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Survey on Ultra-Dense Networks (UDNs) and Applied Stochastic Geometry

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Abstract

Due to rapid growth of demanding data rate, many emerged technologies has been developed for wireless communication. Consequently, the perspective of network design has been shifted to new scale, wherein massive number of machines and people can be handled. Ultra-dense networks (UDNs) represents the bottleneck of 5G system capacity. In this paper, we investigate design criteria of UDNs and discuss the relative technologies which are regarded as the main axes of the current research. Also, coverage performance analysis of dense network is introduced based on stochastic geometry, besides the available software packages of 5G networks. Finally, we introduce the most relevant novel trends and open issues for future research directions in this track. Hence, this survey represents complete paradigm for going through UDNs.

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Notes

  1. RRH performs the task of RF end such as power amplification, ADC, and DAC etc.

  2. UL channel estimates would provide the status of DL channel.

  3. In traditional multi-user hybrid beamforming or beamspace MIMO systems, the maximum allowed number of user equals the number of RF chains deployed at BS [49,50,51]

  4. User-centric concept aims for improving user experience regardless location, mobility conditions via re-centering future services around the user. This can be accomplished by extending network infrastructure to improve content caching, connectivity, and functionality.

  5. Each BS cluster allocates power for selfishly maximizing its own EE [33, Eq.18].

  6. Macro BS has 46 dBm, Pico has 33 dBm, and Femto has 20 dBm.

  7. wired backhaul may be non-ideal with moderate latency and lower capacity.

  8. Network slicing is virtual process which allows multi logical networks to operate along with the physical network. This enables multiplexing different users over a single shared physical resources.

  9. Cryptography based techniques exploit channel randomness as one of simple physical layer security.

  10. Hint: the graph in Fig. 4 is scaled precisely in standard US units.

  11. Given function \(f:X\rightarrow Y\) the set X is the domain (like function argument) of f and Y is the co-domain of f.

  12. H represents channel between typical user and serving BS while \(G_i\) denotes the channel between typical user and \(i{\rm{th}}\) interfere.

  13. using moment generation of exponential random variable x with parameter \(\lambda =1\) is straightforward derivation \({{{\mathbb {E}}}_{x}}\left[ {{e}^{-ax}} \right] =\frac{1}{1+a}.\)

  14. Association probability only requires PDF of \(R_i\) without regarding \(S=i\) since \(a_i\) evaluates probability that typical user is connected or not, i.e. connectivity is still under investigation and may not be achieved.

  15. The probability that at least one of the events \(\left\{ A,B,C\right\}\) occurs is equivalent to \({\mathbb {P}}\left[ A\cup B\cup C \right] ={\mathbb {P}}\left[ A \right] +{\mathbb {P}}\left[ B \right] +{\mathbb {P}}\left[ C \right] -{\mathbb {P}}\left[ A\cap B \right] -{\mathbb {P}}\left[ B\cap C \right] -{\mathbb {P}}\left[ A\cap C \right] +{\mathbb {P}}\left[ A\cap B\cap C \right]\), where the event intersections are reduced to zeros if they are independent. In case of HCN is \(\left\{ {SINR\left( {{{\mathbf {Y}}}_{i}} \right) >{{\tau }_{i}}}\right\} \forall 1\le i \le k\).

  16. if X is discrete random variable, then \({\mathbb {E}}\left[ {{\mathbb {1}}_{X\ge a}} \right] =0.{\mathbb {P}}\left[ X<a \right] +1.{\mathbb {P}}\left[ X\ge a \right] ={\mathbb {P}}\left[ X\ge a \right]\); see Fig. 9.

  17. Recall: standard Campbell’s theorem \({\mathbb {E}}\left[ F \right] ={\mathbb {E}}\left[ \sum \limits _{{{\mathbf {X}}_{i}}\in {\varPhi }}{f({{\mathbf {X}}_{i}})} \right] =\lambda \int \limits _{{{{\mathbb {R}}}^{d}}}{f(X)dX}\).

  18. the moment generation function of for Rayleigh distribute random variable x is \(M(t)={\mathbb {E}}\left[ {{e}^{tx}} \right] =\frac{1}{1-\theta t}\). Where x refers to H and scaling paramter \(\theta =1\) denotes distribution spreading while t is equivalent to \(s{{p}_{j}}{{\left\| {{\mathbf {Y}}_{j}} \right\| }^{-\alpha }}\).

  19. PGFL converts the expectation of product into integral formula which is hopefully evaluated to closed expression.

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  1. Menoufia University, Shibin el Kom, Egypt

    A. Abdelaziz Salem, S. El-Rabaie & Mona Shokair

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Salem, A.A., El-Rabaie, S. & Shokair, M. Survey on Ultra-Dense Networks (UDNs) and Applied Stochastic Geometry. Wireless Pers Commun 119, 2345–2404 (2021). https://doi.org/10.1007/s11277-021-08334-1

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