On the delay reduction of wireless ad hoc networks with directional antennas

Hong-Ning Dai 0 Qinglin Zhao 0 0 Faculty of Information Technology, Macau University of Science and Technology , Macau SAR , China It is shown that the throughput capacity of wireless ad hoc networks using omni-directional antennas (OMN networks) is significantly decreased with the increased number of nodes. One major reason lies in the interference caused by using omni-directional antennas, which just broadcast radio signal in all directions. Thus, a communication with multiple short-ranged hops is suggested in such networks to avoid interference and improve the throughput. However, the multi-hop transmission can also significantly increase the end-to-end delay. In this paper, we investigate the throughput improvement and the delay reduction by using directional antennas in wireless ad hoc networks. We call such wireless ad hoc networks using directional antennas as DIR networks. In particular, we investigate the effective transmission range of directional antennas with consideration of various channel conditions, such as the large scale path loss and the shadow fading effect. We have found that directional antennas can significantly increase the transmission range compared with omni-directional antennas even under the same channel condition. Besides, we derive the throughput and the delay of a DIR network by constructing a routing scheme and a time-division multi-access (TDMA) scheme. We have found that using directional antennas not only can increase the throughput capacity but also can decrease the delay by reducing the number of hops. 1 Introduction Wireless ad hoc networks typically consist of nodes that are sharing the same medium to transmit. It is shown in [1] that in an ad hoc network with n nodes under a random networka, each node has a throughput capacity of ( 1/ n log n). Even under an optimal arbitrary networkb, the network could only offer a per-node throughput of ( 1/n). The per-node throughput is decreased when the number of nodes increases. One of the major reasons of the poor performance of wireless ad hoc networks is that all the nodes within the network share the same medium. When a node transmits, its neighboring nodes are prohibited from transmitting due to the interference. Thus, the network throughput is interference-limited. One implication from [1] is that a small transmission range is necessary to limit the interference and consequently leads to a high throughput. However, a smaller transmission range means that a packet needs to be transmitted through more hops, which inevitably leads to higher transmission delay. It is shown in [2] that the delay due to the multi-hop transmission is increased when the throughput scales. We call such wireless ad hoc networks using omni-directional antennas as OMN networks. Other studies such as [3-11] concentrate on using directional antennas to improve the network throughput. In particular, it is shown in [3] that using directional antenna in random networks achieves a capacity gain of 4 2/(12) over OMN networks when both transmission and reception are directional, where 1 and 2 are transmitter and receiver antenna beamwidths, respectively. We call such wireless ad hoc networks using directional antennas as DIR networks. However, most of all these studies only consider the throughput improvement by using directional antennas. In this paper, we study the scaling rules of the delay due to the multi-hop transmission in DIR networks. The primary research contributions of our paper are summarized as follows. We have analyzed the effective transmission range of DIR networks with consideration of various channels conditions, such as the path loss effect as well as the shadow fading effect. We have derived the capacity and the delay in DIR networks by constructing the routing scheme and the transmission scheme. We have compared our results with those derived under OMN networks. Compared with omni-directional antennas, directional antennas not only can significantly increase the network capacity but also can reduce the transmission delay. We have also found that the capacity incremental gain and the delay reduction gain of DIR networks over OMN networks heavily depend on the antenna beamwidth and the signal path loss factor. Details of our major findings will be presented in Section 1.2. 1.1 Definitions To present the major results, we give some models and definitions, which are necessary for presenting the major results. We will give the detailed models and the complete definitions in Section 3. We consider a static wireless network consisting of n nodes, which are randomly and uniformly distributed in a plane of unit area. In such network, each node can randomly choose its destination. We consider two types of networks in this paper: (i) an OMN networks, in which each node is equipped with a single omnidirectional antenna; (ii) a DIR networks, in which each node is equipped with a single directional antenna with the beamwidth . Details about the models of an omnidirectional antenna and a directional antenna can be found in Section 3.1. We have used the following asymptotic notations. (1) f (n) = O(g(n)) means that there exists a constant k and an integer N such that f (n) kg(n) for n > N . f (n) (2) f (n) = o(g(n)) implies that limn g(n) = 0. (3) f (n) = ( g(n)) means that g(n) = O(f (n)). (4) f (n) = (g(n)) means that g(n) = o(f (n)). (5) f (n) = ( g(n)) means that f (n) = O(g(n)) and g(n) = O(f (n)). We then define the feasible throughput and the delay of a packet due to the multi-hop routing. Definition 1. Feasible Throughput: A throughput of (n) bits per second for each node is feasible if every node can send (n) bits per second on average to its destination. The maximum feasible throughput is T (n) with high probability (w.h.p.c). Definition 2. Delay: The delay of a packet in a network is the time it takes the packet to get to the destination after it leaves the source. In this paper, we just consider the delay due to the routing. Thus, we ignore the queuing delay. We denote D(n) as the average packet delay for a network with n nodes. In a static network, the delay depends on the sum of the times spent at each relay. To counteract the dynamics of the network, we take a similar assumption [2,12], i.e., the service time (transmission delay) is always a constant. 1.2 Main results We summarize our major results and compare our results with OMN networks in Table 1. As shown in Table 1, compared with an OMN network, a DIR network has a capacity improvement 1 4 , which is always 2 4 2 tan2 greater than one since the beamw2idth usually < 2 . This implies that using directional antennas in wireless networks can significantly improve the network capacity. This capacity improvement mainly owes to the reduced interference by using directional antennas. Details about the analysis of the capacity improvement factor will be presented in Section 5.2. Table 1 also shows that a DIR network has a (...truncated)