ECE 445S Real-Time Digital Signal Processing Laboratory - Lecture 14

Lecture by Prof. Brian L. Evans

Announcements: Cellular Business Trends and Ecosystem

Lecture

Lecture 14 slides on Matched Filtering in PowerPoint format.
- Board PAM communication system
- Board Optimal matched filter for a rectangular pulse shape
- YouTube: derivation of bit error probability from 27:33 to 52:20 (Spring 2014 course)
- Board. PAM pulse shaping and matched filter examples
- Board. 8-QAM constellation
Spring 2023 lecture notes part 1 (Jacobellis) and part 2 (Liu)
Additional reading assignment from Communication Systems (3rd edition) by Simon Haykin
- Section 4.6 Random Processes (all)
- Section 4.9 Ergodic Processes (all)
- Section 4.10 Transmission of a Random Process Through a Linear [Time-Invariant] Filter (all)
- Section 4.11 Power Spectral Density (through page 253) especially
  - Equation (4.80) on page 250 for time-averaged autocorrelation and the two limit definitions that immediately follow it.
  - Equation (4.93) on page 253, which is used in the derivation of the matched filter
- Section 4.12 Gaussian Processes, but only the following parts:
  - Subsection on Thermal Noise
  - Subsection on White Noise
  - Example 16 Ideal Low-Pass Filtered White Noise
Spring 2014 lectures on Video: Part 1 - Part 2 - Part 3 - Part 4

Supplemental Material

Spring 2024 marker board notes
- Board. PAM symbol amplitude estimate in the presence of intersymbol interference to the channel impulse response
- Board. Autocorrelation of a Gaussian signal with zero mean is an impulse whose area is the variance
- Board. Optimal match filter impulse response in continuous time and discrete time
- Board. PAM baseband transmitter (after lecture)
- Board. PAM received symbol amplitude (after lecture)
Fall 2023 marker board notes
- Autocorrelation, phase shift, and noise power
- Matched filtering for rectangular pulse shape
Spring 2023 marker board notes
- Part 1: equalization and matched filtering on marker board
- Part 1: In-Lecture Assignment #4
- Part 1: Lecture notes by TA Dan Jacobellis
- Part 2: matched filtering on marker board
- Part 2: Lecture notes by TA Alice Liu
Fall 2022 marker board notes
- Part 1: channel impairments review and two-way communication
- Part 2:
- Part 3: Matched filtering review and bandwidth
Spring 2022 marker board notes
- Eye diagrams and group delay and noise
- Costas loop objective function and steepest descent algorithm for HW 6.1
- Matched filtering: also known as phase reversal and rectangular pulse shape example
- Matched filtering and steepest descent in lecture assignment by Mr. Jacobellis
Fall 2021
- Compensating channel impairments
- Matched filtering slides by Mr. Jacobellis
- Wireless localization
- PAM transmit power
Spring 2021 marker board notes
- Part 1: matched filtering example
- Part 2:
  - baseband channel modeling with Wi-Fi example (with takeaways)
  - matched filtering for rectangular pulse (with takeaways)
  - autocorrelation for the Dirac delta and a Gaussian random signal
- derivation of matched filter from spring 2014 from 0:45 to 52:45, or 41:35 to 52:45 to pick up where the April 19, 2021, lecture ended
- Part 3: optimal matched filtering, rectangular pulse example and generating symbol amplitudes
Fall 2020 lecture notes by Prof. Evans and Mr. Jacobellis: part 1 and part 2
Other marker board notes in recent past semesters
- Spring 2020 Upconverted PAM transmission
- Fall 2019 Slide 14-10: Autocorrelation part 1 and part 2
- Fall 2019 Slide 14-11: Correlation part 1, part 2, and part 3
Karagiannidis and Lioumpas, "An Improved Approximation for the Gaussian Q function", IEEE Communication Letters, August 2007. With
```
       1         x    
Q(x) = - erfc(-------)
       2      sqrt(2) 
```
the authors approximate erfc(x) by g(x) h(x), where
```
             2   
           -x    
          e      
h(x) = ----------
       sqrt(pi) x

            -A x
       1 - e    
g(x) = ---------
          B     
```
where A = 1.98 and B = 1.135 to minimize the absolute error for x in [0, 20].

Last updated 12/08/24. Send comments to (Mailbox) bevans@ece.utexas.edu