Robust identification of a nonminimum phase system: Blind adjustment of a linear equalizer in data communications

TLDR

An unknown linear time‑invariant system driven by white noise is usually assumed minimum‑phase so that least‑squares identification works, but for nonminimum‑phase systems the phase cannot be recovered when the input is Gaussian, rendering second‑order statistics ineffective. This work seeks to identify both gain and phase of a nonminimum‑phase LTI system using only output observations. We introduce an identification procedure that applies to a broad class of non‑Gaussian input distributions and demonstrate it on blind adjustment of a transversal equalizer without a startup period. Numerical results confirm that the method accurately recovers the equalizer parameters in this blind setting.

Abstract

Consider an unknown linear time-invariant system without control, driven by a white noise with known distribution. We are interested in the identification of this system, observing only the output. This problem is well known under the major assumption: the system is minimum (or maximum!) phase, in which the very popular least squares method gives an identification of the system in an autoregressive form. However, we are Interested in the case where the system is nonminimum (nor maximum!) phase, i.e., we want identification of both gain and phase of the system. The literature gives only a negative result: the idenfication of the phase of the system is impossible in the case of a Gaussian driving noise (hence, second-order statistics are irrelevant to our problem). For a large class of other input distributions, we present an identification procedure, and give some numerical results for a concrete case origin of our study: the blind adjustment of a transversal equalizer without any startup period prior to data transmission.