A Statistical Estimation of 5G Massive MIMO Networks’ Exposure Using Stochastic Geometry in mmWave Bands
Abstract
:1. Introduction
1.1. Current Approaches in Exposure Estiamation
1.2. Our Approach and Contributions
2. System Model
2.1. Path Loss Model
2.2. Antenna Model
2.2.1. Element Pattern
2.2.2. Array Pattern
2.3. Channel Model
2.3.1. Array Gain
2.3.2. Channel Gain
3. Exposure Estimation
4. Numerical Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Appendix B
Abbreviation | Meaning |
---|---|
MIMO | Multiple Input Multiple Output |
SNR | Signal to noise ratio |
MISR | Mean interference to signal ratio |
BS | Base station |
mmWave | Millimeter Wave |
ICNIRP | International Commission on Non-Ionizing Radiation Protection |
PPP | Poisson point process |
CDF | Cumulative distribution function |
MT | Mobile terminal |
URA | Uniformly spaced rectangular array |
AoD | Angle of departure |
UMI | Urban microcell |
Probability distribution function | |
MGF | Moment generating function |
PCE | Polynomial chaos expansion |
PFGL | Probability generating functional |
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Symbol | Description |
---|---|
Total Power Received at the center of the cell | |
Power received from the ith BS at the center of the cell | |
Transmitted power from all the BSs | |
Channel and antenna gain from the ith BS to the MT | |
Path loss experienced by the transmitted signal from the ith BS to the MT | |
Zenith and azimuth angles in the local coordinate system centered at the origin of the array | |
Radiation pattern and its vertical and horizontal components respectively | |
Vertical and horizontal beamwidths of the antennas in degrees | |
Numerically smallest number of | |
Antenna’s front-to-back ratio | |
Vertical and horizontal sidelobe attenuation levels | |
Array pattern of the antenna | |
Phase shift due to the antenna element placement | |
Weighting factor due to the antenna element | |
Number of horizontal and vertical antenna elements | |
Zenith and azimuth electrical down-tilt steering angle | |
Vertical and horizontal antenna element spacing | |
Gamma function | |
The Poisson point process and its density describing the BS distribution in the cell | |
Expectation with respect to the random variable | |
Density of the active MTs in the cell | |
Emission probability of the BSs | |
Mobile terminal at the center of the cell | |
the distance between BSi and MT0 | |
Path loss exponent assumed constant in the whole cell | |
Moment generating function and characteristic function of the random variable | |
CDF of the random variable | |
Upper incomplete gamma function | |
Lower incomplete gamma function | |
Iid random variable describing the channel and antenna gains | |
Generalized hypergeometric function |
Parameter | Value |
---|---|
Frequency | |
Scenario | |
Tx Power | |
Array type | |
Number of elements | |
Antenna spacing | |
Half-Power Beamwidth | |
Link Type | |
RF Bandwidth | |
User Terminal Height | |
Base Station Height |
Parameter | Value | Description |
---|---|---|
Gamma distribution shape parameter | ||
Gamma distribution scale parameter | ||
Exponential distribution exponent |
Parameter | Value |
---|---|
Input Variable | Total Sobol Indices |
---|---|
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Al Hajj, M.; Wang, S.; Thanh Tu, L.; Azzi, S.; Wiart, J. A Statistical Estimation of 5G Massive MIMO Networks’ Exposure Using Stochastic Geometry in mmWave Bands. Appl. Sci. 2020, 10, 8753. https://doi.org/10.3390/app10238753
Al Hajj M, Wang S, Thanh Tu L, Azzi S, Wiart J. A Statistical Estimation of 5G Massive MIMO Networks’ Exposure Using Stochastic Geometry in mmWave Bands. Applied Sciences. 2020; 10(23):8753. https://doi.org/10.3390/app10238753
Chicago/Turabian StyleAl Hajj, Maarouf, Shanshan Wang, Lam Thanh Tu, Soumaya Azzi, and Joe Wiart. 2020. "A Statistical Estimation of 5G Massive MIMO Networks’ Exposure Using Stochastic Geometry in mmWave Bands" Applied Sciences 10, no. 23: 8753. https://doi.org/10.3390/app10238753
APA StyleAl Hajj, M., Wang, S., Thanh Tu, L., Azzi, S., & Wiart, J. (2020). A Statistical Estimation of 5G Massive MIMO Networks’ Exposure Using Stochastic Geometry in mmWave Bands. Applied Sciences, 10(23), 8753. https://doi.org/10.3390/app10238753