Semi-blind identification of finite impulse response channels

It is a standard result that a finite impulse response channel of length L can be uniquely identified by feeding in a known (and persistently exciting) sequence of 2L 1 consecutive data points. Equivalently, given only 2L 2 consecutive data points, the channel can be uniquely identified up to a multiplicative constant. This paper significantly extends the identifiability criterion to the case when the known inputs are non-consecutively located. It is argued that by introducing 2L 1 non-consecutively spaced zeros into the input stream, for almost all input sequences, the channel can be uniquely identified up to a multiplicative constant. Furthermore, the result can be extended to the case when the known inputs are non-zero, in which case the channel can almost always be identified uniquely. To arrive at these results, general properties of systems of polynomial equations are derived. These properties do not seem to have appeared in the literature before.