Low complexity timing estimation and resynchronization for asynchronous bidirectional communications with multiple antenna relay

Abstract

In this paper, we consider an asynchronous bidirectional communication system over flat fading channels in which the two source nodes are not perfectly synchronized. A low complexity pilot aided timing estimation and resynchronization scheme is proposed to combat the fractional asynchronous delay between the two source nodes. In the proposed scheme, cyclic prefixed single carrier block transmission is implemented at the two sources and frequency domain orthogonal pilots are transmitted to the relay simultaneously. After timing and channel estimation at the relay, a fractionally spaced frequency domain equalizer is employed at the relay to resynchronize the received mixed signals. With the proposed resynchronization scheme, the data detection at the two sources is the same as in a perfect synchronized system, because the two asynchronous signals are already resynchronized at the relay node. Simulation results show that the performance gap between the proposed scheme and the perfect synchronized system is within 1 dB when there are four antennas at the relay.

Proof of the Equivalency of MSE-Constrained and Rate-Constrained Power Optimization Approaches to Distributed Bi-Directional Beamforming

“…One can then easily find the principal eigenvector of the block diagonal matrix B −1 4 (z)B 2 (z) from the principal eigenvector of that block of this matrix which has the largest principal eigenvalue among all different blocks. Based on these explanations and using the fact that different blocks of B −1 4 (z)B 2 (z) can be extracted as S n B −1 4 (z)B 2 (z)S H n , for n ∈ N , we can rewrite (49) as 12 in (B.1), shown at the bottom of the next page, where in the second equality, we use (44); in the third equality, we use (4); in the fourth equality we use (18); and in the fifth equality, we use the fact that the only non-zero eigenvalue of xy H is y H x; in the seventh equality, we use the fact that B 1 (z) = (zQ 2 + σ 2 I L ) − 1 2 ; and in the eighth equality, we use (6). The derivation of ( 51) is now complete.…”

“…The authors of [17] also study the diversity of linear post-channel equalization schemes, such as zero-forcing and minimum mean squared error (MMSE) receivers. In [18], the authors consider an asynchronous bidirectional relay network, where a single multi-antenna relay enables a two-way information exchange between two transceivers, and devise a channel and timing offset estimation method to re-synchronize the relays. The study in [19] considers a bi-directional relay network, with multiple single-antenna relays.…”

“…Moreover, the authors of [17] study the diversity of linear post-channel equalization schemes, such as zero forcing (ZF) and MMSE receivers, whereas in our work, we focus on obtaining the MSE-constrained poweroptimal values of linear channel equalizers, the relays AF coefficients, and the transceivers' transmit powers with the aim to show the relationship between these values and rate-constrained power-optimal values of the same parameters. The goal in [18] is to develop a channel and timing offset estimation method that can be used to re-synchronization the relays, whereas we herein do not re-synchronize the relays but employ post-channel equalization to suppress the ISI at the two transceivers induced by the relays. Unlike [19], which relies on circularly shifting (cyclic delay) of the CP-free signal at the relays, we assume AF relaying without any cyclic delay for the sake of relay simplicity.…”

On Total Transmission Power Minimization Approach to Decentralized Beamforming in Single-Carrier Asynchronous Bidirectional Relay-Assisted Communication Networks

“…It is worth mentioning that the authors of [15]- [20] have also made important contributions to the research on asynchronous relay networks. However, these authors do not study the same bi-directional relay network which we herein consider.…”

“…Moreover, considering two linear post-channel equalization techniques, namely minimum mean squared error (MMSE) and zero forcing (ZF) receivers, Wang et al [15] study the diversity of these techniques, while we herein do not assume any type of equalizations and aim to determine the power-optimal values of the transceivers' transmit powers and those of the relays' AF coefficients under two data rate constraints at the two end-nodes. Considering an asynchronous bi-directional relay network of two transceivers and a multi-antenna relay, Fang et al [20] devise a timing offset and channel estimation algorithm and use this algorithm for relay re-synchronization. We do not assume any relay re-synchronization.…”