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Unformatted text preview: ECE 5670 : Digital Communications (Spring 2011) Homework 8 Due April 7 in class Instructor: Salman Avestimehr Office 325 Rhodes Hall 1. Consider the 2-tap ISI channel: y [ m ] = h x [ m ] + h 1 x [ m- 1] + w [ m ] , m 1 . (1) We wish to communicate using the OFDM approach. (a) What is the minimum length of the cyclic prefix L needed? (b) For an OFDM symbol of length N c , denote the OFDM channel coefficients, as in the lecture notes, by h ,..., h N c- 1 . Choose h = 1 and h 1 = 0 . 25 and suppose that that the sampling period 1 /W is equal to 1 s. i. With N c = 2, evaluate the OFDM channel coefficients h and h 1 . ii. Plot the magnitude squared of the channel coefficients versus the tone num- ber for different values of N c ; in particular, plot for N c = 32, 64, 128 and 256. Specifically, plot | h k | 2 at point kW N c for k = 0 ,...,N c- 1. iii. Consider the discrete-time Fourier transform of the ISI channel defined as follows: H ( f ) def = L- 1 X l =0 h l exp-...
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- Spring '11