Tools4SDR : Estimation of the RF impairments of the USRP throught channel impulse response estimation

Structure of this article
1 Scripts for the transmitter 2 Scripts for the receiver 3 Results

More about GNU Radio & USRP >> USRP & Matlab
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More about SDR4Teaching >> RF impairments
Frequency offset estimation with linearly modulated sequence of symbols

More about SDR4Teaching >> Linear modulations
Frequency offset estimation with linearly modulated sequence of symbols Transmission of an image with the USRP (matlab/windows) Transmission of linearly modulation of sequences of QPSK and 16-QAM symbols. The received constellation. Channel impulse response estimation with a linearly modulated sequence of symbols Transmission of a binary signal with a linearly modulated sequence of symbols

See also
GNU Radio & USRP >> Generalities GNU Radio & USRP >> Tutorials GNU Radio & USRP >> USRP & Matlab GNU Radio & USRP >> SDR4All tools SDR4Teaching >> Linear modulations SDR4Teaching >> OFDM Signals SDR4Teaching >> RF impairments

Estimation of the RF impairments of the USRP throught channel impulse response estimation

The objective of this demonstration is to estimate the RF impairments of the FLEX 2400 daughterboard of the USRP.

Two USRP have been connected on two PCs running matlab/windows and the Tools4SDR toolbox. The two USRP have been connected thanks to a wire (instead of using antennas):

The two USRP (universal software radio peripheral) connected by wire

On the first PC, a linear modulation of a set of training sequences has been generated, and send through the USRP to the second PC. On this second PC, algorithms have been runned on each training sequence to estimate the channel impulse response and its variation.

These scripts are described on this page, as well as the obtained result. These scripts are available for downloading at the bottom of this page.

1. Scripts for the transmitter

The used scripts are available for downloading : [Transmitter_scripts.zip] To generate the signal, two training sequences have been used:

appr_offset: A training sequence of BPSK symbols to estimate and compensate the frequency offset
appr_symboles: A training sequence of QPSK symbols to estimate the channel impulse response

These sequences are saved into the file [Seqs.mat].

The transmitted symbols have been generated as follows:

NbTrame = 1000;
SymbToTransmit = appr_offset;
for (iNbTrame=1:NbTrame)
SymbToTransmit = [SymbToTransmit ; appr_symboles];
end

A square root cosine filter has been used to modulate these symbols at a rate equal to Tc=5Te. Te is the sampling frequency, and is equal to Te=1us, so that the transmitted signal is 1MHz bandwidth.

Te = 1e-6;
Tc = 5*Te;
g = GetNyquistSqrt(0.2,Tc,-100*Te:Te:100*Te); %0.2 is the bandwidth excess

The transmitted signal has thus been generated as:

Symb = kron(SymbToTransmit,[0 0 1 0 0].');
y = conv(g,Symb);

Finally, it has been transmitted throught the USRP:

USRP_Init();
USRP_SendSignal(y);

The signal y is then transmitted around 10 times into the WiFi bands (channel 3, center frequency 2422MHz), so that on the receiver side, the acquisition script can be runned to record an entire copy of the signal y.

2. Scripts for the receiver

The scripts used for the received can be downloaded at the bottom of this page [Receiver_scripts.zip].
The acquisition script has to be launched just after the PC on which the transmitter is connected prints the transmission begins:

[t,y] = USRP_ReceiveSignal(8);

The signal y is then composed of burts, each being a replica of the signal of interest. The received signal can be downloaded from the bottom of this page ([acqui_flex2400.zip] (around 20Mo), with a script to load the file [ReadAcquiSignal.m]). The signal processing starts with the selection of a burst:

[t2,y2] = SelectUsefulPart(t,y);

Then, the frequency offset is estimated thanks to the BPSK training sequence, and the signal filtered by its adaptative filter:

[z,offset] = CorrectFrequencyOffset(y3,appr_offset,5); % 5 is the oversampling factor (Tc/Te)
[z2] = Adaptative_Filter(z,5,0.2); %0.2 is the bandwidth excess

As the signal is oversampled by a factor 5, we can extract from z2 5 signals sampled at the rate Tc. For each of these signals, the channel impulse response can be estimated as well as the estimation error:

[ Allz ] = Compute_Signals_For_Synchro(z2,5);
[Error,h] = IREst(appr_offset,Allz);

The error variable described the least square error and contains 5 values. It takes its minimal value for the 5th index, meaning that the best synchronized signal is Allz(5,:).

Sig = Allz(5,:);
NbTrames = 1000;
For (iNbTrame = 1:NbTrames)
[Error,h(iT,:)] = IREst(appr_symboles,Sig(length(appr_offset)+(iT-1)*length(appr_symboles):end);
end

3. Results

The mesured variations of the channel impulse response (h(iT,:)) are the following ones:

As the maxima is moving from point 2 to point 3, we can deduce that the sampling frequency is not exactly equal to 1us. Further, the value variation indicates that the oscillator derives.

Attached files:

[ AF1 ] Transmitter_scripts.zip
[ AF2 ] Seqs.mat
[ AF3 ] Receiver_scripts.zip
[ AF4 ] acqui_flex2400.zip
[ AF5 ] ReadAcquiSignal.m