The Effect of Hard Limiting in the Presence of Large Out-of-Band Interfering Signals

The effect of hard limiting on the phase of a test signal was investigated when large out-of-band interfering signals are present at the input to the limiter. First a single and then two discrete interfering signals were considered. The interfering signals and the test signal are restricted to narrow but separated bands. The test signal is recovered after limiting by narrowband filtering. The analysis of the single interfering signal is essentially the same as that performed by Cahn.1 In this correspondence experimental evidence is presented to verify the analysis and, in addition, the case of two interfering signals is considered.     

Hard Limiting in Synthetic Aperture Signal Processing

In synthetic aperture radar a large linear phased array is formed from the rapid movement of a single element through each position in the array. Storage and coherent combining of the successive radar echoes are central to the array-forming process. Optical processing is the most common technique because of the efficiency with which Fourier transformation may be accomplished with simple optics. Real-time operation, however, requires all-electronic processing, which is difficult to accomplish because of the huge quantity of data to be manipulated. Dynamic range compression by hard limiting may ease the problem by reducing the number of bits per frame. The effects of hard limiting are analyzed in this paper. It is shown that large targets simultaneously illuminated by the radar antenna will produce image targets or ghosts displaced in angle. Statistically homogeneous clutter will "linearize" the hard-limited receiver and suppress the ghosts without loss in contrast, as does thermal noise if it is larger than the target echoes. Pulse compression reduces the probability of images from prominent targets. Judicious choice of the pulse-compression waveform is a powerful tool for destroying coherent buildup of images from all large targets not in the same range resolution cell. Linear FM, the most common choice, unfortunately does not exhibit this desirable property.     

Effects of finite weight resolution and calibration errors on theperformance of adaptive array antennas

Adaptive antennas are now used to increase the spectral efficiency in mobile telecommunication systems. A model of the received carrier-to-interference plus noise ratio (CINR) in the adaptive antenna beamformer output is derived, assuming that the weighting units are implemented in hardware, The finite resolution of weights and calibration is shown to reduce the CINR. When hardware weights are used, the phase or amplitude step size in the weights can be so large that it affects the maximum achievable CINR. It is shown how these errors makes the interfering signals “leak” through the beamformer and we show how the output CINR is dependent on power of the input signals. The derived model is extended to include the limited dynamic range of the receivers, by using a simulation model. The theoretical and simulated results are compared with measurements on an adaptive array antenna testbed receiver, designed for the GSM-1800 system. The theoretical model was used to find the performance limiting part in the testbed as the 1 dB resolution in the weight magnitude. Furthermore, the derived models are used in illustrative examples and can be used for system designers to balance the phase and magnitude resolution and the calibration requirements of future adaptive array antennas     

A flexible processor for a digital adaptive array radar

A digital beamforming processor for an adaptive array radar is described. The functionality and the architecture of the processor are strongly driven by a goal of achieving adaptive null depths in the 60-dB to 70-dB range, which necessitates substantial preprocessing of each channel. In particular, conversion to baseband quadrature channels is accomplished digitally using a single A/D converter per channel, and FIR (finite impulse response) equalizing filters are employed in each channel to match channel transfer functions. The processor is highly modular, and this not only distributes the total processing load, but also the I/O (input/output) bandwidth requirement. This is accomplished by distributing the adaptive beamforming algorithm systolically across a linear array of processing nodes. The processor is expandable to a different number of channels and sufficiently flexible to be applied to other problems of an array signal processing nature. Experimental data presented demonstrate that the processor is capable of supporting channel-to-channel cancellation of interfering signals to the level of -65 dB     

Performance of Digital Implementations of an Adaptive Processor

The performance of a digital implementation of an Applebaum-Howells type adaptive processor is analyzed for both a limiter and nonlimiter configuration. The performance is evaluated in terms of steady-state residue power, using either a single-pole filter or a perfect integrator to smooth the output of the correlation mixer. The latter filter is the more commonly used for digital implementations. It is shown that when using the perfect integrator filter for both the limiter and linear digital implementations, the steady-state average weight vector equals the optimum weight vector. Thus, for this filter, the steady-state residue power is the minimum possible for either implementation. When using the single-pole filter, neither implementation achieves the minimum possible steady-state residue power. The relative performance of the two implementations depends upon the relative gain settings. When the gains are adjusted to give comparable servo stability for the design maximum jammer power, a reasonable criterion for digital implementations because of analog to digital saturation, the limiter configuration always has smaller steady-state residue power.     

On a Specific Performance Limitation of Partially Adaptive Antennas

An analysis shows the performance degradation of a sidelobe cancellation system as the consequence of a basic property of partially adaptive antennas when neighboring interference directions are weighted differently in sign by the radar antenna sidelobes.     

Low-Level Signal Detection Using a New Transform Class

A system is developed to detect tracks crossing two-dimensional noise fields. This is accomplished by filtering and integration of signal power in the frequency domain of a new class of generalized transforms which include the FFT and FBT as limiting forms. If the track is essentially parallel to a transform axis and if filters are derived from hard-limited linear approximations to tracks, the FBT offers considerable hardware economy over the FFT in the mechanization algorithm.     

Hard-Limiter Output Autocorrelation Function: Gaussian & Sinusoidal Input

An expression is derived for the autocorrelation function of the output of a hard limiter whose input is stationary Gaussian noise with zero mean plus independent random-phase sinusoidal signal. The output spectrum may then be evaluated. This spectrum is extremely useful in understanding the properties of a filter-limit-filter-detect signal processor whose signal input is an actual sinusoid, or when a sinusoid is used as a test signal.     

Monopulse Radar Angle Tracking Accuracy with Sum Channel Limiting

The variance of angle tracking error is found for an amplitude-comparison form of monopulse radar when the sum channel contains a limiter prior to the angle error detector. The error expression is valid for any shape of transmitted pulse and any duration of range tracking gate but does assume matched filters in signal processing channels. The procedures used are rigorous and an example of results is worked out for the special case of a rectangular transmitted pulse envelope. It is shown, for rectangular pulses, that achievable angle tracking error variance with sum channel limiting is not more than 2.22 dB larger than the theoretical minimum for any processor and not more than 1.29 dB larger than a similar signal processor that uses a "linear" angle error detector. Results apply for large single-pulse signal-to-noise ratio.     

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.     

Spurious Target Generation Due to Hard Limiting in Pulse Compression Radars

A method is presented to calculate the output of a hard limiter if the input consists of a superposition of three phase-coded signals. A detailed investigation is made of the case where the limiter input signals are phase reversal modulated according to a maximum length linear code. It is shown in this case that a false target signal is generated at the limiter output. The amplitude distribution of the false target signal is investigated along with the distribution of the captured true target signals. A digital computer simulation confirms the theoretically predicted effects.     

An Analysis of the Performance of the Oscillating Limiter Driven by FM Signals Corrupted by Noise

The behavior of the oscillating limiter (OL) driven by FM signals is surveyed, and its performance with signal corrupted by noise is investigated. For high values of the carrier-to-noise ratio (CNR), if the frequency deviation of the signal is small in comparison with the locking range of the OL, it is calculated, and experimentally verified, that a system OL discriminator is equivalent to a system bandpass limiter discriminator followed by a linear network whose frequency response has been specified. When the frequency deviation is not so small, the baseband noise power increases with it; a formula is given that allows the calculation of this power when the signal is such that the circuit operates in quasistationary fashion. For low values of the CNR, a mathematical analysis presents unsurmountable difficulties. However, heuristic argumentation leads to an interpretation of the operation of the OL in the threshold region, which is substantiated by an experimental investigation. The results of this paper enable a comparative evaluation of a system OL discriminator and a system bandpass limiter discriminator, to which the former reduces when the feedback path in the OL is open.     

小波消噪在测试信号处理中的应用

结合某测试信号,介绍了阈值消噪的三种方法：强制阈值、默认阈值和给定阈值。通过分析不同阈值消噪后信号波形,计算消噪信号的信噪比、均方根误差和相关系数,对几种方法的准确度进行了对比。结果表明,通过合理选择小波分解的尺度,对小波系数进行阈值重构,能有效地去除信号中含有的噪声,而选用不同规则下的阈值函数或者同一阈值函数对小波系数的处理方式不同,消噪的效果会有很大差异,而阈值函数的选取,更应充分考虑信号的实际特征。     

Detection Performance of Hard-Limited Phase-Coded Signals

The performance of a complex phase-coded waveform digital processor with hard-limiting constant false-alarm rate (CFAR) is presented. Processing losses relative to ideal matched-filter performance are computed and verified by hardware measurement. The losses considered include the consequences of hard limiting, envelope algorithm implementation, range cusping, and the associated effects of code length, IF filter bandwidth, and in-phase and quadrature channel phase offset. The range resolution properties of two closely spaced targets are also considered.     

Multistatic adaptive pulse compression

A new technique denoted as multistatic adaptive pulse compression (MAPC) is introduced which exploits recent work on adaptive pulse compression (APC) in order to jointly separate and pulse compress the concurrently received return signals from K proximate multistatic radars operating (i.e., transmitting) within the same spectrum. For the return signal from a single pulse of a monostatic radar, APC estimates the particular receive filter for a given range cell in a Bayesian sense reiteratively by employing the matched filter estimates of the surrounding range cell values as a priori knowledge in order to place temporal (i.e., range) nulls at the relative ranges occupied by large targets and thereby suppress range sidelobes to the level of the noise. The MAPC approach generalizes the APC concept by jointly estimating the particular receive filter for each range cell associated with each of several concurrently-received radar return signals occupying the same spectrum. As such, MAPC is found to enable shared-spectrum multistatic operation and is shown to yield substantial performance improvement in the presence of multiple spectrum-sharing radars as compared with both standard matched filters and standard least-squares mismatched filters     

The Effect of Limiting a Biphase or Quadriphase Signal Plus Interference

This paper analyzes the case of limiting an incoherent or coherent interference signal at the frequency of a biphase or quadriphase digital signal. The results give the IM products, interference, and attenuation of the digital signal, plus interference through a hard limiter.     

非结构网格限制器研究

研究了6种限制器形式及其参数计算方法,其中新的自适应VenkatakrishnanM限制器能够根据当地流场特征自动调节参数从而实现不同区域不同特性.数值试验表明:非结构网格限制器对邻居集合选择方法较敏感,其中共面法比共点法精度高约15%;高马赫数时压缩型限制器比耗散型限制器计算精度高约10%~40%;参变量算法中,方向梯度法得到的流场比增量法平滑;自适应VenkatakrishnanM限制器能够模拟复杂超声速流动.      

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.     

Modified Generalized Sign Test Processor for 2-D Radar

The modified generalized sign test processor is a nonparametric, adaptive detector for 2-D search radars. The detector ranks a sample under test with its neighboring samples and integrates (on a pulse-to-pulse basis) the ranks with a two-pole filter. A target is declared when the integrated output exceeds two thresholds. The first threshold is fixed and yields a 10-6 probability of false alarm when the neighboring samples are independent and identically distributed. The second threshold is adaptive and maintains a low false-alarm rate when the integrated neighboring samples are correlated and when there are nonhomogeneities, such as extraneous targets, in the neighboring cells. Using Monte Carlo techniques, probability of false-alarm results, probability of detection curves, and angular accuracy curves have been generated for this detector. The detector was built and PPI photographs are used to indicate the detector's performance when the radar is operated over land clutter.     

Median cascaded canceller for robust adaptive array processing

A median cascaded canceller (MCC) is introduced as a robust multichannel adaptive array processor. Compared with sample matrix inversion (SMI) methods, it is shown to significantly reduce the deleterious effects of impulsive noise spikes (outliers) on convergence performance of metrics; such as (normalized) output residue power and signal to interference-plus-noise ratio (SINR). For the case of no outliers, the MCC convergence performance remains commensurate with SMI methods for several practical interference scenarios. It is shown that the MCC offers natural protection against desired signal (target) cancellation when weight training data contains strong target components. In addition, results are shown for a high-fidelity, simulated, barrage jamming and nonhomogenous clutter environment. Here the MCC is used in a space-time adaptive processing (STAP) configuration for airborne radar interference mitigation. Results indicate the MCC produces a marked SINR performance improvement over SMI methods.