Capacity of Ad-Hoc Networks under Multipacket Transmission andReception - eScholarship

Capacity of Ad-Hoc Networks under Multipacket Transmission and Reception Shirish Karande † , Zheng Wang † , Hamid R. Sadjadpour † , J.J. Garcia-Luna-Aceves ‡ Department of Electrical Engineering † and Computer Engineering ‡ University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA Palo Alto Research Center (PARC), 3333 Coyote Hill Road, Palo Alto, CA 94304, USA Email: { karandes,wzgold, hamid, jj } @soe.ucsc. edu Abstract—In this paper we deduce the capacity of ad-hoc networks under the assumptions of physical model for coop- erative multiple input multiple output (MIMO) communication. We show that the capacity of a random wireless ad-hoc network can be improved significantly by adopting MIMO techniques. In particular, when the nodes are endowed with multi-packet transmission and reception capabilities, the per session capacity increases atleast as n 1−2/α R(n) 3−4/α , where α > 2 is the path loss parameter and R(n) is the range of cooperation. The proof for the above results utilizes an edge coloring of an appropriately chosen random geometric graph. This approach, as a by product, provides alternative deductions for some previously established results under the physical model. Consequently, we provide an alternative deduction of the classical result for a point to point communication by Gupta and Kumar. Furthurmore, we also deduce a bound that matches a recent result by Wang et. al., for capacity of ad-hoc networks under multipacket reception, within a poly-log factor. I. I NTRODUCTION The past decade has seen major advances in multiuser detection, multiple input multiple output (MIMO) commu- nication and interference cancelation techniques. Currently, there is an active research interest in modeling and evaluating the impact of these paradigms on the performance of large scale networks. The classical result by Gupta and Kumar [1] essentially states that communication protocols based on point to point communication cannot render networks that perform efficiently with increase in size. It is widely anticipated that advanced cooperative communication can overturn this rather negative conclusion. Recent efforts to realize (static) scalable ad-hoc networks have met with a mixed degree of success. For example, network coding (NC) [2], which is essentially a generalization of routing, has proved to be incapable of improving the throughput order for multipair unicast transmissions [3]. Nev- ertheless, other contemporary efforts, which model relatively classical physical layer co-operative techniques, have met with a greater degree of success. In particular, [4] and [5] have exhbited the feasibility of achieving constant per-session capacity. We provided a more detailed taxonomy of related works in Section II. Section III presents the first contribution of this paper. We model a random network with n nodes, homogeneous transmission power, and unicast traffic for k source-destination (S-D) pairs. We introduce a a new physical model in which nodes have the ability to decode correctly multiple packets transmitted concurrently from different nodes, and transmit concurrently multiple packets to different nodes. We refer to this as the multi-packet transmission and reception (MPTR) physical model. In this section we review some of our recently established results on random geometric graphs Section IV presents our second contribution, where we define a combinatorial interference model based on random geometric graphs. We show that for each of: (a) the classical physical model by Gupta and Kumar [1], (b) the multipacket reception physical model by Wang et. al. [6](c) and the MPTR physical model proposed in Section, there exists a corresponding combinatorial model that performs necessarily worse than the physical model. We utilize this relationship and recently proven poperties of random geometric graphs [7]to deduce the desired lower bounds. We discuss our results in Section V. II. R ELATED W ORK There have been many contributions on the capacity study of wireless ad hoc networks and span unicast, multicast and broadcast traffic. Due to space limitations, however, we only mention a few of them that focus on unicasting. A number of papers have extended the results by Gupta and Kumar [1], which showed a gap between the upper and lower bounds on capacity under the physical model. Franceschetti et al. [8] closed this gap using percolation theory. Several techniques aimed at improving the capacity of wireless ad hoc networks have been analyzed. Grossglauser and Tse [9] demonstrated that a non-vanishing capacity can be attained at the price of long delivery latencies by taking advantage of long-term storage in mobile nodes. Someworks demonstrated that changing physical layer as- sumptions such as using multiple channels [10] or MIMO cooperation [4] can change the capacity of wireless networks. Ozgur et al. [11] proposed a hierarchical cooperation tech- nique based on virtual MIMO to achieve linear capacity. They showed that the optimal per-session capacity of an ad-hoc network is bounded as O(n log n), and a constant per-session capacity of Θ(1) is achievable. Our work is significantly different from this work, in terms of the the model and assumptions used to derive the results. Ozgur et. al. consider the information-theoretic model, and assume that the network