Figure shows a pair of signals s 1 (t) and s 2 (t) that are orthogonal to

Question:

Figure shows a pair of signals s₁ (t) and s₂ (t) that are orthogonal to each other over the observation interval 0 ? t ? 3T. The received signal is defined by below, where w (t) is white Gaussian noise of zero mean and power spectral density N₀/2.

(a) Design a receiver that decides in favor of signals s₁ (t) or s₂ (t), assuming that these two signals are equiprobable.

(b) Calculate the average probability of symbol error incurred by this receiver for E/N₀, where E is the signal energy.