University:
College
Course:
College Engineering
Academic year:

2023
Views:

410

Pages:

1
Author:

Dipin K.

Expression for bit error rate in wired additive white gaussian noise (AWGN) channel Wired Communication Let x be the transmitted signal in wired communication, where additive white gaussian noise channel is considered, then received signal y is represented as 𝑦 =𝑥+𝑛 Where n is the AWGN signal. In AWGN channel Bit error rate(BER) is expressed as, 1 𝐸𝑏 𝐵𝐸𝑅 = 𝑒𝑟𝑓𝑐 (√ ) = 𝑄(√𝑆𝑁𝑅) 2 𝑛0 Where 𝑒𝑟𝑓𝑐(𝑥) is the complementary error function, 𝐸𝑏 is the noise signal energy and 𝑛0 is the variance. This can also represent in terms of probability (Q) function and signal to noise power 𝑃 ratio (SNR), expressed as 𝑆𝑁𝑅 = (𝜎2) So BER = 𝑄 (√ 𝑃 ) 𝜎2 Where 𝑃 is the signal power and 𝜎 2 is the noise power The equation for probability of error in wired system can be formed by applying Chernoff bound, i.e., 𝑄(𝑥) ≤ 1 2 𝑒 −𝑥 2 So 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟(𝑃𝑒) = 1 −𝑆𝑁𝑅 𝑒 2 2 Example: Q: Calculate the SNR required to achieve a probability of error of 10−6 in a wired AWGN system. Solution: We know that for the expression for probability of error in a wired AWGN system is 1 −𝑆𝑁𝑅 𝑃𝑒 = 𝑒 2 2 Here 𝑃𝑒 = 10−6 , So SNR can be calculated as 𝑆𝑁𝑅 = −2𝑙𝑜𝑔𝑒 (2𝑃𝑒 ), So SNR can be calculated as SNR = 14.19dB. Conclusion: The system require 14.19dB of SNR to get a bit error rate of 10−6 .