$($a$)$ A binary transmitter sends two signals with equal probability. The received signals are given by

$s_1(t)=A\sqrt[\phantom{2}]{\frac{T}{2}}cos{}_{c}t,$ and $,s_2(t)=A\sqrt[\phantom{2}]{\frac{T}{2}}sin{}_{c}t$

If the noise spectra density at the receiver is $N_0={10}^{-9}\frac{W}{H}z,$ find the probability of error. What should be the value of $A$ to get an error rate of ${10}^{-5}$ when the data rate is $1M\frac{b}{s}.$

$($b$)$ A digital signal at $4M\frac{b}{s}$ is transmitted using BFSK modulation. The bit error probability $P_e$ measured on the received data is ${10}^{-5}.$ If the measured noise in the signal band is $5\mathrm{.}2$ mW $,$ find the received carrier power.

$($c$)$ Draw the signal space representation of BFSK signal and find the distance between the carriers in terms of $E_b$ and compare the same with BPSK signal.