A new complex system identification method and its application to echo canceller fast initialization

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Abstract
A method is proposed for estimating the impulse response of a complex system based on its complex input and only the real part of its output. A unique periodic white complex testing sequence is constructed, and it is then sent to the system to be estimated. An important feature of the testing sequence is that its real and imaginary parts are mutually orthogonal, i.e. their cross-correlation is zero. Due to this orthogonality, the effects of the system's real imaginary parts are ideally decoupled. The cross-correlation between the complex testing sequence and the system's real part output yields an accurate estimate of the system's complex impulse response. In applications where the unknown system's impulse response is sparse, it is possible to squeeze it and choose a considerably small period for the sequence to reduce complexity. An effective algorithm for this purpose is presented. The application of this new method to fast training of the Nyquist echo cancellers in data modems is described. It is shown that using these techniques, fast and accurate estimation can be achieved efficiently.<>

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