Broadcasting in dense linear networks: To cooperate or not to cooperate?

Abstract

In this paper, the effectiveness of cooperative broadcast in high-density linear networks is studied. In the considered protocol, a single source sends messages continuously causing interference among messages and the goal is to reach to the entire network via cooperating relays. Sufficient conditions for successful broadcast are derived under two different transmission schemes: the unidirectional scheme and the bidirectional scheme. Our analysis shows that the broadcast behavior depends on the pathloss exponent γ and the type of transmission scheme even though the channel between two nodes are affected by small-scale fading. Unlike the noncooperative multihop broadcast, the cooperative broadcast propagates the message to the entire network successfully when γ ≤ 1 provided that network parameters satisfy certain conditions. Furthermore, for γ > 1, cooperative scheme becomes optimal under the bidirectional transmission when the information rate is below a threshold; however if the transmissions are unidirectional, noncooperative scheme becomes optimal. When compared with 2D networks, we demonstrate that the advantages of cooperative broadcast in linear networks are limited.

Introduction

Wireless communication is progressing at an accelerated speed. Anytime, anywhere connectivity is becoming a reality, and wireless networks are becoming increasingly dense. In this paper, we study large-scale, dense, and adhoc linear networks with the goal of broadcasting common messages. At first, it might look like large-scale networks have a chaotic dynamic behavior and are hard to analyze. However, thanks to tools from asymptotic analysis, we can model, simulate and analyze such networks and gain intuition about them.

Broadcasting in linear ad hoc networks have applications such as distributing sensor information in one-dimensional structures and communicating safety-related information in inter-vehicular networks. Ad hoc broadcasting schemes does not require any dedicated infrastructure such as cellular system; hence can be easily employed in any geographical region and weather condition. In most ad hoc networks, transmitting a message to the entire network may result in significant energy consumption or high number of transmissions. Rather than using conventional noncooperative multihop broadcast in ad hoc networks, many authors have proposed cooperative broadcast with a variety of low-complexity protocols [1], [2] and also coding strategies [3] to fully exploit spatial diversity and hence to improve capacity and the power efficiency. Cooperative broadcast is based on the key idea that nodes can combine multiple replicas of the same message transmitted by different transmitters that have overheard the message. The performance of cooperative broadcast and the advantages in high-density 2D ad hoc networks have been fully analyzed in [4], [5]. Motivated by these studies, we are interested to determine if these advantages are still valid in 1D high-density wireless ad hoc networks. Linear network models are used for various applications in vehicular networks including inter-vehicle communication systems [6], [7], [8], [9], [10], [11], highway traffic monitoring [12], safeguarding railway tracks [13], [14]. There are two strong motivations behind studying 1D networks: (i) 1D networks are of practical interest since 2D deployments maybe too costly; (ii) Wireless signals propagate in all dimensions (with an isotropic antenna); however, only one dimension is of interest when the topology is 1D. This creates a fundamentally different behavior in 1D compared to 2D networks.

Fig. 1c and d illustrate a linear network under two types of cooperative broadcast where the source node, colored red in Fig. 1, initiates transmission by broadcasting a message. In the proposed cooperative broadcasting scheme, after source’s transmission, the message is forwarded by a group of nodes simultaneously which is assumed to receive the message successfully. Then, the message is forwarded sequentially over different groups of nodes. If the message is received by the entire network, the broadcast is regarded as successful. We have analyzed the message propagation of this network in [15] under single-shot transmission, in which the source node broadcasts a single message over channels affected only by pathloss attenuation. In [15], a new message is sent by the source after the previous message flushed-out of the network. In this paper, we study a more general scenario in which the source node transmits different messages periodically improving the transmission rate while introducing inter-message interference when compared with single-shot scheme in [15]. We also incorporate small-scale fading into our channel model in addition to the pathloss exponent. Using the continuum approximation initially introduced in [16], we characterize the system behavior under two different transmission protocols; unidirectional transmission (Fig. 1c) and bidirectional transmission (Fig. 1d). Under each transmission protocol, we find the condition for successful propagation that depends on the pathloss exponent γ. Pathloss exponent is related to the type of wireless medium: for indoors/outdoors γ > 1, for underwater γ ≈ 1, and for metallic tunnels γ < 1. Unlike the non-cooperative multihop broadcast which dies off under continuous source transmission for γ ≤ 1 (discussed in Section 3), we demonstrate the possibility of successful cooperative broadcast for any value of γ. Furthermore, cooperative broadcast is shown to be more efficient than noncooperative multihop broadcast under bidirectional transmission for low information rates. Initial results of this work were published in [17].

Performance of linear wireless networks with multiple nodes has been studied for both unicast and broadcast scenarios. Many have shown that the broadcast performance depends on the pathloss exponent of the wireless medium γ [15], [16], [17], [18], [19], [20]. In [19], authors perform asymptotic analysis of extended cooperative 1D networks and show that the capability of nodes to broadcast strongly depends on the pathloss exponent of the channel γ. They also show that the probability that the entire network with any node density receives the message correctly, converges to zero for γ > 1, while it is strictly greater than zero for γ ≤ 1. In [15], we analyzed 1D high-density networks using the deterministic continuum model and unlike [19] we show that the message propagation is always successful for γ > 1 while it fails for γ ≤ 1 for certain value of network parameters. In [20], the authors find an upper bound on the maximum gain of cooperative broadcast in a linear network with the objective of reducing the total power consumption for pathloss exponent γ > 2. They prove that the gain of cooperation is bounded irrespective of the number of devices, the size of network and node placement strategy. In [21], authors introduce the concept of limiting the node participation in a decode-and-forward cooperative network for conserving the energy during transmissions in a 1D and 2D finite node-density network. All these works are based on single-shot transmission in which the source node does not transmit a new message until after the previous message flushed-out of the entire network.

Considering continuous source transmission, in which the source node transmits independent messages periodically, introduces interference in cooperative networks. Broadcast scheduling in order to avoid interference is actually a well-established approach, e.g. in [22], [23]. However, there is a common assumption in [22], [23]; that the transmission range is limited and hence interference beyond a fixed radius is negligible. Only the interference caused by the neighboring nodes or the neighboring cluster of nodes is usually considered. We should note that the aggregate interference of a large number of far transmitting nodes, especially in high-density networks, may significantly reduce SINR (signal-to interference-plus-noise-ratio) depending on the pathloss exponent. This fact is taken into account in [24] and accordingly a cross-layer design is proposed which includes two phases; a simple scheduling algorithm to eliminate strong levels of interference from the neighboring nodes and a distributed power control algorithm to find the optimal power vector for successful transmission. However, to limit the signal power, their approach reduces the received signal to only one signal transmitted by a single neighbor.

Obtaining analytical results for dense networks can be tedious due to the large number of parameters. In [16], the continuum analysis of dense networks was introduced for the first time and using continuum approach, cooperation protocols in 2D high-density networks have been extensively studied in [4], [5], [16], [25]. In these works, a phase transition was observed in the successful propagation of the packets to the entire network, which is dependent on the node transmit powers and the decoding threshold. Power efficiency of cooperation was studied in [25] using continuum model for 2D networks. Furthermore, in [5], the authors determine the upper and the lower bounds on the cooperative broadcast capacity in both high-density and extended networks.

In [26] , authors study the impact of the interference on cooperative broadcast using the continuum and deterministic channel assumptions. For the infinite 2D disk network, they show that the performance is limited when path loss exponent γ is 2, but for higher pathloss attenuations (γ > 2), they analytically show that the continuous transmission is feasible and derive the lower bound of the broadcast throughput. Similarly, in [27], the same authors study 2D strip networks [28] under continuous transmission. In these papers, throughput is defined as the rate at which packets cross a measurement boundary [29]. In [30], the authors study the impact of interference on cooperative broadcast in finite density networks and derive outage probability expression, whereas [26], [27] study dense networks.

In this paper, we formulate the aggregate interference of continuous transmission, yet with no scheduling limitations. Despite the presence of interference, we show that the cooperative broadcast can still succeed for any range of γ under certain conditions. This analysis does not consider the effect of interference from multiple sources with different broadcast messages.

The organization of the paper is as follows. In Section 2, the deterministic system model is presented. In Section 3, the network behavior is characterized under the continuous source transmission. In Section 4, the performance of cooperative broadcast is compared with that of non-cooperative multihop broadcast. In Section 5, we show that our analysis in Section 3 can be applied to systems where nodes experience small-scale fading in addition to pathloss attenuation. We conclude the paper in Section 6.