1572 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 3, MARCH 2009 Network-Coding-Based Signal Recovery for Efficient Scheduling in Wireless Networks Jingyao Zhang, Khaled Ben Letaief, Fellow, IEEE, Pingyi Fan, Member, IEEE, and Kai Cai Abstract—Interference is a serious problem in wireless commu- nications. In a wireless network, the signal sent by a terminal will be received by all its neighboring nodes. If a neighbor (except the destinations) is receiving data from some other terminals at the same time, the signals will collide, and the useful signal will be destroyed, which may result in transmission failure. Previous so- lutions to this problem focused on the avoidance of signal collisions through careful medium access control (MAC) and/or scheduling. However, this needs some sophisticated protocols and may waste system resources such as bandwidth. In this paper, we shall put forward some practical schemes to recover the useful signal from the collided signals for different types of wireless channels; thus, the throughput and network efficiency can greatly be increased. The proposed schemes are based on the network coding technique and performed on the physical layer. One feature of our schemes is that neither strict synchronization nor power control is needed among the different terminals; thus, it is very fit for distributed networks. Simulation results will show that the bit error rate (BER) of the recovered signal by our developed schemes is almost the same as that of the signal with no collision, which proves their efficiency in eliminating the interference. Index Terms—Block fading, network coding, scheduling, time variant, wireless network. I. I NTRODUCTION T HE BROADCAST nature of wireless medium is one of the principal features of wireless networks. Although this feature may somewhat facilitate the broadcast communication, it usually causes interference and collision in other scenarios. In a wireless network, signals sent by a terminal can reach all its neighbors, whereas a terminal may simultaneously receive the signals from all its nearby nodes. In traditional wireless networks, this collision of signals may cause transmission failure if no division technique is adopted. This will degrade the system performance, such as the packet loss rate and energy efficiency. Moreover, in distributed networks such as ad hoc and Manuscript received July 9, 2007; revised November 14, 2007, April 19, 2008, and May 23, 2008. First published June 24, 2008; current version published March 17, 2009. This work was supported in part by the 863 Project of China under Grant 2006AA01Z211 and in part by the National Science Foundation of China under Grant 60572085. The review of this paper was coordinated by Dr. S. Vishwanath. J. Zhang is with the Department of Electronic Engineering, Tsinghua Uni- versity, Beijing 100084, China (e-mail: jy-zhang@mails.tsinghua.edu.cn). P. Fan is with the Department of Electronic Engineering, Tsinghua Univer- sity, Beijing 100084, China (e-mail: fpy@mail.tsinghua.edu.cn). K. B. Letaief is with The Hong Kong University of Science and Technology, Kowloon, Hong Kong (e-mail: eekhaled@ee.ust.hk). K. Cai was with The Hong Kong University of Science and Technology, Kowloon, Hong Kong. He is now with the Institute of ComputingTechnology, Chinese Academy of Sciences, Beijing 100080, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2008.927725 Fig. 1. Traditional wireless multihop scheduling strategy with three frames and three relay nodes. some sensor networks, the absence of control center will in- crease the opportunity of collision and interference, which further reduces the transmission rate and brings about the inevitable hidden- and exposed-node problems. Previous so- lutions to this problem mainly focused on how to avoid sig- nal collision [1], [2] through some well-developed protocols on the medium access control or network layer. For exam- ple, the request-to-send/clear-to-send (RTS/CTS) strategy in IEEE802.11 [3] can reduce the opportunity of signal collision in distributed ad hoc networks. In RTS/CTS, when a terminal is receiving messages, its neighbors cannot transmit until receiv- ing is finished. However, such a mechanism is not efficient, and a lot of bandwidth is wasted. This can be seen from the example shown in Fig. 1. In this wireless network of linear topology, node A intends to transmit three frames of messages a, b, and c to the sink E through the relays B, C, and D. Each link is assumed to be half-duplex. While C is forwarding a to D in time slot 3, A must wait for the next time slot, although the link from A to B is idle. Otherwise, the signals of a and b will collide at B. A closer observation indicates that the throughput of this system is as low as only one third of a frame per time slot. The inefficiency of traditional wireless transmission is main- ly due to the regulation that signal collision is strictly forbidden, which is not always necessary. In fact, for B in time slot 3, the signal of a is not random interference. Since B has received a before, it can regenerate the signal waveform of a, which can help eliminate the interference of a if A and C simulta- neously transmit (as shown in Fig. 2). From the point of view of information theory, a provides the side information to B. In this paper, we shall propose some practical algorithms to eliminate interference and recover the useful signal from the mixed signals such as a ⊕ b at B (Fig. 2). Our strategies are based on the recently proposed net- work coding technique, which was first proposed by 0018-9545/$25.00 © 2008 IEEE