Carrier-Tracking Loop Performance for Quaternary and Binary PSK Signals

By expressing the open-loop response voltage as a Fourier series in terms of the phase-tracking error and then utilizing a very useful mean-value expression, we assess the performance of loops suited to recovering the carrier of four-phase (quaternary) and two-phase (binary) phase-shift-keyed (QPSK and BPSK) signals. At high signal to noise ratios (SNRs) they perform comparably, but at low SNRs the former's performance deteriorates much more rapidly. The loop's ability to maintain the carrier frequency despite the noise accompanying the PSK signal is measured by the mean and the variance of the oscillator's control voltage. In particular, Spilker's loop for QPSK and the Costas loop for BPSK signals are discussed.     

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.     

Coherent Square Wave Demodulation of Ideal Limiter Output

An ideal limiter may be used to single-bit quantize a noisy sinusoidal signal. This digitization is particularly economical if the signal is to be recorded. lt might then be desired to obtain phase coherence with the limited input signal. A single-bit digital phase-locked loop. utilizing a square wave reference, could be used for this purpose. The effects of coherent square wave demodulation on the signal-to-noise ratio and the (signal-to-noise spectral density) ratio are discussed. The latter result is directly applicable to the performance of the digital phase-locked loop.     

基于FPGA的数字Costas环的设计与实现

通过对数字Costas环路原理的分析，提出了新的环路鉴相方式，且环路参数可根据锁定情况及时修改，确保锁相环路稳定工作。详细阐述了环路各部件的参数及电路设计。ChipScopePro实时观测FPGA内部信号和Matlab仿真结果表明．该Costas环路具有十分优良的性能。     

Effects of CW Interference on Narrow-Band Second-Order Phase-Lock Loops

This paper describes an experimental study of the effect of continuous wave (CW) interference and white noise on a second-order phase-lock loop. The reciprocal of the loop mean-square phase error is used as an index of performance, and the effect of interference levels that do not cause cycle skipping or loss of lock is described in terms of this index. Loop thresholds are determined by measurement of cycle-skipping rates. Stationary or slowly-sweeping CW interference caused a degradation in loop threshold of roughly 3 dB for every 6 dB of interference power above the noise power level. The effective loop signal-to-noise ratio was decreased approximately 1 dB at interference-to-noise power ratios of -3 dB. Interference levels equal to the signal level consistently caused loss of lock, regardless of the loop signal-to-noise ratio.     

An Lms Adaptive Array Using a Pilot Signal

A least mean square (LMS) adaptive array requires a reference signal. When the desired signal contains a pilot signal, it may be used as the reference signal. In this paper the steady-state performance of an LMS adaptive array in which the pilot signal is used as the reference signal is examined. It is shown that the LMS adaptive array occasionally suppresses the desired signal. The loop gain, which is an important parameter, is also considered.     

Local SNR considerations in decentralized CFAR detection

We consider the decentralized detection problem, involving N sensors and a central processor, in which the sensors transmit unquantized data to the fusion center. Assuming a homogeneous background for constant false-alarm rate (CFAR) analysis, we obtain the performances of the system for the Swerling I and Swerling III target models. We demonstrate that a simple nonparametric fusion rule at the central processor is sufficient for nearly optimum performance. The effect of the local signal-to-noise ratios (SNRs) on the performances of the optimum detector and two suboptimum detectors is also examined. Finally, we obtain a set of conditions, related to the SNRs, under which better performance may be obtained by using decentralized detection as compared with centralized detection     

On Transient and Periodic Signal Detection in Time-Varying Noise Power

Detectability of periodic and synchronously recurrent transient signals in a noisy environment in which the noise power is time varying is investigated. For at least one noise model, it is shown that the basic nonlinearity of the optimum detector is a limiter. Performance of this optimum detector is compared with analog cross-correlation and clipper cross-correlation (CCC) detectors. It is shown that the CCC performs nearly optimally, especially at low signal-to-noise ratios, and that its performance is significantly better than that of the analog cross correlator.     

Maximun Posterion Probability Demodulation of Angle-Modulated Signals

An algorithm is presented for maximum posterior probability (MPP) demodulation of angle-modulated signals. A sampled data version of the problem is considered, in which additive Gaussian noise and Gaussian modulating signal are assumed. The algorithm is a numerical method for solving the nonlinear equations which are necessary conditions for MPP estimation. Results of a simulation of the algorithm are presented and discussed. Improvements in performance with respect to a phaselocked loop appear to stem from use of data before and after the time position of a phase estimate and from optimization of performance at low signal-to-noise ratio (SNR) as well as at high SNR.     

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.     

Noise analysis of a digital tanlock loop

The noise performance analysis of a nonuniform digital phase-locked loop (DPLL), called the digital tanlock loop (DTL), is investigated by both analytic and computer-simulation methods. The results are presented in terms of phase error probability mass function and mean time to skip cycle versus input signal-to-noise ratio (SNR). These results are compared to the ones obtained with the conventional sinusoidal DPLL loop (DPLL). It is found that, for low-to-moderate input SNR, the DTL has only a slight improvement over the DPLL. The DTL, however, has larger linear characteristics than the conventional DPLL, which makes it attractive for applications that require an increased tracking range or as a first stage in carrier tracking systems based on optimum estimation procedures such as a Kalman smoother     

On the Acquisition Time for an Apollo Ranging Code

An Apollo ranging system is considered whose phase reference is obtained by a phase-locked loop for bit synchronization. The bit phase reference is noisy, and the error probability for the ranging code is shown to depend on the input signal energy per bit to noise density ratio. The procedure of computing the acquisition time for the ranging code is then presented and the acquisition time for a lunar ranging code is plotted versus the input signal-to-noise density ratio.     

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.     

基于小生境遗传算法的分布式OS-CFAR检测系统优化与性能分析

 利用小生境遗传算法,对不同检测窗长度和检测信噪比的三传感器分布式 OS-CFAR检测系统进行了优化设计,给出了一组针对不同检测环境与融合方式的搜索结果。分析表明,对于非一致环境下分布式 OS-CFAR检测系统,小生境遗传算法是一种良好的优化算法。利用搜索结果,研究了不同融合方式下环境变化对分布式 OS-CFAR检测系统的性能影响,结果表明,“或”融合对检测环境的非一致变化具有较强的鲁棒性,而“3选2”融合和“与”融合对检测环境的变化比较敏感。     

Reference Loop Phase Shift in an N-Element Adaptive Array

Adaptive arrays based on the LMS algorithm require the generation of a reference signal which is usually derived from the array output. A particular problem associated with this technique is that of a phase shift in the reference signal loop. The effects of this phase shift on the performance of an N-element adaptive array are discussed. It is shown that a reference loop phase shift causes the array weights to cycle, thereby frequency translating the signals at the output. The weight-cycling frequency is related to various system parameters of an N-element array. In particular, it is observed that the cycling frequency increases as the number of antennas (N) increases.     

Cross-correlation properties of algebraically constructed Costasarrays

The problem of determining the cross-correlation properties of signals based on algebraically constructed Costas arrays is addressed by examining the discrete cross-correlation of the algebraically constructed Costas arrays for a given construction and dimension. Finding two arrays that minimally correlate implies that the signals based on these arrays also minimally correlate. The properties of finite fields are reviewed, and the major algebraic constructions for Costas arrays are presented, i.e. the Welch construction and the Golomb construction. The discrete cross-correlation properties of the Costas arrays are derived for arrays of the same dimension derived from the same construction. The use of Costas arrays in the signal design problem is discussed, and examples are given to show the cross-correlation of the signals based on the algebraically constructed arrays     

Effect of Noncoherent FSK Versus PSK on Waveform Error in PCM Telemetry

In a recent paper [1] the authors presented an optimization strategy for the transmission of analog data over a PCM telemetry link. Constraints imposed included real-time operation and both average and peak power limitations on the transmitter. The selected strategy used Karhunen-Loeve (KL) sampling, unequal bit assignments, optimum uniform quantizing, the natural code, and PSK reception. In this paper, the performance of the above system will be compared to the same system using noncoherent FSK reception instead of PSK. The performance criterion used for the comparison is the mean integral squared error criterion.     

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.     

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.     

Error Probabilities in PCM/FM with Phase-Lock Loop Discriminators

Previous literature has analyzed PCM/FM telemetry systems using idealized FM demodulators at the receiver. However, in many systems operating today, phase-lock loop demodulators are employed which depart noticeably from ideal operation as the loop falls ?out of lock.? In this paper an approximate expression for error probability is derived, which clearly indicates the effect of the loop on the previously published data using ideal discriminators. It is shown that the presence of the loop becomes apparent at input signal-to-noise ratios below approximately 3.5 dB, while the amount of error increase over the ideal case depends, to a large extent, upon the shape of IF filtering being used.