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.
Existing energy accumulation based cooperative broadcast algorithms fall into two groups. The first group includes algorithms (e.g., @cite_0 @cite_35 ) in which receiving nodes can combine signals from all previous transmissions to benefit from transmission diversity. These algorithms are called cooperative broadcast algorithms with memory. The other group includes memoryless'' cooperative broadcast algorithms such as the one proposed in @cite_30 . In these algorithms, a node can only use transmissions in the present time slot to accumulate energy; Signals received from transmissions in previous time slots are discarded. Our work studies cooperative broadcast algorithms with memory as they fully benefit from the energy accumulation. As the result, our derived upper bounds on the cooperation gain also apply to the memoryless'' cooperative broadcast algorithms.
@cite_0 @cite_35 @cite_30
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Broadcasting is a method that allows the distributed nodes in a wireless sensor network to share its data efficiently among each other. Due to the limited energy supplies of a sensor node, energy efficiency has become a crucial issue in the design of broadcasting protocols. In this paper, we analyze the energy savings provided by a cooperative form of broadcast, called the opportunistic large arrays (OLA), and compare it to the performance of conventional multi-hop networks where no cooperation is utilized for transmission. The cooperation in OLA allows the receivers to utilize for detection the accumulation of signal energy provided by the transmitters that are relaying the same symbol. In this work, we derive the optimal energy allocation policy that minimizes the total energy cost of the OLA network subject to the SNR (or BER) requirements at all receivers. Even though the cooperative broadcast protocol provides significant energy savings, we prove that the optimum energy assignment for cooperative networks is an NP-complete problem and, thus, requires high computational complexity in general. We then introduce several suboptimal yet scalable solutions and show the significant energy-savings that one can obtain even with the approximate solutions A fundamental problem in large scale wireless networks is the energy efficient broadcast of source messages to the whole network. The energy consumption increases as the network size grows, and the optimization of broadcast efficiency becomes more important. In this paper, we study the optimal power allocation problem for cooperative broadcast in dense large-scale networks. In the considered cooperation protocol, a single source initiates the transmission and the rest of the nodes retransmit the source message if they have decoded it reliably. Each node is allocated an-orthogonal channel and the nodes improve their receive signal-to-noise ratio (SNR), hence the energy efficiency, by maximal-ratio combining the receptions of the same packet from different transmitters. We assume that the decoding of the source message is correct as long as the receive SNR exceeds a predetermined threshold. Under the optimal cooperative broadcasting, the transmission order (i.e., the schedule) and the transmission powers of the source and the relays are designed so that every node receives the source message reliably and the total power consumption is minimized. In general, finding the best scheduling in cooperative broadcast is known to be an NP-complete problem. In this paper, we show that the optimal scheduling problem can be solved for dense networks, which we approximate as a continuum of nodes. Under the continuum model, we derive the optimal scheduling and the optimal power density. Furthermore, we propose low-complexity, distributed and power efficient broadcasting schemes and compare their power consumptions with those-of-a traditional noncooperative multihop transmission. 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.