Estimation techniques for GMSK using linear detectors in satellite communications

This paper describes data-aided signal level and noise variance estimators for Gaussian minimum shift keying (GMSK) when the observations are limited to the output of a filter matched to the first pulse-amplitude modulation (PAM) pulse in the equivalent PAM representation. The estimators are based on the maximum likelihood (ML) principle and assume burst-mode transmission with known timing and a block of L₀ known bits. While it is well known that ML estimators are asymptotically unbiased and efficient, the analysis quantifies the rate at which the estimators approach these asymptotic properties. It is shown that the carrier phase, amplitude, and noise variance estimators are unbiased and can achieve their corresponding Cramer-Rao bounds with modest combinations of signal-to-noise ratio and observation length. The estimates are used to estimate the signal-to-noise ratio. It is shown that the mean squared error performance of the ratio increases with signal-to-noise ratio while the mean squared error performance of the ratio in decibels decreases with signal-to-noise ratio. Simulation results are provided to confirm the accuracy of the analytic results.     

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.     

Performance of a Two-Sample Mann-Whitney Nonparametric Detector in a Radar Application

The detection of signals in an unknown, typically non-Gaussian noise environment, while attempting to maintain a constant false-alarm rate, is a common problem in radar and sonar. The raw receiver data is commonly processed initially by a bank of frequency filters. The further processing of the outputs from the filter bank by a two-sample Mann-Whitney detector is considered. When the noise statistics in all filters are identical, the Mann-Whitney detector is distribution free, i. e., the false-alarm probability may be prescribed in advance regardless of the precise form of the noise statistics. The primary purpose of this paper is to demonstrate the potential advantage of nonparametric detectors over conventional detectors. The signal detection performance of the Mann-Whitney detector is compared to that of an ordinary linear envelope detector plus integrator in the presence of Gaussian and several hypothetical forms of non-Gaussian noise. This comparison is made for both uniform and nonuniform distributions of noise power across the filter bank. Besides providing a much more constant false-alarm rate than the conventional detector, the Mann-Whitney detector's signal detection performance is found also to be much less sensitive to the form of the noise statistics. In one case, its detection sensitivity is found to be 11 dB better than that of the conventional detector. Even when the noise power density is made moderately nonuniform across the filter bank, the detection performance of the Mann-Whitney detector is found not to be significantly affected.     

Adaptive Radar Detection in Doubly Nonstationary Autoregressive Doppler Spread Clutter

The problem of adaptive radar detection in clutter which is nonstationary both in slow and fast time is addressed. Nonstationarity within a coherent processing interval (CPI) often precludes target detection because of the masking induced by Doppler spreading of the clutter. Across range bins (i.e., fast time), nonstationarity severely limits the amount of training data available to estimate the noise covariance matrix required for adaptive detection. Such difficult clutter conditions are not uncommon in complex multipath propagation conditions where path lengths can change abruptly in dynamic scenarios. To mitigate nonstationary Doppler spread clutter, an approximation to the generalized likelihood ratio test (GLRT) detector is presented wherein the CPI from the hypothesized target range is used for both clutter estimation and target detection. To overcome the lack of training data, a modified time-varying autoregressive (TVAR) model is assumed for the clutter return. In particular, maximum likelihood (ML) estimates of the TVAR parameters, computed from a single snapshot of data, are used in a GLRT for detecting stationary targets in possibly abruptly nonstationary clutter. The GLRT is compared with three alternative methods including a conceptually simpler ad hoc approach based on extrapolation of quasi-stationary data segments. Detection performance is assessed using simulated targets in both synthetically-generated and real radar clutter. Results suggest the proposed GLRT with TVAR clutter modeling can provide between 5–8 dB improvement in signal-to-clutter plus noise ratio (SCNR) when compared with the conventional methods.     

Interception Algorithm of S-cubed Signal Model in Stealth Radar Equipment

Radar equipment of stealth platforms such as aircraft have adopted the newest modern technology to design the signal waveforms. One of the important and effective methods is the hybrid waveform called spread spectrum stretch (S-cubed) which combines linear frequency modulation (LFM) and discrete phase code. In order to investigate the function of enemy’s stealth radar equipment, the interception algorithm of S-cubed is needed. In this paper, a novel detection and parameter estimation approach for the reconnaissance S-cubed radar signal is presented. First, the generalized time-frequency representation of Zhao, Atlas, and Marks (ZAM-GTFR) and Hough transforms (HT) are applied to detecting the signal, and then the initial frequency and modulation slope of LFM are estimated from the ZAM-GTFR. On the basis of LFM information, the reconstructing signal is generated. Finally, the code rate of discrete phase code is extracted from the negative peaks of the ZAM-GTFR. Simulation results show that the proposed algorithm has higher estimation accuracy when the signal to noise ratio (SNR) is above 3 dB.     

Performance Analysis of the Censored Mean-Level Detector

The censored mean-level detector (CMLD) is an alternative to the mean-level detector that achieves robust detection performance in a multiple-target environment by censoring several of the largest samples of the maximum likelihood estimate of the background noise level. Here we derive exact expressions for the probability of detection of the CMLD in a multiple-target environment when a fixed number of Swerling II targets are present. The primary target is modeled by Swerling case II, and only single-pulse processing is analyzed. Optimization of the CMLD parameters is considered, and a comparison to other detectors is presented.     

Limiter-Discriminator Detection Performance of Manchester and NRZ Coded FSK

The theory of limiter-discriminator detection of a frequency shift keyed (FSK) carrier is reviewed and this theory is used to predict the bit error probability performance of Manchester coded and nonreturn-to-zero (NRZ) coded data. A major result of the study is that the predetection time bandwidth product BT and the devia tion ratio h needed to give optimum performance for Manchester coding are seen to be larger than optimum NRZ FSK. Specifically, BT ~ 2 and h ~ 1 will result in Manchester performance about 2 dB worse than optimum NRZ.     

Comparison of various periodograms for sinusoid detection andfrequency estimation

With the advent of the fast Fourier transform (FFT) algorithm, the periodogram and its variants such as the Bartlett's procedure and Welch method, have become very popular for spectral analysis. However, there has not been a thorough comparison of the detection and estimation performances of these methods. Different forms of the periodogram are studied here for single real tone detection and frequency estimation in the presence of white Gaussian noise. The threshold effect in frequency estimation, that is, when the estimation errors become several orders of magnitude greater than the Cramer-Rao lower bound (CRLB), is also investigated. It is shown that the standard periodogram gives the optimum detection performance for a pure tone while the Welch method is the best detector when there is phase instability in the sinusoid. As expected, since the conventional periodogram is a maximum likelihood estimator of frequency, it generally provides the minimum mean square frequency estimation errors     

Optimum detection and location estimation of target lines in the range-time space of a search radar

The average likelihood ratio detector is derived as the optimum detector for detecting a target line with unknown normal parameters in the range-time data space of a search radar, which is corrupted by Gaussian noise. The receiver operation characteristics of this optimum detector is derived to evaluate its performance improvement in comparison with the Hough detector, which uses the return signal of several successive scans to achieve a non-coherent integration improvement and get a better performance than the conventional detector. This comparison, which is done through analytic derivations and also through simulation results, shows that the average likelihood ratio detector has a better performance for different SNR values. This result is justified by showing the disadvantages of the Hough method, which are eliminated by the optimum detector. To have an estimate for the location of the detected target line in the optimum detection method as the Hough method, which detects and localizes the target lines simultaneously, we present the maximum a posteriori probability estimator. The estimation performance of the two methods is then compared and it is shown that the maximum a posteriori probability estimator localizes the detected target lines with a better performance in comparison with the Hough method.     

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。     

基于DDS+PLL的光源调制与功率稳定控制方法CSCD

量子传感器是基于量子操控技术的研究成果,一般具有高精度、小体积等优势。激光器是量子传感器的核心部件,有抽运和检测功能,激光器的稳定性对量子传感器具有重要的意义。提出了一种直接数字合成法(DDS)与锁相回路(PLL)相结合的方法,对激光器进行调制并抑制调制噪声,实现了激光器的稳定输出。基于现有小型量子传感器装置,在DDS生成4kHz参考信号的情况下实现了激光器电流8kHz调制,抑制了调制时调制电流信号噪声约8dB,并提高了激光器输出光功率的稳定性。     

A Sequential Detector

The PRSD detector improves radar performance by controlling the distribution of energy in space, thus making a radar adaptive to its environment. An increase in performance over classical detectors may be realized in any of several ways: 1) greater maximum range; 2) smaller minimum detectable targets; 3) higher data rates; 4) lower average transmitted power, which allows smaller size and weight of equipment. The model of the PRSD detector described herein was tested with a semi-agile beam radar, and gave measured field performance improvement (for this particular radar) equivalent to an S/N increase ranging from 5 to 22 dB with a mean of 9.5 dB. This increase is greater than the 5-dB improvement predicted for the system in a white noise environment because many of the field tests were at locations subjected to heavy interference. The PRSD detector was extremely effective reducing the interference. In this paper, we will briefly review the theory of operation, describe the equipment and the method of test, and present experimental data. The data presented here are essential to a complete understanding of sequential detection since a rigorous theory encompassing multiple range bin radar has not been developed at this time. Finally, an extensive bibliography is appended.     

A comparison of two adaptive detection schemes

Two schemes for adaptive detection are compared: Kelly's generalized likelihood ratio test (GLRT) and the mean level adaptive detector (MLAD). Detection performance, P_D, is predicted for the two schemes under the assumptions that the input noises are zero-mean complex Gaussian random variables that are temporally independent but spatially correlated; and the amplitude of the desired signal is Rayleigh distributed. P_D is computed as a function of the false alarm probability, the number of input channels, the number of independent samples per channel, and the matched filtered output signal-to-noise (S/N) power ratio. In this analysis the GLRT is shown to have better detection performance than the MLAD. The difference in detection performance increases as one uses fewer input samples. However, the required number of samples necessary to have only a 3 dB detection loss for both detection schemes is approximately the same. This is significant since for the present, the MLAD is considerably less complex to implement than the GLRT     

Sonar Array Detection of Gaussian Signals in Gaussian Noise of Unknown Power

A statistical test is postulated for detecting, with an M-element hydrophone array, a Gaussian signal in spatially independent Gaussian noise of unknown power. The test is an extension of the uniformly-most-powerful (UMP) unbiased test for a two-element array. The output signal-to-noise ratio of the test is calculated and, for a large number of independent space-time samples, is shown to be no better than a mean-level detector (MLD). Receiver operating characteristic curves (ROC) for the MLD are computed and compared to the ROC curves for the optimum (Bayes) parametric detector. The input signal-to-noise power ratios required to provide a detection probability of 0.5 differ by less than 0.2 dB for a fifty-element array with wide variation in false-alarm probability and time-bandwidth product. This result suggests that both the extended bivariate UMP unbiased test and the MLD perform close to the unknown UMP unbiased test for independence of a multivariate Gaussian distribution.     

Optimum and mismatched detection against K-distributed plusGaussian clutter

We derive the optimum radar receiver to detect fluctuating and non-fluctuating targets against a disturbance which is modeled as a mixture of coherent K-distributed and Gaussian-distributed clutter. In addition, thermal noise, which is always present in the radar receiver, is considered. We discuss the implementation of the optimum coherent detector, which derives from the likelihood ratio test under the assumption of perfectly known disturbance statistics, and evaluate its performance via a numerical procedure, when possible, and via Monte Carlo simulation otherwise. Moreover, we compare the performance of the optimum detector with those of two detectors which are optimum for totally Gaussian and totally K-distributed clutter respectively, when they are fed with such a mixed disturbance. We conclude that, though the optimum detector has a larger computational cost, it provides sensibly better detection performance than the mismatched detectors in a number of operational situations. Thus, there is a need to derive suboptimum target detectors against the mixture of disturbances which trade-off the detection performance and the implementation complexity     

基于相减式信号抵消的带内隐藏干扰检测

为实现对通信信号的实时监测,提出一种带内隐藏干扰检测方法。该方法先利用解调结果重构期望信号,然后通过时延估计及自适应滤波使其与接收信号中的有用信号在时间、幅度和相位上尽量保持一致,最后利用相减式信号抵消技术将其从接收信号中消除,能够在不中断通信业务的前提下检测出信号带宽内隐藏的干扰。仿真结果表明,当信干比不低于6 dB、信噪比不低于3 dB时,期望信号、干扰信号与各自原信号的相似系数均能达到0.9以上,提取的干扰信号非常准确。将利用文中方法估计出的干扰抵消后,信号的星座图也得到了显著的收敛。     

无需辅助数据的分布式目标自适应检测器

在非高斯背景和没有辅助数据的条件下,研究了高分辨率雷达分布式目标的自适应检测问题.首先采用有序检测理论和协方差矩阵的迭代估计方法粗略估计散射点集合,进一步利用迭代估计方法获得协方差矩阵的近似最大似然估计,提出了无需辅助数据的自适应检测器(ADWSD).ADWSD在非高斯背景下具有近似恒虚警率特性,且检测性能远好于修正的...     

An adaptive array detector with mismatched signal rejection

An adaptive detection algorithm with a sensibility parameter for rejecting unwanted signals is presented. This algorithm is a simple modification of the generalized likelihood ratio (GLR) detector (or test) for detecting a signal in zero mean Gaussian noise with unknown correlation matrix. Specifically, the adaptive detection algorithm is obtained by introducing an arbitrary positive scalar, which is called the sensitivity parameter, into the GLR detector as a multiplier of an already existing quadratic term. The GLR detector then becomes a special case of this detector for the unity sensitivity parameter. It is shown that the sensitivity parameter controls the degree to which unwanted signals are rejected. From numerical examples, it is demonstrated how the sensitivity parameter can be chosen such that unwanted signals, can be rejected while maintaining acceptable detection loss for slightly mismatched signals. Further insight into previous work on adaptive detection is also given     

基于功率复用的椭圆球面波函数非正交调制方法

围绕如何降低基于椭圆球面波函数的非正交调制（PSWF-NPSM）系统误码率，降低信号检测复杂度，引入调制信号功率复用思想，提出基于功率复用的椭圆球面波函数非正交调制（PD-PSWF-NPSM）方法。该方法对载波信号按子波带进行功率分配，增加了调制信号最小欧式距离，降低了系统误码率；在接收端，提出基于检测统计量的串行干扰相消信号检测方法，依据不同支路信号间功率差异，对信号进行分离、检测。理论与仿真分析表明，该方法在不降低系统频带利用率、调制信号功率谱、峰均功率比特性前提下，能够有效提高系统误码性能，降低调制信号检测复杂度；与原非正交调制方法相比，当误比特率（BER）为10^-5时，所提方法系统误码性能提升约1.7 dB。