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 node locations are modeled as a homogeneous Poisson point process (HPPP), a number of results can be applied from stochastic geometry, e.g. @cite_30 @cite_5 , in particular to compute outage probability relative to a signal-to-interference-plus-noise ratio (SINR) threshold. These expressions can be inverted to give the maximum transmit intensity at a specified outage probability, which yields the transmission capacity of the network @cite_32 . This framework provides the maximum number of successful transmission the network can support while simultaneously meeting a network-wide QoS requirement. This framework allows closed-form expressions of achievable throughput to be derived in non-asymptotic regimes, which are useful in examining how various communication technique, channel models, and design parameters affect the aggregate throughput, e.g. @cite_1 @cite_26 @cite_20 @cite_11 @cite_27 @cite_25 @cite_29 @cite_28 ; see @cite_8 for a summary. While the transmission capacity can often be expressed in closed-form without resorting to asymptotics, it is a single-hop or snapshot'' metric. Recent work @cite_9 @cite_12 began to investigate the throughput scaling with two-hop opportunistic relay selection under different channel gain distribution and relay deployment. However, more general multi-hop capacity has not proven tractable.
@cite_30 @cite_12 @cite_26 @cite_8 @cite_28 @cite_29 @cite_9 @cite_1 @cite_32 @cite_27 @cite_5 @cite_25 @cite_20 @cite_11
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This paper addresses three issues in the field of ad hoc network capacity: the impact of (i) channel fading, (ii) channel inversion power control, and (iii) threshold-based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state information (CSI) without requiring cooperation across transmitters. We use the transmission capacity (TC) as our metric, defined as the maximum spatial intensity of successful simultaneous transmissions subject to a constraint on the outage probability (OP). By assuming the nodes are located on the infinite plane according to a Poisson process, we are able to employ tools from stochastic geometry to obtain asymptotically tight bounds on the distribution of the signal-to-interference (SIR) level, yielding in turn tight bounds on the OP (relative to a given SIR threshold) and the TC. We demonstrate that in the absence of CSI, fading can significantly reduce the TC and somewhat surprisingly, channel inversion only makes matters worse. We develop a threshold-based transmission rule where transmitters are active only if the channel to their receiver is acceptably strong, obtain expressions for the optimal threshold, and show that this simple, fully distributed scheme can significantly reduce the effect of fading. In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson cluster process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell-Mecke theorem. 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. We consider transmission of packets in two-hop wireless ad hoc networks in which relay nodes are deployed between the source-destination pairs. Based on results from extreme value theory and product tails, we derive throughput scaling laws when opportunistic relay selection is performed. Assuming partial channel state information at each transmitter (CSIT) and decode- and-forward, half-duplex relays, we investigate how the per-hop throughput depends on the channel gain asymptotic distribution and the relay deployment. In dense networks with lambda t nodes per m 2 and fixed relay distances, we provide specific scaling laws for Rayleigh, lognormal, and Weibull fading, showing that the throughput is upper bounded by thetas(radic(lambda t )). Interestingly, with variable relay distances and location-aware relay selection, we analytically show that regularly varying channel distributions result in enhanced multi-relay diversity gain, achieving linear throughput scaling thetas(radic(lambda t )).