Identification of FIR Systems with Binary Input and Output Observations

TL;DR

This paper develops methods for identifying FIR systems from binary quantized input-output data, using correlation-based equations and stochastic approximation, applicable to various quantizer capabilities and noise distributions.

Contribution

It introduces novel identification schemes for FIR systems with binary data, accommodating both adaptive and fixed quantizers, and handling different noise distributions.

Findings

Proposed algorithms are strongly consistent for Gaussian noise.

Methods work with quantizers having or lacking computational capabilities.

Simulation results demonstrate effectiveness of the proposed schemes.

Abstract

This paper considers the identification of FIR systems, where information about the inputs and outputs of the system undergoes quantization into binary values before transmission to the estimator. In the case where the thresholds of the input and output quantizers can be adapted, but the quantizers have no computation and storage capabilities, we propose identification schemes which are strongly consistent for Gaussian distributed inputs and noises. This is based on exploiting the correlations between the quantized input and output observations to derive nonlinear equations that the true system parameters must satisfy, and then estimating the parameters by solving these equations using stochastic approximation techniques. If, in addition, the input and output quantizers have computational and storage capabilities, strongly consistent identification schemes are proposed which can handle arbitrary input and noise distributions. In this case, some conditional expectation terms are computed at the quantizers, which can then be estimated based on binary data transmitted by the quantizers, subsequently allowing the parameters to be identified by solving a set of linear equations. The algorithms and their properties are illustrated in simulation examples.