University:
College
Course:
College Engineering
Academic year:

2023
Views:

401

Pages:

2
Author:

D. Krishnan

Problem: Q1: For the following power delay profile calculate and analyze the time dispersion parameters. Here the number of paths, L =4, Need to calculate    Maximum excess delay Rms delay spread Coherence bandwidth Maximum excess delay(𝜎𝑚𝑎𝑥 ) is defined as the 𝜏𝑥 − 𝜏0 where , 𝜏0 is the first arriving signal delay and 𝜏𝑥 is the maximum delay at which a multipath component is within X dB of the strongest arriving multipath signal. 𝜎𝑚𝑎𝑥 = 𝜏𝑥 − 𝜏0 𝜏𝑥 = 5µ𝑆𝑒𝑐 𝑎𝑛𝑑 𝜏0 = 0 So 𝜎𝑚𝑎𝑥 = 5 − 0 = 5µ𝑆𝑒𝑐 RMS delay spread (𝜎𝑟𝑚𝑠 ) 𝜎𝑟𝑚𝑠 = √𝜏̅ 2 − (𝜏̅)2 Where 𝜏̅ is mean excess delay and 𝜏̅ 2 is mean square excess delay, can be calculated using following equations. 𝑚𝑒𝑎𝑛 𝑒𝑥𝑐𝑒𝑠𝑠 𝑑𝑒𝑙𝑎𝑦, 𝑚𝑒𝑎𝑛 𝑠𝑞𝑢𝑎𝑟𝑒 𝑒𝑥𝑐𝑒𝑠𝑠 𝑑𝑒𝑙𝑎𝑦, |𝑎𝑖 |2 𝑖𝑛 𝑑𝐵 -20 -10 0 -10 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 𝜏̅ = 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | (𝜏̅)2 = |𝑎𝑖 |2 𝑖𝑛 𝑛𝑜𝑟𝑚𝑎𝑙 𝑠𝑐𝑎𝑙𝑒 10. log(|𝑎𝑖 |2 𝑖𝑛 𝑑𝐵) 0.01 0.1 1 0.1 2 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 µ𝑆𝑒𝑐 0 1 2 3 Calculate mean excess delay: 𝑚𝑒𝑎𝑛 𝑒𝑥𝑐𝑒𝑠𝑠 𝑑𝑒𝑙𝑎𝑦, 𝜏̅ = 𝜏̅ = 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | (0.01 × 0) + (0.1 × 1) + (1 × 3) + (0.1 × 5) 0.01 + 0.1 + 1 𝜏̅ = 3.6 = 2.97 1.21 𝜏̅ ≅ 2.97µ𝑆𝑒𝑐 𝑚𝑒𝑎𝑛 𝑠𝑞𝑢𝑎𝑟𝑒 𝑒𝑥𝑐𝑒𝑠𝑠 𝑑𝑒𝑙𝑎𝑦, 𝜏̅ = (𝜏̅)2 = 2 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | (0.01 × 02 ) + (0.1 × 12 ) + (1 × 32 ) + (0.1 × 52 ) 0.01 + 0.1 + 1 𝜏̅ = 11.6 = 9.59 1.21 𝜏̅ ≅ 9.59µ𝑆𝑒𝑐 RMS delay spread (𝜎𝑟𝑚𝑠 ) 𝜎𝑟𝑚𝑠 = √𝜏̅ 2 − (𝜏̅)2 𝜎𝑟𝑚𝑠 = √9.59 − (2.97)2 𝜎𝑟𝑚𝑠 = 0.877 µ𝑆𝑒𝑐 Coherencce Bandwidth (𝐵𝑐) 𝐵𝑐 = 1 1 = 2𝜎𝑟𝑚𝑠 2 × 0.877 µ𝑆𝑒𝑐 𝐵𝑐 = 570 𝐾𝐻𝑧 Analysis: For GSM system bandwidth 𝐵𝑠 = 200𝐾ℎ𝑧 Here 𝐵𝑐 > 𝐵𝑠 so flat fading will occur, No need of equalizer. If it is WCDMA, 𝐵𝑠 = 5𝑀𝐻𝑧 𝐵𝑠 > 𝐵𝑐, frequency selective fading. So there will be presence of Inter symbol interference (ISI). So need equalizer i.e., System bandwidth decides type of fading