# Scatter Plot and Eye Diagram with MATLAB Functions

This example shows how to visualize signal behavior through the use of eye diagrams and scatter plots. The example uses a QPSK signal which is passed through a square-root raised cosine (RRC) filter.

### Scatter Plot

Set the RRC filter, modulation scheme, and plotting parameters.

span = 10;          % Filter span
rolloff = 0.2;      % Rolloff factor
sps = 8;            % Samples per symbol
M = 4;              % Modulation alphabet size
k = log2(M);        % Bits/symbol
phOffset = pi/4;    % Phase offset (radians)
n = 1;              % Plot every nth value of the signal
offset = 0;         % Plot every nth value of the signal, starting from offset+1

Create the filter coefficients using the rcosdesign function.

filtCoeff = rcosdesign(rolloff,span,sps);

Generate random symbols for an alphabet size of M.

rng default
data = randi([0 M-1],5000,1);

Apply QPSK modulation.

dataMod = pskmod(data,M,phOffset);

Filter the modulated data.

txSig = upfirdn(dataMod,filtCoeff,sps);

Calculate the SNR for an oversampled QPSK signal.

EbNo = 20;
snr = EbNo + 10*log10(k) - 10*log10(sps);

Add AWGN to the transmitted signal.

rxSig = awgn(txSig,snr,'measured');

rxSigFilt = upfirdn(rxSig, filtCoeff,1,sps);

Demodulate the filtered signal.

dataOut = pskdemod(rxSigFilt,M,phOffset,'gray');

Use the scatterplot function to show scatter plots of the signal before and after filtering. You can see that the receive filter improves performance as the constellation more closely matches the ideal values. The first span symbols and the last span symbols represent the cumulative delay of the two filtering operations and are removed from the two filtered signals before generating the scatter plots.

h = scatterplot(sqrt(sps)*txSig(sps*span+1:end-sps*span),sps,offset);
hold on
scatterplot(rxSigFilt(span+1:end-span),n,offset,'bx',h)
scatterplot(dataMod,n,offset,'r+',h)

### Eye Diagram

Display 1000 points of the transmitted signal eye diagram over two symbol periods.

eyediagram(txSig(sps*span+1:sps*span+1000),2*sps)

Display 1000 points of the received signal eye diagram.

eyediagram(rxSig(sps*span+1:sps*span+1000),2*sps)

Observe that the received eye diagram begins to close due to the presence of AWGN. Moreover, the filter has finite length which also contributes to the non-ideal behavior.