1. Lab #5.1 Pulse Amplitude Modulation/ BPSK
EE 445S Real-Time Digital Signal Processing Lab Fall 2013
Lab #5.1 Pulse Amplitude Modulation/ BPSK 1

2. Outline Block Diagram & Expressions of Transmitter
Block Diagram & Expressions of Receiver
Inter Symbol Interference & its Nyquist Criteria
Raised Cosine Filter
Digital Interpolation & Pulse Shaping Filter Banks Examples 2 2

3. Symbol Rate: Rd/J bits/sec
Block Diagram of M-PAM Transmitter
Bit Rate: Rd bits/sec
Symbol Rate: Rd/J bits/sec
Courtesy: Steven Tretters Chapter 11 Recitation Slides
Example of 2J Mapping 3 3

4. Expressions for Transmitter
An Impulse Modulator is
Output of Transmit Filter it
Rectangular pulse shaped BPSK: 4 4

5. Block Diagram of Receiver
Eliminate small deviations
Removes out of band noise
Forms perfect pulse shape with Tx
Courtesy: Steven Tretters Chapter 11 Recitation Slides 5 5

6. Expressions for Receiver
Let us define g(t) as
Output of receive filter is 6 6

7. Inter Symbol Interference
The received filter output:
(Assuming no additive white
Gaussian noise)
We can rewrite this as:
The condition on g(t) that needs to be satisfied for no ISI is: 7 7

8. Inter Symbol Interference (eye pattern)
Superimpose every two symbols on each other for several times
Binary PSK with ISI
Binary PSK without ISI
Courtesy:
Courtesy: 8 8

9. Raised Cosine Filter Frequency Domain Time Domain 9 9
Courtesy: 9 9

10. Square Root Raised Cosine Filter
The system should be designed in such a manner that the combined effect of Tx filter and Rx filter should be a Raised Cosine filter. 10 10

11. Digital Interpolation Example
Upsampling by 4 (denoted by 4)
Output input sample followed by 3 zeros
Four times the samples on output as input
Increases sampling rate by factor of 4
FIR filter performs interpolation
Lowpass filter with stopband frequency stopband   / 4
For fsampling = kHz, =  / 4 corresponds to kHz
Digital 4x Oversampling Filter
16 bits kHz
28 bits kHz 4
FIR Filter
16 bits kHz 1 2
Input to Upsampler by 4 n n’
Output of Upsampler by 4 1 2 3 4 5 6 7 8 1 2
Output of FIR Filter 3 4 5 6 7 8 n’

12. Pulse Shaping Filter Bank Example
L = 4 samples per symbol
Pulse shape g[m] lasts for 2 symbols (8 samples)
bits
…a2a1a0
…000a1000a0
encoding ↑4
g[m]
x[m]
s[m]
s[m] = x[m] * g[m]
s[0] = a0 g[0] s[1] = a0 g[1] s[2] = a0 g[2] s[3] = a0 g[3]
s[4] = a0 g[4] + a1 g[0] s[5] = a0 g[5] + a1 g[1] s[6] = a0 g[6] + a1 g[2] s[7] = a0 g[7] + a1 g[3]
No multiplication by zeros
L polyphase filters
{g[0],g[4]}
{g[1],g[5]}
{g[2],g[6]}
{g[3],g[7]}
s[m]
…,s[4],s[0]
…,s[5],s[1]
…,s[6],s[2]
…,s[7],s[3]
…,a1,a0
m=0
Commutator (Periodic)
Filter Bank