Suboptimum detection of weak signals in non-Gaussian noise (Corresp.)

A suboptimum detector structure is developed for the detection of weak signals in non-Gaussian noise. In contrast to locally optimum detectors, the suboptimum detector structure is relatively easy to implement and is shown to perform well for a wide range of underlying noise distributions. The robustness of simple limiter detectors is discussed. The extension of the concept of a suboptimum detector to an adaptive detector for operating in an unknown noise environment is also discussed.     

Performance of energy detector in the presence of noise uncertainty in cognitive radio networks

Energy detector is simple in structure and easy to implement. Therefore, it is a promising candidate for spectrum sensing in cognitive radio networks. However, its detection performance is typically challenged by the noise uncertainty. Thus, the detection performance of energy detector in the presence of noise uncertainty needs to be evaluated. In this paper, we derive the decision rules for the energy detector in the presence of noise uncertainty by employing a widely used model. Firstly, we derive the decision rule for unknown deterministic signal when the noise power is uncertain. Second, we derive the decision rule for random Gaussian distributed signal when there is noise uncertainty. Then, we analyze the detection performance of the energy detector in the presence of noise uncertainty for both unknown deterministic signal and random Gaussian distributed signal. Both theoretical analyses and simulation results show that in the presence of noise uncertainty, our derived decision rules provide precise sensing thresholds for the energy detector. Furthermore, compared with the conventional decision rule obtained by overestimating the noise power, our decision rules provide performance gains in terms of signal to noise ratio.     

Constant false-alarm rate energy detection of a signal with unknown amplitude and waveform in the presence of a Gaussian interference with unknown variance

A detector of signals with unknown amplitude and waveform in the presence of a Gaussian noise with unknown variance is analyzed. It is shown that the statistics at the detector output is described by the generalized F-distribution. Numerical calculation of the detector’s performance characteristics is performed.     

Optimality of the cell averaging CFAR detector

The cell averaging constant false alarm rate detector has been assumed to be optimal for detecting Swerling I targets embedded in exponential clutter and noise of unknown power. This is because the detector uses a minimum variance unbiased estimate (which is also a maximum likelihood estimate) of the unknown clutter-plus-noise power to set the threshold. The authors prove, using a result concerning least favorable distributions in composite hypotheses testing, that the cell averaging detector is indeed optimal in that it is a uniformly most powerful detector     

An efficient direct-sequence signal detector based onDempster-Shafer theory

The detection of direct-sequence spread-spectrum signals is studied. Consideration is given to the environment of broadband noise jamming with the assumption that jammer state information is unknown. It is shown how the Dempster-Shafer theory can be applied to this problem; in particular, the authors treat the unknown jammer state information as uncertain and use the concept of `confidence discount' and Dempster's combining rule to derive a heuristic detector for the problem. They show that the resulting detector has a better performance than the hard-decision detector and the soft-decision detector when the jammer is significant. The degradation relative to the soft-decision detector is smaller than the hard-decision detector when the jammer is low     

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.     

Robust detection of a known signal in nearly Gaussian noise

A detector that is not nonparametric, but that nevertheless performs well over a broad class of noise distributions is termed a robust detector. One possible way to obtain a certain degree of robustness or stability is to look for a min-max solution. For the problem of detecting a signal of known form in additive, nearly Gaussian noise, the solution to the min-max problem is obtained when the signal amplitude is known and the nearly Gaussian noise is specified by a mixture model. The solution takes the form of a correlator-limiter detector. For a constant signal, the correlator-limiter detector reduces to a limiter detector, which is shown to be robust in terms of power and false alarm. By adding a symmetry constraint to the nearly normal noise and formulating the problem as one of local detection, the limiter-correlator is obtained as the local min-max solution. The limiter-correlator is shown to be robust in terms of asymptotic relative efficiency (ARE). For a pulse train of unknown phase, a limiter-envelope sum detector is also shown to be robust in terms of ARE.     

Data-adaptive algorithms for signal detection in sub-Gaussianimpulsive interference

We address the problem of coherent detection of a signal embedded in heavy-tailed noise modeled as a sub-Gaussian, alpha-stable process. We assume that the signal is a complex-valued vector of length L, known only within a multiplicative constant, while the dependence structure of the noise, i.e. the underlying matrix of the sub-Gaussian process, is not known. We implement a generalized likelihood ratio detector that employs robust estimates of the unknown noise underlying matrix and the unknown signal strength. The performance of the proposed adaptive detector is compared with that of an adaptive matched filter that uses Gaussian estimates of the noise-underlying matrix and the signal strength and is found to be clearly superior. The proposed new algorithms are theoretically analyzed and illustrated in a Monte-Carlo simulation     

A blind detector for Rayleigh flat-fading channels with non-Gaussian interference via the particle learning algorithm

A blind particle learning detector (BPLD) is developed for signal detection in Rayleigh flat-fading channels with non-Gaussian interference. The parameters of the fading channel model and the noise model are all unknown. The impulsive noise is modeled as a mixture of Gaussian distributions, which is capable of representing a broad class of non-Gaussian noise. The particle learning algorithm is employed to simultaneously estimate signal and parameters of the fading channel model and the noise model. The delay weight method is used to improve the performance. Simulation results show that the performance of the BPLD proposed can follow closely the performance of the detector with known parameters of the fading channel model and the noise model.     

Adaptive Bayesian multiuser detection for synchronous CDMA withGaussian and impulsive noise

We consider the problem of simultaneous parameter estimation and data restoration in a synchronous CDMA system in the presence of either additive Gaussian or additive impulsive white noise with unknown parameters. The impulsive noise is modeled by a two-term Gaussian mixture distribution. Bayesian inference of all unknown quantities is made from the superimposed and noisy received signals. The Gibbs sampler (a Markov chain Monte Carlo procedure) is employed to calculate the Bayesian estimates. The basic idea is to generate ergodic random samples from the joint posterior distribution of all unknown and then to average the appropriate samples to obtain the estimates of the unknown quantities. Adaptive Bayesian multiuser detectors based on the Gibbs sampler are derived for both the Gaussian noise synchronous CDMA channel and the impulsive noise synchronous CDMA channel. A salient feature of the proposed adaptive Bayesian multiuser detectors is that they can incorporate the a priori symbol probabilities, and they produce as output the a posteriori symbol probabilities. (That is, they are “soft-input soft-output” algorithms.) Hence, these methods are well suited for iterative processing in a coded system, which allows the adaptive Bayesian multiuser detector to refine its processing based on the information from the decoding stage, and vice versa-a receiver structure termed the adaptive turbo multiuser detector     

The CFAR adaptive subspace detector is a scale-invariant GLRT

The constant false alarm rate (CFAR) matched subspace detector (CFAR MSD) is the uniformly most-powerful-invariant test and the generalized likelihood ratio test (GLRT) for detecting a target signal in noise whose covariance structure is known but whose level is unknown. Previously, the CFAR adaptive subspace detector (CFAR ASD), or adaptive coherence estimator (ACE), was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data. We show here that the CFAR ASD is GLRT when the test measurement is not constrained to have the same noise level as the training data, As a consequence, this GLRT is invariant to a more general scaling condition on the test and training data than the well-known GLRT of Kelly (1986)     

一种非高斯噪声中未知参数的信号的检测方法

研究了非高斯噪声中具有未知参数的信号的渐进最优检测，应用非高斯噪声中线性模型信号以及随机信号的Rao检验，导出了Rao检测的解析式，并与广义似然比检验的性能做比较。仿真结果表明，该检测器性能大大优于传统的能量检测器和高斯噪声假设下的广义似然比检测器。     

A statistical theory for optimal detection of moving objects invariable corruptive noise

In this paper, the classical analysis of variance is extended to three-dimensional (3-D) Graeco-Latin squares design for multiframe processing applications. Conspicuous physical features, including edges, lines, and corners, can then be expressed as contrast functions. This enables the development of a new methodology for detecting moving objects embedded in noise. The new detector exploits spatial and temporal information uniformly most powerful in a Gaussian environment with unknown and time-varying noise variance. Also found is that a moving object detector based on contrast functions coincides with a sufficient statistic of the generalized likelihood ratio test. Extensive image analysis demonstrates the practicality of the detector and compares favorably to other classes of detectors.     

一种高分辨率雷达海上目标自适应检测器

针对海上目标因波浪起伏和转向等导致的姿态变化引起的散射点起伏问题,在未知协方差矩阵的复高斯噪声背景下,研究了高距离分辨率雷达的距离扩展目标自适应检测问题.利用与待检测单元具有相同协方差矩阵结构的辅助教据估计未知噪声协方差矩阵,基于两步法检测策略获得了自适应检测器.恒虚警率特性分析表明,该检测器对不同噪声背景均具有很好的自适应特性.检测性能分析表明,该检测器对不同的目标模型具有很好的鲁棒性,且能有效避免“坍塌损失”.另外,通过增加传感器个数,可有效提高检测器性能.     

A CFAR adaptive subspace detector for second-order Gaussian signals

We study the problem of detecting subspace signals described by the Second-Order Gaussian (SOG) model in the presence of noise whose covariance structure and level are both unknown. Such a detection problem is often called Gauss-Gauss problem in that both the signal and the noise are assumed to have Gaussian distributions. We propose adaptive detectors for the SOG model signals based on a single observation and multiple observations. With a single observation, the detector can be derived in a manner similar to that of the generalized likelihood ratio test (GLRT), but the unknown covariance structure is replaced by sample covariance matrix based on training data. The proposed detectors are constant false alarm rate (CFAR) detectors. As a comparison, we also derive adaptive detectors for the First-Order Gaussian (FOG) model based on multiple observations under the same noise condition as for the SOG model. With a single observation, the seemingly ad hoc CFAR detector for the SOG model is a true GLRT in that it has the same form as the GLRT CFAR detector for the FOG model. We give an approximate closed form of the probability of detection and false alarm in this case. Furthermore, we study the proposed CFAR detectors and compute the performance curves.     

具有未知参数的多输入多输出雷达弱目标检测

针对弱目标检测算法的特点,提出了一种新的多输入多输出(MIMO)雷达检测器。在经典线性模型的基础上,通过最大似然法对未知统计特性的噪声量进行了估计。利用所得到的估计量,分别推导了在信道完全不相关和信道任意相关条件下虚警概率和检测概率的闭合表达式,对具有未知参数的MIMO雷达在任意信道环境下的检测算法进行了分析和比较,有效地解决了具有未知统计特性的噪声的MI-MO雷达目标检测问题。仿真结果证实了该方法的有效性。     

Rank-order statistics for optimum detection of binary signals in the presence of white noise and dc drift (Corresp.)

The well-known technique of detecting binary pulses in white noise and unknown dc drift by means of a high-pass filter followed by a bit-by-bit detector is not theoretically optimum. The optimum procedure is shown to require a rank-ordering operation on the received data.     

Transient signal detection using prior information in thelikelihood ratio test

A uniform approach to the problem of detecting a deterministic transient signal of unknown waveshape in Gaussian noise that is applicable for a general class of signals is provided. It is assumed that the vector representation consists of a group of zero coefficients plus a group of unknown nonzero coefficients, starting at a certain index. Performance indices for a likelihood-ratio-test detector of such a generalized transient signal are derived for three cases: (a) both the starting index and the number of unknown nonzero signal coefficients are known; (b) only the number of unknown nonzero signal coefficients is known; and (c) neither of these is known. It is shown that the performance of detector (a) is always better than that of (b) and (c), and conditions under which the performance of detector (b) is better than that of (c) are derived. The theoretical results are demonstrated by considering signals of different assumed structures     

Signal Activity Detection of Phase-Shift Keying Signals

We propose computationally inexpensive and efficient solutions for signal activity detection of phase-shift keying (PSK) signals in additive white Gaussian noise. We consider the complex amplitude of the signal as well as the information sequence as the unknown parameters. In addition, the noise variance is assumed unknown. We derive the generalized likelihood ratio test (GLRT) and suggest a computationally efficient implementation thereof. Furthermore, we develop a new inexpensive detector for binary PSK signals, which we will refer to as the generalized energy detector. To evaluate the performance of these detectors, we attempt to derive a uniformly most powerful invariant test (UMPI) as an optimal detector. It turns out that the UMPI test exists only if the signal-to-noise ratio is known. We use this UMPI test in order to obtain an upper-bound performance for the evaluation of invariant detectors, such as the above-mentioned GLRT. Simulation results illustrate and compare the performance and the efficiency of the proposed signal activity detectors.     

Realization of the Gauss-in-Gauss detector using minimum-mean-squared-error filters (Corresp.)

Alternative structures for the optimum detection of Gaussian signals in Gaussian noise are derived that can be interpreted in terms of minimum-mean-squared-error (MMSE) estimators of signal and noise. The realization is useful when the statistics of the signal or noise or both are unknown since the detector can be implemented in an adaptive mode by using tapped delay lines whose weights are adjusted recursively to yield the minimum-mean-squared-error estimate of certain components of the incoming waveforms.