Analysis of Outage Probability for Cooperative Networks with HARQ Stefano Tomasin, Marco Levorato and Michele Zorzi Department of Information Engineering University of Padova via Gradenigo 6/B, 35131 Padova, Italy e-mail: {tomasin, levorato, zorzi}@dei.unipd.it Abstract—We derive the expressions of the outage probability for a wireless network that integrates hybrid automatic repeat request (HARQ) and coded cooperation among nodes. The medium access control (MAC) provides a HARQ protocol where the source node, upon a decoding failure at the destination node, transmits additional coded bits for the same data packet. If a neighbor node is able to decode the first transmission, it cooperates with the source by sending additional coded bits. In order to keep nodes simple, we assume half-duplex, single band asynchronous transmissions, and receivers with single user detection techniques. Various configurations of cooperation are considered and the analysis includes key characteristics of wireless communications and interference. I. I NTRODUCTION Cooperation among devices has recently been considered to provide diversity in wireless networks where fading may significantly affect single links [1]. Initial works have focused on relaying, where a cooperator node amplifies (or decodes) and forwards, possibly in a quantized fashion [2], the infor- mation from the source node in order to help decoding at the destination node [3]–[5]. The achieved throughput can be increased with the integration of coding and cooperation, i.e., by letting the cooperator send incremental redundancy to the destination [6]. In particular, it has been shown in [6] that coded cooperation achieves a diversity order of two, while decode-and-forward reaches only a diversity order one, when the transmissions of source and cooperator are orthogonal. The capacity of cooperative networks using both the decode-and- forward and coded cooperation has been extensively studied [6], [7] for simple networks with simple medium access con- trol (MAC) protocols. In [8], a system with two transmission phases that makes use of convolutional codes is analyzed and characterized by means of partner choice and performance regions. Resource allocation for coded cooperative networks has been studied in [9], where an analysis of bit error rate is also derived. The analysis of coded cooperation in [6] assumes that each node is operating in full-duplex. However, full-duplex requires sophisticated electronics for simultaneous operations on two frequency bands and filters to reduce transmitter leakage through the duplexers into the receive path, which may be infeasible for some small devices, such as sensors or portable equipment. In this paper we derive the outage probability of a coded cooperation system, operating on a single band in half-duplex mode. With respect to [6], transmissions from the cooperator and the source are not orthogonal and inter- ference arises. A further distinctive feature of this work is the integration of coded cooperation with a hybrid automatic repeat request (HARQ) protocol that transmits coded packets only when needed. In the HARQ phases, either the source or the cooperator, or both, transmit incremental redundancy upon a transmission failure. We derive outage statistics useful to evaluate network level performance, including the effects of MAC protocols. The outage probability is evaluated as a function of the positions of nodes, and the analysis includes the effects of path loss, Rayleigh fading and possible interference coming from other active devices. II. SYSTEM MODEL We consider a network where all nodes transmit on the same frequency and partially interfere. Although the network has an arbitrary density of nodes, the analysis focuses on three nodes, a source (S) node that aims at transmitting data, a destination (D) node, which attempts to decode the information and a cooperator (C) node. Outage probability results are obtained for given positions of these three nodes and considering the interference coming from other nodes. A. MAC protocol In our cooperative protocol, time is divided into frames, each comprising a data and an acknowledgment slot. In the data slot, coded data are transmitted by node S and/or node C, while in the acknowledgment slot, the correct or wrong reception is reported by node D. The transmission of a single data packet lasts up to (N + 1) frames, according to HARQ, where N is a protocol parameter (e.g., N =2 or 4 in our simulations). The frames belonging to the same data packet may have different durations according to the number of coded bits being sent. Coded cooperation is implemented at node S by encoding the data packet and transmitting different portions of the coded packet during the various frames. For good channel conditions, node D is able to decode the data packet using only the first frame, which already contains all the information. However, for bad channel conditions, node D combines the information received in successive frames and attempts to decode the packet.