Blind identification of sparse Volterra systems

This paper is concerned with blind identification for single‐input single‐output Volterra systems with finite order and memory with the second‐order and the third‐order statistics. For the full‐sized Volterra system (i.e. all its kernels are nonzero) excited by unknown independently and identically distributed stationary random sequences, it is shown that blind identifiability does not hold in the second‐order moment (SOM) and the third‐order moment (TOM) domain. However, under some sufficient conditions, a class of truncated sparse Volterra systems, where some kernels are restricted to being zero, can be identified blindly and more Volterra parameters can be estimated in TOM than in SOM. Numerical examples illustrate the effectiveness of the proposed methods. Copyright © 2007 John Wiley & Sons, Ltd.