Constrained bandwidth waveforms with minimal dilation sensitivity

Bandpass waveforms which have envelopes which are insensitive to this velocity-induced time dilation can be efficiently processed by narrowband receivers in which envelope correlation is fixed and Doppler tested using fast Fourier transform (FFT) processing. The peak level of the waveform ambiguity function (AF) can be used to gauge the distortion of the waveform induced by dilation. The degree of AF attenuation is shown to be proportional to the dilation parameter or velocity, waveform traveling wave (TW) product, and a sensitivity parameter which depends on the envelope function utilized. Classes of symmetric, constrained bandwidth, phase modulated envelope functions which are minimally dilation sensitive (Doppler tolerant) are derived. When the resulting waveforms are used with a simple correlation receiver structure and the echo data is derived from slowly fluctuating point scattering in white Gaussian noise, the receiver becomes an uncoupled joint estimator of delay and dilation (Doppler). In the case of the bandpass waveforms, only odd symmetry of the phase modulation (PM) yields an uncoupled estimator     

Low observable target motion analysis using amplitude information

In conventional passive and active sonar system, target amplitude information (AI) at the output of the signal processor is used only to declare detections and provide measurements. We show that the AI can be used in passive sonar system, with or without frequency measurements, in the estimation process itself to enhance the performance in the presence of clutter where the target-originated measurements cannot be identified with certainty, i.e., for “low observable” or “dim” (low signal-to-noise ratio (SNR)) targets. A probabilistic data association (PDA) based maximum likelihood (ML) estimator for target motion analysis (TMA) that uses amplitude information is derived. A track formation algorithm and the Cramer-Rao lower bound (CRLB) in the presence of false measurements, which is met by the estimator even under low SNR conditions, are also given. The CRLB is met by the proposed estimator even at 6 dB in a cell (which corresponds to 0 dB for 1 Hz bandwidth in the case of a 0.25 Hz frequency cell) whereas the estimator without AI works only down to 9 dB. Results demonstrate improved accuracy and superior global convergence when compared with the estimator without AI. The same methodology can be used for bistatic radar     

Doppler visibility of coherent ultrawideband random noise radar systems

Random noise radar has recently been used in a variety of imaging and surveillance applications. These systems can be made phase coherent using the technique of heterodyne correlation. Phase coherence has been exploited to measure Doppler and thereby the velocity of moving targets. The Doppler visibility, i.e., the ability to extract Doppler information over the inherent clutter spectra, is constrained by system parameters, especially the phase noise generated by microwave components. Our paper proposes a new phase noise model for the heterodyne mixer as applicable for ultrawideband (UWB) random noise radar and for the local oscillator in the time domain. The Doppler spectra are simulated by including phase noise contamination effects and compared with our previous experimental results. A genetic algorithm (GA) optimization routine is applied to synthesize the effects of a variety of parameter combinations to derive a suitable empirical formula for estimating the Doppler visibility in dB. According to the phase noise analysis and the simulation results, the Doppler visibility of UWB random noise radar depends primarily on the following parameters: 1) the local oscillator (LO) drive level of the receiver heterodyne mixer, 2) the saturation current in the receiver heterodyne mixer, 3) the bandwidth of the transmit noise source, and 4) the target velocity. Other parameters such as the carrier frequency of the receiver LO and the loaded quality factor of the LO have a small effect over the range of applicability of the model and are therefore neglected in the model formulation. The Doppler visibility curves generated from this formula match the simulation results very well over the applicable parameter range within 1 dB. Our model may therefore be used to quickly estimate the Doppler visibility of random UWB noise radars for trade-off analysis     

Design and analysis of new p(n,k) polyphase pulse compression codes

P(n,k) codes as a new class of polyphase pulse compression codes are introduced and analyzed in detail. The P(n,k) codes are conceptually derived by step approximation of the phase function of a nonlinear-frequency modulated (NLFM) Chirp signal with a favorable energy density spectrum. The significant advantages of P(n,k) codes over conventional polyphase codes are lower autocorrelation sidelobes and an improved tolerance of low Doppler shifts and precompression bandwidth limitations. The primary disadvantage of the P(n,k) codes over conventional codes is a loss in range resolution. The uniform P(n,k) codes are especially attractive for radars employing digital signal professing because their favorable correlation properties also remain when quantization effects are taken into account     

Some Properties and Effects of Reverberation in Acoustic Surveillance

Following the work of Van Trees,[1] the effect of wide-sense stationary clutter on signal detectability with a matched filter is determined. The improvement to be gained by a high time-bandwidth product in the transmitted waveform for the detection of low-velocity targets is clearly shown. The additional noise contributed by the clutter is reduced by a factor equal to the time-bandwidth product. This reducing effect occurs provided that the transmitted waveform is adjusted properly. The optimum transmitted waveform for detection of low-velocity targets turns out to be one whose energy density spectrum is flat over the bandwidth of interest. This derivation is made by a simple application of Schwarz's inequality rather than the application of the calculus of variations that was done by Manasse.[14] Computations were made of the loss encountered by a narrow-band single-frequency waveform and by a wide-band linear FM waveform, each used in a matched-filter detector. The contrast is especially marked for very low target speeds where the narrow-band waveform is very bad. Its loss drops off sharply with target speed while the loss of the wide-band waveform drops off very slowly in comparison. Beyond a certain small target speed, the narrow-band loss is negligible. However, with enough bandwidth, the wide-band waveform can be made to have acceptable loss at all target speeds.     

Range, radial velocity, and acceleration MLE using radar LFM pulsetrain

An efficient implementation of the maximum likelihood estimator (MLE) is presented for the estimation of target range, radial velocity, and acceleration when the radar waveform consists of a wideband linear frequency modulated (LFM) pulse train. Analytic properties of the associated wideband ambiguity function are derived; in particular the ambiguity function, with acceleration set to zero, is derived in closed form. Convexity and symmetry properties of the ambiguity function over range, velocity, and acceleration are presented; these are useful for determining region and speed of convergence for recursive algorithms used to compute the MLE. In addition, the Cramer-Rao bound (CRB) is computed in closed form which shows that the velocity bound is decoupled from the corresponding bounds in range and acceleration. A fast MLE is then proposed which uses the Hough transform (HT) to initialize the MLE algorithm. Monte Carlo simulations show that the MLE attains the CRB for low to moderate signal-to-noise depending on the a priori estimates of range, velocity, and acceleration     

A Unique Digital Doppler Ambiguity Resolution Technique

This correspondence describes a unique digital Doppler ambiguity resolution technique for a pulsed S-band radar. Whereas conventional methods of resolving ambiguities employ various curve fitting schemes in which the best differentiated range curve fit is compared with the Doppler derived velocity, the method described here uses the opposite approach, i.e., the Doppler derived velocity is integrated and compared with the range change over the integrating interval. The integrating approach offers the following advantages over conventional curve fitting. 1) There are no lag errors due to velocity changes, other than tracker lag induced by jerk. 2) No large storage of past data points and their weighting Constants must be implemented.     

Calculating Detection Probabilities for Adaptive Thresholds

In calculating detection probabiities for radar and sonar systems it is usually assumed that the threshold required to yield a certain probability of false alarm is known. This is often not the case for real systems and therefore the threshold must be estimated using some measure related to the test statistic. This paper presents a calculation technique that handles estimated (adaptive) thresholds in a general framework that can be applied easily to many detection problems. False alarm and detection probabilities are calculated from the characteristic function of the noise or signal plus noise variate and the characteristic function of the threshold estimate. To illustrate the method the detection performance of overlapped discrete Fourier transforms (DFTs) is calculated for a narrowband Gaussian target signal.     

Aperture error mitigation via local-state estimation for frequency-based emitter location

This paper considers the problem of locating a stationary coherent emitter via a single moving platform making frequency measurements in the presence of aperture state uncertainty. It is shown that the estimated emitter location is most sensitive to the receiving aperture velocity uncertainty. The required aperture velocity accuracy is determined through a noninfinitesimal perturbation analysis. A solution to location accuracy enhancement with a minimal hardware addition is attempted. It is shown that this can be achieved by mounting a high-resolution tri-axis microelectromechanical systems (MEMS) accelerometer at the aperture to measure its velocity, which can deviate significantly from that estimated by the on-board navigation system. The Doppler shifts of the GPS signal carrier frequency, whenever it can be acquired through the aperture, are also considered as a way to aid the aperture velocity measurement. A decentralized, federated processing method for the aperture velocity estimate referenced at the aperture, integrating all measurement data, is presented. An upper bound for the error of aperture velocity estimate is derived. The potential for significant accuracy enhancement for emitter location is demonstrated.     

Range and Bearing Estimation in Passive Sonar

Passive sonar systems are used for estimating the range and bearing of signal sources, such as ships or submarines. In this study, the Cramer-Rao bounds on estimation errors are used as measures of the accuracy of the estimates. The bounds show how parameters such as observation time, signal bandwidth, signal-to-noise ratio, and array geometry can be chosen to obtain maximum accuracy. When the array geometry satisfies certain conditions, the bound for range estimate is shown to be independent of the actual source bearing and the bound for bearing estimate independent of both the range and bearing of the source. It is also shown that the same conditions on array geometry ensure that the range or bearing estimation accuracy is not degraded when tne other pammeter is not known.     

Quadrature Sampling with High Dynamic Range

Many radio and sonar systems require signal outputs in complex low-pass form. To achieve this, it is possible to use uniform sampling of the bandpass signal, together with computation of the quadrature component by way of a Hilbert transform. The bandpass to low-pass translation is accomplished by undersampling. A hardware implementation is described which achieves 70 dB spurious-free dynamic range and a bandwidth of 30 kHz.     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

Delay Generated Offset: A Direction Sensitive Pulse-Coherent Doppler Detection Technique

An offset-frequency (heterodyne) direction sensitive coherentpulsed Doppler detection method requiring a single digitally synthesized phase-shiftable oscillator and a single mixer is described. Less stringent demands are imposed on hardware in obtaining offset-frequency stability and rejection of internally generated electrical clutter, as compared with the conventional offset method employing two oscillators. Simplification of hardware and postdetector signal processing as compared with the quadrature method (two parallel homodyne detectors) is anticipated. This technique has direct application in medical ultrasonics and is generally applicable to sonar and radar systems.     

High-Power Wide-Band RF Amplifiers

The theory and procedures pertinent to the design of wide-band high-power amplifiers and the classical theory of broadband voltage amplifiers is briefly reviewed; the differences between the design constraints for voltage amplifiers and for power amplifiers are pointed out. The requisite changes in analytical models of the amplifier are inferred; an analytical model appropriate to the design of high-power wide-band amplifiers is constructed. The observed characteristics of an amplifier are presented and compared with competitive devices. Differences between wide-band voltage amplifiers and wide-band power amplifiers are inferred directly from voltage and power gain; a procedure for designing efficient wide-band power amplifiers is presented; and application of this procedure is shown to be adequate for the design of VHF amplifiers providing average power output of 1 kW over a 50 percent bandwidth with overall efficiency of 33 percent and a power gain of 15 dB.     

Correspondence - Optimum Radar Signal for Detection in Clutter

It is shown that in order to maximize the detectability of a radar target in clutter whose Doppler is unknown and is uniformly distributed over the Doppler bandwidth a simple CW or narrowband signal is optimal. The optimality criterion is the average deflection coefficient, with the averaging being over target Doppler frequency. Most remarkably the result does not depend on the clutter spectrum but holds for any distribution of clutter energy with frequency.     

Synthetic Aperture Processing with Limited Storage and Presumming

The number of transmitted pulses associated with the Doppler histories of a side-looking radar may greatly exceed the desired azimuth compression ratio of the system. This discrepancy is taxing if the storage required for the azimuth processing is provided by cores, magnetic drums, and the like. Thus, as a practical matter, one considers presumming of the data prior to correlation in an attempt to achieve the desired performance with a minimum amount of digital storage. In this paper, the optimum (in terms of resolution) presummer is derived, along with the optimum apportionment of the available storage capacity between the presumming and correlation operations. Under the condition (or generally pessimistic approximation) that the illumination pattern of the antenna uniformly illuminates a Doppler bandwidth equal to the PRF of the radar, the optimum presumming coefficients are the first Np Fourier coefficients of a function which is one of the Doppler bandwidth to be correlated and zero on the remainder of the PRF bandwidth, where Np is the number of transmitted radar pulses over which presumming is provided. Increasing Np reduces the degradation due to presumming, but may leave inadequate storage for correlation. Hence, we optimize the apportionment between the two operations and present the obtainable resolution as a function of total storage and the number of transmitted pulses in the received Doppler history.     

数字域谱估计的GNSS系统信号带宽测试方法

针对传统的单载波扫频法不适于GNSS（全球导航卫星系统）信号生成通道的带宽测量的问题,提出了采用数字信号处理的信号带宽方法.对实际导航信号进行高速采样,在数字域对采样的导航信号和本地数字生成的理想导航信号进行频谱估计和计算,从而得到GNSS信号带宽.分别使用周期图法和Welch法谱估计,对提出的测试方法进行仿真.仿真结果表明,采用Welch法进行理想信号和实际信号谱估计,对谱估计后的结果进行计算,可以完成GNSS信号带宽精密测量,在Welch法估计参数设置合理的情况下,GNSS信号带宽估计的准确度可以达到99.9％以上.     

Clutter Performance of Coherent Pulse Trains for Targets with Range Acceleration

The clutter performance of coherent pulse trains is examined when the duration of the pulse train is increased to values for which range acceleration effects must be taken into account. The problem of target detection against a clutter background with differential Doppler is studied in terms of the range acceleration effects on the conventional Doppler response. Specifically considered are the consequences on the sidelobe level and width of the main Doppler lobe. The analysis shows that the sidelobe level remains essentially unchanged when the range acceleration mismatch becomes significant. However, the main Doppler response broadens in proportion to the magnitude of the acceleration mismatch. Thus, an increase of the signal duration for better Doppler resolution is useful only until acceleration effects spread the Doppler spectrum of the clutter and eliminate the differential Doppler between targets and clutter.     

Emitter Location Accuracy Using TDOA and Differential Doppler

Two methods for locating a radio or sonar transmitter are briefly described: time difference of arrival (TDOA). d differential Doppler. Two formulas are derived which relate the accuracy of the time and frequency measurements the ?one-sigma widths? of the lines of constant TDOA onstant differential Doppler on the surface of the FDOA.     

Target tracking with a network of Doppler radars

By observing a Doppler signal at several points in space, it is possible to determine the position, velocity, and acceleration of a moving target. Parameter identification for a constant-acceleration motion model is studied, and the Cramer-Rao bound on motion parameter uncertainty is obtained for phaseand frequency-based estimation strategies, with the result that the preferred strategy depends upon the sensor/target geometry and target motion. Direct identification of the constant-acceleration trajectory model from the Doppler signal requires a 9-dimensional nonlinear optimization. Exploiting symmetry in the sensing geometry, a novel trajectory representation is presented which reduces the nonlinear optimization to one in 3 dimensions, with additional parameters obtained by linear identification. Baseball tracking using a network of four Doppler radars is experimentally demonstrated