Problem 1: Let the original symbol duration T be 0.1msec and the number of subcarrier is 16 (k=0:15). Guard time TG for cyclic prefix is 0.02msec. The combined symbol period Ts becomes 0.12msec. Let the OFDM signal go though a time varying channel with the following 2-path model:

a.) What is the channel response Hk for subcarrier k=15 (i.e., 16th subcarrier) for t=0msec: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 H0? What is the maximum variation of H8?

c.) Assume channel response is constant in a symbol period, i.e., Hk(t|n+1)=Hk(0.06msec+n*0.12msec) for (n+1)*0.12msec>t>n*0.12msec during the (n+1)th symbol period, If you know, Hk(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, Hk(n) for n=1, 11, 21, ...,101, you use these information to estimate Hk(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)