Question $2$:

Consider a digital communication system using BPSK signaling at a transmission rate of $4\mathrm{.}8$ kbps $.$

a$)$ Find the probability of bit error of BPSK when $\frac{E_b}{N_o}=8dB$ in AWGN channel.

b$)$ Suppose that you need to increase the data rate to $38\mathrm{.}4$ kbps using the same bandwidth as BPSK signaling. You can achieve this increase using M$-$PSK signaling without needing to increase the transmission bandwidth. M can be determined as the number of points in the M$-$PSK constellation and can be increased until the data rate becomes $38\mathrm{.}4$ kbps while the bandwidth remains the same. Determine the number of points $M$ in the new constellation.

Course title: Digital communications