Question

In a binary antipodal signaling scheme, the signals are given by

s₁(t)=−s₂(t)=⎧2At/T, 0≤t≤ T/2
⎨2A(1− t/T) T/2≤t≤T
⎩0, otherwise

The channel is AWGN and Sₙ(f)= N₀/2. The two signals have prior probabilities p and 1−p. 1. Determine the structure of the optimal receiver.
2. Determine an expression for the error probability.
3. Plot the error probability as a function of p for 0≤p≤1.

Answer 1

Questions about a binary antipodal signaling scheme in AWGN channels involve determining the optimal receiver structure, error probability, and plotting error probabilities versus prior probabilities, which are key concepts in signal processing and communications theory at the college level.

Step-by-step explanation:

The questions posed by the student relate to a binary antipodal signaling scheme in the presence of Additive White Gaussian Noise (AWGN) and involve determining the optimal receiver structure and the error probability, as well as plotting the error probability as a function of the prior probabilities. These questions involve advanced concepts in signal processing, modulation, and communications theory which are typically covered in electrical engineering and applied physics programs at the college level.

The optimal receiver for a binary antipodal signaling scheme in an AWGN channel is the matched filter receiver, which maximizes the signal-to-noise ratio. The error probability can be found using the Q-function, which quantifies the tail probabilities of the standard normal distribution.

Superposition, interference, and antipodal signals are key concepts in understanding how the optimal receiver functions in conditions of AWGN, and they also help in the interpretation and plotting of error probability as a function of prior probabilities.