Maximum likelihood estimation for array processing in colored noise

Direction of arrival estimation of multiple sources, using a uniform linear array, in noise with unknown covariance is considered. The noise is modeled as a spatial autoregressive process with unknown parameters. Both stochastic and deterministic signal models are considered. For the random signal case, an approximate maximum likelihood estimator of the signal and noise parameters is derived. It requires numerical maximization of a compressed likelihood function over the unknown arrival angles. Analytical expressions for the MLEs of the signal covariance and the AR parameters are given. Similar results for the case of deterministic signals are also presented     

基于自适应重采样次数的协方差角度估计算法

针对基于Hermitian分解的协方差角度估计算法在低信噪比(SNR)时性能差的问题,提出了基于自适应重采样次数的协方差角度估计算法。该算法首先用接收信号扫描角度空间内的所有导向矢量,划定正确的角度估计区间,并给出判断角度估计结果是否可靠的标准。然后构造协方差矩阵,得到角度估计结果,接着以角度估计结果是否可靠为判断标准自适应地对原始信号进行重采样。若重采样后对应某一信号的多个角度估计结果都不可靠,则对原信号重采样并估计到达角,直到所有信号均有可靠结果为止。仿真结果表明,所提算法修正异常的角度估计结果,提高协方差角度估计算法在低信噪比时的精确度。     

Message delay analysis for TDMA schemes using contiguous-slotassignments

Under a TDMA (time-division multiple-access) scheme, a station shares a multiple-access communications channel by transmitting its messages during its dedicated time slots. An exact result concerning the queue-sizer and message delay analysis of TDMA systems in which a station is allocated multiple consecutive slots per frame is presented. The generating function of the system queue-size for a general independent arrival message process is obtained. Messages consist of a random number of packets, following a geometric distribution. An exact result for the generating function of the message delay for various common message arrival processes and light bounds for the mean message queue-size and delay are then derived. The results are compared to previously derived approximations. It is also proved that a slot allocation scheme which distributes station slots uniformly over the frame yields a message-delay lower bound. The results also apply to the analysis of time-shared reservation schemes     

Relationships between adaptive minimum variance beamforming andoptimal source localization

For many years, the popular minimum variance (MV) adaptive beamformer has been well known for not having been derived as a maximum likelihood (ML) estimator. This paper demonstrates that by use of a judicious decomposition of the signal and noise, the log-likelihood function of source location is, in fact, directly proportional to the adaptive MV beamformer output power. In the proposed model, the measurement consists of an unknown temporal signal whose spatial wavefront is known as a function of its unknown location, which is embedded in complex Gaussian noise with unknown but positive definite covariance. Further, in cases where the available observation time is insufficient, a constrained ML estimator is derived here that is closely related to MV beamforming with a diagonally loaded data covariance matrix estimate. The performance of the constrained ML estimator compares favorably with robust MV techniques, giving slightly better root-mean-square error (RMSE) angle-of-arrival estimation of a plane-wave signal in interference. More importantly, however, the fact that such optimal ML techniques are closely related to conventional robust MV methods, such as diagonal loading, lends theoretical justification to the use of these practical approaches     

Jitter analysis of an IPP tagged traffic stream in an {IPP,M}/M/1 queue

We study a single server queue with two different arriving streams, a tagged arrival process and a background arrival process. The tagged traffic is assumed to be an interrupted Poisson process (IPP) and the background traffic is Poisson. The service time is exponentially distributed, and customers are served in a FIFO manner. We obtain numerically the probability density function of the inter-departure time of the IPP tagged arrival process, from which we calculate its jitter, defined as a percentile of the inter-departure time. Numerical results of the 95th percentile and the squared coefficient of variation of the tagged inter-departure time are given as a function of the arrival rate of the background traffic.     

Maximum likelihood estimation and Cramer-Rao bounds for directionof arrival parameters of a large sensor array

A maximum likelihood (ML) method is developed for estimation of direction of arrival (DOA) and associated parameters of narrowband signals based on the Taylor's series expansion of the inverse of the data covariance matrix R for large M, M specifying number of sensors in the array. The stochastic ML criterion function can thus be simplified resulting in a computationally efficient algorithm for DOA estimation. The more important result is the derivation of asymptotic (large M) expressions for the Cramer-Rao lower bound (CRB) on the covariance matrix of all unknown DOA angles for the general D source case. The derived bound is expressed explicitly as a function of snapshots, signal-to-noise ratio (SNR), sensors, separation, and correlation between signal sources. Using the condition of positive definiteness of the Fisher information matrix a resolution criterion is proposed which gives a tight lower limit on the minimum resolvable angle     

Estimation of the directions of arrival of signals in unknowncorrelated noise. I. The MAP approach and its implementation

The authors propose a method of direction of arrival (DOA) estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary, other than being positive definite. They examine the projection of the data onto the noise subspace. The conditional probability density function (PDF) of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed. The a posteriori PDF of the signal parameters alone is then obtained by assigning a noninformative a priori PDF to the unknown noise covariance matrix and integrating out this quantity. A simple criterion for the maximum a posteriori (MAP) estimate of the DOAs of the signals is established. Some properties of this criterion are discussed, and an efficient numerical algorithm for the implementation of this criterion is developed. The advantage of this method is that the noise covariance matrix does not have to be known, nor must it be estimated     

一种基于矩阵三对角化分解的DOA估计算法

针对DOA（Direction of Arrival）估计在低信噪比的情况下估计性能下降的问题, 根据阵列协方差矩阵共轭对称的特点,采用基于Givens变换的三对角化分解方法对协方 差矩阵进行三对角化,同时利用盖氏(Gerschgorin)圆递推方法准确估计信号子空间的秩, 然后再对三对角 矩阵进行对角化,估计出噪声子空间,利用噪声子空间与导向矢量正交实现波达方向估计, 改善了低信噪比背景下估计的误差性能和稳健性。计算机仿真证明了算法的有效性 。     

基于时间反转的MIMO雷达实值MUSIC算法

针对时间反转(TR)多输入多输出(MIMO)雷达多重信号分类(MUSIC)算法计算量庞大的问题,提出一种基于时间反转的MIMO雷达实值MUSIC算法。首先,通过采用降维思想对TR MIMO回波信号进行降维处理,来减少计算量;然后,为将协方差矩阵转化到实数域,构造酉变换矩阵进行实值变换;最后,分解出实值协方差矩阵的噪声子空间,构造谱函数估计信号波达角。相对于传统的MUSIC算法,该算法借助实值变换剔除了复数运算,极大地降低了计算量,而且不需要空间平滑降低阵列孔径就具有解相干的能力。仿真结果证实了算法的正确性。     

Convergence analysis of adaptive filtering algorithms with singulardata covariance matrix

The paper provides a rigorous analysis of the behavior of adaptive filtering algorithms when the covariance matrix of the filter input is singular. The analysis is done in the context of adaptive plant identification. The considered algorithms are LMS, RLS, sign (SA), and signed regressor (SRA) algorithms. Both the signal and weight behavior of the algorithms are considered. The signal behavior is evaluated in terms of the moments of the excess output error of the filter. The weight behavior is evaluated in terms of the moments of the filter weight misalignment vector. It is found that the RLS and SRA diverge when the input covariance matrix is singular. The steady-state signal behavior of the LMS and SA can be made arbitrarily fine by using sufficiently small step sizes of the algorithms. Indeed, the long-term average of the mean square excess error of the LMS is proportional to the algorithm step size. The long-term average of the mean absolute excess error of the SA is proportional to the square root of the algorithm step size. On the other hand, the steady-state weight behavior of both the LMS and SA have biases that depend on the weight initialization. The analytical results of the paper are supported by simulations     

星载AIS的复值FastICA算法改进

针对星载船舶自动识别系统( AIS )的含噪复值信号盲分离算法分离效果不佳的问题,提出了改进的复值快速独立分量分析算法( FastICA)。该改进算法针对混合信号数目大于源信号数目的超定情况,对含噪混合信号的协方差矩阵进行特征值分解,利用其噪声对应的几个较小特征值估计噪声方差,修正白化矩阵,再应用Huber M估计函数优化该算法的目标函数。实验结果表明,运用该算法信号均方误差( SMSE)变小,信干比( SIR)变大,提高了信号的分离性能;同时,优化后的目标函数使算法具有良好的稳健性。     

Bounds for estimation of multicomponent signals with randomamplitude and deterministic phase

We study a class of nonstationary multicomponent signals, where each component has the form a(t) exp jφ(t), where a(t) is a random amplitude function, and φ(t) is a deterministic phase function. The amplitude function consists of a stationary Gaussian process and a time varying mean. The phase and the amplitude mean are characterized by a linear parametric model, while the covariance of the amplitude function is parameterized in some general manner. This model encompasses signals that are commonly used in communications, radar, sonar, and other engineering systems. We derive the Cramer-Rao bound (CRB) for the estimates of the amplitude and phase parameters, and of functions of these parameters, such as the instantaneous frequencies of the signal components     

Performance Analysis of Fair Channel Sharing Policies in an Integrated Cellular Voice/Data Network

We study channel sharing in an integrated cellular voice/data network with a finite queue for data call requests that cannot be served immediately upon arrival. Using analytical techniques, a comparison of different fair channel sharing policies is made. As a main result, a closed-form expression is derived for the expected sojourn time (waiting time plus transfer time) of a data call, conditional on its size, indicating that the sojourn time is proportional to the call size. This attractive proportionality result establishes an additional fairness property for the channel sharing policies proposed in the paper. Additionally, as a valuable intermediate result, the conditional expected sojourn time of an admitted data call is obtained, given the system state at arrival, which may serve as an appreciated feedback information service to the data source. An extensive numerical study is included to compare the proposed policies and to obtain insight in the performance effects of the various system and policy parameters.     

穿过电离层电子密度不均匀体的脉冲平均到达时间

本文利用前向多重散射理论的新进展，推导了穿过电离层电子密度不均匀体脉冲平均到达时间的理论计算公式，其中包括背景介质折射效应的贡献、色散效应的贡献、电离层电子密度不均匀体的散射效应的贡献和色散效应的贡献，在水平分层背景电离层和高频近似的情况下，给出了背景电离层折射效应、一阶色散效应、电子密度不均匀体的散射效应和一阶色散效应对对称脉冲平均到达时间影响的计算公式。针对特定的电离层情况，分别计算了上述几种     

On the performance of cyclic moments-based parameter estimators ofamplitude modulated polynomial phase signals

Parameter estimation of amplitude-modulated polynomial phase signals embedded in additive white Gaussian noise is considered. The amplitude modulation is modeled as the sum of a real-valued deterministic function and a zero mean correlated stationary random process. It is shown that cyclic moments-based estimators, previously proposed for parameter estimation of polynomial phase signals modulated by stationary random processes, can be adapted to the more general signal model considered here. The covariance matrices of the cyclic moments-based amplitude and phase parameter estimators are derived for large sample lengths. Using this result, it is shown how the lags can be chosen to minimize the large-sample variances of the cyclic moments-based phase parameter estimators. Comparisons with the Cramer-Rao bounds are performed under the assumption of a Gaussian modulating process. The theoretical derivations are confirmed by simulation results     

Joint azimuth, elevation, and time of arrival estimation of diffuse sources

In this paper, we estimate the azimuth, the elevation, and the time of arrival of diffuse sources using the covariance matching estimator (COMET) algorithm. Previous works dealt with azimuth estimation of diffuse sources or azimuth and time of arrival estimation of point sources. However, in realistic situations, a tridimensional diffuse source localization is needed, which is the main objective of this paper. We show that the dimensionality of the COMET algorithm can be reduced by separating the estimation of the different source powers and the noise variance from that of the remaining parameters, namely the azimuth, the elevation, the time of arrival, and the corresponding angular and temporal spreads. As COMET still involves a multidimensional nonlinear optimization, we choose, in this purpose, the alternating projection algorithm to alleviate the corresponding complexity. The multiple signal classification (MUSIC) algorithm is processed to initialize the so-resulted algorithm. Simulations of the proposed algorithm are carried in different contexts and compared to the Cramér-Rao Bound, MUSIC algorithm, and dispersed signal parametric estimation simulation results.     

一种色噪声环境下的DOA估计新算法

本文提出了一种基于色噪声环境下的DOA估计新算法,该算法通过估计噪声协方差矩阵,进行预白化处理,克服了色噪声对空间谱估计的影响误差,计算机仿真结果证实了这一算法的有效性.     

一种低复杂度的信号子空间拟合的新方法

提出一种低复杂度的信号子空间拟合的新方法.证明了多级维纳滤波器的匹配滤波器(或降维矩阵的列矢量)可以张成一个压缩信号子空间.利用其与Krylov子空间等效这一特点,推导出信号子空间拟合一个新的基本公式,进而建立信号子空间拟合一个新的准则函数.分析表明,压缩信号子空间可以由降维矩阵的列矢量有效地张成,而且计算降维矩阵只需要多级维纳滤波器的若干步前向递推,所以本文方法的运算量和复杂度均较小.最后,计算机仿真验证了本文方法的有效性.     

RKHS approach to detection and estimation problems--V: Parameter estimation

Using reproducing-kernel Hilbert space (RKHS) techniques, we obtain new results for three different parameter estimation problems. The new results are 1) an explicit formula for the minimum-variance unbiased estimate of the arrival time of a step function in white Gaussian noise, 2) a new interpretation of the Bhattacharyya bounds on the variance of an unbiased estimate of a function of regression coefficients, and 3) a concise formula for the Cramér-Rao bound on the variance of an unbiased estimate of a parameter determining the covariance of a zero-mean Gaussian process.     

一种用于未知噪声背景中相干源二维波达方向估计的新方法

本文提出了一种用于相干源二维波达方向（DOA）估计的新方法。在该方法中，通过构造一种特别形式的阵列数据协方差矩阵，并利用一次最小平方过程从中提取一个线性算子用以估计噪声子空间，使算法不受信号源相关性的影响，且避免了矩阵的特征值分解。基于噪声的相关性是空间带限的合理假设，新方法选用了一种简单而又特殊的平面阵列结构，用以估计信号源入射的方位角和仰角，使算法不需要特定的传感器加性噪声模型。由于该新方法具有上述优点，因而使其更面向于实时应用。