Let the original symbol duration T be 0.1msec and the number of subcarrier is 16 (k=0:15). G d time TG for cyclic prefix is 0.02msec. The combined symbol period Ts becomes 0.12msec. Let the OFDM signal go through a time varying channel with the following 2-path model:

H(f, t) = ∑ a_n e^{-j2Π(ftΠ - fΠt)} with N=2, a_n=1 for n=1,2, t₁=0, t₂=0.01msec, f₁=20Hz and f₂=-20Hz

a. What is the channel response H_k for subcarrier k=15 (i.e., 16th sub carrier) for t=Omsec:0.02msec:0.12msec (i.e., in a duration of a transmitted OFDM symbol (with cyclic prefix)?

b. If you assume the channel response H15 is constant in a symbol period (0.12msec), what is maximum variation (difference) of H15?

What is the maximum variation of Ho? What is the maximum variation of H8?

c. Assume channel response is constant in a symbol period, ,fed), H_k(t|n+1)=H_k(0.06msec+n*0.12msec) for (n+1)*0.12msec>t>n*0.12 m sec during the (n+1)^th sym1:61 period, If you know, H_k(n) for n=1,3,5,...,11. you use these information to estimate Hk(n) for n=2,4,6,8,10 with a linear approximation. What are the estimation errors?

d. If you know, H_k(n) for n=1, 11, 21, ...,101, )(oboe these information to estimate H_k(n) for n=1,2,...,100 with a linear approximation. What are the estimation errors? (if you cannot program, find the errors for n=6, 16, 26, ...96)