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Homework 1 1. The following table lists a set of empirical path loss measurements. Assume a carrier frequency fc = 2 GHz. Distance from transmitter P/Pt 5 m 60 dB 25 m -80 dB 65 m -105 dB 110 m -115 dB 400 m 135 dB 1000 m -150 dB a. Find the parameters of a single-slope path loss model plus log-normal shadowing that best fit this data assuming K is calculated from free-space path loss at the reference distance dr = 1 m. b. Find the path loss at 2 km based on this model. c. Find the outage probability at a distance d assuming the received power at d due to path loss alone is 10 dB above the required power for non-outage.

Homework 1 1. The following table lists a set of empirical path loss measurements. Assume a carrier frequency fc = 2 GHz. Distance from transmitter P/Pt 5 m 60 dB 25 m -80 dB 65 m -105 dB 110 m -115 dB 400 m 135 dB 1000 m -150 dB a. Find the parameters of a single-slope path loss model plus log-normal shadowing that best fit this data assuming K is calculated from free-space path loss at the reference distance dr = 1 m. b. Find the path loss at 2 km based on this model. c. Find the outage probability at a distance d assuming the received power at d due to path loss alone is 10 dB above the required power for non-outage.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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### Path Loss Measurements and Calculations **Homework 1** 1. The following table lists a set of empirical path loss measurements. Assume a carrier frequency \( f_c = 2 \) GHz. | Distance from transmitter | Path Loss (PL) | |---------------------------|----------------| | 5 m | 60 dB | | 25 m | 75 dB | | 65 m | 90 dB | | 110 m | 105 dB | | 400 m | 115 dB | | 1000 m | 130 dB | **Tasks:** a. Find the parameters of a single-slope path loss model plus log-normal shadowing that best fit this data assuming \( P_{L} \) is calculated from free-space path loss at the referenced distance \( d_0 = 1 \) m. b. Find the path loss at 2 km based on this model. c. Find the outage probability at a distance assuming the received power at \( d \) due to path loss alone is 10 dB above the required power for non-outage. --- **Explanatory Details:** - **Path Loss (PL):** This is the reduction in power density of an electromagnetic wave as it spreads out from a transmitter. The values are provided in decibels (dB). - **Distance from transmitter:** This indicates how far a receiver is situated from the transmitter, measured in meters (m). - **Carrier Frequency:** The frequency of the carrier wave used for transmission. In this case, it is specified to be 2 GHz. **Steps to Solve:** - For **Task a**, determine the parameters such as the path loss exponent and shadowing deviation by fitting the given data to a single-slope path loss model, which uses the measured distances and corresponding path loss values. - For **Task b**, apply the derived model to calculate the path loss at a distance of 2 km. - For **Task c**, use the model to analyze the probability of signal outage based on the specified conditions. This assignment will enhance understanding of empirical measurements and modeling of signal degradation with distance, which is critical in network planning and optimization.
Transcribed Image Text:### Path Loss Measurements and Calculations **Homework 1** 1. The following table lists a set of empirical path loss measurements. Assume a carrier frequency \( f_c = 2 \) GHz. | Distance from transmitter | Path Loss (PL) | |---------------------------|----------------| | 5 m | 60 dB | | 25 m | 75 dB | | 65 m | 90 dB | | 110 m | 105 dB | | 400 m | 115 dB | | 1000 m | 130 dB | **Tasks:** a. Find the parameters of a single-slope path loss model plus log-normal shadowing that best fit this data assuming \( P_{L} \) is calculated from free-space path loss at the referenced distance \( d_0 = 1 \) m. b. Find the path loss at 2 km based on this model. c. Find the outage probability at a distance assuming the received power at \( d \) due to path loss alone is 10 dB above the required power for non-outage. --- **Explanatory Details:** - **Path Loss (PL):** This is the reduction in power density of an electromagnetic wave as it spreads out from a transmitter. The values are provided in decibels (dB). - **Distance from transmitter:** This indicates how far a receiver is situated from the transmitter, measured in meters (m). - **Carrier Frequency:** The frequency of the carrier wave used for transmission. In this case, it is specified to be 2 GHz. **Steps to Solve:** - For **Task a**, determine the parameters such as the path loss exponent and shadowing deviation by fitting the given data to a single-slope path loss model, which uses the measured distances and corresponding path loss values. - For **Task b**, apply the derived model to calculate the path loss at a distance of 2 km. - For **Task c**, use the model to analyze the probability of signal outage based on the specified conditions. This assignment will enhance understanding of empirical measurements and modeling of signal degradation with distance, which is critical in network planning and optimization.
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