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

Abstract

Abstract-Multiple distributed nodes in cooperative networks generally are subject to multiple carrier frequency offsets (MCFOs) and multiple timing offsets (MTOs), which result in time varying channels and erroneous decoding. This paper seeks to develop estimation and detection algorithms that enable cooperative communications for both decode-and-forward (DF) and amplify-and-forward (AF) relaying networks in the presence of MCFOs, MTOs, and unknown channel gains. A novel transceiver structure at the relays for achieving synchronization in AF-relaying networks is proposed. New exact closed-form expressions for the Cramér-Rao lower bounds (CRLBs) for the multi-parameter estimation problem are derived. Next, two iterative algorithms based on the expectation conditional maximization (ECM) and space-alternating generalized expectation-maximization (SAGE) algorithms are proposed for jointly estimating MCFOs, MTOs, and channel gains at the destination. Though the global convergence of the proposed ECM and SAGE estimators cannot be shown analytically, numerical simulations indicate that through appropriate initialization the proposed algorithms can estimate channel and synchronization impairments in a few iterations. Finally, a maximum likelihood (ML) decoder is devised for decoding the received signal at the destination in the presence of MCFOs and MTOs. Simulation results show that through the application of the proposed estimation and decoding methods, cooperative systems result in significant performance gains even in presence of impairments.Index Terms-Cooperative communications, Cramér-Rao lower bounds (CRLB), expectation conditional maximization (ECM), space-alternating generalized expectation-maximization (SAGE), timing and carrier synchronization.

A Study on Orthogonal Space-time Block Codes for Cooperative Function

“…Note also that for the above 2×2 STBC, the transmission rate is one symbol/transmission, and it achieves the maximum diversity order of 4 that is possible with a 2×2 system. The method of Alamouti can be generalized to more than two transmit antennas [15][16][17][18]. The resulting orthogonal codes are still optimally decoded with a linear receiver.…”

DSTBC based DF cooperative networks in the presence of timing and frequency offsets

“…In distributed decode-and-forward (DF) multi-relay networks, the received signal at the destination is the superposition of the relays' transmitted signals that are attenuated differently, are no longer aligned with each other in time, and are experiencing phase rotations at different rates due to different channels, multiple timing offsets (MTOs), and multiple carrier frequency offsets (MCFOs) [1], [2]. Thus, joint estimation and compensation of these impairments is necessary to enable the detection of the received signal at the destination [2].…”

“…Thus, joint estimation and compensation of these impairments is necessary to enable the detection of the received signal at the destination [2]. Different cooperation strategies have been employed at the relays.…”

“…Bandwidth efficiency can be improved by allowing the relays to transmit simultaneously. However, depending on how the relays' signals superimpose at the destination, achieving full diversity is not guaranteed [2], [4]. Recently, it has been shown that full diversity gains can be achieved by employing distributed space-time block code (DSTBC) cooperative strategy, which allows the relays to transmit in the same time slot using the DSTBC structure [5]- [7].…”

“…The joint estimation of multiple channel gains, MTOs, and MCFOs, in DF cooperative networks is well-studied in [2], [8]. However little research has been conducted on the development of compensation algorithms, which can detect the received signal by jointly compensating and removing the effect of multiple channel gains, MTOs, and MCFOs.…”