Clock synchronization for wavelet-based multirate transmissions

Abstract
This paper deals with symbol timing recovery for multirate transmission systems employing wavelets as signaling pulses either at baseband or with linear bandpass modulation. Our analysis is twofold. First, we investigate the impact of clock errors on the bit-error rate of the optimum receiver for a wavelet-based multirate signal. Second, we consider a nondata-aided max- imum-likelihood clock synchronization scheme implemented as a multiple delay-locked loop. We derive a linearized loop model and assess its performance in terms of tracking jitter variance. The analytical results are contrasted with those obtained by simulation and with the relevant modified Cramér-Rao bound. N THE last few years, multimedia consumer applications have made their way inside everybody's life. This class of services envisage the simultaneous transmission of symbol streams conveying information from different data sources, each characterized by a specific information rate. The rapid expansion of this communications segment has fostered worldwide research and development of efficient multirate transmission techniques. Also, recently, several authors have shown that transmission systems employing wavelets as basic signaling waveshapes re- sult inherently well suited to utilization in a multirate environ- ment. A few examples of the use of wavelets over time-varying channels are shown in (1) and (2). The implementation and the performance of a multirate transmission system operating over a Gaussian channel are discussed in (3) and (4), where it is shown how wavelets can be profitably applied to widespread commu- nication services. In this paper, we take up the synchronization issues implied by the use of wavelet-based multirate data signals. These topics have been somewhat overlooked in the literature so far, but they deserve adequate consideration if the feasibility of this uncon- ventional transmission technique is to be ascertained. In the fol- lowing, we limit ourselves to the aspect of data symbol syn- chronization, assuming either that carrier frequency and phase are exactly recovered prior to clock extraction or that the trans- mission is baseband.

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