# BER Aided Energy and Spectral Efficiency Estimation in a Heterogeneous Network

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis

_{b}to the noise spectral density N

_{0}, i.e., EE expresses the count of information bits per energy unit.

_{s}, can be expressed by SE and EE as follows [13]:

_{s}and B, where we consider EE as the ratio C/B, (1) implies that:

_{T}tiers overall.

_{k}, with the transmit power of P

_{k}, BSs density of λ

_{k}, and the SINR threshold of τ

_{k}(often referenced as “bias”) at UE, respectively.

#### 2.1. BER-Based SINR Estimation by AWGN Abstraction of Radio Interference

^{−2}from the middle curve for S/I = 30 dB, to the line crossing with the utmost right curve for S/I = 20 dB (i.e., increasing the interference for 10 dB), is tracked by almost equal increase in the SNR value.

**∞**(representing the no-interference case).

^{−2}at S/N = 20 dB, can be AWGN-abstracted by the utmost left AWGN curve (with S/I =

**∞**), if we consider BER degradation from 2 + 10

^{−4}to 10

^{−2}, upwards the vertical turquoise line.

#### 2.2. Spectral and Energy Efficiency Model

_{1}≤ λ

_{2}… λ

_{k−1}≤ λ

_{k}. For a certain λ

_{k}, the count of tier k

_{i}(i = 1,2,…,N

_{T}) access points within the covered area $\mathcal{A}$ [m

^{2}] is a Poisson random variable with mean value of $\mathcal{A}\xb7{\lambda}_{k}$, being independent of other tiers. Furthermore, all k-tier access points transmit with power P

_{k}.

_{i}distance from BS.

_{open}from Open Access (OA) macro-/femtocells, while the Closed Subscriber Group (CSG) femtocells normally do not provide service to the considered users [8]. So, a certain HetNet is represented by the counts of tiers: N

_{T}= 3 and OA tiers: N

_{open}= 2, respectively, where tier 1, tier 2, and tier 3 represent the macro cells, the OA femtocells, and the CSG femtocells, respectively.

_{k}of a serving tier k

_{i}transmits only the users’ subset U

_{b}served by b

_{k}∈ Φ

_{k}.

_{b}∊ U

_{b}, expressed by BER, according to Equation (5). Then, the spectral efficiency SE

_{k}of the link from b

_{k}to any target u

_{b}is:

_{k}and SE

_{TOT}for individual tiers (k = 1…N

_{T}) and for the whole HetNet, respectively. Furthermore, the selection of serving or candidate-serving cells according to the LTE-A standard is mostly centered around the picocell BSs range extension that enables traffic load balancing, preventing inter-cell radio interference in those areas with evident or expected signal overlapping coverage [13]. The mean levels of the UE-received pilot, originating by the candidate-serving macro and pico BSs, were used for selecting the optimal small-cell tier, which is to serve a particular UE, following two schemes:

_{i}and R

_{j}, we denoted the distances of the UE to the candidate-serving (i.e., the nearest) macro BS and the femto BS, respectively. As we plan to simply model the HetNet SE, we adopt that the power of the instantaneous transmitted signal of any macro BS is considered a random variable close to zero during the ABS state or to ${P}_{1}^{\mathrm{tx}}$ otherwise. Furthermore, we denote the instantaneous transmit power of the serving BS by ${P}_{2}^{\mathrm{tx}}$.

_{i}that is greater than the threshold γ with the probability ${\mathcal{P}}_{i}$.

_{i}and SE

_{j}can be found from:

## 3. Test Results

- -
- single-tier, 5 macro BSs, BS power: 40 W;
- -
- single-tier 250 pico BSs, BS power: 0.25 W;
- -
- two-tier 5 macro and 250 pico BSs.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Parkvall, S.; Dahlman, E.; Furuskar, A.; Jading, Y.; Olsson, M.; Wanstedt, S.; Zangi, K. LTE-advanced-evolving LTE towards IMT-advanced. In Proceedings of the IEEE Conference on Vehicular Technology (VTC), Calgary, AB, Canada, 21–24 September 2008; pp. 1–5. [Google Scholar]
- Slamnik, N.; Okic, A.; Musovic, J. Conceptual radio resource management approach LTE heterogeneous networks using small cells number variation. In Proceedings of the IEEE XI International Symposium (BIHTEL), Sarajevo, Bosnia and Herzegovina, 24–26 October 2016; pp. 1–5. [Google Scholar]
- Slamnik, N.; Musovic, J.; Okic, A.; Krijestorac, I. An approach to analysis of heterogeneous networks’ efficiency. In Proceedings of the XXVI IEEE International Conference ICAT, Sarajevo, Bosnia and Herzegovina, 26–28 October 2017; pp. 1–5. [Google Scholar]
- Bousia, A.; Kartsakli, E.; Antonopoulos, A.; Alonso, L.; Verikoukis, C. Energy efficient schemes for base station management 4G broadband systems. In Broadband Wireless Access Networks for 4G: Theory, Application, and Experimentation; IGI Global: Hershey, PA, USA, 2014; pp. 100–120. [Google Scholar]
- Imran, M.A.; Alonso-Rubio, J.; Auer, G.; Boldi, M.; Braglia, M.; Fazekas, P.; Wajda, W. Most Suitable Efficiency Metrics and Utility Functions. EARTH Project Report. 2011, pp. 1–89. Available online: https://cordis.europa.eu/docs/projects/cnect/3/247733/080/deliverables/001-EARTHWP2D24.pdf (accessed on 23 March 2022).
- ETSI TS 102 706; Environmental Engineering (EE). Measurement Method for Energy Efficiency of Wireless Access Network Equipment, v1.2.1. ETSI: Nice, France, 2011. Available online: https://etsi.org (accessed on 30 January 2021).
- ETSI TR 103 117; Environmental Engineering (EE). Principles for Mobile Network Level Energy Efficiency, v1.1.1. ETSI: Nice, France, 2012. Available online: https://etsi.org (accessed on 30 January 2021).
- Mukherjee, S. Analytical Modeling of Heterogeneous Cellular Networks; Cambridge University Press: Cambridge, UK, 2014; ISBN 978-1-107-05094-5. [Google Scholar]
- Andrews, J.G.; Baccelli, F.; Ganti, R.K. A tractable approach to coverage and rate cellular networks. IEEE Trans. Commun.
**2011**, 59, 3122–3134. [Google Scholar] [CrossRef] - Baccelli, F.; Klein, M.; Lebourges, M.; Zuyev, S. Stochastic geometry and architecture of communication networks. Telecommun. Syst.
**1997**, 7, 209–227. [Google Scholar] [CrossRef] - Baccelli, F.; Błaszczyszyn, B. On a coverage process ranging from the Boolean model to the Poisson-Voronoi tessellation with applications to wireless communications. Adv. Appl. Probab.
**2001**, 33, 293–323. [Google Scholar] [CrossRef] - El Sawy, H.; Hossain, E.; Haenggi, M. Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wireless networks: A survey. IEEE Commun. Surv. Tutor.
**2013**, 15, 996–1019. [Google Scholar] [CrossRef] - Musovic, J.; Lipovac, V.; Lipovac, A. Stochastic Geometry-Based Analysis of Heterogeneous Wireless Network Spectral, Energy and Deployment Efficiency. Electronics
**2021**, 10, 786. [Google Scholar] [CrossRef] - Brown, T.X. Cellular performance bounds via shotgun cellular systems. IEEE J. Sel. Areas Commun.
**2000**, 18, 2443–2455. [Google Scholar] [CrossRef] - Dhillon, H.S.; Ganti, R.K.; Baccelli, F.; Andrews, J.G. Modeling and analysis of K-tier downlink heterogeneous cellular networks. IEEE J. Sel. Areas Commun.
**2012**, 30, 550–560. [Google Scholar] [CrossRef] - Dhillon, H.S.; Ganti, R.K.; Andrews, J.G. Load-aware modeling and analysis of heterogeneous cellular networks. IEEE Trans. Wirel. Commun.
**2013**, 12, 1666–1677. [Google Scholar] [CrossRef] - Mukherjee, S. Distribution of downlink SINR heterogeneous cellular networks. IEEE J. Sel. Areas Commun.
**2012**, 30, 575–585. [Google Scholar] [CrossRef] - Madhusudhanan, P.; Restrepo, J.G.; Liu, Y.; Brown, T.X.; Baker, K.R. Multi-tier network performance analysis using a shotgun cellular system. In Proceedings of the IEEE Global Telecommunications Conference—GLOBECOM, Houston, TX, USA, 5–9 December 2011; pp. 1–6. [Google Scholar]
- Heath, R.W.; Kountouris, M.; Bai, T. Modeling heterogeneous network interference using Poisson point processes. IEEE Trans. Signal Process.
**2013**, 61, 4114–4126. [Google Scholar] [CrossRef][Green Version] - Lipovac, A.; Lipovac, V.; Modlic, B. PHY, MAC, and RLC Layer Based Estimation of Optimal Cyclic Prefix Length. Sensors
**2021**, 21, 4796. [Google Scholar] [CrossRef] [PubMed] - Rumnay, M. LTE and the Evolution of 4G Wireless; Design and Measurements Challenges, 2nd ed.; John Wiley & Sons: Chichester, UK, 2013. [Google Scholar]
- Hanzo, L.; Webb, W.; Keller, T. Single and Multi Carrier Quadrature Amplitude Modulation, 2nd ed.; John Wiley & Sons: Chichester, UK, 2000. [Google Scholar]

Parameter | Value |
---|---|

Maximal size (L) of LTE code-block | 6144 Bytes |

Count of macro cell BSs | 5 |

Maximal output transmit power of macro-cell BS | 40 W |

Maximal output transmit power of small-cell BS | 250 mW |

Count of small-cell BSs | 250 |

Population density per m^{2} | 3.8·10^{−4} |

Maximal distance between BSs in macro cell | 500 m |

Maximal distance between BSs in small cell | 50 m |

Count of resource blocks with LTE 5 MHz channel bandwidth | 25 |

Center of frequency operating band | 2.1 GHz |

LTE channel bandwidth | 5 MHz |

BER | SINR | SE [b/s/Hz] | EE [b/J] |
---|---|---|---|

0.0378 | 11.98 | 17.28 | 0.53 |

0.0550 | 11.06 | 15.96 | 1.04 |

0.0659 | 10.55 | 15.22 | 1.65 |

0.0813 | 9.86 | 14.22 | 3.09 |

0.0921 | 9.45 | 13.63 | 4.45 |

0.0996 | 9.16 | 13.22 | 5.75 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Musovic, J.; Lipovac, A.; Lipovac, V.
BER Aided Energy and Spectral Efficiency Estimation in a Heterogeneous Network. *Computation* **2022**, *10*, 162.
https://doi.org/10.3390/computation10090162

**AMA Style**

Musovic J, Lipovac A, Lipovac V.
BER Aided Energy and Spectral Efficiency Estimation in a Heterogeneous Network. *Computation*. 2022; 10(9):162.
https://doi.org/10.3390/computation10090162

**Chicago/Turabian Style**

Musovic, Jasmin, Adriana Lipovac, and Vlatko Lipovac.
2022. "BER Aided Energy and Spectral Efficiency Estimation in a Heterogeneous Network" *Computation* 10, no. 9: 162.
https://doi.org/10.3390/computation10090162