Problem 1: Let the original symbol duration T be 0.1msec and the number of subcarrier is 16...

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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: 2( ) 1 ( ,) n n N j ft f t n n H f t ae- - p = = ? with N=2, an=1 for n=1,2, t1=0, t2=0.01msec, f1=20Hz and f2=-20Hz 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)
	
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Problem 1: 
 
Let the original symbol duration T be 0.1msec and the number of subcarrier is 16 (k=0:15). Guard time T for cyclic prefix is 
G
0.02msec. The combined symbol period T becomes 0.12msec. Let the OFDM signal go though a time varying channel with the 
s
following 2-path model: 
N
-- jf 2(pt ft)
nn
Hf(,t)= ae with N=2, a =1 for n=1,2, t =0, t =0.01msec, f =20Hz and f =-20Hz 
n XXXXXXXXXX
? n
n=1
th
a.) What is the channel response H for subcarrier k=15 (i.e., 16 subcarrier) for t=0msec:0.02msec:0.12msec (i.e., in a duration of a 
k
transmitted OFDM symbol (with cyclic prefix)? 
b.) If you assume the channel response H is constant in a symbol period (0.12msec), what is maximum variation (difference) of H ? 
15 15
What is the maximum variation of H ? What is the maximum variation of H ? 
0 8
c.) Assume channel response is constant in a symbol period, i.e., H (t|n+1)=H (0.06msec+n*0.12msec) for 
k k
(n+1)*0.12msec>t>n*0.12msec during the (n+1)th symbol period, If you know, H (n) for n=1,3,5,…,11. you use these information 
k
to estimate H (n) for n=2,4,6,8,10 with a linear approximation. What are the estimation errors? 
k
d.) If you know, H (n) for n=1, 11, 21, …,101, you use these information to estimate H (n) for n=1,2,…,100 with a linear 
k k
approximation. What are the estimation errors? (if you cannot program, find the errors for n=6, 16, 26, …96)

David · Accepted Answer

Solution: 
Given That: 
T= 0.1msec 
No of sub carrier= 16. 
TG for cyclic prefix= 0.02 msec 
TS= T + TG= 0.12msec 
a) 
Time varying 2-path channel is given by: 
 (   )  ∑      (       )
The channel response at Kth subcarrier is  
  ( )   
    (        )       (        ) 
         
 
 
 
   ( )   
    (         )       (           
      ) 
    
  
     
         
   ( )   
    (    )       (            
      ) 
   ( )   
    (    )       (      )
b) Variation in H15
Therefore maximum variation is 0.

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...

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