QPSK Mod and Demod

NOTICE! This is a work in progress, but ultimately will replace Guided Tutorial PSK Demodulation.

Introduction

Objectives

• Understand issues of signal distortion and channel effects.
• Recognize the stages required to transmit and receive QPSK signals.

Prerequisites

The student should study each of the sections under the "Flowgraph Fundamentals" heading in Tutorials before attempting to do this tutorial.

References

• Our Suggested Reading list
• The ARRL Handbook "Quadrature Modulation" section (any recent edition)
• J. Feigin, "Practical Costas loop design: Designing a simple and inexpensive BPSK Costas loop carrier recovery circuit," RF signal processing, pp. 20-36, 2002

Notes

This tutorial has been revised and tested with GNU Radio version 3.10.8.0. It strives to provide consistent flowgraphs where each stage builds on the previous one, maintaining the same parameters from one stage to the next.

It is intended that the reader study the flowgraphs and resulting output, but not necessarily build each one. However, links to GRC source files are included.

Transmitting a QPSK Signal

The first stage is transmitting the QPSK signal. We generate a stream of bits and modulate it onto a complex constellation. To do this, we use the Constellation Modulator block, which uses a Constellation Rect. Object and other settings to control the transmitted signal. The Constellation parameter of the Constellation Modulator is the id of the Constellation Rect. Object (qpsk), even though it shows on the flowgraph as something else.

The constellation object specifies how the symbols are coded. The modulator block can then use this modulation scheme with or without differential encoding. The constellation modulator expects packed bytes, so we have a random source generator providing bytes with values of 0 to 255.

When dealing with the number of samples per symbol, we want to keep this value as small as possible (minimum value of 2). Generally, we can use this value to help us match the desired bit rate with the sample rate of a hardware device. But since we're using simulation, the samples per symbol is only important in making sure we match this rate throughout the flowgraph. We'll use 4 here, which is greater than what we need, but useful to visualize the signal in the different domains.

Excess Bandwidth

The constellation modulator uses a root raised cosine (RRC) pulse shaping filter to control the bandwidth of the transmit signal. That parameter is called "Excess BW" (excess bandwidth).

The flowgraph below, Media:Qpsk_rrc_rolloff.grc, generates the following figure showing different values of the excess bandwidth. Typical values used are between 0.2 (red trace) and 0.35 (green trace). We will use 0.35 in this tutorial.

Matched Filters and ISI

The example flowgraph, Media:Qpsk_stage1.grc, transmits a QPSK constellation. It plots both the transmitted signal and part of the receiver chain in time, frequency, and the constellation plot. The variable rrc_taps value is firdes.root_raised_cosine(1.0,samp_rate,samp_rate/sps,excess_bw,11*sps).

In the constellation plot below, we see the effects of the up-sampling (generating 4 samples per symbol) and filtering process. The RRC filter limits the transmit bandwidth so the signal is within our desired bandwidth. If we didn't put a shaping filter on the signal, we would be transmitting square waves which produce a lot of energy in the adjacent channels.

A side effect of the RRC filter is to create inter-symbol interference (ISI). ISI is bad for a received signal because it blurs the symbols together. We'll look into this in-depth during the timing recovery section.

On the receive side, we get rid of ISI by using another filter. Basically, what we've done is used a filter on the transmitter, the RRC filter, which creates the ISI. But when we convolve two RRC filters together, we get a raised cosine filter (which is a form of a Nyquist filter). So, knowing this property of the transmit RRC filter, we can use another RRC filter at the receiver to minimize ISI.