Digital Modulation Primer using GNU Radio

Tom Rondeautom@trondeau.com

GNU Radio Maintainer

July 3, 2012

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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 file for first case study.Images of expected output.Exercises.

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Introduction

“The fundamental problem of communication is that ofreproducing at one point either exactly or approximatelya message selected at another point.”

- Claude Shannon, “A Mathematical Theory of Communication”

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Introduction

GNU Radio is a Development Platform for

Communications

Building Blocks

1 Rapid prototyping of PHY layer systems.

2 Analysis and development of signals.

3 Educational material to teach the workings of various comms.

4 Expose engineering techniques and tricks.

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GNU Radio Information

Information Sources for GNU Radio

Tools and Manuals

Project website: gnuradio.org

Download source:gnuradio.org/redmine/projects/gnuradio/wiki/Download

Online C++ Manual: gnuradio.org/doc/doxygen/

Online Python Manual: gnuradio.org/doc/sphinx/

My website for news and analysis: www.trondeau.com

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GNU Radio Information

Community

Active developer community producing examples.

Large participation on our mailing list.

The Complimentary GNU Radio Archive Network (CGRAN).

Growing list of projects on github.

GNU Radio Conference:www.trondeau.com/gnu-radio-conference-2012

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GNU Radio Information

Available Components (as of v3.7)

Fundamentals

gr-analog

gr-block

gr-digital

gr-fec

gr-fft

gr-filter

gr-runtime

gr-trellis

gr-vocoder

gr-wavelet

Graphical Interfaces

gr-qtgui

gr-wxgui

Hardware Interfaces

gr-audio

gr-comedi

gr-fcd

gr-shd

gr-uhd

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Exploring

Filtering

“The need for filters intrudes on any thought experiment

about the wonders of abundant information.”

- James Gleik, The Information

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Exploring

GNU Radio’s gr filter design Tool

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Exploring

Filtering Noise

filtering.grc

Example of using a filter to shape noise.

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Exploring

Filtering Noise

With a simple low-pass filter, we can adjust the bandwidth of the filter toadjust the shape of the noise.

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Exploring

Sources and Sinks

sources and sinks.grc

Demonstration of using multiple sources to create a noisy sine wave andmultiple sinks to view it in different domains.

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Exploring

Sources and Sinks

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 are translated into 1’sand −1′’s.

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Digital Modulation Study

Information Representation

bits representation.grc

We can do the same for another stream of bits and work actually combinethem 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 orthogonal basis.

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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

0°

45°

90°

135°

180°

225°

270°

315°

0.20.4

0.60.8

1.0

Phase = -3.8096

Phase = 36.0604

Phase = 71.1625Phase = 109.9112

Frequency = 100 HzTime per Sample = 1.0 msRadians per Sample = 36.0

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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 the imaginaryaxis, 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 and timing offsets,and multipath.

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M-PSK Example

The Received Signal

Signal captured using a multipath channel with some AWGN noise andtiming offset. To make the signal recognizable, no frequency offset wasused.

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M-PSK Example

After Timing Recovery

mpsk stage3.grc

We use a control loop algorithm to find the right sampling time to fixclock mismatches between the transmitter and receiver.

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M-PSK Example

After Timing Recovery

Showing a no-noise situation to illustrate ISI (self-interference) issues inthe received signal before timing recovery and matched filtering.

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M-PSK Example

After Timing Recovery - With Noise

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 off objects and hittingthe receiver at different times and with different phases.

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M-PSK Example

Effects of Multipath

mpsk multipath.grc

This simulation allows us to adjust the multipath channel as though weare 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 tries to invertthe multipath so that the combination is a flat frequency response.

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M-PSK Example

Equalizing Multipath

mpsk stage4.grc

Using the constant modulus algorithm (CMA) blind equalizer is used hereto correct multipath distortion.

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M-PSK Example

Equalizing Multipath

Note the similarity between the time-synchronized and filtered output withmultipath and the ISI of the signal before the matched filter with nomultipath.

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M-PSK Example

Equalizing Multipath

Equalization working with noise.

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M-PSK Example

Phase Offset Correction

mpsk stage5.grc

The transmitter and receiver work off different clocks, so there will be afrequency and phase offset. We need to correct for any small frequencyand phase offsets.

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M-PSK Example

After Timing Recovery - With Noise

Left figure shows a rotate constellation. The Costas Loop block fixes theoffset.

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fin.

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