![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 ๐0/2.](https://www.gkseries.com/blog/wp-content/uploads/2023/08/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-๐0-2.jpg)
Q. 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 ๐0/2. Binary signaling, with
0 โฆ ๐(๐ก) and 1 โฆ ๐(๐ก), is used for the transmission, along with an optimal receiver that minimizes the bit-error probability.
Let ๐1(๐ก), ๐2(๐ก) form an orthonormal signal set.
If we choose ๐(๐ก) = ๐1(๐ก) and ๐(๐ก) = โ๐1(๐ก), we would obtain a certain bit-error probability ๐๐.
If we keep ๐(๐ก) = ๐1(๐ก), but take ๐(๐ก) = โ๐ธ ๐2(๐ก), for what value of ๐ธ would we obtain the same bit-error probability ๐๐?
(A) 0
(B) 1
(C) 2
(D) 3
Ans: 3