SYSTEM-IDENTIFICATION WITH PERFECT SEQUENCES BASED ON THE NLMS ALGORITHM

The problem of measuring the impulse response of an unknown linear transmission system has been studied within many papers. One approach for the identification problem represents the so called fast M-sequence transform, where a binary periodic maximal-length sequence is used as excitation signal for the unknown system. This identification process bases on the cross correlation between one period of the maximal-length sequence and its received system response. In this paper an alternative to several existing approaches is proposed by using a periodic perfect sequence stimulus signal for the normalized least mean square (NLMS) algorithm. In contrast to the normally used stochastic white noise process with this deterministic excitation signal the NLMS algorithm is capable to identify a linear noiseless system within one period. Several theoretical aspects of this technique will be discussed. Considering that in many applications such as acoustic echo compensation, acoustic feedback control or active noise reduction the NLMS algorithm is applied, the practical point of view of the proposed method becomes apparent.