A complex adaptive delay filter

Abstract

AbstractImpulse responses of unknown systems for radar and communications are often described in terms of complex numbers. In this paper, a complex‐tap‐selective adaptive filter that allows identification represented by complex numbers for the unknown system localized on the time axis is proposed. In the tap‐selective adaptive filter, the delay time for localized impulse responses is estimated and then the impulse responses in the delay time are estimated. First, temporary weights are set and the delay time is derived in such a way to minimize the mean square of the error signals. However, if the impulse response is described by complex numbers, a large estimation error might be caused when the conventional method of treating unknown systems with real numbers is applied directly for delay time estimation. Hence, two complex numbers that are mutually complex conjugates are set as temporary weights. The performance function based on the sum of the mean squares of the corresponding error signal is used in the proposed method for delay time estimation. In this way, identification of an unknown system with its impulse response located on the time axis and describable with complex numbers is possible. The effectiveness of the proposed method is demonstrated by computer simulation. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(9): 13–21, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10087