This paper addresses the following question, which is of interest in the design of a multiuser decentralized network. Given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W/N should the band be partitioned into in order to maximize the number of simultaneous links in the network? Dividing the available spectrum results in two competing effects. On the positive side, a larger N allows for more parallel, non-interfering communications to take place in the same area. On the negative side, a larger N increases the SINR requirement for each link because the same information rate must be achieved over less bandwidth, which in turn increases the area consumed by each transmission. Exploring this tradeoff and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, the optimal SINR threshold – which directly corresponds to the optimal spectral efficiency – is derived for both the low SNR (power-limited) and high SNR (interference-limited) regimes. This leads to the optimum choice of the number of frequency bands N in terms of the path loss exponent, power and noise spectral density, desired rate, and total bandwidth. I.

We propose and analyze a new paradigm for power control in decentralized wireless networks, termed fractional power control. Transmission power is chosen as the current channel quality raised to an exponent −s, where s is a constant between 0 and 1. Choosing s = 1 and s = 0 correspond to the familiar cases of channel inversion and constant power transmission, respectively. Choosing s ∈ (0, 1) allows all intermediate policies between these two extremes to be evaluated, and we see that neither extreme is ideal. We prove that using an exponent of s ∗ = 1 2 optimizes the transmission capacity of an ad hoc network, meaning that the inverse square root of the channel strength is the optimal transmit power scaling. Intuitively, this choice achieves the optimal balance between helping disadvantaged users while making sure they do not flood the network with interference. I.

A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the throughput over the selection of active links. By deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading (i) the maximum throughput scales like log n (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a decentralized link activation strategy is proposed and analyzed.

The subject of this paper is the long-standing open problem of developing a general capacity theory for wireless networks, particularly a theory capable of describing the fundamental performance limits of mobile ad hoc networks (MANETs). A MANET is a peer-to-peer network with no pre-existing infrastructure. MANETs are the most general wireless networks, with single-hop, relay, interference, mesh, and star networks comprising special cases. The lack of a MANET capacity theory has stunted the development and commercialization of many types of wireless networks, including emergency, military, sensor, and community mesh networks. Information theory, which has been vital for links and centralized networks, has not been successfully applied to decentralized wireless networks. Even if this was accomplished, for such a theory to truly characterize the limits of deployed MANETs it must overcome three key roadblocks. First, most current capacity results rely on the allowance of unbounded delay and reliability. Second, spatial and timescale decompositions have not yet been developed for optimally modeling the spatial and temporal dynamics of wireless networks. Third, a useful network capacity theory must integrate rather than ignore the important role of overhead messaging and feedback. This paper describes some of the shifts in thinking that may be needed to overcome these roadblocks and

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Abstract — The multihop spatial reuse Aloha (MSR-Aloha) protocol was recently introduced by Baccelli et al., where each transmitter selects the receiver among its feasible next hops that maximizes the forward progress of the head of line packet towards its final destination. They identify the optimal medium access probability (MAP) that maximizes the spatial density of progress, defined as the product of the spatial intensity of attempted transmissions times the average per-hop progress of each packet towards its destination. We propose a variant called longest edge routing where each transmitter selects its longest feasible edge, and then identifies a packet in its backlog whose next hop is the associated receiver. The main contribution of this work (and of Baccelli et al.) is the use of stochastic geometry to identify the optimal MAP and the corresponding optimal spatial density of progress. I.

Abstract—This paper studies a cognitive network where licensed primary users and unlicensed but ‘cognitive ’ secondary users share spectrum. Many system design parameters affect the joint performance, e.g., outage and capacity, seen by the two user types in such a scenario. We explore the sometimes subtle system tradeoffs that arise in such networks. To that end, we propose a new simple stochastic geometric model that captures the salient interdependencies amongst spatially distributed primary and secondary nodes. The model allows us to evaluate the performance dependencies between primary and secondary transmissions in terms of the outage probability, node density and transmission capacity. From the design perspective the key design parameters determining the joint transmission capacity and tradeoffs, are the detection radius (detection SINR threshold), decoding SINR threshold, burstiness of coverage and/or transmit powers. We show how the joint transmission capacity region can be optimized or affected by these parameters. Index Terms—cognitive network, stochastic geometry, network information theory, transmission capacity I.

This paper considers the performance of the ALOHA and CSMA MAC protocols in wireless ad hoc networks in the presence of fading. Increasing the rate of successful reception of packets is our objective, and thus, outage probability is used as the performance evaluation metric. In our network model, packets belonging to specific transmitters arrive randomly in space and time according to a 3-D Poisson point process, and are then transmitted to their intended destinations using a fully-distributed MAC protocol. A packet transmission is considered successful if the received SINR is above a predefined threshold for the duration of the packet. Approximate expressions are derived for the outage probability of ALOHA and the different flavors of CSMA, namely CSMA with transmitter sensing, receiver sensing, and joint transmitter-receiver sensing. The introduction of fading adds to the hidden and exposed node problems of CSMA, resulting in an up to 75 % increase in the outage probability. Interestingly, however, the relative difference between the protocols remains unchanged. 1.

Abstract — 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 ad hoc 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. I.

An overview of the transmission capacity of