Loss from Approximations to Square-Law Detectors in Quadrature Systems with Postdetection Integration

The trend toward digital processing of radar and sonar signals has ledto the use of ?baseband? or bipolar video signals. The processingof both the in-phase (I) and quadrature (Q) channels generally allows an exact representation of the signals, and no loss of sensitivity need occur. However, for reasons of economy or weight only one channel is often implemented. This correspondence shows that the sensitivity loss for this case often deviates considerably from the 3-dB rule of thumb.     

Logarithmic Detection with Postdetection Filtering

An analysis is presented of the performance of a logarithmic detector or followed by a low-pass filter, under the assumption of a large ratio of IF bandwidth to postdetection bandwidth. This allows for the probability of detection and similar quantities to be computed in a straightforward manner. The mean and variance of the filter output are found by first deriving the autocorrelation function of the logarithmic detector output and then obtaining the power spectral ral density. A useful engineering approximation is made for the variance which is valid for all signal-to-noise ratios.     

Closed-Form Expressions for Noncoherent Radar Integration Gain and Collapsing Loss

Closed-form formulas allow rapid determination of noncoherent integration gain and integration loss when the single-sample IF signal-to-noise ratio (SNR) is known. In addition, if the required SNR is known for any number of integrated pulses, the required SNR for any other number is easily determined. A closed-form expression is given for radar collapsing loss, expressed in terms of the equivalent integrated signal-to-noise ratio required to produce a given combination of false-alarm and detection probabilities. Alternatively, the single-sample signal-to-noise ratio of a set of samples may be used together with the closed-form expression for integration gain to get the equivalent integrated signal-to-noise ratio.     

Loss in Single-Channel MTI with Post-Detection Integration

The detection performance of a single-channel MTI receiver with post-detection integration, for a Swerling I target, has been evaluated by a Monte Carlo simulation. It is shown that a fairly good approximation is obtained by applying the ?effective number of independent integrated samples? to the standard detection curves. The ?I-only? loss is about 2 dB for integration of more than 20 pulses; thus this receiver is acceptable if implementation constraints dictate it.     

Detectors for Multiomial Input

The binary detection problem is considered. Under an arbitrary noise environment, the input sample space can be transformed into a multinomial vector. Based on observations of this vector, the Neyman-Pearson optimal detector is developed for a known signal. When the signal strength is unknown, the likelihood ratio principle is followed to obtain consistent tests which use the Pearson's chisquare statistic. The resulting detectors are compared to others in terms of asymptotic relative efficiency under some actual noise distributions.     

MTI Loss with Coherent Integration of Weighted Pulses

A moving target indicator (MTI) preceding a coherent integrator causes a degradation in the signal-to-noise ratio (SNR). This negative effect can be reduced by weighting of the MTI output pulses before the integration process. Two examples are given which show the improvement in SNR and detection probability as a result of this weighting.     

Performance Evaluation of Postdetection Integrators with Partially Correlated Noise

A simple procedure for calculating receiver operating characteristics (ROC) for postdetection integration of arbitrary partially correlated noise samples is presented. The approach is based on the application of the ?effective number of independent integrated noise samples? to the classical theory of Marcum and Swerling and has been justified by Monte-Carlo simulation.     

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.     

Two-Stage CFAR Detectors for Multiple-Range-Bin Radars

Two-stage detectors using generalized sign and four-level conditional statistics for signal detection in multiple-range-bin radars are described. The resulting detectors are of constant false-alarm rate (CFAR). Performances are evaluated and compared with singlestage versions. If the a priori probability of either the no-target case or the target-presence case is large (close to 1), a two-stage test can be designed to have the advantage of reducing the average number of samples required without sacrificing detection probability. With the proper choices of parameters, significant improvement in the efficiency can be achieved. Asymptotic relative efficiency of two-stage detectors with respect to single-stage detectors is derived and some numerical results are evaluated.     

Fluctuation Loss and Diversity Gain for In?Phase Systems with Post?Detection Integration

This paper presents a simple method for determining the losses resulting from detecting only the in-phase component of the complex signal vector returned from a Rayleigh-distributed target. A simple rule is given in terms of the fluctuation loss and integration gain of square-law-detected pulses. The integration improvement for the in-phase channel is given for both slow and fast fluctuating Rayleigh targets. The loss associated with failure to use the quadrature signal component is basic in that it accounts for only one Gaussian sample and, therefore, one degree of freedom. The loss incurred with one square-law-detected return as normally implemented in radar receivers represents two degrees of freedom. It is well known that the system performance improves, approaching that for the constant target, with increasing degrees of freedom of the received data. This paper is an extension of earlier work in that it relates previously computed data to a simple rule.     

Detectors for infrared heterodyne mixing and detection

Conclusion For wavelengths < 50m fast and sensitive detectors are available. For wavelengths > 50m the available detectors are far from ideal. Research and development of far infrared detectors for the mixing purpose are highly recommended.     

GLRT Detectors for Aircraft Wake Vortices in Clear Air

 In this article, radar echoes of aircraft wake vortices are modeled as weighted sums of the frequency components of the echoes with a special covariance matrix for the weighted coefficients. With a proposed detection scheme, two generalized likelihood ratio test (GLRT) detectors are derived respectively for aircraft wake vortices with time-varying and time-invariant Doppler spectra. Then the analytical expressions for detection and false alarm probabilities of the detectors are derived and three factors are investigated which mainly influence the detection performance, i.e., the Doppler extension and uncertainty of the aircraft wake vortex, and the number of the detection cells. The results indicate that, the signal-to-noise ratio (SNR) loss induced by Doppler extension is generally several decibels. The SNR loss due to Doppler uncertainty is approximately proportional to the logarithm of the number of spectrum lines in the uncertain Doppler spectrum intervals. For a large number of detection cells, the SNR gain is approximately proportional to the square root of the number of the detection cells.     

A UHF True Logarithmic IF Amplifier

A UHF ?true logarithmic IF? which yields a carrier output proportional in amplitude to the logarithm of the carrier input has been constructed. Although this ?true? form has been known for a number of years, it appears to have been neglected in development. Good performance has been obtained over a 60-dB input signal range with rise and fall times of 2 ns per 20 dB. A high-level, detected dc coupled output without the use of any dc amplifier is obtained. Coherent signal processing of the output carrier is possible, and other important advantages to this type of logarithmic IF are described.     

Logarithmic Compression of Digitally Telemetered Data

To express a number using true logarithmic compression, at least B = log2 [log R log(1 + Q/100 1 - Q/100/)] bits are required. (R = dynamic range, Q = ±error percent.) True logarithmic compression is rarely used in practice, but quasi-logarithmic methods such as normalized floating-point format are used frequently. A partially unnormalized floating-point format provides the best performance in the case of digital data. For this method B = log2 [100 log2 (4R Q/l00 Q 1 - Q/100)]-1. This paper contains analytical and graphical results that facilitate comparison of the various systems.     

A Logarithmic Frequency Allocation Algorithm for Wideband Discrete Frequency Pulse Trains

It is shown that signal waveforms utilizing discrete frequency modulation (DFM) which are generated using a narrowband or frequency shift algorithm have ambiguity sidelobe distortion which is caused by the approximation of time compression by frequency shift. A logarithmic frequency allocation algorithm is presented which couches the signal design problem in terms of band and step ratios, rather than in terms of bandwidth and frequency steps, and is consistent with the wideband formulation of the ambiguity function. The algorithm makes use of the same basic code generating sequence used for narrowband frequency allocation, but the resulting signal will have invariant ambiguity sidelobe positions for any receiver realization in the delay-time compression plane.     

Performance Evaluation of Energy Detectors

The prediction of energy detector performance requires a complicated calculation or a tedious manipulation of nomograms. For a large time-bandwidth product WT, however, it is commonplace to use the formula (E/No) = d?WT to anticipate the required average input energy-to-noise spectral density ratio for a wanted signal detectability parameter d and thus avoid the computational difficulty. This paper proposes a modified formula (E/No) = ?d?WT that is applicable for all range of WT, where ? is the modification factor derived on an empirical basis. The Van Trees measure of the signal detectability parameter of the energy detector also is derived analytically and compared to the modified equation.     

Trimmed Generalized Sign and Modified Median Detectors for Multiple Target Situations

The trimmed generalized sign (TGS) nonparametric detector is introduced. The TGS and the modified median detector (MMD) are considered in situations when more than one target is present. Their performance is obtained through Monte Carlo simulations and compared with that of the generalized sign (GS) detector when detecting nonfluctuating signal in Gaussian noise.     

Design Principles of MIMO Radar Detectors

This paper considers the problem of multiple-input multiple-output (MIMO) radars employing space-time coding (STC) to achieve diversity. To this end, after briefly outlining the model of the received echo, a suitable detection structure is derived, and its performance is expressed in closed form as a function of the clutter statistical properties and of the space-time code matrix. Interestingly, this receiver requires prior knowledge of the clutter covariance, but the detection threshold is functionally independent thereof. At the transmitter design stage, we give two criteria for code construction: the first is based on the classical Chernoff bound, the second is an information-theoretic criterion. Interestingly, the two criteria lead to the same condition for code optimality, which in turn specializes, under the assumption of uncorrelated clutter and square code matrix, in some well-known full-rate space-time codes. A thorough performance assessment is also given, so as to establish the optimum achievable performance for MIMO radar systems.     

Studies of Logarithmic Radar Receiver Using Pulse-Length Discrimination

Using a logarithmic amplifier giving a detected output followed by a high-pass filter is a technique for reducing adverse effects of distributed clutter in radar receivers. A pulse-length discriminator (PLD) used as the high-pass filter is treated here. Theoretical and experimental results for the loss in detectability introduced by this receiver, as compared with a matched filter or a good approximation thereto, have been obtained. For the case of single-hit detection, losses of 4 to 8 dB are introduced by the logarithmic amplifier/pulse-length discriminator (LOG AMP/PLD) combination; for post-detection integration, the losses are reduced to 2 to 4 dB. The latter values would apply where the LOG AMP/PLD output is presented on a PPI (plan position indicator). Some experimental results of the ability of the LOG AMP/PLD receiver to reject signals of incorrect pulse length show that signals exceeding the design pulse length by more than 25 to 50 percent are effectively suppressed. No significant short-pulse discrimination is obtained from the receiver.