On the evaluation of estimated impulse responses

In this letter, we discuss the philosophy of evaluating estimated impulse responses for applications in which the overall scaling or gain is irrelevant, as, for example, in blind channel identification. We argue that no matter how the estimate is obtained, the performance should be independently evaluated using an error measure that is appropriate for a problem of this class. Of several possible error measures, the normalized projection error, which is obtained by minimizing the l(2) norm over all possible gain values, seems to be the most natural and consistent. An example demonstrates that using an inappropriate error measure can produce misleading results.