University:
College
Course:
College Engineering
Academic year:

2023
Views:

214

Pages:

2
Author:

Dipin K.

Problem: Power delay profile is given. Power is given in normal scale. 1. Calculate rms delay spread( 𝜎𝑟𝑚𝑠 ) 2. If the modulation is BPSK find Bit rate (𝑅𝑏). |𝑎𝑖 |2 𝑖𝑛 𝑛𝑜𝑟𝑚𝑎𝑙 𝑠𝑐𝑎𝑙𝑒 10. log(|𝑎𝑖 |2 𝑖𝑛 𝑑𝐵) 1 1 1 RMS delay spread (𝜎𝑟𝑚𝑠 ) 𝜏𝑖 µ𝑆𝑒𝑐 0 1 2 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, 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 𝜏̅ = 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | (𝜏̅)2 𝑚𝑒𝑎𝑛 𝑠𝑞𝑢𝑎𝑟𝑒 𝑒𝑥𝑐𝑒𝑠𝑠 𝑑𝑒𝑙𝑎𝑦, 2 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 = 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | Calculate mean excess delay: 𝑚𝑒𝑎𝑛 𝑒𝑥𝑐𝑒𝑠𝑠 𝑑𝑒𝑙𝑎𝑦, 𝜏̅ = 𝜏̅ = 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | (1 × 0) + (1 × 1) + (1 × 2) 1+1+1 𝜏̅ = 3 =1 3 𝜏̅ ≅ 1µ𝑆𝑒𝑐 𝑚𝑒𝑎𝑛 𝑠𝑞𝑢𝑎𝑟𝑒 𝑒𝑥𝑐𝑒𝑠𝑠 𝑑𝑒𝑙𝑎𝑦, 2 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 𝜏𝑖 𝜏̅ = 2 ∑𝐿−1 𝑖=0 |𝑎𝑖 | 2 (1 × 02 ) + (1 × 12 ) + (1 × 22 ) 𝜏̅ = 1+1+1 2 𝜏̅ 2 = 5 = 1.67 3 𝜏̅ 2 ≅ 1. µ𝑆𝑒𝑐 RMS delay spread (𝜎𝑟𝑚𝑠 ) 𝜎𝑟𝑚𝑠 = √𝜏̅ 2 − (𝜏̅)2 𝜎𝑟𝑚𝑠 = √1.67 − (1)2 𝜎𝑟𝑚𝑠 = 0.816 µ𝑆𝑒𝑐 Symbol duration 𝑇𝑠 = 10𝜎𝑟𝑚𝑠 = 8.16µ𝑆𝑒𝑐 1 1 In BPSK symbol rate = Bit rate( 𝑅𝑏) = 𝑇𝑠 = 8.16µ𝑆𝑒𝑐 = 122.44 𝐾𝑠𝑦𝑚𝑏𝑜𝑙𝑠/𝑠𝑒𝑐 *note In QPSK, symbol duration, 𝑇𝑠 = 2𝑇𝑏 i.e., two times bit duration. So for QPSK, 2𝑥122.44 𝐾𝑠𝑦𝑚𝑏𝑜𝑙𝑠/ sec = 245 𝐾𝑠𝑦𝑚𝑏𝑜𝑙𝑠/𝑠𝑒𝑐