Subspace averaging of steady-state visual evoked potentials

A new algorithm for doing signal averaging of steady-state visual evoked potentials (VEP's) is described. The subspace average is obtained by finding the orthogonal projection of the VEP measurement vector onto the signal subspace, which is based on a sinusoidal VEP signal model. The subspace average is seen to out-perform the conventional average using a new signal-to-noise-ratio-based performance measure on simulated and actual VEP data.     

Matched direction detectors and estimators for array processing with subspace steering vector uncertainties

In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the steering vector but, on the other hand, some knowledge about the steering vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Crame/spl acute/r-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations.     

Robust Gaussian and non-Gaussian matched subspace detection

We address the problem of matched filter and subspace detection in the presence of arbitrary noise and interference or interfering signals that may lie in an arbitrary unknown subspace of the measurement space. A minmax methodology developed to deal with this uncertainty can also be adapted to situations where partial information on the interference or other uncertainties is available. This methodology leads to a hypothesis test with adequate levels of false alarm robustness and signal detection sensitivity. The robust test is applicable to a large class of noise density functions. In addition, generalized likelihood ratio (GLR) detectors are derived for the class of generalized Gaussian noise. The detectors are generalizations of the /spl chi//sup 2/, t, and F statistics used with Gaussian noise, which are themselves motivated in a new way by the robust test. For matched filter detection, these expressions are simpler and computationally efficient. The robust test reduces to the conventional test when unlearned subspace interference is known to be absent. The results demonstrate that when compared with the conventional detector, the robust one trades off some detection performance in the absence of interference for the sake of robustness in its presence.     

Adaptive subspace detectors

We use the theory of generalized likelihood ratio tests (GLRTs) to adapt the matched subspace detectors (MSDs) of Scharf (1991) and of Scharf and Frielander (1994) to unknown noise covariance matrices. In so doing, we produce adaptive MSDs that may be applied to signal detection for radar, sonar, and data communication. We call the resulting detectors adaptive subspace detectors (ASDs). These include Kelly's (1987) GLRT and the adaptive cosine estimator (ACE) of Kaurt and Scharh (see ibid., vol.47, p.2538-41, 1999) and of Scharf and McWhorter (see Proc. 30th Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, 1996) for scenarios in which the scaling of the test data may deviate from that of the training data. We then present a unified analysis of the statistical behavior of the entire class of ASDs, obtaining statistically identical decompositions in which each ASD is simply decomposed into the nonadaptive matched filter, the nonadaptive cosine or t-statistic, and three other statistically independent random variables that account for the performance-degrading effects of limited training data     

训练样本不足时的子空间信号检测方法

为了解决训练样本不足时的子空间信号检测问题,提出了两种有效的降秩检测器.基于主分量分析(PCA)的思想,先把常规自适应子空间检测器中采样协方差矩阵(SCM)的求逆运算用噪声特征子空间矩阵与其共轭转置的乘积代替,构造降秩子空间检测器;为进一步提高算法稳健性,把降秩子空间检测器的求逆运算用Moore-Penrose逆代替.仿真结果表明,所提方法在训练样本充足及不足时,均比现有方法具有更好的检测性能.     

Low-rank detection of multichannel Gaussian signals using blockmatrix approximation

The exact design of an m-channel matched filter with L taps requires the solution of an mL×mL block system of linear equations with Toeplitz entries. Practical cases where m>50 and L>100 are not uncommon. When the individual sensors of an array are closely spaced, the temporal and spatial correlation of the resulting vector noise process may be modeled in a separable fashion. In this case, the noise covariance block matrix attains a special structure where all block entries are just weighted versions of each other. It is shown that in this case, the complexity of the detector design can be reduced drastically by a factor of mL compared to a conventional multichannel matched filter design procedure. It is further shown that the separable vector noise model facilitates a complete exploitation of the rank properties of noise and data matrices. A constructive procedure for the design of “low-rank” detectors in the multichannel case is derived. These detectors consist of two consecutive blocks: a data and noise dependent “compression” stage, which maps the significant signal energy into a subspace of minimal dimension, followed by a minimal set of independent matched filters, which point in the subspace directions in which the signal is much stronger than the noise. This low-rank detector concept enables discrimination with little or no performance penalty at a minimal computational cost     

Insight into detection of deterministic and Gaussian signals incorrelated plus impulsive noise environments

The authors present a different view of the discrete-time detection problem in impulsive noise. The approach used is to examine the geometry from a subspace viewpoint of two detectors: the clairvoyant matched filter and the clairvoyant power detector. They are clairvoyant in that the locations of the impulses in the received data sample are assumed known. In the presence of impulses, both detectors use this knowledge for properly weighting these samples to reduce the effects of the impulses. Unfortunately, since it is never reasonable to assume that the impulse locations are known, these are unrealizable detectors. However, these clairvoyant detectors provide insight into the problem of detection in an impulsive environment when the nominal component is correlated and suggest detectors which are realizable. The results can be used as a theoretical justification of preprocessing the data to eliminate impulsive samples prior to detection     

A near-optimum detector with reduced out-of band response fornarrowband signals

Reduced spectral response in adjacent spectral bins is very desirable for detectors since it gives capability to detect narrowband signals in the presence of unknown interference and colored noise. Conventionally, this is achieved by applying a smoothing window on the signal at the cost of detection performance. In this correspondence, a new method of detecting narrowband signals that uses a close approximation to the matched filter and the extrapolated input signal is proposed. The filter used has a frequency response that is very closely equal to that of the matched filter within a Doppler bin and nearly zero response outside it     

Subspace-based adaptive generalized likelihood ratio detection

Subspace-based adaptive detection performance is examined for the generalized likelihood ratio detector based on Wilks' Λ statistic. The problem considered here is detecting the presence of one or more signals of known shape embedded in Gaussian distributed noise with unknown covariance structure. The data is mapped into a subspace prior to detection. The probability of false alarm is independent of the subspace transformation and depends only on subspace dimension. The probability of detection depends on the subspace transformation through a nonadaptive signal-to-noise ratio (SNR) parameter. Subspace processing results in an SNR loss that tends to decrease performance and a gain in statistical stability that tends to increase performance. It is shown that the statistical stability effect dominates the SNR loss for short data records, and subspace detectors can require substantially less SNR than full space detectors for equivalent performance. A method for designing the subspace transformation to minimize the SNR loss is proposed and illustrated through simulations     

Adaptive array detection of uncertain rank one waveforms

Adaptive array detection of known (within a complex scaling) rank one space time waveforms in unknown spatial noise has received considerable attention. The two published solutions are the adaptive matched filter, and the GLRT. We expand on this work to consider the case of rank one waveforms that are uncertain, i.e., only partially known. More precisely, we model the space time steering vector as the Kronecker product of two vectors, each of which is unknown but is known to lie in a known subspace. Applications for such a model include detection in the presence of multipath and spectral or polarization diversity in both radar processing and wireless communication. Using the principle of invariance, we construct detectors based on the maximal invariant. We show that the SNR required to achieve a given detection probability (for a given false alarm rate) is only weakly impacted by waveform uncertainty. Thus, our detector approaches the performance of earlier detectors, which entail known waveforms     

Detection of stochastic processes

This paper reviews two streams of development, from the 1940's to the present, in signal detection theory: the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance. This treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous-time stochastic processes. The mathematics and intuition behind such developments as the matched filter, the RAKE receiver, the estimator-correlator, maximum-likelihood sequence detectors, multiuser detectors, sequential probability ratio tests, and cumulative-sum quickest detectors, are described     

Wald tests for direction detection in noise and interference

In this paper, we consider the problem of detecting a distributed target in unknown disturbance. The signals reflected by the target are assumed to come from the same direction. However, the exact direction is unknown and yet the signal steering vector lies in a known subspace. The disturbance consists of colored noise and deterministic interference. The interference belongs to a known subspace, linearly independent on the signal subspace. We derive the one-step Wald test and two-step Wald test. Numerical examples show that the proposed detectors can achieve better detection performance than the existing detectors.     

均匀和部分均匀杂波中子空间目标的斜对称自适应检测方法

在雷达目标的自适应检测领域, 当参考单元数不足时, 充分挖掘协方差矩阵的结构信息是有效提高检测性能的途径之一。为此, 针对多维子空间目标的检测问题, 该文在协方差矩阵关于次对角线具有斜对称结构的约束下, 分别基于一步和两步广义似然比(GLRT), 推导了均匀和部分均匀杂波中的斜对称自适应检测器。由于检测器在设计阶段利用了协方差矩阵的结构信息, 仿真结果表明, 与已有检测器相比, 在参考单元数不足时, 斜对称自适应检测器可明显改善检测性能。此外, 分别从协方差估计方法的影响、目标子空间维数的影响、目标子空间失配性能以及目标起伏的影响4个方面对检测性能进行了仿真分析。      

A maximal invariant framework for adaptive detection withstructured and unstructured covariance matrices

We introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing. This involves calculating a low-dimensional basis set of functions called the maximal invariant, the statistics of which are often tractable to obtain, thereby making analysis feasible and facilitating the search for tests with some optimality property. Using this approach, we obtain a locally most powerful invariant test for the unstructured covariance case and show that all invariant tests can be expressed in terms of the previously published Kelly's generalized likelihood ratio (GLRT) and Robey's adaptive matched filter (AMF) test statistics. Applying this framework to structured covariance matrices, corresponding to stochastic interferers in a known subspace, for which the GLRT is unavailable, we obtain the maximal invariant and propose several new invariant detectors that are shown to perform as well or better than existing ad-hoc detectors. These invariant tests are unaffected by most nuisance parameters, hence the variation in the level of performance is sharply reduced. This framework facilitates the search for such tests even when the usual GLRT is unavailable     

A Systematic Approach to Multistage Detectors in Multipath Fading Channels

We consider linear multistage detectors with universal (large system) weighting for synchronous code-division multiple access (CDMA) in multipath fading channels with many users. A convenient choice of the basis of the projection subspace allows a joint projection of all users. Taking advantage of this property, the complexity per bit of multistage detectors with universal weights scales linearly with the number of users on the uplink CDMA channel, while other known multistage detectors with universal weights and different bases of the projection subspace keep the same quadratic complexity order per bit as the linear minimum mean-square error (LMMSE) detector. We focus on the design of two kinds of detectors with linear complexity. The detector of Type I is obtained as an asymptotic approximation of the polynomial expansion detector proposed by Moshavi The detector of Type II has the same performance as the multistage Wiener filter (MSWF) in large systems. Additionally, general performance expressions for large systems, applicable to any multistage detector with the same basis of the projection subspace (e.g., linear parallel interference canceling detectors), are derived. As a by-product, the performance analysis disproves the widespread belief that the MSWF and the polynomial expansion detector are equivalent. We show that, in general, the MSWF outperforms the latter one and they are equivalent only asymptotically in the case of equal received powers.     

Parametric GLRT for Multichannel Adaptive Signal Detection

This paper considers the problem of detecting a multichannel signal in the presence of spatially and temporally colored disturbance. A parametric generalized likelihood ratio test (GLRT) is developed by modeling the disturbance as a multichannel autoregressive (AR) process. Maximum likelihood (ML) parameter estimation underlying the parametric GLRT is examined. It is shown that the ML estimator for the alternative hypothesis is nonlinear and there exists no closed-form expression. To address this issue, an asymptotic ML (AML) estimator is presented, which yields asymptotically optimum parameter estimates at reduced complexity. The performance of the parametric GLRT is studied by considering challenging cases with limited or no training signals for parameter estimation. Such cases (especially when training is unavailable) are of great interest in detecting signals in heterogeneous, fast changing, or dense-target environments, but generally cannot be handled by most existing multichannel detectors which rely more heavily on training at an adequate level. Compared with the recently introduced parametric adaptive matched filter (PAMF) and parametric Rao detectors, the parametric GLRT achieves higher data efficiency, offering improved detection performance in general.     

基于子空间跟踪和卡尔曼滤波的半盲多用户检测

本文研究多载波CDMA(MC-CDMA)上行链路半盲多用户检测技术,提出了一种基于子空间跟踪和卡尔曼滤波的半盲多用户检测算法。利用小区内所有用户的扩频码修改约束条件并采用修正的紧缩近似投影子空间跟踪(PASTd)算法和卡尔曼滤波算法求解优化问题,该算法利用已知的信息消除多址干扰,提高了系统的性能,同时避免了常规卡尔曼滤波算法的特征值分解问题,显著降低了计算复杂度。仿真实验验证了本文算法具有很好的检测性能和较强的抗多址干扰能力。     

Performance analysis of a novel matched filter detector with reduced out-of-band response for narrowband signals

Reduced spectral response in adjacent spectral bins is very desirable for detectors since it provides the capability to detect narrowband signals in the presence of unknown interference and colored noise. Recently, a new method of detecting narrowband signals which uses a close approximation to the matched filter is proposed by Raja Kumar. The impulse response of this filter turns out to be longer than that of the matched filter. In order to support this extra length of filter response, it is proposed that the signal be extrapolated by prediction before the filtering operation. In this paper, the characteristics of this detector are mathematically analyzed and the performance of the detector in the presence of additive white Gaussian noise (AWGN) is studied. The detection method uses predicted signals that are obtained typically from short time data. Hence, in this paper, a method of analyzing the statistics of predicted signals from short time data is presented, and it is applied for the performance analysis of the present detector. The accuracy of the present detection analysis is demonstrated through theoretical and simulation studies. Also the analysis and performance study is extended to fluctuating targets, and it is shown that the proposed method yields near-optimum performance for Swerling's Case-1 and Case-3 targets while giving the excellent advantage of low out-of-bin response.     

Interference estimation with applications to blind multiple-accesscommunication over fading channels

We consider the detection of nonorthogonal multipulse signals on multiple-access fading channels. The generalized maximum-likelihood rule is employed to decode users whose complex fading gains are unknown. We develop geometrical interpretations for the resulting detectors and their corresponding asymptotic efficiencies. The generalized maximum-likelihood detection rule is then applied to find a matched subspace detector for the frequency-selective fading channel, under the assumption of a short coherence time (or long coherence time without the computational power to track the fading parameters). We propose blind implementations of these detectors for nonorthogonal multipulse signaling on both frequency-nonselective and frequency-selective multiple-access fading channels. These blind detectors extend the results of Wang and Poor (see ibid., vol.44, p.677-89, 1998) to multipulse modulation and fast frequency selective fading. For comparison, the minimum mean-squared error decision rules for these channels are derived and blind implementations of their corresponding detectors are developed     

Blind adaptation of zero forcing projections and oblique pseudo-inverses for subspace detection and estimation when interference dominates noise

In much of modern radar, sonar, and wireless communication, it seems more reasonable to model "measurement noise" as subspace interference-plus-broadband noise than as colored noise. This observation leads naturally to a variety of detection and estimation problems in the linear statistical model. To solve these problems, one requires oblique pseudo-inverses, oblique projections, and zero-forcing orthogonal projections. The problem is that these operators depend on knowledge of signal and interference subspaces, and this information is often not at hand. More typically, the signal subspace is known, but the interference subspace is unknown. We prove a theorem that allows these operators to be estimated directly from experimental data, without knowledge of the interference subspace. As a byproduct, the theorem shows how signal subspace covariance may be estimated. When the strict identities of the theorem are approximated, then the detectors, estimators, and beamformers of this paper take on the form of adaptive subspace estimators, detectors, and Capon beamformers, all of which are reduced in rank. The fundamental operator turns out to be a certain reduced-rank Wiener filter, which we clarify in the course of our derivations. The results of this paper form a foundation for the rapid adaptation of receivers that are then used for detection and estimation. They may be applied to detection and estimation in radar, sonar, and hyperspectral imaging and to data decoding in multiuser communication receivers.