# Energy Consumption Analysis for Continuous Phase Modulation in Smart-Grid Internet of Things of beyond 5G

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## Abstract

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## 1. Introduction

- We establish a realistic power consumption model through the analysis of circuit power consumption, transmission power consumption, and reception power consumption on a point-to-point communication link; in particular, we consider three operation modes of the sensors, including sleeping mode, transient mode, and active mode.
- Based on the above power consumption model and a typical automatic repeat request (ARQ)-based wireless transmission protocol, the EC incurred by successfully sending a single information bit is numerically evaluated under different configurations of CPM parameter values. In particular, we consider different waveform pulses of the CPM, including the rectangular pulse, rising cosine pulse, and GMSK pulse, for comprehensive coverage. We also investigate the impact of the distance between the transmitter and the receiver, the impact of the received SNR, the impact of the modulation order, and the average number of transmissions required for sending a single packet, under various modulation schemes considered.
- We compare the EC per successfully transmitted bit of the CPM with that of conventional non-constant envelope modulation methods, such as offset quadrature phase-shift keying (OQPSK) used in the Zigbee standard and QAM modulation supported by the current 5G standard. Our simulation results and analysis demonstrate that CPM enjoys a significantly lower EC than OQPSK and 16QAM in the scenario considered, which is valuable for the standard evolution of beyond 5G tailored for the important use case of low-power SG-IoT.

## 2. The EC Model

#### 2.1. Packet Structure

#### 2.2. Basics of CPM

#### 2.3. Circuit Power Consumption

#### 2.4. Transmission Power Consumption

#### 2.5. EC per Successfully Transmitted Bit

## 3. CPM Parameter Selection

## 4. Evaluation the EC of CPM

#### 4.1. Identification of Major Performance Influencing Factors

#### 4.2. Simulation Results and Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The communication modules and the corresponding power consumption model of a point-to-point wireless communication system.

**Figure 3.**A typical power consumption model of the RF signal processing unit of a point-to-point wireless communication system.

**Figure 4.**The relationship between the EC per successfully transmitted bit (${E}_{b}$) and the received SNR ($\gamma $) for OQPSK, 16QAM, and the CPM signals with different pulse shaping functions (REC, RC, and GMSK), while assuming $M=16$ and $N=3$ for the three CPM waveforms, as well as $d=10$ m and the AWGN channel for all the modulation schemes considered.

**Figure 5.**The relationship between the EC per successfully transmitted bit (${E}_{b}$) and the communication distance (d) for OQPSK, 16QAM, and the CPM signals with different pulse shaping functions (REC, RC, and GMSK) over the AWGN channel, while assuming $M=16$, $N=3$ and $\gamma =8$ dB for the three CPM waveforms, as well as $\gamma =15$ dB for OQPSK and 16QAM signals.

**Figure 6.**The relationship between the EC per successfully transmitted bit (${E}_{b}$) and the modulation efficiency m for the CPM signals with different pulse shaping functions (REC, RC, and GMSK) over the AWGN channel, while assuming $N=3$, $\gamma =8$ dB and $d=10$ m.

**Figure 7.**The relationship between the average number of transmissions required for successfully sending a single packet and the received SNR ($\gamma $), while considering OQPSK, 16QAM, and the CPM signals with different pulse shaping functions (REC, RC, and GMSK) over the AWGN channel. Assume that $M=16$ and $N=3$ for the three CPM waveforms, and $d=10$ m for all the modulation schemes compared.

**Table 1.**The value of ${d}_{\mathrm{min}}^{2}$ when we set $M=2,4,8,16$, $h=0.75$, and $N=3$. For GMSK, the time-bandwidth product $BT$ is set to 0.3, where B is the $-3$ dB bandwidth of the Gaussian pulse.

Waveform | $\mathit{M}=2$ | $\mathit{M}=4$ | $\mathit{M}=8$ | $\mathit{M}=16$ |
---|---|---|---|---|

REC | 2.31648 | 1.41550 | 2.12325 | 2.831 |

RC | 2.96059 | 5.30037 | 6.12447 | 8.16596 |

GMSK | 2.89955 | 4.69275 | 5.95011 | 7.93348 |

Parameters | Values |
---|---|

Symbol rate for transmitted signals | 20 ksps |

${L}_{P}$, ${L}_{H}$, and ${L}_{L}$ | 4, 3, and 30 bytes |

Power spectral density of AWGN at the receiver (${N}_{0}$) | −174 dBm/Hz |

Noise figure of the RF front-end of the receiver (${N}_{f}$) | 10 dB |

Equivalent antenna gain (${A}_{0}$) | 30 dB |

Bandwidth (W) | 20 kHz |

Additional noise (${M}_{\mathrm{l}}$) | 10 dB |

${P}_{\mathrm{T}0}$ | 15.9 mW |

${P}_{R0}$ | 58.2 mW |

M | 2, 4, 8, 16 |

h | 0.75 |

N | 3 |

Path-loss exponent ($\alpha $) | 3.5 |

Drain efficiency ($\eta $) | 0.7 for CPM; 0.35 for OQPSK and 16QAM |

Peak-to-average power ratio ($\xi $) | 0 dB for CPM; 3.5 dB for OQPSK; 6.7 dB for 16QAM |

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**MDPI and ACS Style**

Gao, H.; Lu, Y.; Yang, S.; Tan, J.; Nie, L.; Qu, X.
Energy Consumption Analysis for Continuous Phase Modulation in Smart-Grid Internet of Things of beyond 5G. *Sensors* **2024**, *24*, 533.
https://doi.org/10.3390/s24020533

**AMA Style**

Gao H, Lu Y, Yang S, Tan J, Nie L, Qu X.
Energy Consumption Analysis for Continuous Phase Modulation in Smart-Grid Internet of Things of beyond 5G. *Sensors*. 2024; 24(2):533.
https://doi.org/10.3390/s24020533

**Chicago/Turabian Style**

Gao, Hongjian, Yang Lu, Shaoshi Yang, Jingsheng Tan, Longlong Nie, and Xinyi Qu.
2024. "Energy Consumption Analysis for Continuous Phase Modulation in Smart-Grid Internet of Things of beyond 5G" *Sensors* 24, no. 2: 533.
https://doi.org/10.3390/s24020533