{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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?
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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)?...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern