Adaptive Time Delay and Frequency Estimation for Digital Signal Synchronization in CDMA Systems Saul R. Dooley and Asoke K. Nandi Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, G1 1XW, UK. e-mail:
[email protected]
Abstract
tion to synchronization methods which are computationally inexpensive and thus can be implemented in real time. Synchronization of xk and yk is comprised of two parts: estimation of and compensation for the TDOA (delay synchronization) and FDOA (frequency synchronization). A well-known technique for the estimation of delays is the explicit time delay estimator (ETDE) algorithm [2], which uses the LMS algorithm [3]. However, if is nonzero, the signals are not frequency synchronized and delay synchronization by this method is impossible. Hence, compensation for the FDOA must occur before delay synchronization is possible. For frequency synchronization, one must modulate yk by ? , and to do this, one must estimate first. Short-time Fourier Transform and other time-frequency distribution techniques could be used (see e.g. [4]) but are either high-resolution and computationally very expensive or low resolution and require subsequent interpolation, possibly yielding a biased solution. It should be noted any bias in the FDOA estimate implies the signals are not frequency synchronized and reliable TDOA estimation is still impossible. In this work, the carrier frequency offset and time delay between a narrowband signal and a local carrier are adaptively estimated using fractional sample delay filters (or equivalently, bandlimited interpolation filters), of which there is also growing interest [5] due to their superiority over standard off-line interpolation. The ETDE algorithm uses an adaptive filter constrained to be samples of a sinc fractional delay filter with the delay as the only variable parameter. However, the truncated sinc filter has been shown previously to be a particularly poor choice for accurate delay estimation and subsequent synchronization. Additionally, re-designing the ETDE with a superior fractional delay filter is not straightforward for two reasons. Firstly, the filter must be re-designed on-line every iteration and this process must not impede real-time implementation—implying use of filters of low orders. Secondly, the derivatives of the filter weights with respect to the estimated delay are required at every iteration, implying computationally expensive on-
The problem of synchronization of digital narrowband signals is presented. For non-stationary communication channels, accurate adaptive time delay and carrier frequency offset estimation is required. Modifications to a well-known time delay estimation method (the explicit time delay estimator), including a novel frequency adjustment element, are proposed which are shown through simulation to enable significantly low estimation bias, even at the very short filter lengths desirable in this application.
1. Introduction Recently, there has been growing interest in post digital conversion demodulation (to baseband) in CDMA carrier systems, in order to exploit the power of efficient digital signal processing algorithms to move further towards errorfree communication. Signal synchronization is critical to coherent demodulation, and accurate phase and frequency offset compensation is required between the local carrier xk and the received signal yk (corrupted by zero-mean Gaussian noises k and k ), modelled very simply as complex exponentials:
xk yk
= =
ej!lk + k ej!c (k? ) + k
(1)
where !c is the frequency of the received carrier, and !l is the frequency of the local carrier, k is the discrete time index and is the delay or time difference of arrival (TDOA). !c may differ from !l due to the Doppler effect, and we reasonably assume !c = (!l + ) where the Doppler shift or frequency difference of arrival (FDOA)
