EVM in radial and circumferential directions?

Can comm.EVM measure EVM in the radial and circumferential (i.e., along the unit circle) directions separately?

[Image Analyst]

What is EVM? I don't know that acronymn.

[Jerry Malone]

EVM means error vector magnitude. It's a measure of performance in digital communications systems. It's the distance from the ideal constellation point to the actual (noise+distortion) point as a percentage of the distance from the origin to the ideal point. The RMS value of all such percentages gives you a measure of comms system performance. Lower is better. The Matlab comms package has a function for computing EVM.

Answer 1

[Abhimenyu]

Hi Jerry,

I understand that you want to measure EVM in radial and circumferential direction separately. ‘comm.EVM’ object measures the root mean squared (RMS) EVM, maximum EVM, and percentile EVM of a received signal. It gives overall EVM as a percentage of distance from the origin to ideal point. It does not separate the radial and circumferential components.

Please follow the example code below to understand the EVM measurements in different directions:

% Generate a reference signal (QPSK) 
constellation = [-1-1i, -1+1i, 1-1i, 1+1i]; 
refSignal = constellation(randi([1, 4], 1000, 1)); 

% Generate a modulated signal with noise and distortion 
SNR_dB = 20; % Signal-to-noise ratio in decibels 
modSignal = awgn(refSignal, SNR_dB, 'measured'); % Add white Gaussian noise 
modSignal = modSignal + 0.1 * exp(1i * pi / 4); % Add constant phase offset 
modSignal = modSignal .* (1 + 0.2 * (randn(size(modSignal)))) + 1i * randn(size(modSignal)); % Add random amplitude and phase variation 

% Compute the error vector 
errorVector = modSignal - refSignal; 

% Compute the radial component of the error vector 
radialErrorVector = abs(errorVector); 

% Compute the circumferential component of the error vector 
circumferentialErrorVector = angle(errorVector); 

% Calculate the RMS values of the radial and circumferential errors 
rmsRadialError = rms(radialErrorVector); 
rmsCircumferentialError = rms(circumferentialErrorVector); 

% Normalize the error values by the magnitude of the reference signal to obtain the EVM in each direction 
evmRadial = 100 * rmsRadialError / mean(abs(refSignal)) 

evmRadial = 74.3216

evmCircumferential = 100 * rmsCircumferentialError / mean(abs(refSignal)) 

evmCircumferential = 107.1628

Please follow the MATLAB documentation link below to learn more about the ‘comm.EVM’ object:

https://www.mathworks.com/help/releases/R2023a/comm/ref/comm.evm-system-object.html

I hope this helps!

Thanks,

Abhimenyu

[Jerry Malone]

That is very good, clear, well-documented code. Thanks.

I wish everyone wrote Matlab code like this.

[Jerry Malone]

Here's how I did it:

% Generate a reference constellation (QPSK) 
constellation = [-1-1i, -1+1i, 1-1i, 1+1i]/sqrt(2); 
refSignal = constellation(randi([1, 4], 1000, 1)); 

% Generate a modulated constellation with noise and phase rotation:
SNR_dB = 20;                                        % Signal-to-noise ratio in decibels 
modSignal = awgn(refSignal, SNR_dB, 'measured');    % Add white Gaussian noise 
modSignal = modSignal*.exp(1i*pi/8);                % Constant phase rotation of 22.5 deg.

% Compute radial error vector as a % of reference:
radialErrorVector = 100*(abs(modSignal)-abs(refSignal))./abs(refSignal);

% Compute circumferential error vector as % of reference:
circumferentialErrorVector = 100*(abs(refSignal).*(angle(modSignal)-angle(refSignal)))./abs(refSignal);

mean(radialErrorVector)
mean(circumferentialErrorVector)

rms(radialErrorVector)
rms(circumferentialErrorVector)