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The Lebesgue spectrum filter (LSF), a finite impulse response (FIR) filter whose coefficients decay exponentially with a negative factor r := √3 - 2, is shown to be effective preprocessing for spreading code in asynchronous code-division multiple-access (CDMA) systems. The LSF has only been studied independently from the well-known minimum mean-square error (MMSE) filter, an optimal FIR filter in the mean-square error sense. In this paper, we propose an efficient structure, employing the LSF at the transmitter and the MMSE filter at the receiver, for asynchronous CDMA systems. We employ a spreading code preprocessed by the LSF (referred to as LSF-code), and the LSF-code supplies a "best" initial estimate (among the ones obtained without any a priori information) to an adaptive algorithm for the MMSE filter, leading to significant reduction of iterations in adaptation. This is verified by computer simulations. Also we investigate the link between the LSF and the MMSE filter by examining their autocorrelation properties.

Employing LSF at Transmitter Eases MMSE Adaptation at Receiver in Asynchronous CDMA Systems