John W. Betz

Generalized Theory of Code Tracking with an Early-Late Discriminator Part I: Lower Bound and Coherent Processing

Code tracking is an important attribute of receivers for Global Positioning System (GPS) and other global navigation satellite systems (GNSS). This paper and its sequel provide analytical expressions for performance of code-tracking loops using early-late discriminators, under small-error conditions. Expressions are provided for output signal-to-noise-plus-interference ratio (SNIR) and code-tracking error for arbitrary signal spectra, and Gaussian noise and interference having arbitrary spectral shapes. This first paper addresses coherent early-late processing (ELP) for given receiver precorrelation bandwidth and given early-late spacing, also providing a tight lower bound on code-tracking error independent of discriminator design. Theoretical expressions are derived, showing that code-tracking accuracy depends on more than merely signal-to-noise ratio and early-late spacing - the shape of signal and interference spectra are important, as is the receiver precorrelation bandwidth.

Generalized Theory of Code Tracking with an Early-Late Discriminator Part II: Noncoherent Processing and Numerical Results

Code tracking is an important attribute of receivers for Global Positioning System (GPS) and other global navigation satellite systems (GNSS). This paper and its antecedent provide analytical expressions for performance of code-tracking loops using early-late discriminators, under small-error conditions. Expressions are provided for output signal-to-noise-plus-interference ratio (SNIR) and code-tracking error, for arbitrary signal spectra, and Gaussian noise and interference having arbitrary spectral shapes. This second paper addresses noncoherent early-late processing (NELP) for given receiver precorrelation bandwidth and given early-late spacing, comparing the results to results for coherent early-late processing (CELP) and to a lower bound (LB) on code-tracking error. Theoretical expressions are derived and compared, and numerical results are provided to examine the effect of different modulation designs and interference conditions.

Detection of weak random signals in IID non-Gaussian noise

This paper considers the detection of weak random signals in circularly symmetric, independent, identically distributed noise. Locally optimum detectors and ad hoc nonlinearities are considered, with asymptotic expressions provided for evaluation of detection performance. The analytical expressions are used to evaluate the robustness of detectors to mismatch in the noise models. Finite-sample Monte Carlo simulation results indicate the reliability of these asymptotic measures in cases of practical interest. The results show that, as has been found for detection of weak known signals in non-Gaussian noise, reasonably configured ad hoc nonlinearities are nearly optimum and robust to modest errors in the noise statistics.

Intersystem and intrasystem interference with signal imperfections

Analytical techniques have been developed and accepted as effective ways to assess the approximate effects of interference from Global Navigation Satellite System (GNSS) signals to the reception of signals from the same or other GNSSs. The methodology has been used to determine the effects of interference from different signals transmitted by the same system (intrasystem interference) and interference from signals transmitted by other systems (intersystem interference). However, the current methodology assumes that the set of transmitted signals is merely the superposition of ideally specified signals. In fact, transmitted signals have imperfections, and these imperfections can affect the level of interference. This paper extends the interference assessment methodology to include the effect of signal imperfections, adding consideration of different types of signal imperfections and evaluating their effect on intrasystem and intersystem interference.

Limitations of radiometer performance in spherically invariant noise

The radiometer is a common method for detection of unknown signals in noise. Most analyses of radiometer performance are based on assumptions of stationary Gaussian noise with known marginal statistics. In this note, we use a spherically invariant noise model to derive simple expressions for radiometer performance degradation in noise variance uncertainty. Numerical examples are provided to show that channel uncertainty imposes a substantial penalty in detection performance. >