Hagit Messer

Detection of signals by information theoretic criteria: general asymptotic performance analysis

Detecting the number of sources is a well-known and a well-investigated problem. In this problem, the number of sources impinging on an array of sensors is to be estimated. The common approach for solving this problem is to use an information theoretic criterion like the minimum description length (MDL), or the Akaike information criterion (AIC). Although it has been gaining much popularity and has been used in a variety of problems, the performance of information theoretic criteria-based estimators for the unknown number of sources has not been sufficiently studied, yet. In the context of array processing, the performance of such estimators were analyzed only for the special case of Gaussian sources where no prior knowledge of the array structure, if given, is used. Based on the theory of misspecified models, this paper presents a general asymptotic analysis of the performance of any information theoretic criterion-based estimator, and especially of the MDL estimator. In particular, the performance of the MDL estimator, which assumes Gaussian sources and structured array when applied to Gaussian sources, is analyzed. In addition, it is shown that the performance of a certain MDL estimator is not very sensitive to the actual distribution of the source signals. However, appropriate use of prior knowledge about the array geometry can lead to significant improvement in the performance of the MDL estimator. Simulation results show a good fit between the empirical and the theoretical results.

The use of the wavelet transform in the detection of an unknown transient signal

For the detection of a not-perfectly-known signal in noise, usually no uniformly most powerful test exists, and thus a detector performance depends on the signal representation. The use of the wavelet representation of signals to perform a new detection scheme is discussed. The advantage of using this particular representation is shown. It is shown that prior information regarding the relative bandwidth and the time-bandwidth-product of the signal to be detected is efficiently incorporated into the detection problem formulation. Thus, the proposed detection scheme is most suitable for detection of unknown transient signals when prior information about the signal time-bandwidth product and relative bandwidth exists. In these cases, the wavelet-representation-based detector performs better than any other. The structure of the proposed detectors is discussed and its performance is evaluated using Monte Carlo simulations. >

A Barankin-type lower bound on the estimation error of a hybrid parameter vector

The Barankin (1949) bound is a realizable lower bound on the mean-square error (MSE) of any unbiased estimator of a (nonrandom) parameter vector. We present a Barankin-type bound which is useful in problems where there is a prior knowledge on some of the parameters to be estimated. That is, the parameter vector is a hybrid vector in the sense that some of its entries are deterministic while other are random variables. We present a simple expression for a positive-definite matrix which provides bounds on the covariance of any unbiased estimator of the nonrandom parameters and an estimator of the random parameters, simultaneously. We show that the Barankin bound for deterministic parameters estimation and the Bobrovsky-Zakai (1976) bound for random parameters estimation are special cases of our proposed bound.

Non-data-aided signal-to-noise-ratio estimation

Non-data-aided (NDA) signal-to-noise-ratio (SNR) estimation is considered for binary phase shift keying systems where the data samples are governed by a normal mixture distribution. Inherent estimation accuracy limitations are examined via a simple, closed-form approximation to the associated Cramer-Rao bound which eliminates the need for numerical integration. The expectation-maximization algorithm is proposed to iteratively maximize the NDA likelihood function. Simulation results show that the resulting estimator offers statistical efficiency over a wider range of scenarios than previously published methods.

Rain Rate Estimation Using Measurements From Commercial Telecommunications Links

In this paper, we propose a novel method for estimating the rain rate at any given point within a two-dimensional plain using measurements of the received signal level extracted from power control records of an existing deployed fixed wireless communication network. The path-average rainfall intensity along each microwave radio link is estimated from the rainfall-induced attenuation using an empirical relationship. The proposed algorithm consists of appropriate preprocessing of the links data, followed by a modified weighted least squares algorithm to infer on the rain level at any given point in space. The algorithm can be used to interpolate measurements onto a regular grid to construct a two-dimensional rainfall intensity field. The novelty of the proposed estimation method comes from its ability to be applied on an arbitrary geometry network comprising different microwave links lengths and frequencies and allowing easy integration of rain gauge observations into the model to improve estimation accuracy. The technique has been applied to an existing fixed wireless communication network comprising 22 microwave links covering an area of about 15times15 km2 and operating at carrier frequencies of about 20 GHz. The resulting rainfall field estimates have been compared to rain gauge stations in the vicinity and to weather radar data, showing good agreement.

Narrowband interference suppression in time-hopping impulse-radio systems

Ultra-wideband (UWB) radio systems have drawn a lot of attention during the last few years. These systems use very low transmission power, spread over a bandwidth of several gigahertz. The very low transmission power and the large bandwidth used enable UWB radio systems to coexist with other narrowband systems over the same frequency band without interfering with the narrowband systems. Nevertheless, these narrowband systems may cause interference which jams the UWB receiver completely. Since standard narrowband interference suppression techniques are not applicable, techniques for interference suppression have to be developed. This paper presents novel narrowband interference suppression algorithms for UWB radio systems. Theoretical analysis of these algorithms reveal that they can eliminate the narrowband interference almost completely.

Frontal Rainfall Observation by a Commercial Microwave Communication Network

Abstract A novel approach for reconstruction of rainfall spatial–temporal dynamics from a wireless microwave network is presented. It employs a stochastic space–time model based on a rainfall advection model, assimilated using a Kalman filter. The technique aggregates the data in time and space along the direction of motion of the rainfall field, which is recovered from the simultaneous observation of a multitude of microwave links. The technique is applied on a standard microwave communication network used by a cellular communication system, comprising 23 microwave links, and it allows for observation of near-surface rainfall at the temporal resolutions of 1 min. The accuracy of the method is demonstrated by comparing instantaneous rainfall estimates with measurements from five rain gauges, reaching correlations of up to 0.85 at the 1-min time interval with a bias and RMSE of −0.2 and 4.2 mm h−1, respectively, and up to 0.96 with RMSE of 1.6 mm h−1 at the 10-min time interval for a 22-h intensive rainsto...

Suboptimal detection of non-Gaussian signals by third-order spectral analysis

The use of higher-order spectra (HOS) is proposed for improving detection performance in non-Gaussian signals. The method comprises two stages. First, the higher-order spectra of the received signal are estimated using conventional spectral estimation techniques; then, a (maximum) likelihood ratio test (LRT) is performed in the higher-order-spectra domain. It is shown that, under certain low signal-to-noise ratio (SNR) conditions, the HOS-based method performs much better than the conventional energy one. The required processor is derived and its performance is analyzed. While the method is demonstrated using the third-order spectrum (called bispectrum), it can easily be extended to higher-order analysis (e.g. trispectrum, etc.). >

Notes on the Tightness of the Hybrid CramÉr–Rao Lower Bound

In this paper, we study the properties of the hybrid Cramer-Rao bound (HCRB). We first address the problem of estimating unknown deterministic parameters in the presence of nuisance random parameters. We specify a necessary and sufficient condition under which the HCRB of the nonrandom parameters is equal to the Cramer-Rao bound (CRB). In this case, the HCRB is asymptotically tight [in high signal-to-noise ratio (SNR) or in large sample scenarios], and, therefore, useful. This condition can be evaluated even when the CRB cannot be evaluated analytically. If this condition is not satisfied, we show that the HCRB on the nonrandom parameters is always looser than the CRB. We then address the problem in which the random parameters are not nuisance. In this case, both random and nonrandom parameters need to be estimated. We provide a necessary and sufficient condition for the HCRB to be tight. Furthermore, we show that if the HCRB is tight, it is obtained by the maximum likelihood/maximum a posteriori probability (ML/MAP) estimator, which is shown to be an unbiased estimator which estimates both random and nonrandom parameters simultaneously optimally (in the minimum mean-square-error sense).

Highlights of statistical signal and array processing

The Statistical Signal and Array Processing Technical Committee (SSAP-TC) deals with signals that are random and processes an array of signals simultaneously. The field of SSAP represents both solid theory and practical applications. Starting with research in spectrum estimation and statistical modeling, study in this field is always full of elegant mathematical tools such as statistical analysis and matrix theory. The area of statistical signal processing expands into estimation and detection algorithms, time-frequency domain analysis, system identification, and channel modeling and equalization. The area of array signal processing also extends into multichannel filtering, source localization and separation, and so on. This article represents an endeavor by the members of the SSAT-TC to review all the significant developments in the field of SSAP. To provide readers with pointers for further study of the field, this article includes a very impressive bibliography-close to 500 references are cited. This is just one of the indications that the field of statistical signals has been an extremely active one in the signal processing community. The article also introduces the recent reorganization of three technical committees of the Signal Processing Society.