Question

Find the probability of bit error, PB, for the coherent matched filter detection of the equally likely binary FSK signals s1(t)-0.5 Cos(2000? t) and s2 (t) = 0.5 Cos(2020? t), where the two-sided AWGN power spectral density is No2 = 0.0001. Assume that the symbol duration is T-0.01 sec.

Answer 1

Given: To find out the probability of bit rimon Frequency shift keying: s_1(t)=0.5 cos(2000ft) s_2(t)=0.5 cos(2020 pit) power speed density is N_0/2=10^-4 symbol duration T = 0.01sec Amplitude A = 0.5 N_0=2 times 10^-4 probability error P_e = Q squareroot E_d/2N_0 E_d = A^2T P_e = Q squareroot A^2T/2M_0 squareroot A^2T/2M_0 = squareroot (0.5)^2 times 0.01 /2 times alpha times 10^-4 = squareroot 6.25 =2.5 we know: p = 1-2.5=-1.5 proportional 1