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.
The best-known metric for studying end-to-end network capacity is the transport capacity @cite_14 @cite_31 @cite_4 . This framework pioneered many notable studies on the limiting scaling behavior of ad hoc networks with the number of nodes @math by showing that the maximum transport capacity scales as @math in arbitrary networks @cite_14 . The feasibility of this throughput scaling has also been shown in random networks by relaying all information via crossing paths constructed through the network @cite_21 . Several other researchers have extended this framework to more general operating regimes, e.g. @cite_16 @cite_13 . Their findings have shown that nearest neighbor multihop routing is order-optimal in the power-limited regime, while hopping across clusters with distributed multiple-input and multiple-output (MIMO) communication can achieve order-optimal throughput in bandwidth-limited and power-inefficient regimes. However, most of these results are shown and proven for asymptotically large networks, which may not accurately describe non-asymptotic conditions. Moreover, scaling laws do not provide much information on how other network parameters imposed by a specific transmission strategy affect the throughput.
@cite_14 @cite_4 @cite_21 @cite_31 @cite_16 @cite_13
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We determine the asymptotic scaling for the per user throughput in a large hybrid ad hoc network, i.e., a network with both ad hoc nodes, which communicate with each other via shared wireless links of capacity W bits s, and infrastructure nodes which in addition are interconnected with each other via high capacity links. Specifically, we consider a network model where ad hoc nodes are randomly spatially distributed and choose to communicate with a random destination. We identify three scaling regimes, depending on the growth of the number of infrastructure nodes, m relative to the number of ad hoc nodes n, and show the asymptotic scaling for the per user throughput as n becomes large. We show that when m spl lsim spl radic n logn the per user throughput is of order W spl radic n log n and could be realized by allowing only ad hoc communications, i.e., not deploying the infrastructure nodes at all. Whenever spl radic n log n spl lsim m spl lsim n log n, the order for the per user throughput is Wm n and, thus, the total additional bandwidth provided by m infrastructure nodes is effectively shared among ad hoc nodes. Finally, whenever m spl gsim n log n, the order of the per user throughput is only W log n, suggesting that further investments in infrastructure nodes will not lead to improvement in throughput. The results are shown through an upper bound which is independent of the routing strategy, and by constructing scenarios showing that the upper bound is asymptotically tight. We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful end-to-end transmissions, multiplied by the communication distance, and normalized by the network area. We show that a simple upper bound on this quantity is computable in closed-form in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops and optimal per hop success probability and show that our result follows the well-known square root scaling law while providing exact expressions for the preconstants, which contain most of the design-relevant network parameters. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability. Scaling results for the sum capacity of the multiple access, uplink channel are provided for a flat-fading environment, with multiple-input-multiple-output (MIMO) links, when there is interference from other cells. The classical MIMO scaling regime is considered in which the number of antennas per user and per base station grow large together. Utilizing the known characterizations of the limiting eigenvalue distributions of large random matrices, the asymptotic behavior of the sum capacity of the system is characterized for an architecture in which the base stations cooperate in the joint decoding process of all users (macrodiversity). This asymptotic sum capacity is compared with that of the conventional scenario in which the base stations only decode the users in their cells. For the case of base station cooperation, an interesting "resource pooling" phenomenon is observed: in some cases, the limiting performance of a macrodiversity multiuser network has the same asymptotic behavior as that of a single-user MIMO link with an equivalent amount of pooled received power. This resource pooling phenomenon allows us to derive an elegant closed-form expression for the sum capacity of a new version of Wyner's classical model of a cellular network, in which MIMO links are incorporated into the model. In this paper, we study the asymptotic throughput capacity of a static multi-channel multi-interface infrastructure wireless mesh network (InfWMN) wherein each infrastructure node has m interfaces and c channels of unequal bandwidth are available. First, an upper bound on the InfWMN per-user capacity is established. Then, the feasible lower bound is derived by construction. We prove that both lower and upper bounds are tight. We limit our analysis for more practical case of @math . However, for the asymptotic upper bound, our analysis can be used for the general case in which there is no constraint on m and c. Our study shows that in such a network with Nc randomly distributed mesh clients, Nr regularly placed mesh routers, and Ng gateways, the asymptotic per-client throughput capacity has different bounds, which depend on the ratio between the total available bandwidth for the network and the sum of m first greatest data rates of c available channels, i.e., @math . The results of this paper are more general compared to the existing published researches. In addition, in the case that @math , our results reduce to the previously reported studies. This implies that our study is comprehensive compared to the formerly published researches.