Comparing CSI-RS results with NeoRadium
% To save a new set of files, you need to set the saveFiles to true.
saveFiles = true;
outPath = fileparts(matlab.desktop.editor.getActiveFilename);
disp(outPath);
Initialize Carrier abd CSI-RS objects
Create a carrier configuration object representing a 5 MHz carrier with subcarrier spacing of 15 kHz.
carrier = nrCarrierConfig;
carrier.NSizeGrid = 25;
carrier.SubcarrierSpacing = 15;
carrier.NSlot = 1;
carrier.NFrame = 0
Create a CSI-RS configuration object representing two CSI-RS resources, NZP with row number 3 and ZP with row number 5.
csirs = nrCSIRSConfig;
csirs.CSIRSType = {'nzp','zp'};
csirs.CSIRSPeriod = {[5 1],[5 1]};
csirs.Density = {'one','one'};
csirs.RowNumber = [3 5];
csirs.SymbolLocations = {1,6};
csirs.SubcarrierLocations = {6,4};
csirs.NumRB = 25
Consider the power scaling of CSI-RS in dB.
powerCSIRS = 0;
disp(['CSI-RS power scaling: ' num2str(powerCSIRS) ' dB']);
Generate CSI-RS Symbols and Indices
Generate CSI-RS symbols for the specified carrier and CSI-RS configuration parameters. Apply power scaling.
sym = nrCSIRS(carrier,csirs);
csirsSym = sym*db2mag(powerCSIRS);
if (saveFiles)
save(strcat(outPath,'/csirsSym.mat'),'csirsSym');
end
csirsSym(201:210)
The variable csirsSym is a column vector containing CSI-RS symbols.
Generate CSI-RS indices for the specified carrier and CSI-RS configuration parameters.
csirsInd = nrCSIRSIndices(carrier,csirs);
The variable csirsInd is also a column vector of same size as that of csirsSym.
When you configure both ZP and NZP resources, the generation of ZP signals takes priority over the generation of NZP signals.
Initialize Carrier Grid
Initialize the carrier resource grid for one slot.
ports = max(csirs.NumCSIRSPorts); % Number of antenna ports
txGrid = nrResourceGrid(carrier,ports);
size(txGrid)
Map CSI-RS Symbols Onto Carrier Grid
Perform resource element mapping.
txGrid(csirsInd) = csirsSym;
if (saveFiles)
save(strcat(outPath,'/txGrid.mat'),'txGrid');
end
size(txGrid)
txGrid(128,:,1)'
Perform OFDM Modulation
Perform OFDM modulation to generate the time-domain waveform.
[txWaveform,ofdmInfo] = nrOFDMModulate(carrier,txGrid, "Nfft",2048);
if (saveFiles)
save(strcat(outPath,'/txWaveform.mat'),'txWaveform');
end
size(txWaveform)
txWaveform(3001:3010,1)
Pass Time-Domain Waveform Through Channel and Add AWGN Noise
Configure the number of receiving antennas.
R = 4;
Configure the channel.
channel = nrCDLChannel;
channel.SampleRate = 30720000;
channel.DelayProfile = 'CDL-D';
channel.DelaySpread = 10e-9;
channel.CarrierFrequency = 4e9;
channel.MaximumDopplerShift = 10;
channel.AngleScaling = true;
channel.MeanAngles = [130 70 80 110];
channel.RandomStream = 'Global stream'; % Use this to be able to match the random numbers in python
channel.TransmitAntennaArray.Size = [1 2 2 1 1]; % 2x2 antenna panel
% channel.TransmitAntennaArray.Element = '38.901';
channel.TransmitArrayOrientation = [10; 20; 30]; % Transmit antenna orientation bearing(α), downtilt(β), and slant(γ) angles in degrees
channel.ReceiveAntennaArray.Size = [1 2 2 1 1]; % 2x2 antenna
channel.ReceiveAntennaArray.Element = '38.901' % Make sure we are using 3GPP antennas. (Default is not 3GPP)
chInfo = info(channel)
Based on the configured channel, append zeros to the transmitted waveform to account for the channel delay.
maxChDelay = ceil(max(chInfo.PathDelays*channel.SampleRate)) + chInfo.ChannelFilterDelay
maxChDelay = 11
txWaveform = [txWaveform; zeros(maxChDelay,size(txWaveform,2))];
Pass waveform through channel.
rng(123); % For Reproducibility (Making sure the same random numbers are used by Matlab and NeoRadium)
[rxWaveform,pathGains,sampleTimes] = channel(txWaveform);
if (saveFiles)
save(strcat(outPath,'/rxWaveform.mat'),'rxWaveform')
end
rxWaveform(3001:3010,1)
To produce the actual propagation channel H_actual, perform perfect channel estimation.
pathFilters = getPathFilters(channel);
offset = nrPerfectTimingEstimate(pathGains,pathFilters)
offset = 7
NRB = 25;
SCS = 15;
nSlot = 0;
H_actual = nrPerfectChannelEstimate(pathGains,pathFilters,...
NRB,SCS,nSlot,offset,sampleTimes,"Nfft",2048);
if (saveFiles)
save(strcat(outPath,'/H_actual.mat'),'H_actual')
end
Add AWGN noise to the waveform. For an explanation of the SNR definition that this example uses, see SNR Definition used in Link Simulations.
% Use the following to generate random noise
SNRdB = 50; % in dB
SNR = 10^(SNRdB/10); % Linear value
N0 = 1/sqrt(2.0*R*double(ofdmInfo.Nfft)*SNR); % Noise variance
rng(0);
noise = N0*complex(randn(size(rxWaveform)),randn(size(rxWaveform)));
if (saveFiles)
save(strcat(outPath,'/noise.mat'),'noise')
end
% noise=load(strcat(outPath,'/noise.mat')).noise;
rxWaveform = rxWaveform + noise;
Perform timing synchronization using NZP-CSI-RS. To estimate timing offset, use nrTimingEstimate and consider the NZP-CSI-RS as a reference.
% Disable ZP-CSI-RS resource, not going to be used for timing and channel
% estimation
csirs.CSIRSPeriod = {[5 1],'off'};
% Generate reference symbols and apply power scaling
refSym = db2mag(powerCSIRS)*nrCSIRS(carrier,csirs);
% Generate reference indices
refInd = nrCSIRSIndices(carrier,csirs);
offset = nrTimingEstimate(carrier,rxWaveform,refInd,refSym,"Nfft",2048)
offset = 7
rxWaveform = rxWaveform(1+offset:end,:);
OFDM demodulate the received time-domain waveform.
rxGrid = nrOFDMDemodulate(carrier,rxWaveform,"Nfft",2048); % Of size K-by-L-by-R
if (saveFiles)
save(strcat(outPath,'/rxGrid.mat'),'rxGrid')
end
size(rxGrid)
rxGrid(121,:,1)'
Compare Estimated Channel Against Actual Channel
Perform practical channel estimation using NZP-CSI-RS. Make sure the CSI-RS symbols csirsSym are of the same CDM type.
cdmLen = [2 1]; % Corresponds to CDMType = 'FD-CDM2'
[H_est,nVar] = nrChannelEstimate(carrier,rxGrid,refInd,refSym,'CDMLengths',cdmLen);
size(H_est)
estSNR = -10*log10(nVar);
disp(['estimated SNR = ' num2str(estSNR) ' dB'])
Plot the estimated channel and actual channel between first transmitting antenna and first receiving antenna.
figure;
% Plot the estimated channel
subplot(1,2,1)
imagesc(abs(H_est(:,:,1,1)));
colorbar;
title('Estimated Channel')
axis xy;
xlabel('OFDM Symbols');
ylabel('Subcarriers');
% Plot the actual channel
subplot(1,2,2)
imagesc(abs(H_actual(:,:,1,1)));
colorbar;
title('Actual Channel')
axis xy;
xlabel('OFDM Symbols');
ylabel('Subcarriers');
Calculate the channel estimation error.
H_err = (H_est - H_actual(:,:,:,1:size(H_est,4)));
[minErr,maxErr] = bounds(abs(H_err),'all');
disp(['Absolute value of the channel estimation error is in the range of [' num2str(minErr) ', ' num2str(maxErr) ']'])
Local Functions
function plotGrid(gridSize,csirsInd,csirsSym)
% plotGrid(GRIDSIZE,CSIRSIND,CSIRSSYM) plots the carrier grid of size GRIDSIZE
% by populating the grid with CSI-RS symbols using CSIRSIND and CSIRSSYM.
figure()
cmap = colormap(gcf);
chpval = {20,2};
chpscale = 0.25*length(cmap); % Scaling factor
tempSym = csirsSym;
tempSym(tempSym ~= 0) = chpval{1}; % Replacing non-zero-power symbols
tempSym(tempSym == 0) = chpval{2}; % Replacing zero-power symbols
tempGrid = complex(zeros(gridSize));
tempGrid(csirsInd) = tempSym;
image(chpscale*tempGrid(:,:,1)); % Multiplied with scaling factor for better visualization
axis xy;
names = {'NZP CSI-RS','ZP CSI-RS'};
clevels = chpscale*[chpval{:}];
N = length(clevels);
L = line(ones(N),ones(N),'LineWidth',8); % Generate lines
% Index the color map and associate the selected colors with the lines
set(L,{'color'},mat2cell(cmap( min(1+clevels,length(cmap) ),:),ones(1,N),3)); % Set the colors according to cmap
% Create legend
legend(names{:});
title('Carrier Grid Containing CSI-RS')
xlabel('OFDM Symbols');
ylabel('Subcarriers');
end