Broadcast is a fundamental network operation, widely used in wireless networks to disseminate messages. The energy-efficiency of broadcast is important particularly when devices in the network are energy constrained. To improve the efficiency of broadcast, different approaches have been taken in the literature. One of these approaches is broadcast with energy accumulation. Through simulations, it has been shown in the literature that broadcast with energy accumulation can result in energy saving. The amount of this saving, however, has only been analyzed for linear multi-hop wireless networks. In this work, we extend this analysis to two-dimensional (2D) multi-hop networks. The analysis of saving in 2D networks is much more challenging than that in linear networks. It is because, unlike in linear networks, in 2D networks, finding minimum-energy broadcasts with or without energy accumulation are both NP-hard problems. Nevertheless, using a novel approach, we prove that this saving is constant when the path loss exponent alpha is strictly greater than two. Also, we prove that the saving is theta(log n) when alpha=2, where n denotes the number of nodes in the network.
We formulate the problem of delay constrained energy-efficient broadcast in cooperative multihop wireless networks. We show that this important problem is not only NP-complete, but also o(log(n)) inapproximable. We derive approximation results and an analytical lower-bound for this problem. We break this NP hard problem into three parts: ordering, scheduling and power control. We show that when the ordering is given, the joint scheduling and power-control problem can be solved in polynomial time by a novel algorithm that combines dynamic programming and linear programming to yield the minimum energy broadcast for a given delay constraint. We further show empirically that this algorithm used in conjunction with an ordering derived heuristically using the Dijkstra's shortest path algorithm yields near-optimal performance in typical settings. We use our algorithm to study numerically the trade-off between delay and power-efficiency in cooperative broadcast and compare the performance of our cooperative algorithm with a smart non-cooperative algorithm. Cooperative broadcast aims to deliver a source message to a locally connected network by means of collaborating nodes. In traditional architectures, node cooperation has been at the network layer. Recently, physical layer cooperative schemes have been shown to offer several advantages over the network layer approaches. This form of cooperation employs distributed transmission resources at the physical layer as a single radio with spatial diversity. In decentralized cooperation schemes, collaborating nodes make transmission decisions based on the quality of the received signal, which is the only parameter available locally. In this case, critical parameters that influence the broadcast performance include the source relay transmission powers and the decoding threshold (the minimum signal-to-noise ratio (SNR) required to decode a transmission). We study the effect of these parameters on the number of nodes reached by cooperative broadcast. In particular, we show that there exists a phase transition in the network behavior: if the decoding threshold is below a critical value, the message is delivered to the whole network. Otherwise, only a fraction of the nodes is reached, which is proportional to the source transmit power. Our approach is based on the idea of continuum approximation, which yields closed-form expressions that are accurate when the network density is high. 