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.     

M-ary CPSK Detection with Noisy Reference and Interferences

A general expression of the error probability on an M-ary coherent phase-shift-keyed (MCPSK) signal purturbed by a noisy reference carrier, multiple interferences, and additive Gaussian noise is presented taking into account the frequencey divider in the carrier recovery circuit. First, a new expression for the probability density function (pdf) of the phase of a composite wave of signal, multiple interferences, and additive Gaussian noise is derived. Then this result and a pdf of the phase error modified from the Tikhonov distribution are used to obtain the erro probability of an MCPSK detector. In addition, the comparison between the error probabilities with and without the frequency divider is given, and it is found that the estimation is more pessimistic when the frequency divider is included.     

Interference between FM Carriers and a Digitally Modulated SCPC Circuit

The interference from the digital single channel per carrier (SCPC) circuits into frequency-modulated carrier systems has been calculated by convolving the desired and the interfering spectra extending the previously published works. Resulting interference noise power in FDM/FM systems covering a wide range of modulation indices and basebands has been presnted. Also plots of interference noise power as a function of the number of SCPC circuits have been presented for various values of carrier power to interference power ratios.     

Performance analysis of GPS carrier phase observable

The accuracy analysis of Global Positioning System (GPS) carrier phase observable measured by a digital GPS receiver is presented. A digital phase-locked loop (DPLL) is modeled to extract the carrier phase of the received signal after a pseudorandom noise (PRN) code synchronization system despreads the received PRN coded signal. Based on phase noise characteristics of the input signal, the following performance of the first, second, and third-order DPLLs is analyzed mathematically: (1) loop stability and transient process; (2) steady-state probability density function (pdf), mean and variance of phase tracking error; (3) carrier phase acquisition performance; and (4) mean time to the first cycle-slipping. The theoretical analysis is verified by Monte Carlo computer simulations. The analysis of the dependency of the phase input noise and receiver design parameters provides with an important reference in designing the carrier phase synchronization system for high accuracy GPS positioning     

Applications of level crossing theory to target intervisibility: to be seen or not to be seen?

Here we discuss intervisibility (the existence of an unobstructed line of sight (LOS) between two points) accounting for the vertical and horizontal errors in the estimated locations of both points as well as elevation errors in the database of the terrain that could obstruct the LOS between these points. The errors are first simply treated as a "white" noise sequence: we assume no correlation between the intervisibility at two different times, and the probability of an instantaneous intervisibility event is in this case developed. This is useful; but perhaps of greater concern is whether or not a target remains visible long enough and/or often enough that its motion can be tracked? Consequently, we present a second treatment in which the errors are stochastic processes of a certain bandwidth, and both the probability density function (pdf) of an intervisibility interval and the average number of intervisibility intervals over a certain time period are developed.     

Radiometric detection of spread-spectrum signals in noise ofuncertain power

The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval     

Single Channel Per Carrier Satellite Repeater Channel Capacity

This paper analyzes the performance of a number of modulation and speech processing techniques that have been considered for single voice channel per carrier transmissions via satellite. This transmission mode is applicable to demand assignment systems, which make possible the most efficient loading of the satellite transponder in applications where the traffic at individual Earth terminals is not sufficient to justify a substantial number of dedicated channels. The analysis basically determines the operating point for the satellite transponder which minimizes the required Earth terminal G/T. The fraction of the total link noise allocated to uplink noise is treated as a parameter, so that the cost of improving G/T may be traded against the cost of providing increased Earth terminal transmitter power. Both analog and digital modulation techniques are considered, together with various practical combinations of syllabic companding, voice-actuated carriers, and error-correcting codes. The results are presented in general analytic form, applicable to any modulation technique for which carrier-to-noise density ratio, channel width, and guardband width may be specified. Curves showing required G/T as a function of the total number of voice channels per transponder are also presented for the above-mentioned signal processing techniques, assuming "CCIR/CITT type" speech quality and transponder EIRP and bandwidth typical of current domestic satellite configurations.     

Interference Immunity Effects in CPSK Systems with Hard-Limiting Transponders

Transmission characteristics are described for M-ary coherent phase-shift keyed (CPSK) systems with N-stage hard-limiting transponders where noise and multiple continuous wave (CW) interference sources are additively combined in each link. A general expression for the probability density function of the composite phase at the final link is derived; the overall error probability is then obtained from this general expression. Comparisons with N-cascaded linear amplifier systems clearly show the noise and interference immunity that result from the use of bandpass hard limiters (BPHLs). The BPHL system's error probability improvement versus interference sources is shown to be much larger than the improvement versus noise.     

A Useful Approximation to Binary FSK Probability of Error

A technique for calculating a simple approximation to the probability of error for binary frequency-shift keying (FSK) systems when the predetection bandwidth-bit duration product is large enough so that the signal portion of the detector output is relatively undistorted is described. The results are mathematically simple and avoid the calculation of the density function of the nonclick noise part of the output phase noise.     

Imperfect Carrier Recovery Effect on Filtered PSK Signals

Coherent demodulation of a PSK signal requires the generation of a local carrier phase reference. Methods are given to determine the detection loss caused by noisy phase recovery and its use in the coherent detection of filtered BPSK and QPSK signals. It is assumed that the phase noise can have a static part and a random component with a Tikhonov-type distribution. The static part is mostly due to offset frequency tracking of the PLL used to recover the carrier, while the random component is due to thermal noise present in the carrier recovery loop and is also due to the random nature of the phase modulation. It is shown that the probability of error of BPSK and QPSK can be expressed as a finite sum of a set of strictly alternating converging series when the number of ISI terms is finite. Upper and lower bounds on the probability of error have been derived when this number becomes infinite and we show how this error rate can be computed with any desired accuracy. Numerical results are presented for various values of static error and phase noise variance when the transmit and receive filters are 4-pole Butterworth filters. For filtered PSK signals and for a bit error rate of 10-6, our results show that the additional degradation in presentday receiver systems due to imperfect carrier recovery can be less than 0.1 dB for BPSK and less than 1 dB for QPSK.     

Dynamics of the Phase-Locked Loop without a Limiter

The general (nth order) phase-locked loop is analyzed, of which the amplitude is not constant. The input carrier signal is amplitude-modulated by wide-band stationary Gaussian noise, and the signal, superposed with the additive white stationary Gaussian noise, enters the nonlimited phase-locked loop. Under the above assumptions the loop can be shown to constitute an n-dimensional vector Markov process, so that the process satisfies the n-dimensional Fokker-Plank equation. The probability density function depends on the effective loop signal-to-noise ratio and the effective modulation power.     

Noncoherent Detection of Sinusoidal Signals in Sinusoidal Clutter

Probability density expressions associated with the noncoherent detection of a sinusoidal signal have been obtained. The signal is assumed to be imbedded in sinusoidal clutter at the same frequency and narrow-band Gaussian noise. The density expressions are shown to be a function of the signal-to-noise power ratio and the clutter-to-noise power ratio. The expressions have been numerically evaluated for a number of conditions, and the results under each reception hypothesis are presented graphically. Under large-sample conditions, the probability density for a multisample test statistic is shown to be Gaussian, and the probability of detection expression is written such that commonly available tabulated data can be utilized to determine the probabilities.     

The Output Pdf of a Polarity Coincidence Correlation Detector

A general expression is derived for the probability density function of the output of a cross correlator, the inputs of which are assumed to consist of clipped sine waves of similar frequency plus uncorrelated, stationary Gaussian noise. The correlator output is shown to be a piecewise linear function of the random phase difference between the two input processes; hence, the density function for the correlator output is obtained by a relatively simple transformationfrom the probability density function of the random phase difference.     

Single Channel Per Carrier Satellite Repeater Capacity, Part 2

This paper analyzes the performance of a number of speech processing techniques that have been considered for single voice channel per carrier transmissions via satellite. This transmission mode is applicable to demand assigiment systems, which make possible the most efficient loading of the satellite transponder applications where the traffic at individual earth terminals is not sufficient to justify a substantial number of dedicated channels. The analysis basically determines the operating point for the satellite transponder which minimizes the required earth terminal G/T. Both analog and digital modulation techniques are considered, and the effects of syllabic companding and voice actuation of carriers are demonstrated. The results are presented in general analytic form, applicable to any modulation technique for which carrier-to-noise density ratio, channel width, and guardband width may be specified. Full carrier modulation is assumed. Curves are also furnished showing the required G/T and uplink per carrier EIRP as a function of the number of voice channels per transponder and the transponder gain. "CCIR/CCITT type" speech quality is assumed, together with a transponder El RP and bandwidth typical of current domestic satellite configurations.     

Experiments in Adaptive Estimation of Unknown Binary Waveforms

A special-purpose adaptive machine is described which carries out estimation in real time of an unknown binary waveform which is perturbed with additive Gaussian noise. Unknown waveforms of over 103 samples in duration can be recovered. The unknown waveforms are of unknown epoch and can reappear at either random or periodic time intervals. The observed signal is received at moderate or low signal-to-noise ratios so that a single observation of the received data (even if one knew the precise signal arrival time) is not sufficient to provide a good estimate of the signal waveshape. Experimental results are described which show transient behavior waveform estimate. The transient behavior is expressed as the number of errors in the current estimate of the signal plotted vs. time. In a noisy environment, each ``learning' transient is a random time function. These learning transients are shown for several different signal-to-noise ratios and indicate the threshold noise levels for various types of initial states of the machine memory.     

未知测量噪声分布下的多目标跟踪算法

 粒子概率假设密度滤波(SMC-PHDF)在进行粒子更新时需要知道测量噪声的概率分布以计算似然函数,这使得SMC-PHDF依赖于测量噪声的概率模型。针对这一点不足,提出一种未知测量噪声分布下的多目标跟踪算法——基于风险评估的概率假设密度滤波(RE-PHDF)。该算法在SMC-PHDF进行概率假设密度(PHD)粒子更新时采用风险函数计算每个PHD粒子的风险值,并通过一个风险评估函数评估每个PHD粒子,然后用评估后的结果更新粒子的权值。由于粒子更新时避免了在多维测量空间中计算似然函数,算法不仅不依赖于测量噪声的概率分布,还可以节省大量计算时间。仿真结果表明：和SMC-PHDF相比,RE-PHDF在未知的复杂测量噪声环境下具有更高的鲁棒性和稳定性;同时,在两种算法跟踪精度接近的情况下,所提算法节省了50%的运行时间。     

A noncoherent adaptive detection technique

An adaptive detection technique suitable for both stationary and nonstationary noise environments based upon a generalized likelihood ratio test (GLRT) formulation is presented. The detector, which is statistically equivalent to a special form of the Wilks's lambda test, noncoherently combines the information contained in a pulse train of arbitrary length for decision-making purposes. The probability density function of the test under the noise only hypothesis is shown to be central χ². Under the signal plus noise hypothesis, an exact statistical characterization of the test cannot be obtained, and, therefore, a Chernoff bound is derived. Results in terms of the probability of detection versus signal-to-noise ratio (SNR) obtained from Monte Carlo simulation, the Chernoff bound, and the optimal matched filter case are examined. The performance of the noncoherent detector is shown to be a function of the covariance matrix estimate and the number of data samples     

A robust exponential mixture detector applied to radar

Exponential mixture probability density functions (pdfs) are shown to be useful models of radar sea clutter. The variability of certain parameters leads to estimation error and degradation in the performance of detection algorithms derived from this model. Robust implementations are introduced by assuming that parameters are known within certain intervals and selecting values to prevent an excessive number of false alarms. An empirical study demonstrates an average 6-9 dB gain in comparison with a constant false-alarm rate (CFAR) processor     

High resolution radar clutter statistics

The generalized compound probability density function (GC-pdf) is presented for modeling high resolution radar clutter. In particular, the model is used to describe deviation of the speckle component from the Rayleigh to Weibull or other pdfs with longer tails. The GC-pdf is formed using the generalized gamma (GΓ) pdf to describe both the speckle and the modulation component of the radar clutter. The proposed model is analyzed and thermal noise is incorporated into it. The validation of the GC-pdf with real data is carried out employing the statistical moments as well as goodness-of-fit tests. A large variety of experimental data is used for this purpose. The GC-pdf outperforms the K-pdf in modeling high resolution radar clutter and reveals its structural characteristics     

基于提前停止判决的编码软信息辅助载波同步

 针对目前编码辅助载波同步算法中复杂度较高、延时大的问题,提出了引入辅助停止判决机制的编码辅助载波同步算法。在现有的编码辅助载波同步结构基础上,该算法能对环路信噪比(SNR)进行实时判定,在环路SNR满足限定条件后提前停止编码辅助载波同步迭代,而不影响译码性能。采用新的相位估计方式估计含相位噪声的载波相位,提升了该条件下的环路信噪比。仿真采用码率为1/2的低密度奇偶校验(LDPC)码作为编码方式,结果表明:在误码率为10^-5时,该算法减少了约50%的编码辅助载波同步迭代次数;在含相位噪声的信号条件下,与理想解调译码相比,性能损失不超过0.15 dB。