The Cost of Complexity in Identification of FIR Systems

In this paper we investigate the minimum amount of input power required to estimate a given linear system with a prescribed degree of accuracy, as a function of the model complexity. This quantity is defined to be the ‘cost of complexity’. The degree of accuracy considered is the maximum variance of the discrete-time transfer function estimator over a frequency range [−ωB, ωB]. It is commonly believed that the cost increases as the model complexity increases. The objective of this paper is to quantify this dependence. In particular, we establish several properties of the cost of complexity. We find, for example, a lower bound for the cost asymptotic in the model order. For simplicity, we consider only systems described by FIR models and assume that there is no undermodelling.