6G channel design

How channel stattistics at receiver side will be extracred?

[Torsten]

Answer from AI:

In 6G channel design using MATLAB, extracting channel statistics at the receiver side is essential for evaluating key performance indicators (KPIs) like path loss, delay spread, angular spread, and Doppler shifts.

The exact method depends on whether you are using the 5G Toolbox (which supports CDL/TDL models up to 100 GHz, often used as the baseline for 6G), the Phased Array System Toolbox (for ray tracing), or the Communications Toolbox.

Here is how you can extract these statistics from a simulated 6G channel.

1. Extracting Statistics via Channel Object Outputs

When you pass a signal through a MATLAB channel object (like nrCDLChannel or a custom 6G tapped delay line), you can request a channel information structure (info) that contains the statistical properties of the channel.

matlab

% Example using a CDL channel object
cdl = nrCDLChannel;
cdl.DelayProfile = 'CDL-A';
cdl.DelaySpread = 30e-9; % 30 ns
cdl.CarrierFrequency = 140e9; % Sub-THz 6G frequency

% Call the info method to extract channel statistics
chnInfo = info(cdl);

What you can extract from chnInfo:

• Path Delays & Gains: chnInfo.PathDelays and chnInfo.AveragePathGains give you the Power Delay Profile (PDP) at the receiver.
• Angles of Arrival (AoA & ZoA): chnInfo.AzimuthAnglesOfArrival and chnInfo.ZenithAnglesOfArrival provide the spatial statistics at the receiver.
• Maximum Doppler Shift: chnInfo.MaximumDopplerShift represents the mobility statistics.

2. Extracting Statistics from the Channel Impulse Response (CIR)

For advanced 6G scenarios (like time-varying channels or ray tracing), you filter your signal to get the time-varying Channel Impulse Response (CIR) matrix, denoted as \(H(t, \tau)\).

matlab

% Run the channel simulation
% txWaveform: transmitted signal
% pathGains: [Time steps x Paths x Rx Antennas x Tx Antennas]
[rxWaveform, pathGains, sampleTimes] = cdl(txWaveform);

From pathGains and chnInfo.PathDelays, you can mathematically extract the following receiver-side statistics using standard MATLAB functions:

📊 Root-Mean-Square (RMS) Delay Spread

RMS delay spread measures the multipath richness in time.

matlab

pdp = mean(abs(pathGains).^2, [1 3 4]); % Average power over time and antennas
meanDelay = sum(pdp .* chnInfo.PathDelays) / sum(pdp);
rmsDelaySpread = sqrt(sum(pdp .* (chnInfo.PathDelays - meanDelay).^2) / sum(pdp));

🌀 Doppler Power Spectrum & Coherence Time

Taking the Fast Fourier Transform (FFT) of the path gains over time yields the Doppler shift seen by the receiver.

matlab

% FFT over the time dimension of a dominant path
dopplerSpectrum = fftshift(fft(pathGains(:, 1, 1, 1))); 

📡 Spatial Correlation (MIMO Capacity)

To analyze how correlated the receiver antennas are (crucial for 6G Ultra-Massive MIMO):

matlab

% Reshape pathGains to compute correlation matrix between Rx antennas
rxSignals = squeeze(sum(pathGains, 2)); % Sum over paths
R_rx = corrcoef(rxSignals); % Receiver spatial correlation matrix

3. Ray Tracing for 6G Site-Specific Statistics

6G heavily relies on Ray Tracing for Sub-THz and Visible Light Communications (VLC). MATLAB allows you to launch rays in a 3D scene and extract exact receiver statistics directly from the propagation paths.

matlab

% Assuming you have a site viewer and a scene setup
pm = propagationModel("raytracing", "Method", "sbr", "MaxNumReflections", 3);
rays = raytrace(txSite, rxSite, pm);

% Extract stats per ray at the receiver

for i = 1:numel(rays{1})
    aoa = rays{1}(i).AngleOfArrival;  % [Azimuth; Elevation]
    dist = rays{1}(i).PropagationDistance;
    loss = rays{1}(i).PathLoss;       % Path loss in dB
end

Summary of Extraction Dimensions

Statistic MATLAB Source KPI Target for 6G

Path Loss & Shadowing rays.PathLoss or pathGains magnitude Coverage & Link Budget

RMS Delay Spread Calculated from chnInfo.PathDelays & pathGains CP length & OFDM

numerology

Angular Spread (AoA/ZoA) chnInfo.AzimuthAnglesOfArrival Beamforming & spatial

multiplexing

Doppler Spread fft(pathGains) over time dimension High-mobility robustness

(e.g., LEO satellites)