System Identification with Perfect Sequence Excitation - Efficient NLMS vs. Inverse Cyclic Convolution

Linear transmission systems are often characterized by their impulse responses. A simple and fast approach to acquire these impulse responses is the normalized leastmean-square (NLMS) algorithm in combination with a perfect sequence excitation. It is not only applicable to static impulse response measurements, but has been optimized especially for the tracking of time varying linear systems. In this paper, different implementation strategies of the perfect sequence excited NLMS algorithm, namely the efficient NLMS and the inverse cyclic convolution algorithm, are discussed and compared in terms of performance, complexity, and applicability. As a main result it is shown that for certain conditions all algorithmic variants can be transferred to each other.