ELCT562_PA2

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Clemson University *

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562

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Electrical Engineering

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Apr 3, 2024

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ELCT 562 PA#2 1. (40 pts) In https://www.mathworks.com/help/lte/ug/propagation-channel- models.html, three different power delay profiles (i.e., EPA, EVA, and ETU) for 4G LTE are provided. For each model, determine the following: a. Average delay spread The following equation can be used to determine the average delay spread given the power delay profiles below. T mean = ∑ T i ∗ 10 A dB 10 10 A dB 10 b. RMS delay spread The following equation can be used to determine the RMS delay spread given the average delay spread calculated from part A. T rms = √ ∑ ( τ i − T mean ) 2 10 A db 10 ∑ 10 A db 10 c. Coherence bandwidth The following equation can be used to determine the coherence bandwidth given the average deay spread calculated from part B. B c ≈ 1 5 T rms for r = 0.5 Solution: Figure 1: EPA Delay Profile

Figure 2: EVA Delay Profile Figure 3: ETU Delay Profile The following table was calculated using the delay profiles and Matlab code mentioned below. Profile EPA EVA ETU Average Delay Speed [ns] 0.442 0.0254 0.0561 RMS Delay Speed [ns] 0.431 0.0356 0.0991 Coherence Bandwidth [MHz] 4.637 0.561 0.561 Matlab code: %ELCT562 HW clc clear all % Power delay profile (EPA) EPA_tList = [0 30 70 90 110 190 410]*1e-9; % ns EPA_aList = [0 -1 -2 -3 -8 -17.2 -20.8]; % dB EPA_aListLin = 10.^(EPA_aList/10); EPA_Taverage = sum(EPA_tList.*EPA_aListLin)/sum(EPA_aListLin) EPA_Trms = sqrt(sum((EPA_tList-EPA_Taverage).^2.*EPA_aListLin)/sum(EPA_aListLin)) EPA_Bc=0.2/EPA_Trms % Power delay profile (EVA) EVA_tList = [0 30 150 310 370 710 1090 1730 2510]*1e-9; % ns EVA_aList = [0 -1.5 -1.4 -3.6 -0.6 -9.1 -7 -12 -16.9]; % dB EVA_aListLin = 10.^(EVA_aList/10); EVA_Taverage = sum(EVA_tList.*EVA_aListLin)/sum(EVA_aListLin) EVA_Trms = sqrt(sum((EVA_tList-EVA_Taverage).^2.*EVA_aListLin)/sum(EVA_aListLin))

EVA_Bc=0.2/EVA_Trms % Power delay profile (ETU) ETU_tList = [0 50 120 200 230 500 1600 2300 5000]*1e-9; % ns ETU_aList = [-1 -1 -1 0 0 0 -3 -5 -7]; % dB ETU_aListLin = 10.^(ETU_aList/10); ETU_Taverage = sum(ETU_tList.*ETU_aListLin)/sum(ETU_aListLin) ETU_Trms = sqrt(sum((ETU_tList-ETU_Taverage).^2.*ETU_aListLin)/sum(ETU_aListLin)) ETU_Bc=0.2/EVA_Trms 2. (20 pts) Assume that the maximum Doppler spread frequency is 50 Hz. Calculate the coherence time based on the rule-of-thump rule. Coherence Time = T c = √ 9 16 π f d max 2 = 0.423 f d max T c = 0.423 50 = 0.00846 s 3. (40 pts) Consider communications between two cars approaching each other. Assume that the channel coherence bandwidth is larger than the signal bandwidth. a. Does the wireless channel model follow flat-fading or frequency-selective fading? Why? The problem states that the coherence bandwidth is larger than the signal bandwidth which causes flat-fading. This is due to the channels frequency response at the bandwidth for the signal being considered constant or “flat-fading”. b. Is the 𝐾 -factor of the small-scale channel model (i.e., Rician model) small (e.g., 0) or large (e.g., 20)? Why? The K-factor for this example would be large. This is due to strong domiant path from the Doppler effect from two cars directly approaching each other, essentially increasing the k factor. c. If the speed of each car is 10 m/s and 𝑓 c = 3 GHz, what would be the carrier frequency of the received signals at the receiver end? Is it still 3 GHz? Since both cars are moving towards each other at the same rate the carrier frequency should stay the same at the receiver end. It would be still 3 GHz.

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