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MPSK Tutorial Tom Rondeau

2012-09-22

Tom Rondeau ()

MPSK Tutorial

2012-09-22

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Outline

1

Introduction

2

Digital Modulation Study

3

M-PSK Example

Tom Rondeau ()

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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 sine wave and multiple sinks to view it in dierent domains. Tom Rondeau ()

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Introduction

Sources and Sinks sources_and_sinks.grc

Showing both the frequency and time domain of the noisy signal. Tom Rondeau ()

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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 0 translated into 1's and −1 's. Tom Rondeau ()

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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 combine them into a single signal. Tom Rondeau ()

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Digital Modulation Study

Information Representation bits_representation.grc

We combine these by using complex numbers as an orthogonal basis. Tom Rondeau ()

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Digital Modulation Study

Complex Numbers

z (t ) = x (t )cos (2π ft + φ(t )) + jy (t )sin(2π ft + φ(t ))

z (t ) = c (t )e −j 2πft +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 the imaginary axis, we can combine these on two orthogonal planes. The constellation plot on the right is just a polar plot. Tom Rondeau ()

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M-PSK Example

Modulating & Transmitting a Signal mpsk_stage1.grc

Using a pre-build PSK modulator block from GNU Radio. Tom Rondeau ()

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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 osets, and multipath. Tom Rondeau ()

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M-PSK Example

The Received Signal mpsk_stage2.grc

Signal captured using a multipath channel with some AWGN noise and timing oset. To make the signal recognizable, no frequency oset was used. Tom Rondeau ()

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M-PSK Example

After Timing Recovery mpsk_stage3.grc

We use a control loop algorithm to nd the right sampling time to x clock mismatches between the transmitter and receiver. Tom Rondeau ()

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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. Tom Rondeau ()

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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 and hitting the receiver at dierent times and with dierent phases.

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M-PSK Example

Eects of Multipath mpsk_multipath.grc

This simulation allows us to adjust the multipath channel as though we are adjusting a stereo's equalizer. (See also: multipath_sim.grc) Tom Rondeau ()

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M-PSK Example

Equalizing Multipath

Cartoon showing signal corrupted by multipath. Equalizer tries to invert the multipath so that the combination is a at frequency response.

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M-PSK Example

Equalizing Multipath mpsk_stage4.grc

Using the constant modulus algorithm (CMA) blind equalizer is used here to correct multipath distortion. Tom Rondeau ()

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M-PSK Example

Equalizing Multipath mpsk_stage4.grc

Note the similarity between the time-synchronized and ltered output with multipath and the ISI of the signal before the matched lter with no multipath. Tom Rondeau ()

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M-PSK Example

Equalizing Multipath mpsk_stage4.grc

Equalization working with noise. Tom Rondeau ()

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M-PSK Example

Phase Oset Correction mpsk_stage5.grc

The transmitter and receiver work o dierent clocks, so there will be a frequency and phase oset. We need to correct for any small frequency and phase osets. Tom Rondeau ()

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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 oset. Tom Rondeau ()

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