Post on 03-Oct-2021
transcript
MPSK Tutorial
Tom Rondeau
2012-09-22
Tom Rondeau () MPSK Tutorial 2012-09-22 1 / 26
Outline
1 Introduction
2 Digital Modulation Study
3 M-PSK Example
Tom Rondeau () MPSK Tutorial 2012-09-22 2 / 26
Introduction
Download Materials
http://www.trondeau.com/gr-tutorial
Presentation PDF
Case Study materials
GNU Radio apps to run examples.
Links to source code for analysis.
Data �le for �rst case study.
Images of expected output.
Exercises.
Tom Rondeau () MPSK Tutorial 2012-09-22 3 / 26
Introduction
Sources and Sinks
sources_and_sinks.grc
Demonstration of using multiple sources to create a noisy sinewave and multiple sinks to view it in di�erent domains.
Tom Rondeau () MPSK Tutorial 2012-09-22 4 / 26
Introduction
Sources and Sinks
sources_and_sinks.grc
Showing both the frequency and time domain of the noisy signal.
Tom Rondeau () MPSK Tutorial 2012-09-22 5 / 26
Digital Modulation Study
Information Representation
bits_representation.grc
We can visualize bits as a series of 1's and 0's that aretranslated into 1's and −1′'s.Tom Rondeau () MPSK Tutorial 2012-09-22 6 / 26
Digital Modulation Study
Information Representation
bits_representation.grc
We can do the same for another stream of bits and workactually combine them into a single signal.
Tom Rondeau () MPSK Tutorial 2012-09-22 7 / 26
Digital Modulation Study
Information Representation
bits_representation.grc
We combine these by using complex numbers as an orthogonalbasis.Tom Rondeau () MPSK Tutorial 2012-09-22 8 / 26
Digital Modulation Study
Complex Numbers
z(t) = x(t)cos(2πft + φ(t)) + jy(t)sin(2πft + φ(t))
z(t) = c(t)e−j2πft+φ(t)
Tom Rondeau () MPSK Tutorial 2012-09-22 9 / 26
Digital Modulation Study
Complex Numbers: Polar Plots}
Tom Rondeau () MPSK Tutorial 2012-09-22 10 / 26
Digital Modulation Study
Information as a Complex Number
bit_representations.grc
Putting one signal on the real axis and another signal on theimaginary axis, we can combine these on two orthogonal planes.The �constellation� plot on the right is just a polar plot.
Tom Rondeau () MPSK Tutorial 2012-09-22 11 / 26
M-PSK Example
Modulating & Transmitting a Signal
mpsk_stage1.grc
Using a pre-build PSK modulator block from GNU Radio.
Tom Rondeau () MPSK Tutorial 2012-09-22 12 / 26
M-PSK Example
Modulating & Transmitting a Signal
Tom Rondeau () MPSK Tutorial 2012-09-22 13 / 26
M-PSK Example
The Received Signal
mpsk_stage2.grc
We can simulate a channel model with noise, frequency andtiming o�sets, and multipath.
Tom Rondeau () MPSK Tutorial 2012-09-22 14 / 26
M-PSK Example
The Received Signal
mpsk_stage2.grc
Signal captured using a multipath channel with some AWGNnoise and timing o�set. To make the signal recognizable, nofrequency o�set was used.
Tom Rondeau () MPSK Tutorial 2012-09-22 15 / 26
M-PSK Example
After Timing Recovery
mpsk_stage3.grc
We use a control loop algorithm to �nd the right sampling timeto �x clock mismatches between the transmitter and receiver.
Tom Rondeau () MPSK Tutorial 2012-09-22 16 / 26
M-PSK Example
After Timing Recovery
mpsk_stage3.grc
Showing a no-noise situation to illustrate ISI (self-interference)issues in the received signal before timing recovery and matched�ltering.
Tom Rondeau () MPSK Tutorial 2012-09-22 17 / 26
M-PSK Example
After Timing Recovery - With Noise
mpsk_stage3.grc
Even with noise, we can still recover the proper timing.
Tom Rondeau () MPSK Tutorial 2012-09-22 18 / 26
M-PSK Example
Multipath in Brief
Multipath channels result from a signal bouncing o� objects andhitting the receiver at di�erent times and with di�erent phases.
Tom Rondeau () MPSK Tutorial 2012-09-22 19 / 26
M-PSK Example
E�ects of Multipath
mpsk_multipath.grc
This simulation allows us to adjust the multipath channel asthough we are adjusting a stereo's equalizer. (See also:multipath_sim.grc)
Tom Rondeau () MPSK Tutorial 2012-09-22 20 / 26
M-PSK Example
Equalizing Multipath
Cartoon showing signal corrupted by multipath. Equalizer triesto invert the multipath so that the combination is a �atfrequency response.
Tom Rondeau () MPSK Tutorial 2012-09-22 21 / 26
M-PSK Example
Equalizing Multipath
mpsk_stage4.grc
Using the constant modulus algorithm (CMA) blind equalizer isused here to correct multipath distortion.
Tom Rondeau () MPSK Tutorial 2012-09-22 22 / 26
M-PSK Example
Equalizing Multipath
mpsk_stage4.grc
Note the similarity between the time-synchronized and �lteredoutput with multipath and the ISI of the signal before thematched �lter with no multipath.
Tom Rondeau () MPSK Tutorial 2012-09-22 23 / 26
M-PSK Example
Equalizing Multipath
mpsk_stage4.grc
Equalization working with noise.
Tom Rondeau () MPSK Tutorial 2012-09-22 24 / 26
M-PSK Example
Phase O�set Correction
mpsk_stage5.grc
The transmitter and receiver work o� di�erent clocks, so therewill be a frequency and phase o�set. We need to correct for anysmall frequency and phase o�sets.
Tom Rondeau () MPSK Tutorial 2012-09-22 25 / 26
M-PSK Example
After Timing Recovery - With Noise
mpsk_stage5.grc
Left �gure shows a rotate constellation. The Costas Loop block�xes the o�set.Tom Rondeau () MPSK Tutorial 2012-09-22 26 / 26