This paper develops upper bounds on the end-to-end transmission capacity of multihop wireless networks. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form lower bound on the outage probability is derived in terms of the expected number of potential paths. This is in turn used to provide an upper bound on the number of successful transmissions that can occur per unit area, which is known as the transmission capacity. The upper bound results from assuming independence among the potential paths, and can be viewed as the maximum diversity case. A useful aspect of the upper bound is its simple form for an arbitrary-sized network, which allows insights into how the number of hops and other network parameters affect spatial throughput in the nonasymptotic regime. The outage probability analysis is then extended to account for retransmissions with a maximum number of allowed attempts. In contrast to prevailing wisdom, we show that predetermined routing (such as nearest neighbor) is suboptimal, since more hops are not useful once the network is interference-limited. Our results also make clear that randomness in the location of relay sets and dynamically varying channel states is helpful in obtaining higher aggregate throughput, and that dynamic route selection should be used to exploit path diversity.
If several other strong assumptions are made, e.g. that all relays are placed equi-distant on a straight line and all outages are independent, then closed-form multi-hop transmission capacity can be derived @cite_22 . Stamatiou @cite_6 also investigated multihop routing in a Poisson spatial model, whose focus is to characterize the end-to-end delay and stability, again based on predetermined routes. Other recent works analyzing the throughput of multihop networks using stochastic geometric tools include @cite_0 , which extended @cite_22 to non-slotted ALOHA and @cite_23 , which also adopted a similar framework to @cite_23 to study the throughput-delay-reliability tradeoff with an ARQ protocol, and didn't require all hops to be equidistant. However, all of these used predetermined routing selection. In fact, the outage of a predetermined route does not preclude the possibility of successful communication over other routes. Separately, multihop capacity has also been studied in a line network without explicitly considering additional interference @cite_24 @cite_17 . This approach is helpful in comparing the impact of additional hops in bandwidth and power-limited networks, but fails to account for the interference inherent in a large wireless network.
@cite_22 @cite_6 @cite_0 @cite_24 @cite_23 @cite_17
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This paper presents the evaluation of the multi-hop aggregate information efficiency of the slotted and unslotted ALOHA protocols. We consider a multi-hop wireless network where the nodes are spatially characterized by a Poisson point process and the traffic generation also follows a Poisson distribution. By applying the properties of stochastic geometry, we derive a closed-form lower bound on the outage probability as a function of the required communication rate, the single-hop distance, the number of hops and the maximum number of retransmissions. The results indicate that slotted ALOHA always outperforms its unslotted version, demonstrating the importance of synchronization in distributed networks. In addition, we show that it is always possible to optimize the network efficiency by properly setting the required rate for a given packet density. Finally, in the scenario considered, the use of retransmissions and multiple hops never achieves the best performance if compared to the option of single-hop links without retransmissions. We evaluate the end-to-end delay of a multihop transmission scheme that includes a source, a number of relays, and a destination, in the presence of interferers located according to a Poisson point process. The medium access control (MAC) protocol considered is a combination of TDMA and ALOHA, according to which nodes located a certain number of hops apart are allowed to transmit with a certain probability. Based on an independent transmissions assumption, which decouples the queue evolutions, our analysis provides explicit expressions for the mean end-to-end delay and throughput, as well as scaling laws when the interferer density grows to infinity. If the source always has packets to transmit, we find that full spatial reuse, i.e., ALOHA, is asymptotically delay-optimal, but requires more hops than a TDMA-ALOHA protocol. The results of our analysis have applications in delay-minimizing joint MAC routing algorithms for networks with randomly located nodes.We simulate a network where sources and relays form a Poisson point process, and each source assembles a route to its destination by selecting the relays closest to the optimal locations. We assess both theoretically and via simulation the sensitivity of the end-to-end delay with respect to imperfect relay placements and route crossings. The goal of this paper is to establish which practical routing schemes for wireless networks are most suitable for power-limited and bandwidth-limited communication regimes. We regard channel state information (CSI) at the receiver and point-to-point capacity-achieving codes for the additive white Gaussian noise (AWGN) channel as practical features, interference cancellation (IC) as possible, but less practical, and synchronous cooperation (CSI at the transmitters) as impractical. We consider a communication network with a single source node, a single destination node, and N-1 intermediate nodes placed equidistantly on a line between them. We analyze the minimum total transmit power needed to achieve a desired end-to-end rate for several schemes and demonstrate that multihop communication with spatial reuse performs very well in the power-limited regime, even without IC. However, within a class of schemes not performing IC, single-hop transmission (directly from source to destination) is more suitable for the bandwidth-limited regime, especially when higher spectral efficiencies are required. At such higher spectral efficiencies, the gap between single-hop and multihop can be closed by employing IC, and we present a scheme based upon backward decoding that can remove all interference from the multihop system with an arbitrarily small rate loss. This new scheme is also used to demonstrate that rates of O(log N) are achievable over linear wireless networks even without synchronous cooperation. We consider a network where each route comprises a backlogged source, a number of relays and a destination at a finite distance. The locations of the sources and the relays are realizations of independent Poisson point processes. Given that the nodes observe a TDMA ALOHA MAC protocol, our objective is to determine the number of relays and their placement such that the mean end-to-end delay in a typical route of the network is minimized.We first study an idealistic network model where all routes have the same number of hops, the same distance per hop and their own dedicated relays. Combining tools from queueing theory and stochastic geometry, we provide a precise characterization of the mean end-to-end delay. We find that the delay is minimized if the first hop is much longer than the remaining hops and that the optimal number of hops scales sublinearly with the source-destination distance. Simulating the original network scenario reveals that the analytical results are accurate, provided that the density of the relay process is sufficiently large. We conclude that, given the considered MAC protocol, our analysis provides a delay-minimizing routing strategy for random, multihop networks involving a small number of hops.