Signal-to-noise ratio (SNR) estimation is considered for phase-shift keying communication systems in time-varying fading channels. Both data-aided (DA) estimation and nondata-aided (NDA) estimation are addressed. The time-varying fading channel is modeled as a polynomial-in-time. Inherent estimation accuracy limitations are examined via the Cramer-Rao lower bound, where it is shown that the effect of the channel's time variation on SNR estimation is negligible. A novel maximum-likelihood (ML) SNR estimator is derived for the time-varying channel model. In DA scenarios, where the estimator has a simple closed-form solution, the exact performance is evaluated both with correct and incorrect (i.e., mismatched) polynomial order. In NDA estimation, the unknown data symbols are modeled as random, and the marginal likelihood is used. The expectation-maximization algorithm is proposed to iteratively maximize this likelihood function. Simulation results show that the resulting estimator offers statistical efficiency over a wider range of scenarios than previously published methods.

In this paper, we consider training-based symbol timing synchronization for continuous phase modulation over channels subject to flat, Rayleigh fading. A high signal-to-noise-ratio maximum-likelihood estimator based on a simplified channel correlation model is derived. The main objective is to reduce algorithm complexity to a single-dimensional search on the delay parameter, similar to that of the static-channel (slow fading) estimator. The asymptotic behavior of the algorithm is evaluated, and comparisons are made with the Cramer-Rao lower bound for the problem. Simulation results demonstrate highly improved performance over the conventional, static-channel delay estimator.

Data-Aided Signal-to-Noise-Ratio (SNR) estimation is considered for time selective fading channels whose time variation is described by a polynomial time model. The inherent estimation accuracy limitations associated with the problem are quantified via a Cramer-Rao Bound analysis. A maximum likelihood type class of estimators is proposed and its exact, non-asymptotic performance is computed. The standard, constant channel SNR estimator performance is determined in the presence of channel polynomial order mismatch. Simulations results are presented which verify the effectiveness of the technique as well as its performance advantage over previously proposed methods.

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.

We define a generalized scattering function for the spatio-temporal propagation channel. The definition is free of the restrictive assumption that there is a finite number of scatterers. We derive the time-varying vector channel between the source and the array in a unified manner and define a correlation function and a power spectrum that incorporate the spatial parameter-directly giving rise to the new scattering function of the spatio-temporal channel. In practice, the scattering function can be estimated by applying a well-known non-parametric spectrum estimation method to data obtained from an appropriately designed channel sounding experiment. The estimator's performance is evaluated theoretically and by simulation.

In this paper we consider a time synchronization problem for a minimum shift keying (MSK) signal received over a time-selective, fast fading channel. We calculate the Cramer Rao bound (CRB) for the case when the transmitted data bits are a-priori known and examine the effects of parameters such as signal-to-noise ratio (SNR) and temporal correlation of the channel on the synchronization performance. In addition, we derive an explicit high SNR approximation to the CRB. Lastly, we use the bound to study how the choice of transmitted bits (the training sequence) influences synchronization performance thus enabling us to identify the best and worst case bit sequences.

The problem of using antenna array measurements to estimate the bearing of a mobile communications user surrounded by local scatterers is considered. The concept of "partial coherence" is introduced to account for the temporal as well as spatial correlation effects often encountered in mobile radio propagation channels. A simple, intuitive parametric model for temporal channel correlation is presented. The result is an overall spatio-temporal channel model which is more realistic than formerly proposed models (which assume either full or zero temporal channel correlation). Thus, previously posed bearing estimation problems for a "distributed" or "scattered" source are generalized to a joint spatio-temporal parameter estimation problem. A study of the associated Cramer-Rao Bound for the case of known transmitted signal of constant modulus indicates that the inherent accuracy limitations associated with this generalized problem lie somewhere between the cases of zero and full temporal correlation and become more severe as temporal channel correlation increases.

The problem of passive localization of coherently scattered sources with an array of sensors is considered. The spatial extent of such a source is typically characterized by an angular mean and an angular spreading parameter. The maximum likelihood (ML) estimator for this problem requires a complicated search of dimension equal to twice the number of sources. However, a previously reported sub-optimal MUSIC type method reduces the search dimension to two (independently of the number of sources). In this paper, the search over the angular mean parameter in the above MUSIC type technique is replaced by a possibly more efficient polynomial rooting procedure. Computer simulations verify the effectiveness of the proposed method compared to the performance of the ML and MUSIC estimators as well as to the Cramer-Rao bound.

An algorithm for the joint tracking of source DOAs and sensor positions is presented to address the problem of DOA tracking in the presence sensor motion. Initial maximum likelihood estimates of source DOAs and sensor positions are refined by Kalman filtering. Spatio-temporally correlated array movement is considered. Source angle dynamics are used to achieve correct data association. The new technique is capable of performing well for the difficult cases of sources that cross in angle, fully coherent sources, as well as sources of identical or vastly different (possibly time-varying) power. Computer simulations show that the approach is robust in the presence of array motion modeling uncertainty and effectively reduces dependence on expensive and possibly unreliable hardware.

A new algorithm for signal selective tracking of the directions-of-arrival (DOAs) of multiple moving targets with an array of passive sensors is presented. A new method based on the principles of maximum likelihood estimation and cyclostationarity is used to generate initial angle estimates which, in turn, are refined by a Kalman filter. Source angle dynamics are used to achieve correct data association. High performance is obtained with relatively low computational complexity.