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HierHybNET: Cut-set upper bound of ad hoc networks with cost-effective infrastructure

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Abstract

This paper introduces an information-theoretic upper bound on the capacity scaling law for a hierarchical hybrid network (HierHybNET), consisting of both n wireless ad hoc nodes and m base stations (BSs) equipped with l multiple antennas per BS, where the communication takes place from wireless nodes to a remote central processor through BSs in a hierarchical way. We deal with a general scenario where m, l, and the backhaul link rate scale at arbitrary rates relative to n. Then, a generalized cut-set upper bound under the HierHybNET model is derived by cutting not only the wireless connections but also the wired connections. In addition, the corresponding infrastructure-limited regime is identified.

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Notes

  1. We use the following notation: (1) \(f(x)=O(g(x))\) means that there exist constants C and c such that \(f(x)\le Cg(x)\) for all \(x>c\), (2) \(f(x)=o(g(x))\) means that \(\lim _{x\rightarrow \infty }\frac{f(x)}{g(x)}=0\), (3) \(f(x)=\Omega (g(x))\) if \(g(x)=O(f(x))\), (4) \(f(x)=w(g(x))\) if \(g(x)=o(f(x))\), and (5) \(f(x)=\varTheta (g(x))\) if \(f(x)=O(g(x))\) and \(g(x)=O(f(x))\) [22].

  2. To simplify notations, \(T_n(\alpha ,\beta ,\gamma ,\eta )\) will be written as \(T_n\) if dropping \(\alpha\), \(\beta\), \(\gamma\), and \(\eta\) does not cause any confusion.

  3. Here and in the sequel, the noise variance is assumed to be one to simplify the notation.

  4. To simplify notations, the terms including \(\epsilon\) are omitted if dropping them does not cause any confusion.

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Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054577) and by the research fund of Dankook University(BK21 Plus) in 2014. This paper was presented in part at the 2014 IEEE International Symposium on Information Theory, Honolulu, HI, June/July 2014.

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  1. DMC R&D Center, Samsung Electronics, Suwon, 443-742, Republic of Korea

    Cheol Jeong

  2. Department of Computer Science and Engineering, Dankook University, Yongin, 448-701, Republic of Korea

    Won-Yong Shin

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Correspondence to Won-Yong Shin.

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Jeong, C., Shin, WY. HierHybNET: Cut-set upper bound of ad hoc networks with cost-effective infrastructure. Wireless Netw 22, 1133–1144 (2016). https://doi.org/10.1007/s11276-015-1017-x

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