Performance of Millimeter Wave Dense Cellular Network Using Stretched Exponential Path Loss Model
Abstract
:1. Introduction
Motivation and Contribution
- The SEPLM is validated for mmwave NLOS link using experimental measurement data from NYUSIM for an urban outdoor scenario.
- A system model is proposed where LOS links follow the standard distance-dependant path loss model and NLOS links are modeled using SEPLM. A 3GPP LOS probability is employed to determine the LOS and NLOS link state, and the impact of blockages in the surroundings is modeled as path loss parameters.
- Based on the system model, stochastic geometry is used to derive generalized mathematical expressions for SINR coverage probability and ASE. The expressions are numerically analyzed to observe the performance over a range of SINR thresholds and BS densities.
2. System Model
2.1. Spatial Network Model
2.2. Path Loss and Channel Model
- , defines the environment where the obstacles scale linearly with the path length between UE and BS. (3) can be written as . This case captures obstacles distribution similar to the one defined in [22], based on random shape theory that is widely adopted for performance analysis of mmwave networks. The randomly oriented obstacles are uniformly distributed over the plane intersecting the path length r between BS and UE and scales linearly with the distance r. in this case depends upon the attenuation of each blocking object.
- , defines the environment where the obstacle scales with . Assuming UE to be located at the centre of a disc and signal propagates within the disc sector extending to the BS, (3) can be written as and takes the form analogous to LOS probability function in [43] expressed as , where L depends upon the density of large obstructing objects in the propagation environment. A larger value of signifies a sparse environment having high LOS probability with distance.
- defines the case similar to the ray propagation in lattice modeling of urban areas with regular building blockage [28]. Here, depends on the properties of the considered lattice and the reflectivity of the obstacle.
- The special values of and in SEPLM reduces to multislope path loss model [44] consistent with the one adopted in 3GPP standardization.
2.3. Antenna Model
3. SINR Coverage Probability and Area Spectral Efficiency
3.1. SINR Coverage Probability
3.1.1. , Where p Is a Positive Integer
3.1.2.
3.1.3.
3.2. Area Spectral Efficiency
3.2.1. ASE for
3.2.2. ASE for
4. Simulation Results and Discussions
Fitting the Path Loss Model
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Derivation of SINR Coverage Probability
Appendix A.1. Laplace Transform of Interference
Appendix A.2. Laplace Transform for
Appendix A.3. Laplace Transform for ζ = 1
Appendix B. Fitting Stretched Exponential Path Loss Model to the Measurement Data
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Notation | Definition |
---|---|
BS, UE and Interfering UE point process | |
BS and UE densities | |
Path loss at distance r | |
LOS path loss exponent | |
NLOS path loss parameter | |
Operating frequency | |
B | Channel Bandwidth |
Cell radius, | |
Noise power | |
PDF of distance r between typical UE and tagged BS | |
Distance between interfering UE and tagged BS | |
Path loss on the link | |
Small-scale fading on the link from serving BS to typical UE | |
Small scale fading on interfering link | |
Maximum directivity gain, | |
Antenna HPBW, | |
Side lobe gain, | |
Directivity gain of interfering UE | |
Beamwidth of interfering UE | |
SINR coverage probability at threshold T | |
SINR coverage probability, on l link for | |
Probability of link being in l condition for | |
Laplace Transform of interference component | |
ASE | Area spectral efficiency |
kth order logarithmic function |
Parameter | Value |
---|---|
f | 28 GHz |
B | 500 MHz |
Scenario | UMi |
Environment | NLOS |
Lower-Upper bound of transmitter-receiver separation | 10–350 m |
Transmit Power | 30 dBm |
Number of receiver locations | 100 |
Other parameters | default |
Parameter | Value |
---|---|
f | 28 GHz |
B | 500 MHz |
, | 10 dB |
, | −10 dB |
, | 30 |
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Mariam, H.; Ahmed, I.; Ali, S.; Aslam, M.I.; Rehman, I.U. Performance of Millimeter Wave Dense Cellular Network Using Stretched Exponential Path Loss Model. Electronics 2022, 11, 4226. https://doi.org/10.3390/electronics11244226
Mariam H, Ahmed I, Ali S, Aslam MI, Rehman IU. Performance of Millimeter Wave Dense Cellular Network Using Stretched Exponential Path Loss Model. Electronics. 2022; 11(24):4226. https://doi.org/10.3390/electronics11244226
Chicago/Turabian StyleMariam, Hira, Irfan Ahmed, Sundus Ali, Muhammad Imran Aslam, and Ikram Ur Rehman. 2022. "Performance of Millimeter Wave Dense Cellular Network Using Stretched Exponential Path Loss Model" Electronics 11, no. 24: 4226. https://doi.org/10.3390/electronics11244226
APA StyleMariam, H., Ahmed, I., Ali, S., Aslam, M. I., & Rehman, I. U. (2022). Performance of Millimeter Wave Dense Cellular Network Using Stretched Exponential Path Loss Model. Electronics, 11(24), 4226. https://doi.org/10.3390/electronics11244226