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practice_final

# practice_final - EE 5505 Wireless Communication Prof Jindal...

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EE 5505 Prof. Jindal Wireless Communication May 4, 2010 Practice Final 1. Signalling in Wideband Channels Consider a wideband channel in which the channel response is given by: h ( t ) = 9 i =0 α i δ ( t - τ i ) , where the delays satisfy 0 = τ 0 < τ 1 < · · · < τ 9 = 10 microseconds. Furthermore, assume each of the attenuation coeﬃcients α 0 , . . . , α 9 is iid Rayleigh. The available bandwidth is 1 MHz, and thus the symbol period is T s = 1 microsecond. (a) Approximately what length (in terms of number of taps) equalizer would be nec- essary for this channel? (b) Now assume OFDM is used over this channel. i. What length cyclic prefix is necessary? ii. How would frequency diversity be obtained in this system and what is the (approximate) maximum diversity order achievable over this channel? 2. Diversity in Fixed Access Schemes In this question we compare the available diversity when using two different fixed access schemes, FDMA and TDMA. (a) Consider a narrowband ( B << B c ) downlink channel in which a single access point serves 10 users. The AP wishes to send a single codeword to each of the users, e.g., a different voice packet to each of the users. A single block lasts T b seconds, and each voice packet must be served during this block (i.e., a codeword cannot be spread over multiple blocks). Assume the coherence time of the channel is half the block time: T c = 1 2 T b . The transmitter does not know the channel quality, and thus must use a fixed access scheme. i. Consider traditional FDMA, in which the bandwidth B is split into 10 equal parts: user 1 is allocated the first B 10 Hz, user 2 the next B 10 Hz, etc. How could each user obtain diversity in such a system? What is the maximum diversity order achievable by each user? ii. Consider traditional TDMA, in which the block T b is split into 10 equal parts: user 1 gets the channel for the first T b 10 seconds, user 2 for the next T b 10 seconds, and so forth. How could each user obtain diversity in such a system? What is the maximum diversity order achievable by each user? iii. Is there a different TDMA strategy that could provide each user with more diversity than the strategy in (ii)? 1

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(b) Now consider a wideband downlink channel with B = 10 B c , again with 10 users that each need to be sent a single codeword during a block. This time we assume that the coherence time is much larger than the block time T b . i. Consider traditional FDMA, in which the bandwidth B is split into 10 equal parts: user 1 is allocated the first B 10 Hz, user 2 the next B 10 Hz, etc. How could each user obtain diversity in such a system? What is the maximum diversity order achievable by each user? ii. Consider traditional TDMA, in which the block T b is split into 10 equal parts: user 1 gets the channel for the first T b 10 seconds, user 2 for the next T b 10 seconds, and so forth. Assume OFDM is used within each time slot. How could each user obtain diversity in such a system? What is the maximum diversity order achievable by each user?
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practice_final - EE 5505 Wireless Communication Prof Jindal...

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