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.     

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.     

Time jitter analysis for quadrature sampling

Time jitter in the quadrature sampling processes is modeled and the performance of an adaptive cancellation system in the presence of such time jitter is analyzed. It is shown that the decorrelation due to time jitter depends on the magnitude of the jitter, the sampling scheme used, the bandwidth of the signal and the intermediate frequency (IF) preceding the analog-to-digital (A/D) conversion stages. The performance of a sidelobe cancellation system in the presence of time jitter, for several sampling approaches, is evaluated numerically as well as simulated. The results show that the direct quadrature sampling scheme with a lower IF provides superior performance for an adaptive cancellation system     

Degradation of Probability of Error Due to IF Filtering

The probability of error P(e) is computed in a binary communication system with a single-pole IF filter. The effect of time-bandwidth product foT and IF frequency to band width ratio f1/Ifo on P(e) is shown. The sampling time is optimized and the effect of nonoptimal sampling time on P(e) is calculated.     

The effect of the clutter-to-noise ratio on Doppler filterperformance

The effect of the clutter-to-noise ratio on the performance of a Doppler filter is considered. Clutter is assumed to have a power level which is unknown and varies in range. The assessment of the performance of a Doppler filter is based on the gain of the filter, which is the normalized output signal-to-interference ratio improvement at a given Doppler. The gain is generally a complex function of the statistics of the clutter. New upper and lower bounds on the gain differential between the expected design point clutter-to-noise ratio and the actual clutter-to-noise ratio are found. These bounds are independent of the clutter covariance matrix and are only a function of the unknown clutter-to-noise ratio. The bounds are valid for both Gaussian and non-Gaussian noise and for arbitrary linear filters. The upper and lower bounds differ by the theoretical coherent integration gain, 10 logN dB, where N is the number of pulses. A tighter lower bound is found for the case when the filters are matched filters. A simple exact expression is found for matched filters assuming a Gaussian Markov clutter model as the clutter spectral width approaches zero. An easily implementable adaptive procedure is given which improves performance due to the unknown clutter-to-noise ratio. This work extends a previous result, valid for the Emerson filter, that shows the effect of clutter-to-noise ratio on performance in terms of an average quantity, the improvement factor     

Filter Selection for Receivers Using Square-Law Detection

A numerical method is described for predicting the detection probability performance of a pulse receiver which uses square-law detection. The method is useful for receivers where the ratio of RF bandwidth to video bandwidth is in the range from 2 to 40; a range where numerical results have previously been hard to obtain. A key feature of the approach is that it takes into account the actual filter transfer functions, pulse envelope shape, and pulse frequency.     

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.     

Performance Degradation of MTI Circuits Due to Amplitude Limiting

The loss in output signal-to-noise ratio (SNR) due to amplitude limiting is obtained for a radar circuit consisting of a bandpass limiter, coherent demodulator, matched filter, and moving-target-indicator (MTI) filter. The circuit is used in scanning MTI radars. The tandem connection of the limiter and coherent demodulator is a model for the saturation of the intermediate-frequency (IF) demodulator of an MTI radar. Results on special functions are used to obtain simple formulas for the loss in output SNR relative to a linear IF demodulator when the input SNR is less than -15 dB and the number of hits per 3-dB beamwidth exceeds 15.     

Computer Optimization of FM/FM Telemetry Systems

In this correspondence, the threshold carrier power of FM/FM systems and the receiver IF bandwidth are optimized through a computer program. For a typical set of IRIG (inter-range instrumentation group) channels, it is demonstrated that the required carrier signal-to-noise ratio can be as low as 5 dB (much less than the conventional 12 dB value) in order to maintain the subcarrier signal-to-noise ratio at 12 dB, the threshold level. comparison of the optimized and the conventional taper analysis is tabulated.     

A digital quadrature demodulation system

Existing digital quadrature demodulation techniques sample the input at either 2B Hz or 4B Hz, select the even samples as the in-phase (I), and interpolate the odd samples to give the quadrature (Q), output. The signal bandwidth is B. We propose a demodulation system to produce I and Q samples at arbitrary sampling rate greater than 2B Hz. The system eliminates the IF downconversion step with a special sampling scheme. The even samples correspond to the I component, while the Q components are the filtered output. The filter can be a lowpass or least squares (LS) filter. The lowpass filter design is based on trade-offs between the filter length and the degree of oversampling. It produces similar results as previous work when the sampling rate is 2B Hz or 4B Hz. Unlike existing methods which assume the input is white, a LS filter, on the other hand, can make use of input signal characteristics to achieve a better result. The higher the correlation in the input the larger the improvement. The cost for LS filtering is a coefficient update step if the input is time varying. A scheme to cancel dc offset from analog to digital (A/D) converters is also given     

短波信道数字传输脉冲成形技术研究

短波窄带信道上的数据传输,要求将信号的带宽限制在3kHz语音频带内,当系统带宽小于数据信息所需的奈奎斯特最小带宽时,脉冲时域范围的扩展产生的码间串扰会降低系统的误差性能。文章阐明了脉冲成形技术可以压缩信号的频谱,分析了恰当选择的平方根升余弦脉冲成形滤波器可以明显提高短波信道数据传输的误差性能。     

Binary Communication with Large Bandwidth to IF Frequency Ratios

The effect of I F filter bandwidth to I F frequency ratio on the probability of error in a binary bandpass communication system with nonreturn-to-zero (NRZ) and split-phase (SP) signals is investigated. ed. Explicit results are given for the case when the bandpas I F filter is transformed from a single-pole low-pass filter.     

Maximizing the Usable Bandwidth of MTI Signal Processors

A technique is presented for maximizing the percentage of usable Doppler bandwidth throughout which a radar return can be detected while maintaining an acceptable clutter suppression. The technique employs the weighted Chebyshev approximation to the design of a transversal high-pass digital filter which has an optimal passband ripple for a given number of filter weights and associated integration gain consistent with the required increase in signal-to-noise ratio needed for acceptable probabilities of detection and false alarm. Conventional approaches to the design of a movingtarget arget indictor (MTI) filter which maximizes the improvement factor by clutter suppression typically improve the signal-to-background noise ratio over less than 50 percent of the range between dc and the pulse-repetition frequency fT. This technique can increase the usable bandwidth to 80 percent or more of fT. Two examples are included which utilize parameter values from the Army Missile Command's experimental radar and demonstrate the interactive influence of such filter parameters as the number of weights, passband ripple and bandedge, and stopband attenuation and cutoff.     

The Susceptivity of MTI Systems to White Noise

The performance of various coherent MTI systems in the presence of white noise is investigated. The single-pulse signal-to-noise ratios at the output of the filters are presented for the case of large system bandwidth. Generalized results, calculated as a function of the system's bandwidth, are given. Finally, those results are compared to the optimum signal-to-noise acheivable by a matched filter.     

Reconciling steady-state Kalman and alpha-beta filter design

The deterministic design of the alpha-beta filter and the stochastic design of its Kalman counterpart are placed on a common basis. The first step is to find the continuous-time filter architecture which transforms into the alpha-beta discrete filter via the method of impulse invariance. This yields relations between filter bandwidth and damping ratio and the coefficients, α and β. In the Kalman case, these same coefficients are related to a defined stochastic signal-to-noise ratio and to a defined normalized tracking error variance. These latter relations are obtained from a closed-form, unique, positive-definite solution to the matrix Riccati equation for the tracking error covariance. A nomograph is given that relates the stochastic and deterministic designs     

An Analysis of Helicopter Rotor Modulation Interference

In satellite-to-helicopter communications, interference exists on the incoming signal when the receiving antenna is located below the rotor blades. A bound is established for the performance of a coherent fixed-tone ranging system operating at L band in this interference environment. The scalar diffracted field beneath the rotating blades, at L band and above, is found to satisfy the criterion of Fresnel diffraction, and is computed using the techniques of Fourier optics. The diffracted field is expressed in terms of a narrow-band signal. The amplitude and phase components are calculated from a Fourier Series expansion using the FFT algorithm. The significant harmonics of the phase component of the interference combine with the baseband of the narrow-band, phase-modulated ranging signal. This results in CW interference, and in rearrangement of the first-order, sideband, ranging-tone channel powers. The degradation in ranging accuracy is evaluated by computing the signal-to-interference (SIR) ratio for a set of ranging tones. The post-detection (SIR)PD at the output of the correlator is shown to be a function of the amplitude of the phase harmonics of the interference, the relative difference between the ranging tone and interference center frequencies (a function of rotor speed), the rangetone modulation indices, and the post-detection filter noise bandwidth.     

Specification and Performance of Passive Sonar Spectral Estimators

The application of existing estimation theory to the problem of specification and performance of passive sonar spectral estimators is considered. The classification function is addressed, so that the signal is assumed to be present, and so that the energy arrival angle is known. The spatial filter considered is a line array of M equally spaced omnidirectional hydrophones. Signal and ambient noise are both zero-mean, wide-sense, stationary Gaussian random processes that differ in their spatial correlation across the face of the array. The signal is a plane wave that can be made totally spacially corrected between array elements by inserting delays between sensors to invert the signal propagation delay. The noise correlation is a function of frequency, bandwidth, element separation, and the relative time delay between sensors. Under these assumptions, the Cramer-Rao lower bound is derived for the class of unbiased estimates of signal power in a narrow frequency band at the hydrophone in the presence of correlated ambient noise of known power. The bound is examined numerically, resulting in a threshold phenomenon with M that constitutes a new design consideration. In addition, there is a striking insensitivity to realistic values of ambient noise correlation, and there are ranges in signal-to-noise ratio for which one gains more by increasing M than by increasing the bandwidth-time product. Specific processors, including a new unbiased estimator when noise power is unknown, are developed.     

An Upper Bound on Detection Probability for Fluctuating Signals

In the theory of signal detectability, the signal-to-noise ratio (SNR), defined as the quotient of the average received signal energy and the spectral density of the white Gaussian noise, is a fundamental parameter. For a signal which is exactly known, or known except for a random phase, this ratio uniquely defines the detection performance which can be achieved with a matched filter receiver. However, when the signal amplitude is a random parameter, the detection performance is changed and must be determined from the probability density function (pdf) of the amplitude. Relative to the case of a constant signal amplitude, such signal amplitude fluctuation usually degrades performance when a high probability of detection (Pd) is required, but improves performance at low values of Pd; the corresponding change in the required SNR is the so-called signal fluctuation loss Lf. Thus, since Lf in some cases represents an improvement in performance for low values of Pd, a question of at least theoretical interest is: how large might this improvement be, when the class of all signal amplitude pdf's is considered. The solution, presented here, results in a lower bound on the signal fluctuation loss Lf as a function of Pd, or equivalently an upper bound on Pd as a function of SNR. The corresponding most favorable pdf was determined using the Lagrange multiplier technique and results of a numerical maximization are included to provide insight into the general properties of the solution.     

Phase-Shift-Keyed Signal Detection with Noisy Reference Signals

This paper derives and graphically illustrates the performance characteristics of Phase-Shift-Keyed communication systems where the receiver's phase reference is noisy and derived from the observed waveform by means of a narrow-band tracking filter (a phase-locked loop). In particular, two phase measurement methods are considered. One method requires the transmission of an auxiliary carrier (in practice, this signal is usually referred to as the sync subcarrier). This carrier is tracked at the receiver by means of a phase-locked loop, and the output of this loop is used as a reference signal for performing a coherent detection. The second method is self-synchronizing in that the reference signal is derived from the modulated data signal by means of a squaring-loop. The statistics (and their properties) of the differenced-correlator outputs are derived and graphically illustrated as a function of the signal-to-noise ratio existing in the tracking filter's loop bandwidth and the signal-to-noise ratio in the data channel. Conclusions of these results as well as design trends are presented.     

The Effects of Filtering and Limiting a Double-Binary PSK Signal

This paper describes a digital computer simulation of a double-binary phase-shift keying system. This simulation program is used to investigate the effects of limiting action and of the shape and bandwidth of the filter on the system performance, expressed in terms of error probability