Performance Analysis for Time-of-Arrival Estimation with Oversampled Low-Complexity 1-bit A/D Conversion

Analog-to-digtial (A/D) conversion plays a crucial role when it comes to the design of energy-efficient and fast signal processing systems. As its complexity grows exponentially with the number of output bits, significant savings are possible when resorting to a minimum resolution of a single bit. However, then the nonlinear effect which is introduced by the A/D converter results in a pronounced performance loss, in particular for the case when the receiver is operated outside the low signal-to-noise ratio (SNR) regime. By trading the A/D resolution for a moderately faster sampling rate, we show that for time-of-arrival (TOA) estimation under any SNR level it is possible to obtain a low-complexity $1$-bit receive system which features a smaller performance degradation then the classical low SNR hard-limiting loss of $2/\pi$ ($-1.96$ dB). Key to this result is the employment of a lower bound for the Fisher information matrix which enables us to approximate the estimation performance for coarsely quantized receivers with correlated noise models in a pessimistic way

Asymptotic Signal Detection Rates with 1-bit Array Measurements

This work considers detecting the presence of a band-limited random radio source using an antenna array featuring a low-complexity digitization process with single-bit output resolution. In contrast to high-resolution analog-to-digital conversion, such a direct transformation of the analog radio measurements to a binary representation can be implemented hardware and energy-efficient. However, the probabilistic model of the binary receive data becomes challenging. Therefore, we first consider the Neyman-Pearson test within generic exponential families and derive the associated analytic detection rate expressions. Then we use a specific replacement model for the binary likelihood and study the achievable detection performance with 1- bit radio array measurements. As an application, we explore the capability of a low-complexity GPS spectrum monitoring system with different numbers of antennas and different observation intervals. Results show that with a moderate amount of binary sensors it is possible to reliably perform the monitoring task

Performance Analysis for Time-of-Arrival Estimation with Oversampled Low-Complexity 1-bit A/D Conversion

Analog-to-digtial (A/D) conversion plays a crucial role when it comes to the design of energy-efficient and fast signal processing systems. As its complexity grows exponentially with the number of output bits, significant savings are possible when resorting to a minimum resolution of a single bit. However, then the nonlinear effect which is introduced by the A/D converter results in a pronounced performance loss, in particular for the case when the receiver is operated outside the low signal-to-noise ratio (SNR) regime. By trading the A/D resolution for a moderately faster sampling rate, we show that for time-of-arrival (TOA) estimation under any SNR level it is possible to obtain a low-complexity $1$-bit receive system which features a smaller performance degradation then the classical low SNR hard-limiting loss of $2/\pi$ ($-1.96$ dB). Key to this result is the employment of a lower bound for the Fisher information matrix which enables us to approximate the estimation performance for coarsely quantized receivers with correlated noise models in a pessimistic way

Measurement-driven Quality Assessment of Nonlinear Systems by Exponential Replacement

We discuss the problem how to determine the quality of a nonlinear system with respect to a measurement task. Due to amplification, filtering, quantization and internal noise sources physical measurement equipment in general exhibits a nonlinear and random input-to-output behaviour. This usually makes it impossible to accurately describe the underlying statistical system model. When the individual operations are all known and deterministic, one can resort to approximations of the input-to-output function. The problem becomes challenging when the processing chain is not exactly known or contains nonlinear random effects. Then one has to approximate the output distribution in an empirical way. Here we show that by measuring the first two sample moments of an arbitrary set of output transformations in a calibrated setup, the output distribution of the actual system can be approximated by an equivalent exponential family distribution. This method has the property that the resulting approximation of the statistical system model is guaranteed to be pessimistic in an estimation theoretic sense. We show this by proving that an equivalent exponential family distribution in general exhibits a lower Fisher information measure than the original system model. With various examples and a model matching step we demonstrate how this estimation theoretic aspect can be exploited in practice in order to obtain a conservative measurement-driven quality assessment method for nonlinear measurement systems.Comment: IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Taipei, Taiwan, 201