# Spectrum-Aware Energy Efficiency Analysis in K-tier 5G HetNets

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

- We use tools of stochastic geometry to model and analyze D2D communication underlying a multi-tier and multi-channel cellular network where the D2D transmitters are capable of harvesting RF energy from ambient interference arising from concurrent cellular downlink transmissions. Note that we analyze the impact of RF EH on both the SE and EE of the D2D-aided HetNet. In addition, we propose a framework for wireless video sharing to consider D2D requirements under realistic application scenarios and specific business requirements, where users are equipped with cache memory to store popular video files and exchange files through D2D communication.
- Our analysis is conducted for two D2D spectrum sharing scenarios (will be discussed later): overlay and underlay in-band D2D. In underlay in-band D2D, we consider cognitive D2D communication, where cognition is integrated into the cache-enabled D2D communication underlying the multi-tier/multi-channel cellular network. Specifically, by incorporating CR techniques, the cache-enabled D2D transmitter performs spectrum sensing to provide opportunistic access to a predefined non-exclusive D2D channel. As common to all schemes, errors in the form of false alarms and misdetections occur in spectrum sensing, and such errors can lead to degradation in the performance. Thus, the impact of sensing errors by the D2D transmitters is studied in our work.
- Considering the described model, we use tools from stochastic geometry to evaluate the performance of the proposed communication system model in terms of SE and EE. In general, we derive simple and closed-form expressions for the coverage probability of cellular and D2D users under the overlay and underlay in-band D2D, and also the probability of harvesting sufficient energy is obtained; finally, the EE expression of the cache-enabled cognitive D2D-aided HetNet with EH is derived. In our derivations, in contrast to previous related studies in which a traditional single-tier macrocell deployment is assumed, we consider a cellular network that consists of $K$ tiers of BSs with distinct and general network parameters in each tier, which enables us to discover further insights into the behavior of the SE and EE in dense HetNets. Furthermore, unlike those works, in our analysis, we consider more general D2D scenarios by randomly modeling the distance between D2D pairs instead of assuming a fixed distance between the pairs.
- The possible impact of the TPC $\beta $ (identified for SC BSs) as well as the D2D layer added on the network EE and SE will be studied. Furthermore, we demonstrate that EH can effectively power D2D communications underlying cellular networks. A higher SE under various parameter settings of the proposed system model is also corroborated. Finally, we will observe that cognitive channel access will help to increase the QoS of D2D users under the same network conditions as in the non-cognitive situation. As will be shown in the simulations, the proposed framework brings a considerable advantage in terms of EE and SE. More specifically, the power control/adjustment strategy of SCs, the caching placement, D2D establishment, and cognition and EH capabilities altogether can lead to a considerable improvement in the achieved network EE and SE.

## 3. System Model

#### 3.1. Network Topology

#### 3.2. Spectrum Allocation

#### 3.3. Multi-Tier EH Model

#### 3.4. Spectrum Sensing Model of D2D Users

- The D2D channel ${c}_{d}$ is used by nearby cellular BSs, and a typical D2D transmitter correctly detects the presence of cellular transmissions. The probability of this situation is $(1-{p}_{f}^{\mathrm{D}2\mathrm{D}}){p}_{DE}$, where ${p}_{f}^{\mathrm{D}2\mathrm{D}}$ is the probability that the D2D channel (i.e., ${c}_{d}$) is free, and therefore $(1-{p}_{f}^{\mathrm{D}2\mathrm{D}})$ indicates the probability of the presence of nearby cellular transmissions on channel ${c}_{d}$. In this case, the typical D2D transmitter cannot utilize the channel to transmit information.
- The channel ${c}_{d}$ is in use by nearby cellular BSs, but the typical D2D transmitter misdetects the presence of cellular transmissions. The probability of this situation is $(1-{p}_{f}^{\mathrm{D}2\mathrm{D}})(1-{p}_{DE})$. In this case, the typical D2D transmitter attempts to utilize the occupied channel ${c}_{d}$ for data transmission. However, to avoid any severe interference, the typical D2D transmitter should not be allowed to perform data transmission.
- The channel ${c}_{d}$ is not being utilized by nearby cellular BSs, and the typical D2D transmitter falsely detects the presence of cellular transmissions. The probability of this situation is ${p}_{f}^{\mathrm{D}2\mathrm{D}}{p}_{FA}$. Further, in this case, the typical D2D transmitter does not utilize the channel to transmit data.
- The channel ${c}_{d}$ is not in use by nearby cellular BSs, and the typical D2D transmitter correctly detects the absence of cellular transmissions. The probability of this situation is ${p}_{f}^{\mathrm{D}2\mathrm{D}}\left(1-{p}_{FA}\right)$. In this case, the typical D2D transmitter utilizes ${c}_{d}$ to transmit information.

#### 3.5. Spectrum Access Model for Cellular Transmissions

**Proof.**

## 4. Problem Formulation

#### 4.1. The Load-Dependent TPC

#### 4.2. Overlay Mode: Downlink Cellular and D2D Coverage Probabilities

**Theorem**

**1.**

**Proof.**

**Remark**

**1.**

**Corollary**

**1.**

**Theorem**

**2.**

**Remark**

**2.**

**Corollary**

**2.**

#### 4.3. Underlay Mode: Downlink Cellular and D2D Coverage Probabilities

**Theorem**

**3.**

**Proof.**

**Remark**

**3**

**Corollary**

**3.**

**Theorem**

**4.**

**Proof.**

**Remark**

**4.**

**Corollary**

**4.**

#### 4.4. Cellular and D2D Links Coexistence

- i.
- Calculation of ${p}_{f}^{\mathrm{D}2\mathrm{D}}$: In a $K$-tier HetNet, for a generic D2D transmitter, the probability that the D2D channel (i.e., ${c}_{d}$) is free inside the D2D protection region is given by$${p}_{f}^{\mathrm{D}2\mathrm{D}}={\displaystyle \prod}_{k\in \mathcal{K}}\mathrm{exp}\left[-{\theta}_{k}{q}_{d,k}\right]$$$${\theta}_{k}=\pi {\mathsf{\lambda}}_{k}{\left(\frac{{P}_{T}^{k}}{{\mu}_{k}\gamma}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.}\mathsf{\Gamma}\left(1+\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.\right)k=1,\dots ,K$$

**Proof.**

- ii.
- Calculation of ${p}_{s}^{\mathrm{D}2\mathrm{D}}$: Although the random variable ${r}_{d}$ ($0\le {r}_{d}\le d$) is the distance between each D2D transmitter and its receiver, we consider the worst-case scenario for the calculation of ${p}_{s}^{\mathrm{D}2\mathrm{D}}$, where the receiver is at the boundary of the circle (i.e., at a distance $d$). Notice that this presumption gives an upper bound on the amount of transmission power needed for the communication link to be established, thus providing a lower bound on the probability of sufficient energy being harvested. Relaxing this presumption, without providing further insights, complicates the derived expressions [43]. We define the probability ${p}_{s}^{\mathrm{D}2\mathrm{D}}$ that a D2D transmitter harvests sufficient energy as follows:$${p}_{s}^{\mathrm{D}2\mathrm{D}}=\mathbb{P}\left[{P}_{EH}>{P}_{EH}^{th}\right]$$

**Theorem**

**5.**

**Proof.**

#### 4.5. Cellular and D2D Data Rate Analysis

**Overlay Mode:**Firstly, if a typical user obtains data via the traditional cellular network, i.e., directly from a BS in the $k$-th tier, the average achievable rate is given as follows:

**Underlay Mode:**Firstly, if a typical user receives data via the traditional cellular network, $\overline{{R}_{k}}$ can be written as follows (considering an interference-limited regime (${\sigma}^{2}\to 0$) and following the derivation in Appendix A.3)

#### 4.6. Network EE Metric

**Overlay in-band D2D mode:**In Equation (51), $\overline{{p}_{k}^{cov}}$ and $\overline{{p}_{\mathrm{D}2\mathrm{D}}^{cov}}$, i.e., the average cellular and D2D coverage probability expressions, are, respectively, taken from those in Equations (16) and (19). In addition, the $\overline{{R}_{k}}$ and $\overline{{R}_{\mathrm{D}2\mathrm{D}}}$ are, respectively, taken from those in Equations (42) and (44). Moreover, in the ${N}_{\mathrm{D}2\mathrm{D}}$ expression, ${p}_{t}^{\mathrm{D}2\mathrm{D}}={p}_{s}^{\mathrm{D}2\mathrm{D}}$.

**Underlay in-band D2D mode:**In Equation (51), $\overline{{p}_{k}^{cov}}$ and $\overline{{p}_{\mathrm{D}2\mathrm{D}}^{cov}}$ expressions are, respectively, taken from those in Equations (22) and (29). In addition, the $\overline{{R}_{k}}$ and $\overline{{R}_{\mathrm{D}2\mathrm{D}}}$ are, respectively, taken from those in Equations (45) and (47). Further, in the ${N}_{\mathrm{D}2\mathrm{D}}$ expression, ${p}_{t}^{\mathrm{D}2\mathrm{D}}=\left(1-{p}_{FA}\right){p}_{f}^{\mathrm{D}2\mathrm{D}}{p}_{s}^{\mathrm{D}2\mathrm{D}}$.

## 5. Simulation Results

_{d}as much as possible. In addition, for the same reasons mentioned for Figure 4 and Figure 5, the probability of channel C

_{d}being occupied by the macro tier (${q}_{d,1}^{\mathrm{PSA}}$ and ${q}_{d,1}^{\mathrm{RSA}}$) is higher for all values of ${\lambda}_{U}$ when compared to the femto tier (${q}_{d,2}^{\mathrm{PSA}}$ and ${q}_{d,2}^{\mathrm{RSA}}$). Figure 10 depicts the effect of varying the density of users on ${q}_{c,k}^{\mathrm{PSA}}$. As it can be seen, the probability that a BS of tier $k$ uses a generic channel ${c}_{i}\in {\mathrm{C}}_{k}\backslash \left\{{c}_{d}\right\}$ to serve one of its associated cellular users is an increasing function of ${\lambda}_{U}$. Similar reasons and arguments to those we had for the previous figures hold here as well.

## 6. Conclusions and Future Research Directions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Derivation of ${\mathcal{N}}_{k}$

#### Appendix A.2. Derivation of ${p}_{s}^{D2D}$

#### Appendix A.3. Derivation of $\overline{{R}_{k}}$

**Overlay mode:**From the expression of $\overline{{R}_{k}}$ in Equation (41), we have

**Underlay mode:**Similarly, from the expression of $\overline{{R}_{k}}$ in Equation (41), we have

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**Figure 1.**System model: a multi-cell network topology for a D2D-enabled two-tier cellular network composed of a macrocell tier overlaid with a femtocell tier.

**Figure 2.**The probability of finding a file from the cache-enabled D2D UEs vs. the maximum allowable D2D distance (i.e., $d$) and the number of network cache files (i.e., $m$). Here, the $z$ value is set to 10.

**Figure 3.**Coverage simulations for the proposed spectrum-aware D2D-enabled HetNet. The D2D connections are shown by solid black lines. The green and black points, respectively, represent the users connected to the femto base stations (FBSs) and macro base stations (MBSs). The white points are inactive users.

**Figure 4.**The impact of the FBSs’ TPC (i.e., ${\beta}_{2}$) on the ${q}_{c,k}^{\mathrm{PSA}}$ and ${q}_{d,k}^{\mathrm{PSA}}$ in the underlay in-band D2D mode.

**Figure 5.**The ${q}_{c,k}^{\mathrm{PSA}}$ and ${q}_{d,k}^{\mathrm{PSA}}$ in the underlay in-band D2D mode vs. the total number of available channels $|\mathrm{C}|$ in each macrocell.

**Figure 6.**The probability that the D2D channel ${c}_{d}$ is free inside the D2D protection region (i.e., ${p}_{f}^{\mathrm{D}2\mathrm{D}}$) as a function of the spectrum sensing threshold $\gamma $ (in dBm).

**Figure 7.**${p}_{f}^{\mathrm{D}2\mathrm{D}}$ vs. the density of users for the prioritized spectrum access (PSA) and random spectrum access (RSA) policies in the $K$-tier HetNet.

**Figure 8.**The percentage of D2D links with the desired quality of service (QoS) vs. the cognitive radio sensing threshold $\gamma $ (in dBm) for both the RSA and PSA policies. Higher $\gamma $: moving toward the non-cognitive D2D scenario. Lower $\gamma $: moving toward the cognitive D2D scenario.

**Figure 9.**The ${q}_{d,k}^{\mathrm{PSA}}$ and ${q}_{d,k}^{\mathrm{RSA}}$ in the underlay in-band D2D mode vs. the intensity of users when both the RSA and PSA policies are used.

**Figure 10.**The ${q}_{c,k}^{\mathrm{PSA}}$ in the underlay in-band D2D mode vs. the density of users when the PSA policy is used.

**Figure 11.**The ${q}_{c,k}^{\mathrm{PSA}}$ and ${q}_{d,k}^{\mathrm{PSA}}$ in the underlay in-band D2D mode vs. the density of MBSs when the PSA policy is used.

**Figure 12.**The average downlink cellular/D2D coverage probabilities (i.e., $\overline{{p}_{k}^{cov}\left(c\right)}$ and $\overline{{p}_{\mathrm{D}2\mathrm{D}}^{cov}}$ ) in underlay in-band D2D mode and when the PSA policy is used vs. the corresponding SINR thresholds ${\tau}_{k}$ ($k\in \mathcal{K}$ ) and ${\tau}_{\mathrm{D}2\mathrm{D}}$.

**Figure 13.**The percentage of D2D links with the desired quality of service (QoS) vs. the misdetection probability (i.e., ${p}_{MD}$) for different sizes of $|\mathrm{C}|$.

**Figure 14.**The D2D transmission probability (${p}_{t}^{\mathrm{D}2\mathrm{D}}$) vs. the probability of false alarm (i.e., ${p}_{FA}$ ) and the predetermined energy harvesting (EH) threshold (i.e., ${P}_{EH}^{th}$) of the cognitive D2D transmitters.

**Figure 15.**The D2D transmission probability (${p}_{t}^{\mathrm{D}2\mathrm{D}}$) vs. the predetermined EH threshold (i.e., ${P}_{EH}^{th}$ ) and the predefined sensing threshold (i.e., $\gamma $) of the cognitive D2D transmitters.

**Figure 16.**The total network power consumption vs. the total number of available channels in each macrocell (i.e., $|\mathrm{C}|$) and the probability of false alarm ${p}_{FA}$.

**Figure 17.**The total network power consumption vs. the maximum allowable D2D distance $d$ and the probability of false alarm ${p}_{FA}$.

**Figure 18.**The sensitivity of the spectral efficiency (SE) and energy efficiency (EE) with respect to variations of the network parameters.

**Figure 19.**The impact of varying the maximum allowable D2D distance (i.e., $d$) and the total number of available channels in each macrocell (i.e., $|\mathrm{C}|$ ) on the achievable sum of D2D rates (i.e., ${R}_{total}^{\mathrm{D}2\mathrm{D}}$).

**Figure 20.**The relationship between the network SE, the maximum allowable D2D distance $d$, and the predetermined EH threshold (i.e., ${P}_{EH}^{th}$ ). Higher ${P}_{EH}^{th}$: moving toward non-EH-based D2D communications. Lower ${P}_{EH}^{th}$: moving toward EH-based D2D communications.

**Figure 21.**The relationship between the network SE, the maximum allowable D2D distance $d$, and the cache size (i.e., $z$) of each cache-enabled D2D UE; (

**b**) shows a high-angle view of (

**a**). $m$ is set to be 100 here.

**Figure 22.**The relationship between the network SE (

**a**)/EE (

**b**), the FBSs’ TPC (i.e., ${\beta}_{2}$), and $\mathbb{P}\left\{{c}_{d}\in {\mathrm{C}}_{k}\right\}=\frac{|{\mathrm{C}}_{k}|}{|\mathrm{C}|}$ (in this figure, $k$ is set to 2, i.e., the femto tier). Note that $\mathbb{P}\left\{{c}_{d}\in {\mathrm{C}}_{k}\right\}$ is the probability that the D2D channel ${c}_{d}$ belongs to the channels allocated to the $k$-th tier.

**Figure 23.**The impact of the total number of available channels in each macrocell (i.e., $|\mathrm{C}|$) and the density of users (${\lambda}_{U}$) on the network EE.

Symbol | Value | Description |
---|---|---|

${P}_{MBS}^{T}$ | $37$ dBm | MBS transmit power |

${P}_{FBS}^{T}$ | $23$ dBm | FBS transmit power |

${P}_{U}^{T}={P}_{\mathrm{D}2\mathrm{D}}^{T}$ | $20$ dBm | User transmit power |

${\lambda}_{MBS}$ | $1\times {10}^{-7}{m}^{-2}$ | MBS initial density |

${\lambda}_{FBS}$ | $3{\lambda}_{M}$ | FBS initial density |

${\lambda}_{U}$ | $4\times {10}^{-5}{m}^{-2}$ | User initial density |

${\lambda}_{UD}$ | $50\%$${\lambda}_{U}$ | Cache-enabled D2D UEs density |

${\mu}_{MBS}={\mu}_{FBS}={\mu}_{\mathrm{D}2\mathrm{D}}$ | 1 | Rayleigh fading parameter |

$d$ | 200 m | Maximum allowable D2D distance |

$|\mathrm{C}|$ | 200 | Macrocell bandwidth |

$\gamma $ | $-80$ dBm | D2D sensing threshold |

${P}_{EH}^{th}$ | $-90$ dBm | EH threshold |

${\tau}_{FBS}={\tau}_{MBS}$ | 0 dB | Cellular SINR threshold |

${\tau}_{\mathrm{D}2\mathrm{D}}$ | $0$ dB | D2D SINR threshold |

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**MDPI and ACS Style**

Panahi, F.H.; Panahi, F.H.; Ohtsuki, T.
Spectrum-Aware Energy Efficiency Analysis in *K*-tier 5G HetNets. *Electronics* **2021**, *10*, 839.
https://doi.org/10.3390/electronics10070839

**AMA Style**

Panahi FH, Panahi FH, Ohtsuki T.
Spectrum-Aware Energy Efficiency Analysis in *K*-tier 5G HetNets. *Electronics*. 2021; 10(7):839.
https://doi.org/10.3390/electronics10070839

**Chicago/Turabian Style**

Panahi, Fereidoun H., Farzad H. Panahi, and Tomoaki Ohtsuki.
2021. "Spectrum-Aware Energy Efficiency Analysis in *K*-tier 5G HetNets" *Electronics* 10, no. 7: 839.
https://doi.org/10.3390/electronics10070839