# A Fuzzy-Based Optimization Technique for the Energy and Spectrum Efficiencies Trade-Off in Cognitive Radio-Enabled 5G Network

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## Abstract

**:**

_{s(LUT)}= 20 ms. Furthermore, optimizing the sensing time and the secondary user (SU) transmission power, yielded a maximum EE and provided a QoS provisioned cognitive radio-enabled 5G network.

## 1. Introduction

**(problem P**. Second, EE-CRNs provide a greater spectrum for wireless portable devices while consuming less energy [20]. EE policies are becoming more critical to achieving green communication because of traditional grid-powered or replaceable battery-powered devices which emit 2% of the total CO

_{1})_{2}. Ref. [21] developed an efficient sensing time optimization algorithm, which we have modified using the concept of a look-up table and then used it throughout the study. Due to this severe issue, recently researchers have focused on developing energy harvesting wireless communication systems (LUT). On the other hand, an LUT-incorporated EH system with spectrum and energy efficiencies is yet to be explored

**(problem P**[22,23,24,25,26,27,28,29,30,31,32,33,34].

_{2})#### Highlights of this Investigation

- In a traditional CSS, a large amount of time is consumed while reporting, which contributes little to the sensing performance and hence makes the system inefficient. Therefore, we have designed a novel super frame with a look-up table for reporting and hence, the ability to further reduced the sensing time. The LUT updates regularly and thus acts as a sensing database for other SUs connected in co-operative communication.
- To enhance the EE using CSS the sensing time and transmission power were jointly considered when optimizing EE under PU transmission constraints. We derived an optimized co-operative sensing model by maximizing the EE under QoS provisioning while optimizing the sensing time using an LUT. Another problem of CR with QoS provisioning is formulated, i.e., satisfying the SE requirements under the constraint of maximizing EE. For this issue, we analyzed the effect of the spectrum efficiency on the energy efficiency. The literature shows that for different SEs, different values of the sensing time are required. To overcome this problem, we optimized the LUT incorporated EH systems to obtain a trade-off between the sensing time and power utilized during transmission under EE Constraints with QoS provisioning.
- We further implemented a fuzzy-based selection switch in the proposed system to optimize sensing time to provide a symmetrical trade-off between the EE and the SE for 5G-CRN networks

## 2. Materials and Methods

#### 2.1. Network Models

#### 2.2. Primary Network Model

_{i}with Ch

_{i}= 0 (for the channel in idle state) and Ch

_{i}= 1 (for an occupied channel). The state diagram of the primary spectrum utilization is shown in Figure 1. In this model, the spectrum in state ”0” corresponds to idle with probability P

_{0}, and it transits from state ”0” to ”1” with probability (1 − P

_{0}). Conversely, if the spectrum is in state ”1” with probability P

_{1}is moving towards state ”0”, with probability (1 − P

_{1}). Therefore the steady-state probability in two cases is ${\Phi}_{0}\left({P}_{0,}{P}_{1}\right)=\frac{1-{P}_{1}}{2-\left({P}_{1}+{P}_{0}\right)}$ and ${\Phi}_{1}\left({P}_{0,}{P}_{1}\right)=\frac{1-{P}_{0}}{2-\left({P}_{1}+{P}_{0}\right)}$ respectively.

_{s}) be the transmission frame with total frame time duration in T. The modified sensing time ${\tau}_{s(LUT)}\text{}$ is the suggested LUT time that is exploited for co-operative sensing, as shown in Figure 2. Let δ

_{min}be the minimum time frame for SUs to sense the spectrum and τ

_{R}

_{(LUT)}be the reporting time to the cognitive radios base station ${\tau}_{R\left(LUT\right)}<<{\tau}_{s(LUT)}\text{}$:- for example. for T = 20 ms, the reporting time for the maximum τ

_{R}

_{(LUT)}= 0.1 ms [15,21].

_{D}and P

_{FA}using the following relations:

_{s}is the sampling frequency, and γ denotes the average power consumed

#### 2.3. Problem Formulation

_{i}is the probability that the spectrum is vacant ${R}_{1}={\mathrm{log}}_{2}(1+\frac{{P}_{t}{h}_{s}}{{\sigma}_{s}^{2}})$, P

_{t}is the power utilized by the SU during transmission, h

_{s}is the CR link gain, and ${\sigma}^{2}{}_{s}$ denotes the power due to unwanted signals (noise). During miss detection (i.e., the spectrum falsely detected as vacant), the probability is calculated as ${\pi}_{i}(1-{P}_{d})$ and hence the average SE, in this case, using [12] is as follows:

_{i}is the probability of vacant spectrum ${R}_{2}={\mathrm{log}}_{2}(1+\frac{{P}_{t}{h}_{s}}{{P}_{PU}{h}_{PU}+{\sigma}_{s}{}^{2}})$, P

_{PU}is the power utilized by the PU during transmission, and h

_{PU}denotes PU gain. Hence the average value of the spectral efficiency is calculated as follows:

_{s}is the sensing power and P

_{c}is the power consumed by the circuit. During reporting to the LUT stage, the average power consumption is ${\tau}_{R(LUT)}N({\mathrm{P}}_{R}+{P}_{c})$, where ${\mathrm{P}}_{R}$ is the power consumed during reporting to the cognitive radio-base station(CR-BS).

_{s}

_{(LUT)}) as well as the SUs power (P

_{t}) use such that the energy efficiency will be maximized under the constraint that the primary user’s rights are always protected, i.e.,

_{d}) ≤ threshold detection probability ($\widehat{{P}_{d}}=0.9$).

#### 2.4. Solution to the Problem

**(Problem P**. Then an optimal solution of P

_{1})_{1}is provided by achieving a sensing time that provides maximum energy efficiency for a given transmission power of the SUs

**(Problem P**. To achieve this, we took a partial derivative of the energy efficiency w.r.t the sensing time using LUT.

_{1})_{s}

_{(LUT)}is equal to

_{t}, there must be one unique value of ${\tau}_{s(LUT)}\u2019$ for which ${f}_{1}({\tau}_{s(LUT)})$ = 0.

**(Problem P**. Where an optimal solution of P

_{2})_{2}is found by taking the second-order partial derivative of the energy efficiency w.r.t the transmission power.

_{t}for which the energy efficiency is a maximum is equal to:

_{t}. For a particular value of P

_{t}, there must be one unique value of ${P}_{t}{}^{\u2020}$ for which ${f}_{2}({P}_{t})=0$. Therefore $\frac{\partial {\eta}_{EE}}{\partial {P}_{t}}\ge 0\text{}\mathrm{for}\text{}{P}_{t}\in (0,{P}_{t}{}^{\text{\u2020}})\text{}\mathrm{and}\text{}\frac{\partial {\eta}_{EE}}{\partial {P}_{t}}0for\text{}{P}_{t}\in ({P}_{t}{}^{\u2020},\infty )$. Therefore the energy efficiency of the cognitive radio network ${\eta}_{EE}$ has one optimal value of ${P}_{t}$ that maximizes ${\eta}_{EE}$.

## 3. Energy Efficiency-Spectrum Efficiency Trade-Off

## 4. LUT Enabled Energy Harvested Optimization in 5G-CRN

_{H}represents the energy stored in the buffer

_{,}if the energy utilized when sensing is $({P}_{S}{\tau}_{s(LUT)})$${P}_{T}(T-\text{}{\tau}_{s(LUT)})$. M is the number of available channels, and N is the number of SUs. The Algorithm 1 for the sensing energy minimization is shown below.

Algorithm1: Look-up-table-based minimization of the sensing energy (LUT-MSE) |

Pre-requisites: P_{D}, M, N, Signal to noise ratio of primary users (SNR_{PUs}), T, SUs sensing frame (δ_{min}) |

Step 1: Remaining transmission time [n] = T − ${\tau}_{s(LUT)}$ Ɐn |

Step 2: for Ch_{i} = 1 to M do |

Step 3: Sorting of all SUs sensing channels data in terms of decreasing SNR_{PUs}. |

Step 4: Start sensing for M channels by N SUs, for SNR = 0, k = 1 |

Step 5: while sensing < δ_{min} do |

Step 6: update LUT = index [k] |

Step 7: For each SU monitor ${\tau}_{s(LUT)}$ calculate P_{D} by applying step 3 |

Step 8: if ${\tau}_{s(LUT)}<\mathrm{total}\text{}\mathrm{time}\text{}\mathrm{remained}\left[\mathrm{n}\right]$ then |

Step 9: if $\mathrm{total}\text{}\mathrm{time}\text{}\mathrm{remained}\left[\mathrm{n}\right]=\mathrm{total}\text{}\mathrm{time}\text{}\mathrm{remained}\left[\mathrm{n}\right]-{\tau}_{s(LUT)}$ then |

Step 10: Increment the LUT [index] = LUT [index + 1] |

Step 11: end if |

Step 12: k = k + 1 |

Step 13: end while |

Step 14 end for |

_{n}= 0), thereby saving energy. Sensing of the channel starts immediately when the radio comes into “on” mode (A

_{n}= 1) as shown in Figure 4a. While sensing if the channel is found to be busy and another channel near it is found to be idle, handoff occurs immediately to that idle channel, leading to the system’s good throughput.

_{Saved}). Furthermore, the LUT incorporated EH model also saves E

_{.H}

_{.}energy also, as shown in Figure 4b. Therefore, the total energy saved (residual energy) in a fixed frame (T), depending upon the amount of residual energy E

_{r}= E

_{H}+E

_{saved}is left in the battery unit of the SUs. ${P}_{s}{\tau}_{s}$ helps in the calculation of the energy and the power used in sensing. Therefore minimizing ${\tau}_{s}\text{}$ will lead to overcoming two problems, namely less energy consumption while sensing and maximizing the transmission time, which improves the throughput of the system.

_{r}< E

_{s}+ E

_{T}

_{,}then the whole E

_{r}was left unutilized. Here we have proposed a novel fuzzy-based approach that will decide whether the residual energy is utilized for next slot sensing, transmission, or both. The fuzzy switch regularly checks whether the consumption of energy in sensing and transmitting is always less than the residual energy

## 5. Results

_{t}= 25%, 50%, 75% of P

_{t}

_{(max)}and optimal transmission power. Figure 7 shows that the optimal value for the transmission power at ${\tau}_{s(LUT)}=3$ ms yielded a maximum energy efficiency of 58–60%.

_{t}

_{(max)}and optimal power. Solutions 1, 2, and 4 gave the worst EE since the time and power were fixed whereas, for solutions 3 and 5, the EE increased with an increase in the signal-to-noise ratio (SNR), but was almost constant for higher SNR (SNR > 4 dB) values. In solution 6, joint optimization (optimal τ

_{s(LUT)}and optimal P

_{t}) gave better results for low and high SNR, and reached a mark of 88% at the optimal sensing time and transmission power.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Look-up table incorporated into an energy harvesting secondary user (SU) cognitive radio network (CRN) and primary user network.

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**MDPI and ACS Style**

Khalaf, O.I.; Ogudo, K.A.; Singh, M.
A Fuzzy-Based Optimization Technique for the Energy and Spectrum Efficiencies Trade-Off in Cognitive Radio-Enabled 5G Network. *Symmetry* **2021**, *13*, 47.
https://doi.org/10.3390/sym13010047

**AMA Style**

Khalaf OI, Ogudo KA, Singh M.
A Fuzzy-Based Optimization Technique for the Energy and Spectrum Efficiencies Trade-Off in Cognitive Radio-Enabled 5G Network. *Symmetry*. 2021; 13(1):47.
https://doi.org/10.3390/sym13010047

**Chicago/Turabian Style**

Khalaf, Osamah Ibrahim, Kingsley A. Ogudo, and Manwinder Singh.
2021. "A Fuzzy-Based Optimization Technique for the Energy and Spectrum Efficiencies Trade-Off in Cognitive Radio-Enabled 5G Network" *Symmetry* 13, no. 1: 47.
https://doi.org/10.3390/sym13010047