Distributed Space-Frequency Coding over Broadband Relay Channels

Abstract

Abstract-Designing diversity achieving schemes over the wireless broadband fading relay channels is crucial to achieve higher diversity gains. These gains are achieved by exploiting the multipath (frequency) and cooperative diversities to combat the fading nature of wireless channels. The challenge is how to design spacefrequency codes, distributed among randomly located nodes that can exploit the frequency diversity of the wireless broadband channels. In this paper, the design of distributed space-frequency codes (DSFCs) for wireless relay networks is considered. The proposed DSFCs are designed to achieve the frequency and cooperative diversities of the wireless relay channels. The use of DSFCs with the decode-and-forward (DAF) and amplify-andforward (AAF) protocols is considered. The code design criteria to achieve full diversity, based on the pairwise error probability (PEP) analysis, are derived. For DSFC with the DAF protocol, a two-stage coding scheme, with source node coding and relay nodes coding, is proposed. We derive sufficient conditions for the proposed code structures at the source and relay nodes to achieve full diversity of order NL, where N is the number of relay nodes and L is the number of paths per channel. For the case of DSFC with the AAF protocol, a structure for distributed space-frequency coding is proposed.

High-Rate Distributed Space-Time-Frequency Coding for Wireless Cooperative Networks

“…There has been a growing attention on the design of cooperative OFDM systems [6]- [8]. Seddik and Liu have proposed distributed space-frequency codes (DSFCs) assuming both decode-and-forward (DF) and amplify-and-forward (AF) relaying [7]. The proposed code structure of AF DSFC is only shown to achieve full diversity for some special cases [7].…”

“…Seddik and Liu have proposed distributed space-frequency codes (DSFCs) assuming both decode-and-forward (DF) and amplify-and-forward (AF) relaying [7]. The proposed code structure of AF DSFC is only shown to achieve full diversity for some special cases [7]. In [6], Zhang et al have introduced some AF DSFCs and provided diversity analysis for arbitrary number of relay nodes and channel lengths based on some approximations.…”

“…In [6], Zhang et al have introduced some AF DSFCs and provided diversity analysis for arbitrary number of relay nodes and channel lengths based on some approximations. The maximal rate of AF-DSFCs proposed in both [7] and [6] is one OFDM block per two-phase cooperative OFDM transmission, which is termed as "full rate". Wang, et al have proposed two lower-rate (i.e., less than full rate) DSFCs to combat multiple carrier frequency offsets (CFO) [8].…”

“…The proposed designs achieve full-rate for any number of cooperative nodes, and allow channel variations over multiple OFDM blocks within one DSTFC codeword. Unlike the designs of AF DSFC which were based on diversity analyses using average pairwise error probability (PEP) [6], [7], we design AF DSFC using oneside-channel conditioned PEP based diversity analysis, which enables to shed light on code construction. In addition, we also provide some discussions on average PEP based diversity analysis for our design creteria, and show some insights on .…”

On the Detection of Distributed STBC AF Cooperative OFDM Signal in the Presence of Multiple CFOs

“…Moreover, the flexible timing requirement of OFDM, which allows perfect timing within the inter-block interference (IBI) free range of the cyclic prefix (CP), can accommodate minor timing misalignments among distributed nodes. Therefore, cooperative OFDM has gained a lot of attention recently when combined with distributed space time block coding (STBC) [3]- [7] or distributed space frequency coding (DSFC) [8], [9].…”