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Throughput Scaling of Primary and Secondary Ad Hoc Networks With Same-Order Dimensions

Chengzhi Li, Huaiyu Dai

2014
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IEEE Transactions on Vehicular Technology
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In this paper, the scaling law of the network throughput of a special type of heterogeneous networks is studied, where a secondary network composed of cognitive users shares the same resources opportunistically with a primary network of licensed users. Some pioneering works in this area showed that this type of heterogeneous networks performs as well as two stand-alone networks, under the dense network model. A key assumption behind this conclusion is that the density of the secondary network
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... secondary network is higher than that of the primary one in the order sense, which essentially decouples the two overlaid networks, as the secondary network dominates asymptotically. In this work we endeavor to investigate this problem with a weaker condition that the dimensions of the two overlaid networks are on the same order, under the extended network model. Our analysis shows that with the ratio of the two network sizes larger than a threshold, this weaker (and arguably more practical) condition does not degrade either network throughput scaling. Our result further reveals the potentials of cognitive radio technology in real applications. network. Due to its secondary role, the CR network should prevent any unacceptable interference to the primary network, while tolerate the interference from the primary transmissions. One primary concern for CR networks is network throughput. In [3] , the authors showed that an n-node primary network and an m-node secondary network, while coexisting, can achieve the per-node throughput Θ( √ 1 n log n ) and Θ( √ 1 m log m ), respectively. The same results were achieved in [4] with a more practical assumption, requiring only the knowledge of the locations of primary transmitters, rather than the locations of all the primary nodes as in [3] . Both [3] and [4] focus on the dense network model, where the number of nodes grows with the node density in a fixed area, and assume that m = n β (β > 1), i.e., the density of the secondary network is higher than that of the primary one in the order sense. Under this assumption the influence of the primary network on the secondary network becomes increasingly negligible (so that full connectivity 1 of the secondary network is guaranteed); in addition, it is only valid in the dense network model and does not hold in the extended network model, where the number of nodes grows with the area with a fixed density. These facts motivate us to study a more practical scenario where m n = constant in this paper, i.e., the dimensions of the two overlaid networks are on the same order. We mainly consider an extended network 2 and show that even with this weaker condition the per-node throughput of both networks can be further boosted to Θ( 1 √ n ) and Θ( 1 √ m ), respectively, if m/n is larger than a threshold. Our results are derived with the help of intelligent design of "highway" systems originally proposed in [6] . It should be noted that 1) the weaker condition m n = constant no longer maintains full connectivity of the secondary 1 Given a transmission range r there is always a path connecting two arbitrary nodes in the network. 2 In many scenarios, the (scaling law) results obtained in the dense and extended network model coincide; this holds for the results of this paper as well. As a side note, it is felt that the extended network model is more realistic, where one is free from the concern of the near field effects of electromagnetic propagation [5] . This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available at http://dx.

doi:10.1109/tvt.2014.2310424
fatcat:szedq2bjyngelfxijguof33b5u