Ariela Zeira

A low bias algorithm to estimate negative SNRs in an AWGN channel

Signal-to-noise ratio (SNR) is an important parameter in many receivers. In this letter, we derive a maximum-likelihood estimate of the amplitude of a binary phase-shift keying modulated signal and develop an iterative SNR search algorithm. Low bias is achieved for low SNR.

Realizable lower bounds for time delay estimation

The accuracy of time delay estimates obtainable in active localization systems is studied, focusing on the effect of ambiguities in the time delay estimates. Such ambiguities occur when the transmitted signal has small relative bandwidth. Then, for signal to noise ratios below a certain threshold, the commonly used Cramer-Rao lower bound is not realizable. The study concentrates on the region of intermediate SNR values, where the Cramer-Rao bound is no longer achievable, but useful information on time delays can still be obtained from the measurement. Realizable bounds for the single and two echo cases are obtained by deriving a new form of the Barankin (1949) bound for active time delay estimation. This form maintains the realizability property of the most general form, but is of reasonable complexity. New bounds are derived for the multiple echo case. Examples are presented to illustrate the dependence of the bound on parameters such as SNR, relative bandwidth, and echo separation. >

Realizable lower bounds for time delay estimation. 2. Threshold phenomena

In time delay estimation of narrowband signals the mean square error (MSE) plotted as a function of the signal to noise ratio (SNR) exhibits threshold phenomena. The thresholds divide the domain of SNR values into several disjoint segments. For very low SNR values the observations are dominated by noise and are essentially useless for delay estimation. Here the MSE is determined largely by the available a priori information. For intermediate SNR values, time delay estimates are possible, but are subject to ambiguities resulting from the oscillatory nature of the signal sample correlation. For very high SNR values, these ambiguities are resolvable and the Cramer-Rao bound (CRB) yields a realistic bound for the attainable performance. A previous paper by Zeira and Schultheiss (see IEEE Trans. Signal Processing, vol.41, p.3102-3113, Nov. 1993) used the Barankin (1949) bound to obtain a realizable lower bound for the intermediate SNR region but left open the question where the transitions from low to medium and medium to high SNR operation occur. Since the attainable MSE in the three regions can be very different, the location of the SNR thresholds is of considerable practical interest. The present paper addresses this issue. It obtains threshold values for the single and two echo problems, with emphasis on the effect of echo separation in the two echo case. It concludes that the location of the thresholds is only weakly dependent on echo separation, even though the attainable MSE in both the intermediate and high SNR regions varies drastically as the echo separation changes. >

Frequency domain Cramer-Rao bound for Gaussian processes

An expression is derived for the asymptotic frequency-domain Cramer-Rao bound (CRB) on the parameters of Gaussian processes with information in their means. The general result extends Whittles (1953) formula which is applicable to Gaussian processes with information in their covariance matrices or spectra. It is useful in many fields such as system identification, radar, and sonar. Examples of its application to system deconvolution and time-delay estimation in colored noise are given. >

Direction finding with time-varying arrays

This paper considers the problem of finding the directions of narrowband signals using a time-varying array, whose elements move during the observation interval in an arbitrary but known way. Assuming a Gaussian signal model, we derive the Cramer-Rao bound (CRB) and the maximum likelihood estimator for the directions of arrival. The single source case is studied in detail. Time-varying arrays are shown to be more robust to ambiguity errors than static arrays of comparable dimensions. >

Oversampled Gabor representation for transient signals

Considers the Gabor representation that uses a one-sided exponential window for detection and analysis of transient signals. Earlier results on the critically sampled case are extended to the more practically useful oversampled case. For oversampling by an integer factor, the authors derive an explicit analytical expression for the dual window (dual frame) function required for computing the Gabor representation. Based on this expression they develop an efficient procedure for computing the Gabor coefficients. Finally, they demonstrate the performance of the method by numerical examples. >

Direction of arrival estimation using parametric signal models

We consider the problem of estimating the directions-of-arrival (DOAs) of narrowband sources with known center frequency. The paper evaluates the potential improvement in estimation accuracy by using spatial-temporal processing for signals obeying a deterministic parametric model. One would expect that prior information about the temporal structure of the signals will yield some gain in performance. By deriving the Cramer-Rao bound (CRB) on the DOA estimates, we quantify this gain and identify the cases for which the gain is significant. We show that for the single-source case, spatial-temporal processing does not yield any gain in performance relative to conventional spatial processing. For multiple noncoherent signals, incorporating temporal processing can achieve the single-source performance, yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array. However, spatial-temporal processing cannot yield any gain in performance for multiple coherent signals.

Eigenstructure-based algorithms for direction finding with time-varying arrays

This paper considers the problem of finding the directions of narrowband signals using a time-varying array whose elements move during the observation interval in an arbitrary but known way. We derive two eigenstructure-based algorithms for this problem, which are modifications of techniques developed originally for time-invariant arrays. The first uses array interpolation, and the second uses focusing matrices. Like other eigenstructure-based methods, these algorithms require a modest amount of computations in comparison with the maximum likelihood (ML) estimator. The performance of the algorithms is evaluated by Monte-Carlo simulations, and is compared with the Cramer Rao Bound (CRB). Although both techniques were successful for wideband array processing with time-invariant arrays, we found that only the interpolated array algorithm is useful for direction finding (DF) with time-varying arrays.

Time delay estimation for closely spaced echoes

The Cramer-Rao bound (CRB) for the time delays of closely spaced echoes is derived. It is shown that the variance of the ith echo delay estimate depends on the relative delays of all other echoes, but not on their amplitudes. This results from the restriction that the estimator must be unbiased. A single replica correlation algorithm is suggested for the case of two echoes with highly unequal amplitudes, and its performance is evaluated. For echo spacings below some threshold, the estimate for the dominant echo is slightly biased, but its mean square error is significantly lower than the CRB. The estimation of the weak echo is discussed.<<ETX>>

New results on SNR estimation of MPSK modulated signals

Signal-to-noise ratio (SNR) is an important parameter in many receivers. In a previous letter B Li et al., (2002) we derived a maximum-likelihood amplitude estimator and obtained a low bias SNR estimation algorithm for a binary phase-shift keying (BPSK) modulated signal. We now extend the result and obtain a low bias SNR estimator for multiple phase-shift keying (MPSK) modulation. We compare our algorithm with others, such as a decision-directed approach. Simulations show that the new algorithm provides not only much lower bias and but also much smaller mean square error (MSE).