Turbo equalisation in non-Gaussian impulsive noise

Turbo equalisation is a state-of-the-art receiving scheme for coded data transmission over channels introducing intersymbol interference (ISI). The author investigates turbo equalisation performance in the presence of ISI and impulsive noise. The design imperfections contributing to the non-robustness of the standard turbo equaliser to outliers are identified, and a novel turbo equaliser, at almost no additional increase in complexity, is proposed for joint mitigation of ISI and impulsive noise. The proposed turbo equaliser incorporates a Talwar penalty function into the maximum a posteriori (MAP) component equaliser to serve two purposes. First, it improves the estimation of the transition probabilities for all transitions through the trellis and for subsequent determination of the a posteriori log-likelihood ratio. Secondly, it absorbs the outliers and prevents them from spreading into the MAP constituent decoder. Simulation results based on Proakis's channel models show that the proposed turbo equaliser achieves a dramatic improvement over the standard turbo equaliser in impulsive noise. At a bit error rate (BER) of 10/sup -2/, the performance gain is as large as 3.5 to 5 dB, and as large as 7 to 8 dB at a BER of 10/sup -3/.     

Threshold parameter estimation in nonadditive non-Gaussian noise

Threshold or weak-signal locally optimum Bayes estimators (LOBEs) of signal parameters, where the observations are an arbitrary mixture of signal and noise, the latter being independent, are first derived for “simple” as well as quadratic cost functions under the assumption that the signal is present a priori. It is shown that the desired LOBEs are either a linear (simple cost function) or a nonlinear (quadratic cost function) functional of an associated locally optimum and asymptotically optimum Bayes detector. Second, explicit classes of (threshold) optimum estimators are obtained for both cost functions in the coherent as well as in the incoherent reception modes. Third, the general results are applied to amplitude estimation, where two examples are considered: (1) coherent amplitude estimation in multiplicative noise with simple cost function (SCF) and (2) incoherent amplitude estimation with quadratic cost function (QFC) of a narrowband signal arbitrarily mixed with noise. Moreover, explicit estimator structures are given together with desired properties (i.e. efficiency of the unconditional maximum likelihood (ML) estimator) and Bayes' risks. These properties are obtained by employing contiguity-a powerful concept in modern statistics-implied by the locally asymptotically normal character of the detection algorithms     

Detection of weak signals in non-Gaussian noise

A locally optimum detector structure is derived for the detection of weak signals in non-Gaussian environments. Optimum performance is obtained by employing a zero-memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise Gaussian. The asymptotic detection performance of the locally optimum detector under non-Gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in Gaussian noise. Numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest.     

Passive time delay estimation in non-Gaussian noise

This article deals with the structure of the maximum-likelihood (ML) estimator for time delay with arbitrary signal and noise statistics. At high signal-to-noise ratios (SNRs), the ML estimation performs a nonlinear operation on the delayed difference of the two received waveshapes. The required nonlinearity depends only on the noise statistics. At low SNR, a closed-form simple expression for the ML, which depends only on the noise statistics and on the second-order statistics of the signal, is provided. With statistically independent noise processes, the estimator correlates two vectors generated by separate nonlinear operations on the two received waveshapes     

Threshold detection in correlated non-Gaussian noise fields

Classical threshold detection theory for arbitrary noise and signals, based on independent noise samples, i.e., using only the first-order probability density of the noise, is generalized to include the critical additional statistical information contained in the (first-order) covariances of the noise. This is accomplished by replacing the actual, generalized noise by a “quasi-equivalent” (QE-)model employing both the first-order PDF and covariance. The result is a “near-optimum” approach, which is the best available to date incorporating these fundamental statistical data. Space-time noise and signal fields are specifically considered throughout. Even with additive white Gaussian noise (AWGN) worthwhile processing gains per sample (Γ^(c)) are attainable, often O(10-20 dB), over the usual independent sampling procedures, with corresponding reductions in the minimum detectable signal. The earlier moving average (MA) noise model, while not realistic, is included because it reduces in the Gaussian noise cases to the threshold optimum results of previous analyses, while the QE-model remains suboptimum here because of the necessary constraints imposed in combining the PDF and covariance information into the detector structure. Full space-time formulation is provided in general, with the important special cases of adaptive and preformed beams in reception. The needed (first-order) PDF here is given by the canonical Class A and Class B noise models. The general analysis, including the canonical threshold algorithms, correlation gain factors Γ^(c), detection parameters for the QE-model, along with some representative numerical results for both coherent and incoherent detection, based on four representative Toeplitz covariance models is presented     

Locally optimal detection in multivariate non-Gaussian noise

The detection of a vanishingly small, known signal in multi-variate noise is considered. Efficacy is used as a criterion of detector performance, and the locally optimal detector (LOD) for multivariate noise is derived. It is shown that this is a generalization of the well-known LOD for independent, identically distributed (i.i.d.) noise. Several characterizations of multivariate noise are used as examples; these include specific examples and some general methods of density generation. In particular, the class of multivariate densities generated by a zero-memory nonlinear transformation of a correlated Gaussian source is discussed in some detail. The detector structure is derived and practical aspects of obtaining detector subsystems are considered. Through the use of Monte Carlo simulations, the performance of this system if compared to that of the matched filter and of the i.i.d. LOD. Finally, the class of multivariate densities generated by a linear transformation of an i.i.d, noise source is described, and its LOD is shown to be a form frequently suggested to deal with multivariate, non-Gaussian noise: a linear filter followed by a memoryless nonlinearity and a correlator.     

Maximum likelihood time delay estimation in non-Gaussian noise

In a non-Gaussian noise environment, it is theoretically possible to design a delay estimator that performs significantly better than the conventional linear correlator. We study the maximum likelihood estimator for passive time delay in non-Gaussian noise. We show that the form of the best estimator depends strongly on signal-to-noise ratio (SNR), and the estimator optimal at low SNR can fail catastrophically at high values of SNR. The paper uses simulations to examine this sensitivity problem and proposes an ad hoc instrumentation that is reasonably robust over a wide range of SNR values     

Locally optimum detection in moving average non-Gaussian noise

Detection algorithms that are locally optimum Bayes, and also asymptotically optimum, are developed for both coherent and incoherent signaling for arbitrary interference and signal waveforms when the dependence in the noise samples is represented by a moving-average model. This leads to receiver structures, which are prewhitened versions of the locally optimum detectors in the independent case. A probability-of-error expression (in the ideal-observer symmetric case), the processing gain, and the minimum-detectable signal are derived in both cases. These demonstrate, by means of an expression comparing performance between this and the independent case, that for the same large sample size (n≫1), an improvement in performance is always achieved when the noise samples are dependent, without any additional complexity in receiver structure     

On the non-Gaussian noise in erbium-doped fiber amplifiers

The non-Gaussian character of the probability density functions (PDFs) of binary signals dominated by signal-spontaneous and spontaneous-spontaneous beat noise in erbium-doped fiber amplifiers (EDFAs) is experimentally verified and their impact on the operation of decision circuits in optically preamplified digital receivers discussed     

Neural networks for signal detection in non-Gaussian noise

We employ neural networks to detect known signals in additive non-Gaussian noise. Training of the neural network for signal detection and its operation at some specified probability of false alarm are discussed. Performance of neural detectors are presented under several non-Gaussian noise environments and are compared with those of matched filter and locally optimum detectors     

Harmonic retrieval in colored non-Gaussian noise using cumulants

This paper addresses the harmonic retrieval problem in colored linear non-Gaussian noise of unknown covariance and unknown distribution. The assumptions made in the reported studies that the non-Gaussian noise is asymmetrically distributed and no quadratic phase coupling occurs are released. Using the elaborately defined fourth-order cumulants of the complex noisy observations, which are obtained by Hilbert transform, we can estimate either the correlation or the AR polynomial of the non-Gaussian noise via cumulant projections or ARMA modeling; then, the prewhitening or prefiltering techniques can be employed to retrieve harmonics, respectively. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms     

非高斯色噪声条件下的最小二乘单音频率估计

提出一种非高斯色噪声条件下的最小二乘单音频率估计算法,该算法首先将待估计单音频率搬移至零频附近,然后通过抽取滤波把噪声转换为高斯白噪声,最后引入相位差分最小二乘频率估计构成整个算法.该方法摆脱了FFT类算法频率分辨率的束缚,可以为自动调制识别等应用提供高精度的符号速率估计.     

Detection of weak random signals in IID non-Gaussian noise

This paper considers the detection of weak random signals in circularly symmetric, independent, identically distributed noise. Locally optimum detectors and ad hoc nonlinearities are considered, with asymptotic expressions provided for evaluation of detection performance. The analytical expressions are used to evaluate the robustness of detectors to mismatch in the noise models. Finite-sample Monte Carlo simulation results indicate the reliability of these asymptotic measures in cases of practical interest. The results show that, as has been found for detection of weak known signals in non-Gaussian noise, reasonably configured ad hoc nonlinearities are nearly optimum and robust to modest errors in the noise statistics     

Estimation and detection in non-Gaussian noise using higher orderstatistics

One of the primary applications of higher order statistics has been for detection and estimation of nonGaussian signals in Gaussian noise of unknown covariance. This is motivated by the fact that higher order cumulants of Gaussian processes vanish. We study the opposite problem, namely, detection and estimation in nonGaussian noise. We estimate cumulants of nonGaussian processes in the presence of unknown deterministic and/or Gaussian signals, which allows either parametric or nonparametric estimation of the covariance of the nonGaussian noise. Our approach is to augment existing second-order detection methods using cumulants. We propose solutions for detection of deterministic signals based on matched filters and the generalized likelihood ratio test which incorporate cumulants, where the resulting solutions are valid under either detection hypotheses. This allows for single record detection and obviates the need for noise-only training records. The problem of estimating signal strength in the presence of nonGaussian noise of unknown covariance is also considered, and a cumulant-based solution is proposed which uses a single data record. Examples are used throughout to illustrate our proposed methods     

Signal interception: performance advantages of cyclic-featuredetectors

The problem of detecting the presence of spread-spectrum phase-shift-keyed signals in variable noise and interference backgrounds is considered, and the performances of four detectors are evaluated and compared. The detectors include the optimum radiometer, the optimum modified radiometer that jointly estimates the noise level and detects the signal, and the maximum-SNR spectral-line regenerator for spectral-line frequencies equal to the chip rate and the doubled carrier frequency. It is concluded that the spectral-line regenerators can outperform both types of radiometers by a wide margin. The performance advantages are quantified in terms of receiver operating characteristics for several noise and interference environments and receiver collection times     

Nearest neighbor decoding for additive non-Gaussian noise channels

We study the performance of a transmission scheme employing random Gaussian codebooks and nearest neighbor decoding over a power limited additive non-Gaussian noise channel. We show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white Gaussian noise channel with signal and noise power equal to those of the original channel. The results are presented for single-user channels as well as multiple-access channels, and are extended to fading channels with side information at the receiver     

A hybrid approach to harmonic retrieval in non-Gaussian ARMA noise

Addresses the harmonic retrieval problem in colored noise. As contrasted to the reported studies in which Gaussian noise was assumed, this paper focuses on additive non-Gaussian ARMA noise. Our approach is hybrid in the sense that third-order cumulants are first used to identify the AR part of the non-Gaussian noise process, and then correlation-based high-resolution methods are used for the filtered process to estimate the number of harmonics and their frequencies. Simulation examples are presented to demonstrate the high resolution of this approach     

Adaptive nonparametric locally optimum Bayes detection in additive non-Gaussian noise

A nonparametric generalization of the locally optimum Bayes (LOB) parametric theory of signal detection in additive non-Gaussian noise with independent sampling is presented. From a locally asymptotically normal (LAN) expansion of the log-likelihood ratio the nonparametric detector structure, in both coherent and incoherent modes, is determined. Moreover, its statistics under both hypotheses are obtained. The nonparametric LAN log-likelihood ratio is then reduced to a least informative (i.e., having minimum variance under the hypothesis, H/sub 0/) local parametric submodel, which is referred to as adaptive. In the adaptive submodel, certain nonlinearities are replaced by their efficient estimates. This is accomplished such that no information is lost when the noise first-order density is no longer parametrically defined. Adaptive nonparametric LOB detectors are thus shown to be asymptotically optimum (AO), canonical in signal waveform, distribution free in noise statistics, and identical in form (in the symmetric cases) to their parametric counterparts. A numerical example is provided when the underlying density is Middleton's (see ibid., vol.45, p.1129-49, May 1999)Class-A noise, which demonstrates that even with a relatively small sample size (O(10/sup 2/)) adaptive LOB nonparametric detectors perform nearly as well as the classical LOB detectors.     

具有非高斯相关噪声的目标跟踪

为实现强杂波背景下视频的鲁棒跟踪,在常 用非线性系统模型的基础上引入柯 西高斯混合噪声模型,充分考虑了非高斯噪声前 后时刻的状态相关性,并以权重条件最小方差为标准,推导了非高斯相关噪声的最优建议分 布 函数,在粒子滤波框架内实现了非高斯相关噪声模型时系统状态的准确估计。在新算法的框 架内采用多特征自适应融合的方法,实现了强噪声背景下视频目标的鲁棒跟踪。实验结果表 明,本文方法扩展了粒子滤波的适用范围,有效提升了强噪声环境下视频目标跟踪的精度和 稳定性。