Performance of Doppler Radar in the Presence of Random Fading

This paper deals with the performance of pulse Doppler radar in the presence of random fading. The behavior of this radar is studied as a statistical problem to bring out the limiting bounds of the ambiguity diagram and the nature of variance with respect to the Doppler frequency. The performance of the radar insofar as the first sidelobe is concerned, is shown to be better in the presence of fading than in the normal case. In a particular case where 75 pulses out of an aggregate of 250 pulses are missing, the first sidelobe level is 20.0 dB down from the main lobe with a probability of 23 percent.     

A Quantitative Analysis of Sea Clutter Decorrelation with Frequency Agility

A brief statement of the sea clutter problem in surface-search radar operation illustrates the need for some form of signal-to-clutter enhancement. Post-detection integration used in the simpler radars is limited by the pulse-to-pulse correlation of the clutter. Analysis of the effect of changing frequency from pulse to pulse leads to an expression for the correlation between pulses in the sequence. Knowing this correlation, the reduction in the fluctuating clutter component produced by integration can be determined. This is described by an equivalent number of independent pulses, Nc. For the particular case of sinusoidal modulation of the transmitted frequency, N6 is computed. The critical dependecne of Nc upon the modulating frequency fm is illustrated by spectrum photographs. Choice of an optimum fm is discussed. The results of computations of N4 for optimum fm are presented as a family of normalized curves. These data permit the tradeoff of the radar parameters against their quantitative effect on radar performance.     

CFAR integration processors in randomly arriving impulseinterference

Time diversity transmission is often used to circumvent the high probability of a deep fade on a single transmission which may result in loss of the signal. One way to combat deep fades is to postdetection integrate the received observations from each range resolution cell. The false alarm rate of the postdetection integrator (PI) is extremely sensitive to randomly arriving impulse interference. Such interfering pulses may be unintentionally generated by nearby radars or intentionally generated by pulse jammers seeking to destroy the visibility of the radar. The binary integrator (PI) which uses an M-out-of-L decision rule is insensitive to at most M-1 interfering pulses. We consider the adaptive implementation of the PI and BI detectors for constant false alarm rate (CFAR) operation. We show that the CFAR BI detector when the “AND” (L-out-of-L) decision rule is used exhibits more robust false alarm control properties in the presence of impulse interference at the expense of severe detection loss when no interference is present. The CFAR adaptive PI (API) detector is proposed to alleviate this problem. The CFAR API detector implements an adaptive censoring algorithm which determines and censors with high probability the interference samples thereby achieving robust false alarm control in the presence of interference and optimum detection performance in the absence of interference     

Detection probability for partially correlated chi-square targets

The probability of detection of the sum of N square-law-detected pulses is derived for the case where the signal fluctuation obeys chi-square statistics with four degrees of freedom. P. Swerling's (1960) case III and IV represent the cases where the signal is completely correlated and completely decorrelated, respectively, from pulse to pulse. An exact expression for probability of detection is derived for the condition of partial signal correlation. The results given are compared with the approximate technique commonly used to handle partial signal correlation     

Sidelobe blanking with integration and target fluctuation

In radar systems, sidelobe blanking (SLB) is used to mitigate impulsive interference that enters the radar through sidelobes of the main antenna. SLB employs an auxiliary antenna channel with the output being compared with that of the main antenna channel and a decision is then made as to whether or not to blank the main channel output. SLB performance determination involves the evaluation of several probability functions. Based on the classical Maisel SLB architecture, this work extends previous performance results, in which detection was limited to the case of a single radar pulse with either Marcum or Swerling I target fluctuation. Probability expressions have been generalized to include both an arbitrary number of integrated pulses and target fluctuation models based on the gamma distribution. The Swerling fluctuation models are all special cases of the gamma distribution. Results are derived in terms of two generalized probability functions, one for detection and the other for blanking. With these generalized probability functions, the SLB design and performance results can be determined. Examples are presented and discussed.     

Target Track Pulse Scheduling

The problem of scheduling radar tracking pulses in a dense target environment where the position estimation error must be constrained to avoid false return with track correlations is considered. The problem is to schedule n fixed energy pulses such that the rangerate error is minimized at some final time subject to the constraint that the position error will be smaller than some value for the whole time interval. For a fixed time interval, the problem of finding the minimum number of radar measurements required to satisfy the position estimation error constraint is solved. A closed-form solution for the optimum schedule is given in the case where the number of pulses is equal to the minimum number of pulses. For cases where one extra pulse is available, a solution method is described and an algorithm is derived.     

Probability of Pulse Coincidence in a Multiple Radar Environment

Elementary probability theory is used to develop three formulas for the probability of two or more pulses being coincident at an observer's aircraft position in a multiple radar environment. The first formula is for nonscanning tracking type radars with different pulsewidths (PWs) and pulse repetition frequencies (PRFs), the second is for generically identical nonscanning radars with similar PWs and PRFs, and the third is for scanning type radars such as air search radars with similar PWs and PRFs. The probability of coincidence is related to the mean-time-between-coincidences (MTBC) and to the average coincidence rate. Two sample problems are given.     

Frequency Agility Radar Range Calculation Using Number of Independent Pulses

A method for accurately calculating the radar range improvement introduced by frequency agility is presented. This calculation is made by using the concept of independent pulses. The number of independent target or clutter pulses is calculated by a simple method based on such basic combinatorial probability theory as drawing differently colored balls from an urn.     

Reduction of sidelobe self-interference in an agile beam radar

In an agile beam phased array radar, the beam is often multiplexed over several angular positions, and “listens” in each position only over an instrumented range that may be a fraction of the unambiguous range as determined by the pulse repetition period in each position. After transmitting a pulse in a given direction, the beam is switched, essentially instantaneously, to another position, after the instrumented range delay. In this second position, echoes from the first position, from multiple trips of the instrumented range, enter the one-way angular sidelobes of the first position. This interference is compounded if there are several beam positions in a pulse repetition period. The author proposes a method of phase coding the pulses in such a way that the pulse-to-pulse phase variation in each direction is orthogonal to every other phase code in the other directions. The codes are Walsh functions. These are sets of binary valued (+1 or -1) functions such that all of the functions in the set are mutually orthogonal. Not every possible number N of pulses in each direction and number K of beam positions can be accommodated, but a large variety of such combinations can be accommodated. Several examples are given. The combination of low one-way sidelobes and orthogonality (or near orthogonality) of the phase codes should provide for very stringent sidelobe self interference rejection     

Interference Effects of Pseudo-Random Frequency-Hopping Signals

When a pseudo-random frequency-hopping signal is intercepted by a conventional receiver operating within the same frequency band, the interfering signal has the form of a pulse-amplitude modulated signal. Each pulse amplitude is dependent upon the hopping frequency and the selectivity characteristic of the victim receiver. The probability density function for the interfering pulse amplitude prior to demodulation is determined when the probability density function for the hopping frequency is uniform and the victim-receiver characteristic is 1) ideal flat bandpass, 2) single tuned, and 3) Gaussian shaped. It is shown that the average interfering pulse amplitude and interference power decrease as the frequency-hopping bandwidth increases with respect to the victim-receiver bandwidth. Fast Fourier transform computer techniques are used to obtain the probability density function of the interference amplitude in a Gaussian receiver when several (from 2 to 10) pseudo-random frequency-hopping systems are simultaneously using the same frequency band. The probability that the interference exceeds a prescribed threshold value is computed from the derived probability density functions. This probability may be used in signal-to-interference ratio calculations, to describe the capture effect, or to compute the expected number of clicks produced in an FM discriminator.     

Signal-to-Noise Ratio Calculations in Pulse and Pulse Doppler Radars

In low pulse-repetition frequency (PRF) pulse radars, signal-to-noise ratio (SNR) is usually calculated on a per pulse basis and this value is then multiplied by the number of pulses integrated to obtain the SNR for a given duration of target illumination. In high PRF pulse Doppler radars, SNR is usually calculated by using the centerline power of the transmitted signal spectrum as the target return power because the centerline is kept in the receiver and returns of the PRF lines are notched out [1]. We show here that both methods of SNR calculations are entirely equivalent for matched transmit-receive radar systems.     

Envelope Threshold Detection in a Class of Non-Gaussian Interference

This paper considers the detection of a sinusoidal or chirp signal imbedded in wideband FM interference (as might be generated by some types of active jamming), such that after pulse compression or other integration, the interference can be approximated by a sum of sinusoids of independent phase. The detection probability in such non-Gaussian noise is compared to that for Gaussian noise, with the Gaussian result approached, as required, in the limit that the number of sinusoids in the sum increases without bound. For detection using a comparison of the envelope with a threshold which yields a given false-alarm probability (CFAR detection), the detection probability is improved over the case of Gaussian noise, so that the usual approach basing the design on Gaussian noise would be conservative. Using a threshold determined from the envelope mean, the FM interference yields a lower false-alarm probability than for Gaussian noise, with detection probability only slightly degraded.     

Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

A Clutter Reduction Technique for Random Signal Radars

The performance of certain radars is degraded in environments with significant clutter returns, and since the clutter is signal-generated, increasing the transmitted power does not improve the situation. However, changing the pulse width and pulse period of the transmitted signal can increase the input signal-to-interference ratio. In this correspondence, the transmitted signal is made up of pulses of random waveforms and the receiver is a correlator where the reference signal extends over many pulses. An expression for input signal-to-interference ratio as a function of pulse width and period is obtained for the case of a distributed target. This expression could be maximized by any of several methods, but to further elucidate the clutter reduction technique, contour plots of the input signal-to-interference ratio are presented.     

Analysis of queuing behavior of automatic ESM systems

Radar electronic support measures (ESM) systems detect active emitters in a given area and determine their identities and bearings. The high arrival rate of radar pulses in dense emitter environments demands fast automatic processing of arriving pulses so that the ESM system can fulfill its functions properly in real time. Yet, the performance analysis of automatic ESM system in real life Is difficult since both pulse arrivals and widths can be specified only probabilistically. The success of queuing theory in many applications such as computer communication networks and flow-control has encouraged designers to utilize queuing theory in qualifying and judging the performance of automatic ESM systems in dense emitter environments. The queuing behavior of these systems is analytically evaluated under different service disciplines and elaborate computer simulations validate the results. The analysis involves statistical modeling of arrival and departure processes as well as distribution of service times. It permits estimating the blocking probability due to high arrival rates of intercepted radar pulses or due to limited speed of the deinterleaver processor. Queuing analysis is shown to be quite useful to quantitatively assess tradeoffs in ESM systems design     

Target detection trials with a millimeter wave radar system

Unobstructed, large RCS targets, similar radar targets surrounded by moving foliage, and small targets in severe clutter have been used as test cases for two pre-processing algorithms and several threshold levels in an experimental millimeter wave radar system. The rather conventional "six-out-of-eight" pulse radar selection method with binary output has been compared to an algorithm that accepts a target if the pre-defined trigger level is crossed by the average of the eight consecutive pulses. In this case, however, the output is an analog value corresponding to the relative average video amplitude. In terms of plotted video, this process seems to give a slightly better combination of false alarm rate and detection probability. Large targets are easier to detect from foliage clutter with the conventional method.     

一种改善防渗碳性能的脉冲镀铜工艺优化

为了实现对航空发动机零件非渗碳区域的有效防护,需要进行局部镀铜工艺的优化。通过脉冲镀铜正交试验和镀层孔隙率极差分析,确定了脉冲镀铜的主要和次要影响参数,优化了脉冲镀铜工艺参数。优化工艺脉冲制备的铜镀层结合力良好,表面形貌、孔隙率、防渗效果均优于直流镀铜层,将镀铜厚度由50~70μm降低到20μm,节约镀铜成本,且提高了工作效率。     

Probability of Detecting a Fluctuating Target Immersed in Both Noise and Clutter

The probability of detecting either a Swerling 1 or Swerling 2 target immersed in both Rayleigh-distributed noise and log-normally distributed clutter is calculated. Results are presented which demonstrate the effect of noise-to-clutter ratio, signal-to-noise ratio, and number of pulses integrated on the detection statistics.     

Resolution in Doppler and Acceleration with Coherent Pulse Trains

The resolution properties and clutter performance of a simultaneous Doppler and acceleration measurement are investigated in detail with particular emphasis given to coherent pulse trains. The analysis is based on the concept of a matched-filter receiver, although receiver weighting of the type that reduces Doppler sidelobes is also analyzed in detail. Near the main lobe of the acceleration response is a pedestal-ike sidelobe region, the height of which is about 1/N of the main response lobe power where N is the number of pulses in the train. The extent of this pedestal along the acceleration axis is proportional to N. The acceleration measurement in a clutter environment is best performed when both targets and clutter are confined to this pedestal region, since some response sidelobes outside of this region are extremely large.     

Mitigating Range Ambiguity in High PRF Radar using Inter-Pulse Binary Coding

The paper proposes a way to increase the energy within a coherent processing interval (CPI) using more pulses instead of longer pulses. Long coded pulses result in masking targets at close range and poor Doppler tolerance. Increasing the number of pulses implies high pulse repetition frequency (PRF), which suffers from range ambiguity and target folding. These drawbacks of a high PRF can be mitigated by inter-pulse coding. The approach suggested here should be attractive for close and mid range applications of radar, ground penetrating radar, ultrasound imaging, and more.