Area Spectral Efficiency of Ultradense Networks
Area spectral efficiency refers to the data rate that can be achieved per unit bandwidth and in a unit area of the wireless network. It has the unit of b/s/Hz/m2 or b/s/Hz/km2.
Network densification has been the main driver of wireless network capacity increase in the past and will play an even more crucial role in the development of the next generation mobile communication systems (5G). Network densification refers to the deployment of more base stations (BSs) and wireless access points per unit area and the associated technological advances to support such densification. There are three primary ways of increasing the wireless network capacity: (1) adding more spectrum, (2) enhancing spectral efficiency through advanced communication techniques, and (3) enhancing spatial reuse of frequency spectrum through network densification. The area spectral efficiency (ASE) is a major metric to measure the efficiency in the spatial reuse of frequency spectrum. According to a study by Webb (Henderson, 2007), among the 1-million-fold increase in wireless network capacity achieved in 50 years from 1950 to 2000, 15× improvement was achieved from a wider spectrum, 5× improvement from better Medium Access Control (MAC) and modulation schemes, 5× improvement by designing better coding techniques, and an astounding 2700× gain through network densification and reduced cell sizes. As we move to the next generation mobile communication systems and seek further capacity increases, network densification, manifested through heterogeneous and ultradense networks, will play an even more important role. First, the combined amount of spectrum available for licensed mobile broadband and unlicensed Wi-Fi is scarce. Spectrum approaching millimeter wavelengths is more abundant but is yet to be proven for cellular and Wi-Fi use due to difficulty in penetration and supporting significant mobility (Andrews et al., 2016a; Kutty and Sen, 2016). Second, the scope for enhanced spectral efficiency may be limited as many current wireless systems are already running at a spectral efficiency close to the performance limit prescribed by the Shannon. Therefore, mobile operators have increasingly turned to network densification and small cell technology to meet the 1000× capacity increase expected on 5G. Small cells are now deployed in massive numbers (Small Cell Forum, 2016), which drives the paradigm shift into ultradense networks. Ultradense networks feature a very dense deployment of BSs and wireless access points.
The ASE and wireless network capacity can be used interchangeably in the sense that the total capacity achieved by a network deployed in a given geographical area and using a specific amount of bandwidth is equal to the ASE times the size of the area and the amount of bandwidth. It is of crucial interest to investigate how the ASE varies as more and more BSs are deployed and the network becomes denser and denser.
The SINR Invariance Principle for Low-to-Medium BS Density
The SINR invariance principle implies that as the network densifies and the distances between transmitters and receivers reduce, the increase in interference will be counterbalanced by the increase in the desired signal. Consequently, the SINR will stay approximately the same. The principle suggests that other things being equal, the spectral efficiency, or equivalently the capacity, per BS cell is invariant as network densifies. Therefore, from the network perspective, the ASE, or equivalently the overall network capacity, will linearly increase with the number of cells per unit area; from the user perspective, as each user maintains the same SINR but shares its BS with an ever-smaller number of other users, each user can achieve approximately linear growth in its achievable data rate as BSs are added, until the limit of one user per cell is reached. The SINR invariance principle is not affected by the BS layout, transmit power, shadowing and fading distributions, and path loss exponent (Andrews et al., 2016b).
Area Spectral Efficiency for Ultradense BS Regime
Recent research suggested however that the SINR invariance principle may no longer apply when the BS density becomes very large and that there may exist a limit in network densification, beyond which further densification will not bring the expected linear increase in capacity and may even reduce the capacity (Ding et al., 2015, 2016a,b; Ge et al., 2016; Liu et al., 2016a,b; Andrews et al., 2016b; Zhang and Andrews, 2015). Specifically, by incorporating those effects that have negligible impacts on the ASE when the BS density is small or moderate but become dominant factors determining the ASE when the BS density is very large, it was shown that the ASE may either exhibit a sublinear increase with the BS density, or reduce at certain region of the BS density, or even monotonically reduce to zero beyond a certain BS density threshold.
when the BS density is small, the ASE quickly increases with the BS density because the network is generally noise-limited and adding more BSs immensely benefits the ASE by reducing the transmission distance between the BS and the mobile user (MU). Most transmissions in this regime are NLoS transmissions; however the transmission between a MU and its desired BS has a higher probability of being LoS transmission, and as the BS density further increases, this probability increases to a non-negligible value. Therefore, in this region, the ASE considering LoS/NLoS transmissions is higher than that without considering LoS/NLoS transmissions, but their trend is the same;
when the network is dense enough, i.e., greater than 20 BS/km2 in Fig. 1, the growth of the ASE with the BS density, when considering LoS/NLoS transmissions, becomes flat or even exhibits a decrease (for γ0 = 3 dB and γ0 = 6 dB), which is distinctly different from that predicted without considering LoS/NLoS transmissions. This can be explained by the so-called NLoS-LoS transition effect. Particularly, in this region, the transmissions between MSs and their desired BS are already dominated by LoS transmissions but in the beginning signals from interfering BSs, are mainly NLoS transmissions suffering higher loss. As BS density further increases and the distances between a MU and BSs, including both the desired BS and interfering BSs, further reduce, signals from interfering BSs start to transit from NLoS transmissions to LoS transmissions. Consequently, as the BS density increases, interference experiences a larger increase compared with the desired signal, causing the SINR to reduce sharply in this region. Therefore, the ASE remains largely flat with the increase in BS density or may even reduce;
when the network becomes very dense, i.e., greater than 100 BS/km2 in Fig. 1, the dominant interfering BSs have completed their NLoS-LoS transitions. Both the desired signal and the dominant interference are now LoS transmissions. However, non-dominant interfering BSs further away from the MS may still experience the NLoS-LoS transition effect. Therefore, in this region, the SINR may still reduce modestly with the increase in BS density. This modest decrease in the SINR combined with the increase in the BS density causes the ASE to increase but at a rate below that predicted without considering LoS/NLoS transmissions.
In summary, distinct from conventional low-to-medium density networks, in ultradense networks, impacts of LoS/NLoS transmissions, the different radio propagation conditions in the near-field and far-field of BSs, and network geometric constraints may play an important role in determining the ASE.
The ASE is a fundamental performance metric of ultradense networks and more general wireless networks. The ASE determines the capacity that can be achieved by a wireless network and measures the efficiency in the spatial reuse of frequency spectrum. Knowledge of the ASE helps to guide the design and deployment of wireless networks.
- Andrews JG, Baccelli F, Ganti RK (2011) A tractable approach to coverage and rate in cellular networks. IEEE Trans Commun 59(11):3122–3134Google Scholar
- Andrews JG, Gupta AK, Dhillon HS (2016a) A primer on cellular network analysis using stochastic geometry. eprint arXiv:1604.03183Google Scholar
- Andrews JG, Zhang X, Durgin GD, Gupta AK (2016b) Are we approaching the fundamental limits of wireless network densification? IEEE Commun Mag 54(10):184–190Google Scholar
- Ding M, Lopez-Perez D, Mao G, Wang P, Lin Z (2015) Will the area spectral efficiency monotonically grow as small cells go dense? In: IEEE GLOBECOM, pp 1–7Google Scholar
- Ding M, Perez DL (2016) Please lower small cell antenna heights in 5G. In: IEEE Globecom, pp 1–6Google Scholar
- Ding M, Wang P, López-Pérez D, Mao G, Lin Z (2016a) Performance impact of LoS and NLoS transmissions in dense cellular networks. IEEE Trans Wirel Commun 15(3):2365–2380Google Scholar
- Ding T, Ding M, Mao G, Lin Z, López-Pérez D (2016b) Uplink performance analysis of dense cellular networks with LoS and NLoS transmissions. In: IEEE ICC, pp 1–6Google Scholar
- Ge X, Tu S, Mao G, Wang CX, Han T (2016) 5G ultra-dense cellular networks. IEEE Wirel Commun 23(1):72–79Google Scholar
- Gruber M (2016) Scalability study of ultra-dense networks with access point placement restrictions. In: IEEE ICC workshops, pp 650–655Google Scholar
- Haenggi M, Andrews JG, Baccelli F, Dousse O, Franceschetti M (2009) Stochastic geometry and random graphs for the analysis and design of wireless networks. IEEE J Sel Areas Commun 27(7):1029–1046Google Scholar
- Henderson W (2007) Webb report, ofcom.Google Scholar
- Kutty S, Sen D (2016) Beamforming for millimeter wave communications: an inclusive survey. IEEE Commun Surv Tutor 18(2):949–973Google Scholar
- Liu J, Sheng M, Liu L, Li J (2016a) Effect of densification on cellular network performance with bounded pathloss model. IEEE Commun Lett 21(2):346–349Google Scholar
- Liu J, Sheng M, Liu L, Li J (2016b) How dense is ultra-dense for wireless networks: from far- to near-field communications. eprint arXiv:1606.04749Google Scholar
- Small Cell Forum (2016) Small cell market status report, May 2016Google Scholar