Blind System Identification in Noise Using a Dynamic-Based Estimator

In this work we consider the problem of blind system identification in noise driven by an independent and identically distributed (i.i.d) non-Gaussian signal generated from a deterministic nonlinear chaotic system. A new estimator for the phase space volume (PSV) which is a dynamic-based property of chaos is derived using the maximum likelihood formulation. This novel estimator of PSV is denoted as the maximum likelihood phase space volume (ML-PSV). The Cramer Rao Lower Bound (CRLB) of the ML-PSV estimator has also been derived. We have shown that the mean square error of the ML-PSV estimate gradually approaches its CRLB asymptotically. An algorithm is formulated that applies the ML-PSV estimator as an objective function in the task of blind system identification of autoregressive (AR) and moving average (MA) models. The proposed technique is shown to improve blind identification performance at low signal-to-noise ratio (SNR) when the system is driven by both chaotic numeric and symbolic signals. The efficiency of our proposed method is compared with conventional blind identification methods through simulations. Our technique is further validated through experimental evaluation based on a software defined radio (SDR). Results show that the ML-PSV method outperforms the existing blind identification methods producing estimates at a low SNR of $\le20$ dB.