A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density N0/2. Binary signaling, with 0 ↦ p(t) and 1 ↦ q(t), is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. Let φ1 (t), φ2(t) form an orthonormal signal set. If we choose p(t) = φ1 (t) and q(t) = −φ1 (t), we would obtain a certain bit-error probability Pb. If we keep p(t) = φ1(t), but take \(q\left( t \right) = \sqrt E\) φ2 (t) for what value of E would we obtain the same bit-error probability Pb?

A single bit, equally likely to be 0 and 1, is to be sent across an ad

1.	A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density N0/2. Binary signaling, with 0 ↦ p(t) and 1 ↦ q(t), is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. Let φ1 (t), φ2(t) form an orthonormal signal set. If we choose p(t) = φ1 (t) and q(t) = −φ1 (t), we would obtain a certain bit-error probability Pb. If we keep p(t) = φ1(t), but take \(q\left( t \right) = \sqrt E\) φ2 (t) for what value of E would we obtain the same bit-error probability Pb?
A.	0
B.	1
C.	2
D.	3
Answer» E.