Timing Synchronization for Cooperative Communications with Detect and Forward Relaying

Abstract

A non-data-aided near maximum likelihood (NDA-NML) symbol timing estimator is presented, which is applied to a cooperative communication system with a source, relay and destination. A Cramer rao bound (CRB) for the estimator for asymptotically low signal-to-noise (SNR) ratio case is derived. The timing complexity of the NDA-NML estimator is derived and compared with the correlation based data-aided maximum likelihood (DA-ML) estimator. It is demonstrated that the complexity of the NDA-NML estimator is much less than that of correlation based DA-ML estimator. The bit-error-rate (BER) performance of this system operating in a detect-and-forward (DAF) mode is studied where the channel state information (CSI) is available at the receiver and the symbol timings are estimated independently for each channel. SNR combining (SNRC) and equal ratio combining (ERC) methods are considered. It is found that timing estimation error has a significant effect on BER performance. It is also found that for large timing error the benefit of cooperative diversity could vanish. It is demonstrated that significant gains can be made with both combining methods with cooperation and timing estimation, where the gains are the same for both estimators.

Timing and Carrier Synchronization With Channel Estimation in Multi-Relay Cooperative Networks

“…As anticipated, the CRLBs in (14) and (15b) are also dependent on the TS length and the choice of the TSs broadcasted from both and the relays. Based on the CRLBs in (19a) and (19b), similar dependencies can be also deduced for the case of DF relaying.…”

“…The CRLB for the estimation of MCFOs and MTOs is given by diagonal elements of the matrix, in (11), and can be written in closed-form as (14) where the second equality in (14) follows from the matrix inverse identity for invertible matrices and in [30]. In this case, , and in (14) correspond to , and , respectively.…”

“…Remark 3: The CRLBs for the estimation of and for AF relaying in (14) and (15b) depend on source-relay-destination carrier frequency offsets, , timing offsets, , and channel gains, , through the matrices and in (10). As anticipated, the CRLBs in (14) and (15b) are also dependent on the TS length and the choice of the TSs broadcasted from both and the relays.…”

“…Most of the existing work in the literature focuses on estimating either MCFOs while assuming perfect timing synchronization [8]- [13] or MTOs while assuming perfect carrier synchronization [6], [7], [14], [15]. Cramér-Rao lower bounds (CRLBs) and different techniques for estimating MCFOs in MIMO systems are addressed in [9]- [12].…”

“…However, the algorithms in [9]- [12] are not applicable to the case of amplify-and-forward (AF)-relaying cooperative networks and are based on the assumption of perfect timing synchronization. Novel CRLBs and maximum likelihood (ML) estimators to obtain MTOs for detect-and-forward, decode-and-forward (DF), and AF systems are derived in [14], [15], and [6], [7], respectively. Similarly, in [8], [13], [16] the estimation of multiple channel gains and MCFOs in DF and AF cooperative systems are analyzed.…”