by generating a cancelling component in a square-law device. The cancelling component tracks the unwanted component in both frequency and amplitude over a wide bandwidth of signal frequencies. Reductions in magnitude of the unwanted components by at least 16 dB are predicted; reductions of better than 14 dB have been achieved in practice.     

Evaluation and reduction of multipath-induced bias on GPS time-of-arrival

New expressions are presented for the multipath-induced pseudorange error (i.e. bias) and variance introduced by multipath onto the time-of-arrival estimate obtained using a noncoherent early-late gate discriminator. The results include the effect of front-end bandwidth and early-late gate spacing. We also investigate a blind method for cancelling the multipath, in order to improve the time-of-arrival estimate. Our approach uses early-late gate processing on an objective function derived from an adaptive finite impulse response (FIR) filter that attempts to match the crosscorrelation of the received signal with a multipath-free replica of the desired crosscorrelation. This method performs reasonably well, and decreases the multipath-induced pseudorange error by approximately a factor of 2, even in very stressing multipath environments.     

Detection of Target Maneuver Onset

A classical maneuvering target tracking (MTT) problem (detection of the onset of a target maneuver) is presented in two parts. The first part reviews most traditional maneuver onset detectors and presents results from a comprehensive simulation study and comparison of their performance. Six algorithms for maneuver onset detection are examined: measurement residual chi-square, input estimate chi-square, input estimate significance test, generalized likelihood ratio (GLR), cumulative sum, and marginalized likelihood ratio (MLR) detectors. The second part proposes two novel maneuver onset detectors based on sequential statistical tests. Cumulative sums (CUSUM) type and Shiryayev sequential probability ratio (SSPRT) maneuver onset detectors are developed by using a likelihood marginalization technique to cope with the difficulty that the target maneuver accelerations are unknown. The proposed technique gives explicit solutions for Gaussian-mixture prior distributions, and can be applied to arbitrary prior distributions through Gaussian-mixture approximations. The approach essentially utilizes a~priori information about the maneuver accelerations in typical tracking engagements and thus allows to improve detection performance as compared with traditional maneuver detectors. Simulation results demonstrating the improved capabilities of the proposed onset maneuver detectors are presented.     

Noncoherent Detection of Split-Phase FSK by Multiple Predetection Filtering

When the cumulative drift in the center frequency of a binary split-phase FSK signal exceeds the peak deviation of the signal, a conventional noncoherent receiver (i.e., one provided with only two IF filters) may be unable to achieve the probability of error per bit which the designer desires. This limitation may be overcome if the receiver is provided with a bank of more than two contiguous filters (each followed by an envelope detector) tospan the total IF band the instantaneous IF signal might occupy. It is shown that the probability of error per bit for such a receiver is a function of 1) the ratio F of peak frequency deviation to peak frequency drift, 2) the number M of IF filter/detectors, and 3) the signal-to-noise ratio ? in the output of the filter containing the signal. It is further shown thatfor a given value of F an increase in M reduces the amount of transmitter power the communication system designer must provide to yield a given probability of error per bit.     

Second time around radar return suppression using PRI modulation

A technique for suppressing second-time-around radar returns using pulse-repetition interval (PRI) modulation is presented and analyzed. It is shown that a staggered PRI radar system can offer considerable improvement over a nonstaggered radar system in rejecting second-time-around returns which cause false alarms. This improvement is a function of detector implementation (noncoherent integrator or binary integrator), the number of staggered PRIs, the quiescent false alarm number, the Swerling number of the false return, the transmitted signal power, the second-time-around noise power, and the quiescent noise power of the radar. Small changes in transmitted signal power can be traded off with the quiescent false alarm number to suppress the bogus return significantly. In addition, for a noncoherent integrator, all other parameters being equal, if the second-time-around return is a Swerling case II or IV target, then there is an optimum number of staggered PRIs that can be chosen to minimize the likelihood of its detection. It is also shown that the binary integrator significantly reduces the number of second-time-around return detections when compared with the noncoherent integrator. However, there is an accompanying loss of detection     

Importance sampling for characterizing STAP detectors

This paper describes the development of adaptive importance sampling (IS) techniques for estimating false alarm probabilities of detectors that use space-time adaptive processing (STAP) algorithms. Fast simulation using IS methods has been notably successful in the study of conventional constant false alarm rate (CFAR) radar detectors, and in several other applications. The principal objectives here are to examine the viability of using these methods for STAP detectors, develop them into powerful analysis and design algorithms and, in the long term, use them for synthesizing novel detection structures. The adaptive matched filter (AMF) detector has been analyzed successfully using fast simulation. Of two biasing methods considered, one is implemented and shown to yield good results. The important problem of detector threshold determination is also addressed, with matching outcome. As an illustration of the power of these methods, two variants of the square-law AMF detector that are thought to be robust under heterogeneous clutter conditions have also been successfully investigated. These are the envelope-law and geometric-mean STAP detectors. Their CFAR property is established and performance evaluated. It turns out the variants have detection performances better than those of the AMF detector for training data contaminated by interferers. In summary, the work reported here paves the way for development of advanced estimation techniques that can facilitate design of powerful and robust detection algorithms