Tools4SDR : Symbol rate estimation of linearly modulated sequence of symbols

Discussion
The last comment is from Pierre J.: Not yet. An update of the toolbox will be made to support this feature in november. Add a comment

Structure of this article
1 Using the USRP to make the simulations more realistics *2 The classical* method 3 The proposed method**

More about SDR4Research >> Signal processing
Detection of DVB-T signals (with USRP, GNU Radio and matlab)

More about GNU Radio & USRP >> USRP & Matlab
Test the installation of the Tools4SDR toolbox USRP interface with Matlab and Windows Estimation of the RF impairments of the USRP throught channel impulse response estimation The "hello world !" of the communication with two USRPs, matlab and windows

See also
SDR4Research >> Cognitive radio SDR4Research >> Signal processing GNU Radio & USRP >> Generalities GNU Radio & USRP >> Tutorials GNU Radio & USRP >> USRP & Matlab GNU Radio & USRP >> SDR4All tools

Symbol rate estimation of linearly modulated sequence of symbols

The objective of this tutorial is to estimate without prior information the baudrate of a received linearly modulation of i.i.d. symbols. The algorithms used in these simulations have been published in the signal processing journal [1].

We assume that we receive a linear modulation of symbols, with the following model:

$y(nT_e) = \sum_ka_k f(nT_e-kT_c)$

where $f$ is the result of the convolution between the shaping filter and the channel impulse response. We expect to estimate the parameter $T_c$.

1. Using the USRP to make the simulations more realistics

Despite using the USRP does not allow to draw conclusions about the performance of the algorithm, it allows to test it on real signals, with a real propagation channel and reals RF impairments.

The communication system

The transmitted signal has been generated using 1000 QPSK symbols oversampled of a rate 5. The used code is available for downloading at the bottom of this page [Transmitter.zip].

The signal has been received on a second PC with a second USRP. The received signal is available for downloading [acqui.zip] (with a script [ReadAcquiSignal.m] for reading this file). After selecting the useful part of the signal (see this demo for more information), two symbol rate estimation algorithms have been tested. These scripts are also available for downloading [Receiver.zip].

2. The classical method

The classical method consists in computing the Fourier transform of the autocorrelation function of the received signal. It can indeed be proved that the autocorrelation function of the received signal is time periodic (the signal is cyclostationary), and that this period depends on the symbol rate (see the cited article).

On the figure below, this Fourier transform of the received signal has been plotted:

Fourier transform of the autocorrelation function of the received signal

Two peaks are expected at -0.2 and 0.2 (Te/Tc) and can be observed. Nevertheless, these peaks are lower that the values reached by this function around the lowest frequency.

3. The proposed method

The method proposed is based on the fact that is the received signal is filtered by an-hoc filter, the peak value at Te/Tc is not affected, but the estimation noise significantly reduced.
A cost function can be build based on this constatation. We illustrate it with the received signal on the figure below:

Proposed cost function

As illustrated, the peak at 0.2 remains, and the estimation noise has been enough reduced so that the value reached at 0.2 is the maximal value of the function.

References:

[1] P. Jallon, A. Chevreuil, Estimation of the symbol rate of linearly modulated sequences of symbols, Signal processing, August 2008

Attached files:

[ AF1 ] Transmitter.zip
[ AF2 ] acqui.zip
[ AF3 ] ReadAcquiSignal.m
[ AF4 ] Receiver.zip