This paper studies the asymptotic properties of average area spectral efficiency (ASE) of a downlink cellular network in the limit of very dense base station (BS) and user densities. This asymptotic analysis relies on three assumptions: 1) interference is treated as noise; 2) the BS locations are drawn from a Poisson point process; and 3) the path loss function is bounded above satisfying mild regularity conditions. We consider three possible definitions of the average ASE, all of which give units of bits per second per unit bandwidth per unit area. When there is no constraint on the minimum operational signal-to-interference-plus-noise ratio (SINR) and instantaneous full channel state information (CSI) is available at the transmitter, the average ASE is proven to saturate to a constant, which we derive in a closed form. For the other two ASE definitions, wherein either a minimum SINR is enforced or CSI is not available, the average ASE is instead shown to collapse to zero at high BS density. We provide several familiar case studies for the class of considered path loss models, and demonstrate that our results cover most previous models and results on ultradense networks as special cases.
The study of dense wireless network capacity has a rich history, in particular for the case of ad hoc multihop networks. The seminal result of Gupta and Kumar @cite_47 showed that the transport capacity of an infrastructure-less network increases with the number of nodes @math roughly as @math , assuming a given node wishes to transmit with a randomly selected other node. Many subsequent results extended this scaling law'' approach to a wide variety of models and communication techniques, well summarized in @cite_28 . A main intuition from these results is that the best network-wide throughput scaling is achieved by short-range local communication coupled with multi-hopping towards the intended receiver, a form of spatial reuse. A key subsequent paper showed that this square-root scaling is a fundamental property of the electromagnetic propagation @cite_0 , thus attempts to improve the scaling law through exotic communication strategies would be futile.
@cite_28 @cite_47 @cite_0
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We consider a wireless device-to-device (D2D) network in which the nodes are uniformly distributed at random over the network area and can cache information from a library of possible messages (files). Each node requests a file in the library independently at random, according to a given popularity distribution, and downloads from other nodes having the requested file in their local cache via multihop transmission. Under the classical “protocol model” of wireless ad hoc networks, we characterize the optimal throughput scaling law by presenting a feasible scheme formed by a decentralized caching policy for the parameter regimes of interest and a local multihop transmission protocol. The scaling law optimality of the proposed strategy is shown by deriving a new throughput upper bound. Surprisingly, we show that decentralized uniform random caching yields optimal scaling in most of the system interesting regimes. We also observe that caching improves the throughput scaling law of classical ad hoc networks, and that multihop improves the previously derived scaling law of caching wireless networks under one-hop transmission. This paper deals with throughput scaling laws for random ad hoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio lambda(n) of achievable network sum capacity to the sum of the point-to-point capacities of source-destinations (S-D) pairs operating in isolation. Our focus in this paper is on fixed signal-to-noise ratio (SNR) networks, i.e., networks where the worst case SNR over the S-D pairs is fixed independent of n. For such fixed SNR networks, which include fixed area networks as a special case, we show that collaborative strategies yield a scaling law of lambda(n)=Omega(1 n1 3) in contrast to multihop strategies which yield a scaling law of lambda(n)=Theta(1 radicn). While networks where worst case SNR goes to zero do not preclude the possibility of collaboration, multihop strategies achieve optimal throughput. The plausible reason is that the gains due to collaboration cannot offset the effect of vanishing receive SNR. This suggests that for fixed SNR networks, a network designer should look for network protocols that exploit collaboration We consider a wireless Device-to-Device (D2D) network where communication is restricted to be single-hop. Users make arbitrary requests from a finite library of files and have pre-cached information on their devices, subject to a per-node storage capacity constraint. A similar problem has already been considered in an infrastructure'' setting, where all users receive a common multicast (coded) message from a single omniscient server (e.g., a base station having all the files in the library) through a shared bottleneck link. In this work, we consider a D2D infrastructure-less'' version of the problem. We propose a caching strategy based on deterministic assignment of subpackets of the library files, and a coded delivery strategy where the users send linearly coded messages to each other in order to collectively satisfy their demands. We also consider a random caching strategy, which is more suitable to a fully decentralized implementation. Under certain conditions, both approaches can achieve the information theoretic outer bound within a constant multiplicative factor. In our previous work, we showed that a caching D2D wireless network with one-hop communication, random caching, and uncoded delivery, achieves the same throughput scaling law of the infrastructure-based coded multicasting scheme, in the regime of large number of users and files in the library. This shows that the spatial reuse gain of the D2D network is order-equivalent to the coded multicasting gain of single base station transmission. It is therefore natural to ask whether these two gains are cumulative, i.e.,if a D2D network with both local communication (spatial reuse) and coded multicasting can provide an improved scaling law. Somewhat counterintuitively, we show that these gains do not cumulate (in terms of throughput scaling law). In this paper we study the capacity of wireless ad hoc networks with infrastructure support of an overlay of wired base stations. Such a network architecture is often referred to as hybrid wireless network or multihop cellular network. Previous studies on this topic are all focused on the two-dimensional disk model proposed by Gupta and Kumarin their original work on the capacity of wireless ad hoc networks. We further consider a one-dimensional network model and a two-dimensional strip model to investigate the impact of network dimensionality and geometry on the capacity of such networks. Our results show that different network dimensions lead to significantly different capacity scaling laws. Specifically, for a one-dimensional network of n nodes and b base stations, even with a small number of base stations, the gain in capacity is substantial, increasing linearly with the number of base stations as long as b log b ≤ n. However, a two-dimensional square (or disk) network requires a large number of base stations b = Ω(√n) before we see such a capacity increase. For a 2-dimensional strip network, if the width of the strip is at least on the order of the logarithmic of its length, the capacity follows the same scaling law as in the 2-dimensional square case. Otherwise the capacity exhibits the same scaling behavior as in the 1-dimensional network. We find that the different capacity scaling behaviors are attributed to the percolation properties of the respective network models.