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(ELEC343)03Fall_MidTerm2_solution.pdf
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ELEC 343 Wireless Communications
Midterm #2
Fall 2003
November18, 2003
1. (26%) In a 1-way communication system, the transmitter has 1 transmit antenna and the receiver has 3 receive antennas. Assume that all these antennas are separated far enough from each other so that the channels seen by different (TX,RX) pairs are all independent flat fading channels. Further assume that the coherence time of the channel is 1ms and the data rate is 100kbps. a) (5%) Is there any diversity and what is the order of diversity if the system transmits uncoded
data?
Yes, spatial or receive antenna diversity will be achieved and the order of diversity is
3.
b) (6%) If the transmitter uses a (24,12) forward error correcting code with dmin=4 to achieve diversity, design the interleaver by specifying its dimension (assuming that you fill it row-by-row and take it out column-by-column for transmission). (Assume that delay is not a problem and the block size can be arbitrarily large.)
Since data rate is 100kbps and after the (24,12) code, the coded bit rate is 200kbps, 200 bits will be transmitted in 1ms. Hence, the interleaver should be M rows by 24 columns and M should be at least equal to 200.
c) (5%) What is the order of diversity can you achieve in part (b) (including both time and spatial diversity)?
The total order of diversity is 3*4=12.
d) (5%) If the interleaver size of the coded bits is 720 (i.e. length x width = 720), what can you say about the order of diversity achieved by this system?
Since not all the bits in the codeword can be separated by coherence time, the order
of diversity will only be 3 (spatial diversity).
e) (5%) In part (b), the (24,12) code doubles the bandwidth. An engineer tries to compensate for that by increasing the number of transmit antenna from 1 to 2. By doing that, (s)he expects to increase the order of diversity as well. Comment on whether this approach will work and if it works, what is the new order of diversity?
Without using spread spectrum or advanced receiver signal processing, the signals transmitted on 2 transmit antennas will interferes with each other. Hence, this scheme cannot work. [ This following answer is not what I expect, but is also correct.] However, since there are multiple receive antennas at the receiver, the receiver can separate the 2 transmit signals from the 2 transmit antenna using advance signal processing techniques, this approach will increase the transmit antenna diversity order and the total order of diversity is 2*3=6.
2. (20%) On average, a mobile phone subscriber will make 5 calls per day and each call will last on average 4 minutes. a) (5%) What is the traffic intensity, in Erlang, for each subscriber? 5*4/(60*24) = 1/72= 0.013889 b) (5%) If the number of subscribers in each cell is 2160, how many pairs of GSM frequency channels (each pair can support 8 2-way voice calls simultaneously) are needed to support a 0.2% blocking probability? Total Erla