4.12 Performance analysis of binary orthogonal signals with

Orthogonal signals with equally likely bits, $r_t=s_m(t)+N_t$ for $0\le t\le T$ , $m=1$ , $m=2$ , and $s_1\cdot s_2=0$ .

Correlation (correlator-type) receiver

$r_t\implies (r=\left(\begin{array}{c}{r}_1\\ r_2\end{array}\right)=s_m+)$ (see )

Decide $s_1(t)$ was transmitted if $r_1\ge r_2$ .

Alternatively, if $s_1(t)$ is transmitted we decide on the wrong signal if $r_2> r_1$ or ${}_2> {}_1+\sqrt{E_s}$ or when ${}_2-{}_1> \sqrt{E_s}$ .