Parameter estimation of 2-D random amplitude polynomial-phasesignals

Phase information has fundamental importance in many two-dimensional (2-D) signal processing problems. In this paper, we consider 2-D signals with random amplitude and a continuous deterministic phase. The signal is represented by a random amplitude polynomial phase model. A computationally efficient estimation algorithm for the signal parameters is presented. The algorithm is based on the properties of the mean phase differencing operator, which is introduced and analyzed. Assuming that the signal is observed in additive white Gaussian noise and that the amplitude field is Gaussian as well, we derive the Cramer-Rao lower bound (CRB) on the error variance in jointly estimating the model parameters. The performance of the algorithm in the presence of additive white Gaussian noise is illustrated by numerical examples and compared with the CRB     

Estimate-maximize algorithms for multichannel time delay and signalestimation

Computationally efficient iterative algorithms are developed for the joint maximum-likelihood estimation of the time delays and the spectral parameters of stationary Gaussian signals radiated from a stationary source and observed in the presence of uncorrelated additive noise at two or more spatially distributed receivers. The first set of algorithms is based on the estimate-maximize approach, while the second set achieves superlinear performance by using a modified approach. These algorithms decouple the estimation of all the unknowns, separately estimating the signal, the signal spectral parameters, and each channel's delay, attenuation, and noise power. This decoupling considerably simplifies the estimator's structure and computation. Convergence is guaranteed to the set of stationary points of the likelihood function, and each iteration increases the likelihood. The convergence rates are analyzed theoretically, and the algorithm's performance demonstrated via simulation     

A general likelihood-ratio formula for random signals in Gaussian noise

It is shown that the likelihood ratio for the detection of a random, not necessarily Gaussian, signal in additive white Gaussian noise has the same form as that for a known signal in white Gaussian noise. The role of the known signal is played by the casual least-squares estimate of the signal from the observations. However, the "correlation" integral has to be interpreted in a special sense as an Itô stochastic integral. It will be shown that the formula includes all known explicit formulas for signals in white Gaussian noise. However, and more important, the formula suggests an "estimator-correlator" philosophy for engineering approximation of the optimum receiver. Some extensions of the above result are also discussed, e.g., additive finite-variance, not necessarily Gaussian, noise plus a white Gaussian noise component. Purely colored Gaussian noise can be treated if whitening filters can be specified. The analog implementation of Itô integrals is briefly discussed. The proofs of the formulas are based on the concept of an innovation process, which has been useful in certain related problems of linear and nonlinear least-squares estimation, and on the concept of covariance factorization.     

实时高精度雷达噪声信号产生方法与FPGA实现

针对各种典型分布的噪声信号在雷达系统半实物仿真和噪声雷达波形设计中的实际需求,基于Box-Muller算法提出了一种能够实时产生多种分布特性噪声的信号生成方法。首先使用线性反馈移位寄存器产生均匀分布随机序列,然后利用能够实现高精度、低延迟的坐标旋转数字算法(Coordinate Rotation Digital Computer,CORDIC)实现Box-Muller变换中复杂函数的快速计算,将均匀随机序列转换成高斯分布随机序列,最后利用高斯随机序列经过相关数学运算得到其他复杂分布的随机序列,在此基础上产生具有各种分布特性的噪声信号。基于Xilinx XC7VX415T 现场可编程门阵列(Field Programmable Gate Array,FPGA)芯片的实验结果表明,所提方法在保证小数位数据精度为20 b时,可实时产生速率为2.5 Gb/s的高精度随机数据序列,进而生成服从多种函数分布下的噪声信号。所提方法整体资源占用率较少,具有较强的实用性。     

Analysis of CDMA signal spectral regrowth and waveform quality

Closed-form expressions for the spectral regrowth and waveform quality of a reverse-link code divison multiple access (CDMA) signal passed through a weakly nonlinear circuit are derived using the power series and statistical methods. The third-order nonlinearity is expressed in terms of IP₃ to include the memory effects of the circuit in-band and out-of-band reactances. The analysis is based on a time-domain model of the signal that gives more accurate distortion estimates than the widely used Gaussian approximation. The model is used to derive the probability density function and other statistical properties of the CDMA signal to compare them to the Gaussian noise properties. Differences in statistics and distortions of OQPSK and QPSK modulated signals are discussed     

主动声纳的混沌波形设计和解调方法

该文为解决主动声纳隐蔽性差的问题,提出了一种新的波形设计方法：将特定编码调制到混沌信号中,作为主动声纳的发射信号。文中全面考虑了水声信道滤波和加性噪声对回波的影响,采用自适应滤波器解调回波,通过识别编码检测回波信号。提出了改进的相平面Lyapunov自适应滤波器作为解调算法。仿真结果表明：该解调算法在加性白噪声和滤波情况均有较好的解调效果,并能满足实时性的要求。与现有的主动声纳发射信号相比,提高了主动声纳的隐蔽性。     

A further note on a general likelihood formula for random signals in Gaussian noise

A general likelihood ratio formula of the author's for the detection of signals in independent white Gaussian noise is extended to allow a "one-sided" dependence in which only the future white noise is required to be independent of past signal and noise. The assumption of Gaussian additive noise is also somewhat relaxed. The proof is based on some recent martingale theorems and on the concept of the innovations process.     

Optimum and reduced complexity multiuser detectors for asynchronous CPM signaling

Maximum likelihood detector algorithms are developed for the matrix of transmitted symbols in a multiuser system in which the received signal is the sum of K cochannel continuous phase modulated (CPM) signals and additive white Gaussian noise. We illustrate that the maximum likelihood matrix detector, which provides optimum detector performance, consists of K sets of front-end matched filters followed by a Viterbi algorithm. We also derive two reduced complexity receivers, demonstrating through simulation that they perform within 1-2 dB of the optimal while substantially reducing complexity. The paper demonstrates how performance can be traded off against complexity, giving particular attention to cochannel Gaussian minimum shift keyed (GMSK) signals.     

基于小波分析的脉冲信号波形检测方法

通过对多种小波函数的分析、比较,提出了一种基于小波分析的脉冲信号时域波形检测方法,该方法利用小波变换模的极大值特性,较好地实现了对脉冲成形信号波形参数的检测。理论分析和仿真研究结果表明,该方法对高斯噪声信道具有较强的适应能力,并且算法简单、运算量小、信号参数检测精度高,具有较好的工程应用前景。     

Robust L-estimation based forms of signal transforms and time-frequency representations

The L-estimation based signal transforms and time-frequency (TF) representations are introduced by considering the corresponding minimization problems in the Huber (1981, 1998) estimation theory. The standard signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. For signals corrupted by an impulse noise, the median-based transforms produce robust estimates of the non-noisy signal transforms. When the input noise is a mixture of Gaussian and impulse noise, the L-estimation-based signal transforms can outperform other estimates. In quadratic and higher order TF analysis, the resulting noise is inherently a mixture of the Gaussian input noise and an impulse noise component. In this case, the L-estimation-based signal representations can produce the best results. These transforms and TF representations give the standard and the median-based forms as special cases. A procedure for parameter selection in the L-estimation is proposed. The theory is illustrated and checked numerically.     

Lateral inhibition net and weighted matching algorithms for speechrecognition in noise

The authors address the problem of speech recognition with signals corrupted by white Gaussian additive noise at moderate SNR. The energy of the noise is not required. A technique based on a lateral inhibition process approximation with a multilayer neural net (the lateral inhibition net (LIN)) and neural net processing efficacy weighting in acoustic pattern matching algorithms is proposed. In the recognition procedure, the local SNR is computed by means of the autocorrelation function and is employed to estimate the efficacy of LIN in noise cancelling which is taken into account as a weight in a pattern matching algorithm. A general criterion based on weighting the frame influence in decisions according to the reliability in noise reduction is suggested, and modified versions of both HMM and DTW algorithms have been designed. To be more coherent with the conditions that define LIN, a modification in the backpropagation algorithm is also proposed     

Relation of signal set choice to the performance of optimalnon-Gaussian detectors

The optimal procedure for detecting the presence of discrete-time signals in additive noise can be derived from the likelihood ratio test. When the noise has statistically independent, identically distributed components, the dependence of the detector's performance on signal characteristics can be related to the Kullback-Leibler (KL) distance between the distributions governing the hypotheses. Performance predictions based on the central limit theorem are shown to be poor approximations to the true performance. Performance of the optimal detector has long been known to increase exponentially with increasing KL distance. Symmetric noise amplitude distributions yield a symmetric dependence on the difference between the signals' amplitudes at each time index. Small-signal (locally optimal) detection performance is shown to depend on signal energy, whereas large-signal performance depends on the signal waveform. When a distance measure can be defined, performance depends on a different measure than that used in the detector with one exception (the Gaussian)     

Estimation for discrete Markov random fields observed in Gaussiannoise

A finite state Markov random field is observed in Gaussian noise. Changes of measures are defined under which all random variables of the signal are independent and uniformly distributed over the finite state space and all random variables of the observation are independent and N(0,1). The problem of estimating the most likely signal given the observations is treated in a related form by introducing probabilities over the possible signals     

Signal Design for Low-Error Probability in Fading Dispersive Channels

The signal design problem for FSK communication via fading dispersive channels is considered. The channel is modeled as a linear filter whose time-varying impulse response is a sample function from a zero-mean Gaussian random field of arbitrary WSSUS type. The additive noise component in the received waveforms is supposed to be a zero-mean white Gaussian random process, and maximum likelihood demodulation is assumed. The signal design procedure here adopted consists of minimizing a known upper bound on the error probability, whereas the previous similar design method by Daly intended maximizing an upper bound on the detection probability for radar-astronomy targets. Though with slightly different optimal numerical values, here, as in Daly's problem, the signal design depends on a single parameter which is a simple functional of the channel timefrequency covariance function and of the signal envelope ambiguity function. A detailed example shows how the results of this concise paper can be used to optimize signal parameters and to predict the performance loss due to nonoptimal signal envelopes.     

离散信号空间上的最小能量框架在升余弦脉冲信号上的去噪算法

利用离散信号空间上的最小能量(小波)框架对升余弦脉冲信号展开去噪算法的研究。对于所给的2组不同最小能量框架,升余弦脉冲信号和加性高斯白噪声的抽样离散信号在这2组框架的各个子数列下的分解系数将出现明显不同的统计特征。据此给出了2个具体的阈值去噪算法,两者都充分利用了最小能量框架在信号去噪应用上的优点,在保持发送原始信号成分的同时去除了部分噪声成分,获得了较好的处理效果。仿真结果表明,当调制方式为BPSK且升余弦脉冲信号受加性高斯白噪声影响时,如果利用2个算法对接收波形进行去噪预处理,则接收信号的信噪比大幅度提升,在误码率上可以分别获得3.1dB和2.7dB左右的性能增益。     

Constrained iterative speech enhancement with application to speechrecognition

The basis of an improved form of iterative speech enhancement for single-channel inputs is sequential maximum a posteriori estimation of the speech waveform and its all-pole parameters, followed by imposition of constraints upon the sequence of speech spectra. The approaches impose intraframe and interframe constraints on the input speech signal. Properties of the line spectral pair representation of speech allow for an efficient and direct procedure for application of many of the constraint requirements. Substantial improvement over the unconstrained method is observed in a variety of domains. Informed listener quality evaluation tests and objective speech quality measures demonstrate the technique's effectiveness for additive white Gaussian noise. A consistent terminating point of the iterative technique is shown. The current systems result in substantially improved speech quality and linear predictive coding (LPC) parameter estimation with only a minor increase in computational requirements. The algorithms are evaluated with respect to improving automatic recognition of speech in the presence of additive noise and shown to outperform other enhancement methods in this application     

Binary communication over the Gaussian channel using feedback with a peak energy constraint

We consider binary communication over the additive white Gaussian noise channel with no bandwidth constraint on the channel input signals, assuming the availability of a noiseless delayless feedback link. Although the signals at timetcan depend on the noise at timestau < tand are therefore random functions, we require that the signal energy never exceed a fixed level. We show that the optimal probability of error is attainable without the use of the feedback channel by using antipodal signals.     

Waveform recognition in the presence of domain and amplitude noise

In this paper, we discuss the problem of recognizing single-dimensional, real-valued, functions in the presence of domain noise (i.e., noise that affects the domain rather than the amplitude). This problem is inspired by the field of on-line character recognition where it is more natural to view the hand as deforming the domain of the character rather than adding noise to its amplitude. The results obtained illustrate the difficulties one faces when dealing with both domain and amplitude deformation of waveforms or images. Our major result is a set of sufficient conditions that a recognition metric has to satisfy. Examples of metrics that satisfy these conditions, and hence are appropriate for recognition when the deformation affects the domain rather than the amplitude, include the supnorm metric and the total variation metric. Furthermore, we extend the results to the case when a waveform is corrupted by both amplitude and domain deformation     

On the error probability of linearly modulated signals on Rayleighfrequency-flat fading channels

Consideration is given to optimal detection of linearly modulated signals subject to multiplicative Rayleigh-distributed distortion and additive white Gaussian noise. For coherent detection, regenerated amplitude and phase references are employed at the receiver to compensate for amplitude and phase deviations from the correct values. A system model is formulated under the assumption of perfect symbol timing and in the absence of intersymbol interference, producing a final additive noise term, applied just before the detection, which contains the effects of the original additive and multiplicative distortions and of the errors in the phase and amplitude references. By determining the probability density function of this final noise term for arbitrary types of linear modulation, it is possible to perform exact calculations of error probabilities     

Locally optimum rank detection of correlated random signals inadditive noise

Nonparametric detection of a zero-mean random signal in additive noise is considered. The locally optimum detector based on signs and ranks of observations is derived, for good weak-signal detection performance under any specified noise probability density function. This detector is shown to have interesting similarities to the locally optimum detector for random signals. It may also be viewed as a generalization of the locally optimum rank detector for known signals. Examples of the test statistic of the detector are given for some specific noise probability density functions. Asymptotic and finite sample-size performance of the locally optimum rank detector is also considered