Question

Let us consider the binary digital communication system in which bit 1 is represented by the waveform Acos(ωt) of bit duration T, where ω is the carrier radial frequency and A is the constant amplitude. On the hand, the bit 0 is represented by the following waveform instead (A/10)cos(ωt). During the transmission the channel has introduced the uniform random phase shift Φ and transmitted waveform is affected by zero-mean white Gaussian noise of variance σ². To demodulate, we perform the multiplication with the extracted carrier 2cos(ωt+Ѳ), where Ѳ is the estimated phase of transmitted signal; followed by low-pass filtering and threshold detection. If the phase difference of received signal and estimated phase is Φ-Ѳ=20° and the average signal-to-noise ratio is 9 dB determine the average error probability assuming equal probable transmission.

Answer 1