Gaussian Cramer-Rao bound for direction estimation of noncircular signals in unknown noise fields

This paper focuses on the stochastic Cramer-Rao bound (CRB) on direction of arrival (DOA) estimation accuracy for noncircular Gaussian sources in the general case of an arbitrary unknown Gaussian noise field parameterized by a vector of unknowns. Explicit closed-form expressions of the stochastic CRB for DOA parameters alone are obtained directly from the Slepian-Bangs formula for general noncircular complex Gaussian distributions. As a special case, the CRB under the nonuniform white noise assumption is derived. Our expressions can be viewed as extensions of the well-known results by Stoica and Nehorai, Ottersten et al., Weiss and Friedlander, Pesavento and Gershman, and Gershman et al. Some properties of these CRBs are proved and finally, these bounds are numerically compared with the conventional CRBs under the circular complex Gaussian distribution for different unknown noise field models.     

Linear prediction analysis of speech signals in the presence ofwhite Gaussian noise with unknown variance

A simple method is presented to compensate for noise effects before performing linear prediction analysis of speech signals in the presence of white noise with unknown variance. The method determines a suitable bias that should be subtracted from the zero-lag autocorrelation function, rather than deriving the exact noise variance. The resulting linear prediction filter is guaranteed to be stable. Since the bias used is always smaller than the minimum eigenvalue of the autocorrelation matrix. In addition to a comparison with other methods, the proposed method is examined from various viewpoints, including the degree of formant intensity, signal-to-noise ratio (SNR), deviation of compensated spectra and objective distortion measures. The improvements observed across a data set, consisting of four sentences uttered by six speakers, indicate that the compensated spectra measured with low SNRs are comparable to the uncompensated counterparts measured with approximately 5 dB higher SNRs     

Nonsingular detection and likelihood ratio for random signals in white Gaussian noise

This paper is concerned with the mathematical aspect of a detection problem (a random signal in white Gaussian noise). Specifically, we obtain a sufficient condition for nonsingular detection and derive a likelihood-ratio expression in terms of least-mean-square estimates. The problem itself is old, and the likelihood-ratio expression is also well known. The contribution of this paper is a relatively elementary and self-contained derivation of the likelihood-ratio expression as well as the nonsingularity condition.     

Estimation of randomly occurring stochastic signals in Gaussian noise (Corresp.)

This note applies the general likelihood ratio for the minimum-mean-square-error estimation of the signal when the presence of the signal at the receiver is uncertain during the entire observation interval.     

Estimation of frequency-delay of arrival (FDOA) using fourth-orderstatistics in unknown correlated Gaussian noise sources

A new family of nonparametric and parametric methods based on fourth-order statistics for the estimation of the frequency-delay of arrival (FDOA) between two sensor signal measurements, corrupted by correlated Gaussian noise sources in an unknown way, is presented. The new family of FDOA estimation methods utilizes the fourth-order cumulants or 1-D Fourier transforms of sliced fourth-order cumulants of the two signal measurements. It is demonstrated that the new family of FDOA estimation methods suppresses the effect due to correlated Gaussian measurement noises and outperforms existing second-order statistics-based FDOA estimation methods using either cross-ambiguity function or MUSIC algorithm. Various simulation results are presented for different types of signals, different lengths of data, and different signal-to-noise ratios     

Adaptive AR modeling in white Gaussian noise

Autoregressive (AR) modeling is widely used in signal processing. The coefficients of an AR model can be easily obtained with a least mean square (LMS) prediction error filter. However, it is known that this filter gives a biased solution when the input signal is corrupted by white Gaussian noise. Treichler (1979) suggested the γ-LMS algorithm to remedy this problem and proved that the mean weight vector can converge to the Wiener solution. In this paper, we develop a new algorithm that extends works of Vijayan et al. (1990), for adaptive AR modeling in the presence of white Gaussian noise. By theoretical analysis, we show that the performance of the new algorithm is superior to the γ-LMS filter. Simulations are also provided to support our theoretical results     

The optimum constant false alarm probability detector for relatively coherent multichannel signals in Gaussian noise of unknown power

In this paper, the method of "most powerful similar tests" is used to obtain the optimum (largest probability of detection) constant false alarm probability detector for multichannel signals received in the presence of additive Gaussian noise of unknown power. The signals are assumed to contain a common random phase angle, and hence are relatively coherent over the multiple channels. The noise is assumed to be correlated from channel to channel. The performance of the optimum detector is calculated. Finally, for illustrative purposes, the technique is applied to the detection of a signal in the presence of a jammer, and to the detection of a single channel signal in white and colored noise of unknown power.     

Expansion of likelihood ratio for signals in Gaussian noise

It is shown that the coefficients of the Taylor expansion of the likelihood ratio for random signals in Gaussian noise are proportional to the mean-square estimates of the successive powers of the signal evaluated at zero. A similar relationship holds for the expansion of the logarithm of the likelihood ratio.     

超宽带信号在高斯噪声中传播性能的研究

超宽带无线通信技术使用微弱的、持续时间极短的脉冲进行短距离通信。超宽带信号具有极宽的射频带宽和较低的中心频率，这种特性可使短距无线通信利用较低的发射功率进行高速传输。根据信号的频谱及其在高斯噪声中的传播性能，研究超宽带信号的减少衰减余量特性，给出不同进制波形的PPM调制超宽带信号比特误码率仿真分析。     

A sharp upper bound for the probability of error of the likelihoodratio test for detecting signals in white Gaussian noise

A new sharp upper bound for the probability of error of the likelihood ratio test is given for the detection in white Gaussian noise of any random vector whose norm is greater than, or equal to, a given value and whose probability of presence is less than, or equal to, one half. Also, a new test for the detection of such vectors is described. This test does not depend on the distribution of the signal vector but nevertheless its probability of error is less than, or equal to, the given upper bound     

On the performance of ultra-wide-band signals in Gaussian noise anddense multipath

An ultra-wide-band (UWB) signal is characterized by a radiated spectrum with a very wide bandwidth around a relatively low center frequency. In this paper, we study the reduced fading margin property of UWB signals. To evaluate the fading margin, we compare the performance of UWB signals in an environment with only additive white Gaussian noise (AWGN) versus the performance of UWB signals in a dense multipath environment with AWGN. The assumption here is that the presence of multipath causes a small increase in the signal-to-noise ratio required to achieve reasonable levels of bit error rate. A numerical example confirms this assumption, more specifically, the example shows that to achieve a bit error rate equal to 10^-5, we require about 13.5 dB in the AWGN case and about 15 dB in the multipath case, resulting in a fading margin of just 1.5 dB. This small fading margin can be understood by the ability of the UWB signal to resolve the dense multipath     

Artifacts in Wiener kernels estimated using Gaussian white noise

Wiener's nonlinear system identification theory characterizes a system function with a set of kernels of integrals. One method of determining these Wiener kernels is the cross-correlation technique proposed by Lee and Schetzen, which uses Gaussian white noise as the input to the unknown system. Because a test stimulus is only an approximation of infinitely long Gaussian white noise, it is possible that artifacts are generated during the estimation of the kernels. To help identify and characterize these artifacts, Wiener kernel estimates for two simple nonlinear model systems were made using a pseudorandom Gaussian white noise sequence. The results showed that because of the approximation of a Gaussian distribution, artifacts appear in the estimated kernels due to a form of aliasing. These artifacts can be reduced by increasing the sequence length of the input noise.     

Estimation of the number of orthogonal signals with unknown parameters

Algorithms for estimation of the number of signals with unknown amplitudes and several non-energy parameters are synthesized on the basis of the modified maximum likelihood method. Asymptotic values of the probabilities of the error in estimation of the signal number are determined. The effect of a reduced volume of the a priori domain of possible values and the dimensionality of the vector of unknown non-energy parameters on the quality of operation of the algorithms for estimation of the number of signals is investigated.     

The equivalence- singularity problem for Gaussian signals in Gaussian noise (Corresp.)

The structural properties and sample path behavior of Gaussian signals which can and which cannot be perfectly detected in a given Gaussian noise are described.     

Hard-limiting of two signals in random noise

Two sinusoidal signals and Gaussian noise lying in a narrow band are passed through an ideal band-pass limiter that confines the output spectrum to the vicinity of the input frequencies. The output spectrum, consisting of both discrete and continuous components, is studied in terms of its corresponding autocorrelation function. The discrete output components are identified with the output signals and intermodulation products due to interference between the two input signals. The continuous part of the spectrum is associated with the output noise. The effects of limiting are expressed by ratios among the average powers of the output spectral components. Performance curves are given that show signal suppression, the ratio of output to input SNR's, and the relative strength of the intermodulation terms.     

高斯白噪声环境下电磁辐射测量修正

噪声对电磁辐射准确测量影响较大,特别是对一些弱信号电磁辐射测量,噪声影响不容忽视,需要对测量结果进行修正。目前传统修正办法是合理设置频谱分析仪参数,但不同频谱分析仪,参数设置会存在差别,这种方法通用性不强,而且对电磁辐射测量结果精确度提高不明显。对此,本文研究了频谱分析仪基底噪声及测量环境中噪声的特征,提出了基于高斯白噪声的修正方法,并通过实验进行分析验证。该方法能为电磁辐射准确测量与评估提供新的思路。     

高斯白噪声中单频复正弦信号频率估计

本文提出了一种在加性复高斯白噪声中对单频复正弦信号频率的估计方法。该方法是基于利用自相关系数对Kay的方法和扩展。它从自相关系数的相位差的最佳线性组合中提取频率值。相对于Kay的方法，自相关系数中相位差信息的信噪比提高了。新的估计方法的方差具有更低的输入信噪经阈值，而保持了Kay的方法的无偏性和频率估计范围。我们给出了新方法的均方误差分析及其数值结果。该方差分析适用于中等以上的信噪比或大样本长度的情况。给出了估计其估计方差输入信噪比阈值的近似公式，该公式得出的阈值与样本长度大于24的模拟结果相当接近。     

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.     

MSK-type signals in the presence of adjacent channel interferenceand white noise

In this letter, the problem of adjacent channel interference (ACI) caused by the close packing of constant envelope MSK-type users in a given frequency band is considered. An optimal receiver filter, based on the theory of matched filtering, is found, and it serves as an upper bound on the signal-to-interference ratio. The intersymbol interference (ISI) caused by the time response of the matched filter is eliminated by a decision feedback equalizer (DFE) which, however, degrades performance. It was found that the matched-filter upper bound allows about 3-15 dB more ACI than the performance of a classical correlation detector (for additive white Gaussian noise only), depending on the frequency separation between channels. The DFE performance is only a little bit worse than that of the matched filter