MPSK Tutorial

Tom Rondeau

2012-09-22

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Outline

1 Introduction

2 Digital Modulation Study

3 M-PSK Example

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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.

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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.

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Introduction

Sources and Sinks

sources_and_sinks.grc

Showing both the frequency and time domain of the noisy signal.

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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.

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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)

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Digital Modulation Study

Complex Numbers: Polar Plots}

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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.

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M-PSK Example

Modulating & Transmitting a Signal

mpsk_stage1.grc

Using a pre-build PSK modulator block from GNU Radio.

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M-PSK Example

Modulating & Transmitting a Signal

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M-PSK Example

The Received Signal

mpsk_stage2.grc

We can simulate a channel model with noise, frequency andtiming o�sets, and multipath.

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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.

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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.

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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.

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M-PSK Example

After Timing Recovery - With Noise

mpsk_stage3.grc

Even with noise, we can still recover the proper timing.

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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.

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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)

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M-PSK Example

Equalizing Multipath

Cartoon showing signal corrupted by multipath. Equalizer triesto invert the multipath so that the combination is a �atfrequency response.

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M-PSK Example

Equalizing Multipath

mpsk_stage4.grc

Using the constant modulus algorithm (CMA) blind equalizer isused here to correct multipath distortion.

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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.

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M-PSK Example

Equalizing Multipath

mpsk_stage4.grc

Equalization working with noise.

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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.

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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