rev3s.pdf - EE 284 F Tobagi Autumn 2017-2018 EE284 Review...

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EE 284 F. Tobagi Autumn 2017-2018 EE284 Review Session #3 Topics: Physical Layer October 13, 2017 1 Interference and Noise in Wireless Transmission a. Consider a wireless communication channel of bandwidth W Hz. Suppose we have a transmitter receiver pair on this channel. The transmitter is a distance L from the receiver. See the figure below: We denote P t as the signal power at the transmitter, and P r as the signal power at the receiver. In this channel, signal power at a distance of x away from the transmitter is given by: P x = P t ( k x 2 ) where k is a constant term. Assume a constant noise of power N env everywhere. What is the capacity of this channel? What happens to the capacity as noise decreases to 0? Why is this the case? b. Now consider a similar situation, but with two parallel transmitter-receiver pairs. Both pairs operate on the same frequency, thus their transmissions can interfere with one another. The transmitters and receivers are a distance d away from each other. See the figure below: 1
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What is the capacity of each channel, given a significant environmental noise power N env compared to interference noise? What is the capacity of each channel, given a negligible environmental noise compared to interference noise? Solution a. To find channel capacity in a noisy environment, apply Shannon’s theorem: C = Wlog 2 (1 + S N ) . In this case, the signal S at the receiver is given by S = P r = P t ( k L 2 ) Thus, we can find the capacity as follows: C = Wlog 2 (1 + P t k L 2 N env ) As N env 0, C → ∞ . This is because as we approach an noiseless channel, we can theoretically transmit infinite information with a single symbol (imagine an infinitely precise signal on a wire). Thus, the capacity of the channel also approaches infinity. b. In this case, there is interference noise from the other transmitter. Because of the symmetry of the setup, both channels experience the same interference, and will thus have the same capacity.
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