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# PS07 - (c What is the average probability of error for such...

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University of Illinois Spring 2011 ECE 361: Problem Set 7 Communication over Band-Limited Channels Due: Thursday March 31 at 9:30 a.m. Reading: Lecture Notes: Lectures 14-18 1. [The pleasure that you get is less than the pain that you have to endure] Let Q ( x ) = 1 - Φ( x ) denote the complementary cumulative unit Gaussian distribution function. Show that for any x > 0 and any a 6 = 0, Q ( x + a ) + Q ( x - a ) > 2 Q ( x ) . 2. [Error probability when ISI is ignored] The discrete-time model for a band-limited channel has as channel response the sequence 0 . 1 , 1 . 0 , 0 . 2 , - 0 . 1. The ratio E T 2 is 10 (or 10 dB). Assume that the demodulator ignores the presence of ISI and simply makes a decision about X [ m ] from the value of Y [ m ]. (a) What is the maximum probability of error for such a decision? (b) What is the minimum probability of error for such a decision?
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Unformatted text preview: (c) What is the average probability of error for such a decision? Is it larger than, smaller than, or the same as Q ( √ SINR )? 3. [Error probability when a matched ﬁlter is used] The discrete-time model for a band-limited channel has as channel response the sequence 0 . 1 , 1 . , . 2 ,-. 1. The ratio E T /σ 2 is 10 (or 10 dB). Assume that the demodulator uses a matched ﬁlter to gather up all the transmitted energy. (a) What is the impulse response of the matched ﬁlter? (b) Compute SINR for the matched ﬁlter. (c) What is the maximum probability of error when a matched ﬁlter is used? How does your answer compare to that of Problem 2(a)?...
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