# Analysis of outage probability and throughput for half-duplex hybrid-ARQ Relay Channels

Behrouz Maham, Aydin Behnad, Mérouane Debbah

Research output: Contribution to journalArticle

33 Citations (Scopus)

### Abstract

We consider a half-duplex wireless relay network with hybrid-automatic retransmission request (HARQ) and Rayleigh fading channels. In this paper, we analyze the average throughput and outage probability of the multirelay delay-limited (DL) HARQ system with an opportunistic relaying scheme in decode-and-forward (DF) mode, in which the best relay is selected to transmit the source's regenerated signal. A simple and distributed relay selection strategy is considered for multirelay HARQ channels. Then, we utilize the nonorthogonal cooperative transmission between the source and selected relay for retransmission of source data toward the destination, if needed, using space-time codes. We analyze the performance of the system. We first derive the cumulative density function (cdf) and probability density function (pdf) of the selected relay HARQ channels. Then, the cdf and pdf are used to determine the exact outage probability in the $l$th round of HARQ. The outage probability is required to compute the throughput-delay performance of this half-duplex opportunistic relaying protocol. The packet delay constraint is represented by $L$, which is the maximum number of HARQ rounds. An outage is declared if the packet is unsuccessful after $L$ HARQ rounds. Furthermore, simple closed-form upper bounds on outage probability are derived. Based on the derived upper bound expressions, it is shown that the proposed schemes achieve the full spatial diversity order of $N + \hbox{1}$, where $N$ is the number of potential relays. Our analytical results are confirmed by simulation results. In addition, simulation shows that our proposed scheme can achieve higher average throughput, compared with direct transmission and conventional two-phase relay networks.

Original language English 6213570 3061-3070 10 IEEE Transactions on Vehicular Technology 61 7 https://doi.org/10.1109/TVT.2012.2203342 Published - 2012

### Keywords

• Hybrid ARQ
• outage probability
• performance analysis
• relay channels
• throughput

### ASJC Scopus subject areas

• Automotive Engineering
• Aerospace Engineering
• Electrical and Electronic Engineering
• Applied Mathematics