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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An Aloha-type access control mechanism for large mobile, multihop, wireless networks is defined and analyzed. This access scheme is designed for the multihop context, where it is important to find a compromise between the spatial density of communications and the range of each transmission. More precisely, the analysis aims at optimizing the product of the number of simultaneously successful transmissions per unit of space (spatial reuse) by the average range of each transmission. The optimization is obtained via an averaging over all Poisson configurations for the location of interfering mobiles, where an exact evaluation of signal over noise ratio is possible. The main mathematical tools stem from stochastic geometry and are spatial versions of the so-called additive and max shot noise processes. The resulting medium access control (MAC) protocol exhibits some interesting properties. First, it can be implemented in a decentralized way provided some local geographic information is available to the mobiles. In addition, its transport capacity is proportional to the square root of the density of mobiles which is the upper bound of Gupta and Kumar. Finally, this protocol is self-adapting to the node density and it does not require prior knowledge of this density. We consider a time-slotted two-hop wireless system in which the sources transmit to the relays in the even time slots (first hop) and the relays forward the packets to the destinations in the odd time slots (second hop). Each source may connect to multiple relays in the first hop. In the presence of interference and without tight coordination of the relays, it is not clear which relays should transmit the packet. We propose four decentralized methods of relay selection, some based on location information and others based on the received signal strength (RSS).We provide a complete analytical characterization of these methods using tools from stochastic geometry. We use simulation results to compare these methods in terms of end-to-end success probability. The transmission capacity (TC) of a wireless ad hoc network is defined as the maximum spatial intensity of successful transmissions such that the outage probability does not exceed some specified threshold. This work studies the improvement in TC obtainable with successive interference cancellation (SIC), an important receiver technique that has been shown to achieve the capacity of several classes of multiuser channels, but has not been carefully evaluated in the context of ad hoc wireless networks. This paper develops closed-form upper bounds and easily computable lower bounds for the TC of ad hoc networks with SIC receivers, for both perfect and imperfect SIC. The analysis applies to any multiuser receiver that cancels the K strongest interfering signals by a factor z isin [0, 1]. In addition to providing the first closed-form capacity results for SIC in ad hoc networks, design-relevant insights are made possible. In particular, it is shown that SIC should be used with direct sequence spread spectrum. Also, any imperfections in the interference cancellation rapidly degrade its usefulness. More encouragingly, only a few - often just one - interfering nodes need to be canceled in order to get the vast majority of the available performance gain. This paper surveys and unifies a number of recent contributions that have collectively developed a metric for decentralized wireless network analysis known as transmission capacity. Although it is notoriously difficult to derive general end-to-end capacity results for multi-terminal or adhoc networks, the transmission capacity (TC) framework allows for quantification of achievable single-hop rates by focusing on a simplified physical MAC-layer model. By using stochastic geometry to quantify the multi-user interference in the network, the relationship between the optimal spatial density and success probability of transmissions in the network can be determined, and expressed-often fairly simply-in terms of the key network parameters. The basic model and analytical tools are first discussed and applied to a simple network with path loss only and we present tight upper and lower bounds on transmission capacity (via lower and upper bounds on outage probability). We then introduce random channels (fading shadowing) and give TC and outage approximations for an arbitrary channel distribution, as well as exact results for the special cases of Rayleigh and Nakagami fading. We then apply these results to show how TC can be used to better understand scheduling, power control, and the deployment of multiple antennas in a decentralized network. The paper closes by discussing shortcomings in the model as well as future research directions. Spectrum sharing between wireless networks improves the efficiency of spectrum usage, and thereby alleviates spectrum scarcity due to growing demands for wireless broadband access. To improve the usual underutilization of the cellular uplink spectrum, this paper addresses spectrum sharing between a cellular uplink and a mobile ad hoc networks. These networks access either all frequency subchannels or their disjoint subsets, called spectrum underlay and spectrum overlay, respectively. Given these spectrum sharing methods, the capacity trade-off between the coexisting networks is analyzed based on the transmission capacity of a network with Poisson distributed transmitters. This metric is defined as the maximum density of transmitters subject to an outage constraint for a given signal-to-interference ratio (SIR). Using tools from stochastic geometry, the transmission-capacity trade-off between the coexisting networks is analyzed, where both spectrum overlay and underlay as well as successive interference cancellation (SIC) are considered. In particular, for small target outage probability, the transmission capacities of the coexisting networks are proved to satisfy a linear equation, whose coefficients depend on the spectrum sharing method and whether SIC is applied. This linear equation shows that spectrum overlay is more efficient than spectrum underlay. Furthermore, this result also provides insight into the effects of network parameters on transmission capacities, including link diversity gains, transmission distances, and the base station density. In particular, SIC is shown to increase the transmission capacities of both coexisting networks by a linear factor, which depends on the interference-power threshold for qualifying canceled interferers. We study the transmission capacities of two coexisting wireless networks (a primary network vs. a secondary network) that operate in the same geographic region and share the same spectrum. We define transmission capacity as the product among the density of transmissions, the transmission rate, and the successful transmission probability (1 minus the outage probability). The primary (PR) network has a higher priority to access the spectrum without particular considerations for the secondary (SR) network, where the SR network limits its interference to the PR network by carefully controlling the density of its transmitters. Assuming that the nodes are distributed according to Poisson point processes and the two networks use different transmission ranges, we quantify the transmission capacities for both of these two networks and discuss their tradeoff based on asymptotic analysis. Our results show that if the PR network permits a small increase of its outage probability, the sum transmission capacity of the two networks (i.e., the overall spectrum efficiency per unit area) will be boosted significantly over that of a single network. 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 )). 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 this paper, upper and lower bounds on the transmission capacity of spread-spectrum (SS) wireless ad hoc networks are derived. We define transmission capacity as the product of the maximum density of successful transmissions multiplied by their data rate, given an outage constraint. Assuming that the nodes are randomly distributed in space according to a Poisson point process, we derive upper and lower bounds for frequency hopping (FH-CDMA) and direct sequence (DS-CDMA) SS networks, which incorporate traditional modulation types (no spreading) as a special case. These bounds cleanly summarize how ad hoc network capacity is affected by the outage probability, spreading factor, transmission power, target signal-to-noise ratio (SNR), and other system parameters. Using these bounds, it can be shown that FH-CDMA obtains a higher transmission capacity than DS-CDMA on the order of M sup 1-2 spl alpha , where M is the spreading factor and spl alpha >2 is the path loss exponent. A tangential contribution is an (apparently) novel technique for obtaining tight bounds on tail probabilities of additive functionals of homogeneous Poisson point processes. This paper derives the outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques, for a general class of signal distributions. This analysis allows system performance to be quantified for fading or non-fading environments. The transmission capacity is given for interference-limited uniformly random networks on the entire plane with path loss exponent alpha > 2 in which nodes use: (1) static beamforming through M sectorized antennas, for which the increase in transmission capacity is shown to be thetas(M2) if the antennas are without sidelobes, but less in the event of a nonzero sidelobe level; (2) dynamic eigenbeamforming (maximal ratio transmission combining), in which the increase is shown to be thetas(M 2 alpha ); (3) various transmit antenna selection and receive antenna selection combining schemes, which give appreciable but rapidly diminishing gains; and (4) orthogonal space-time block coding, for which there is only a small gain due to channel hardening, equivalent to Nakagami-m fading for increasing m. It is concluded that in ad hoc networks, static and dynamic beamforming perform best, selection combining performs well but with rapidly diminishing returns with added antennas, and that space-time block coding offers only marginal gains. Preface. Preface to Volume II. Contents of Volume II. Part IV Medium Access Control 1 Spatial Aloha: the Bipole Model 2 Receiver Selection in Spatial 3 Carrier Sense Multiple 4 Code Division Multiple Access in Cellular Networks Bibliographical Notes on Part IV. Part V Multihop Routing in Mobile ad Hoc Networks: 5 Optimal Routing 6 Greedy Routing 7 Time-Space Routing Bibliographical Notes on Part V. Part VI Appendix:Wireless Protocols and Architectures: 8 RadioWave Propagation 9 Signal Detection 10 Wireless Network Architectures and Protocols Bibliographical Notes on Part VI Bibliography Table of Notation Index. The transmission capacity of an ad-hoc network is the maximum density of active transmitters in an unit area, given an outage constraint at each receiver for a fixed rate of transmission. Assuming channel state information is available at the receiver, this paper presents bounds on the transmission capacity as a function of the number of antennas used for transmission, and the spatial receive degrees of freedom used for interference cancelation at the receiver. Canceling the strongest interferers, using a single antenna for transmission together with using all but one spatial receive degrees of freedom for interference cancelation is shown to maximize the transmission capacity. Canceling the closest interferers, using a single antenna for transmission together with using a fraction of the total spatial receive degrees of freedom for interference cancelation depending on the path loss exponent, is shown to maximize the transmission capacity. Multicast transmission, wherein the same packet must be delivered to multiple receivers, is an important aspect of sensor and tactical networks and has several distinctive traits as opposed to more commonly studied unicast networks. Specially, these include 1) identical packets must be delivered successfully to several nodes, 2) outage at any receiver requires the packet to be retransmitted at least to that receiver, and 3) the multicast rate is dominated by the receiver with the weakest link in order to minimize outage and retransmission. A first contribution of this paper is the development of a tractable multicast model and throughput metric that captures each of these key traits in a multicast wireless network. We utilize a Poisson cluster process (PCP) consisting of a distinct Poisson point process (PPP) for the transmitters and receivers, and then define the multicast transmission capacity (MTC) as the maximum achievable multicast rate per transmission attempt times the maximum intensity of multicast clusters under decoding delay and multicast outage constraints. A multicast cluster is a contiguous area over which a packet is multicasted, and to reduce outage it can be tessellated into v smaller regions of multicast. The second contribution of the paper is the analysis of several key aspects of this model, for which we develop the following main result. Assuming τ v transmission attempts are allowed for each tessellated region in a multicast cluster, we show that the MTC is Θ(ρkxlog(k)vy) where ρ, x and y are functions of τ and v depending on the network size and intensity, and k is the average number of the intended receivers in a cluster. We derive ρ, x, y for a number of regimes of interest, and also show that an appropriate number of retransmissions can significantly enhance the MTC. The performance benefits of two interference cancellation methods, successive interference cancellation (SIC) and joint detection (JD), in wireless ad hoc networks are compared within the transmission capacity framework. SIC involves successively decoding and subtracting out strong interfering signals until the desired signal can be decoded, while higher-complexity JD refers to simultaneously decoding the desired signal and the signals of a few strong interferers. Tools from stochastic geometry are used to develop bounds on the outage probability as a function of the spatial density of interferers. These bounds show that SIC performs nearly as well as JD when the signal-to-interference ratio (SIR) threshold is less than one, but that SIC is essentially useless for SIR thresholds larger than one whereas JD provides a significant outage benefit regardless of the SIR threshold.