Question

Assume you are designing a digital communication system to control an automated assembly plant that operates continuously 24 hours/day. Safety regulations require that the communication system make no more 10 bit errors per day on average. You choose a noncoherent (differentially coherent), binary DPSK system with a data rate of 250 bits/second. The single-sided AWGN PSD is No = 2 x 10-10 W/Hz. a) What is the maximum bit error rate, Pb, for this system?

Answer 1

The maximum bit error rate, Pb, for a noncoherent (differentially coherent), binary DPSK system with a data rate of 250 bits/second and a single-sided AWGN PSD of No = 2 x 10^-10 W/Hz is approximately 0.4999999997.

Step-by-step explanation:

The maximum bit error rate, Pb, for a noncoherent (differentially coherent), binary DPSK system can be calculated using the formula:

Pb = 0.5 * exp(-Eb/No)

where Eb/No is the energy per bit to noise power spectral density ratio. In this case, we have a data rate of 250 bits/second and a single-sided AWGN PSD of No = 2 x 10^-10 W/Hz.

Using the given information, we can calculate the maximum bit error rate:

Pb = 0.5 * exp(-Eb/No) = 0.5 * exp(-250 * 2 x 10^-10) = 0.5 * exp(-5 x 10^-8) ≈ 0.5 * 0.9999999995 ≈ 0.4999999997

So, the maximum bit error rate, Pb, for this system is approximately 0.4999999997.