Quantization error for weak RF simultaneous signal estimation

In a congested signal environment, it is difficult to obtain estimates of weak RF signal parameters. Determining signal parameter estimates in real time is a challenge for electronic warfare receivers that aim to receive multiple simultaneous signals. Prior work provided estimates of weak signal parameters (weak signal frequency and weak signal amplitude) without taking into account any error introduced by analog-to-digital converters that are inherently part of digital signal processing systems. In order to obtain realistic estimates, we need to take error introduced by an ADC into account. The primary aim of this paper is to quantify error introduced by a single ideal ADC as a function of angle. This paper presents a method to estimate angle resolution and quantization levels in N-bit analog-to-digital converters (ADCs) for use in a weak radiofrequency (RF) simultaneous signal estimation process. The paper quantifies the error in the angle quantization of an N-bit ADC for an input complex signal that is the instantaneous frequency obtained for the situation in which there are two simultaneous signals (with one strong signal and one weak signal) in a weak RF simultaneous signal estimation process. The presented method describes the process to determine the angle quantization range, angle quantization uncertainty, and angle quantization error. This approach has potential applications in electronic warfare (EW) systems. The approach also has potential for assessing ADC performance for measurements that approach the quantum limit. Results are presented for 1-bit, 2-bit, 3-bit, and 10-bit ADCs.