In an attempt to test modem performance deterministically through dropout conditions and partial fades selective, we added the fading model and selective fading model to GNU Radio a few years ago. Recently Bastian Bloessl pointed out that the auto-correlation properties of these channel responses were degrading over time and did a great write up on it here.
Flat Fader Corrections
After looking into the issue we now have stable auto-correlation properties not degrading with the phase accumulation and large non-dense floating point representation that occurred after very long runs of the original channel model. Here we see the autocorrelation at the beginning of a run, and 500 MSamples into a run both follow the analytically expected ACF closely with the patch introduced here. Soon to be squashed and merged in a cleaner fashion.
Selective Fading Model 2
The selective fading model in GNU Radio takes N flat fading models at fixed fractional delays measured in samples to define a power delay profile [PDP]. For instance delays of [0,1,1.5] and amplitude of [1,1,0.5] would introduce three flat fading components to a PDP at 0 samples delay, 1 sample delay, and 1.5 samples delay, with magnitudes of 1,1, and 0.5 respectively. This is a standard way to form a frequency-selective fading channel out of a small number of flat fading components. However, this is a rather contrived fading channel because the PDP components are a fixed delays in time which don’t change during the simulation! In the real world, we are moving around, reflectors are moving around, direct and indirect path lengths change over time, and so the delays corresponding to these paths shift earlier or later in time.
In an attempt to simulate this effect, we’ve introduced the selective fading model 2, which adds a delay_std and delay_maxdev parameter to each PDP component. The delay_std, defines a standard deviation of a gaussian random walk in time per sample, measured in samples, while the delay_maxdev defines a maximum distance in time to deviate from the initial delay value. Experimentally, this significantly helps to reduce repetitious behavior and create a more realistic seeming fading environment for some scenarios.
Using gr-fosphor, we can see a brief excerpt of white noise sent through a fading channel using selective model 2 below.
Improved Channel Diagnostics and Visualization
A useful step in the validation of this or any other channel model is that of inspecting the impulse response of the channel. To enable this we add a message output port to the selective_model2 block which passes the complex channel taps at the end of every work function forward. For now we can simply plot these complex vector messages so that we can visually see the effect of the channel on the time domain while observing the effect on the spectrogram. These could of course also be used to cheat in an equalizer or other channel estimation algorithm and use channel state information, CSI, that would otherwise not be available in a real system. This could be very useful for validation or performance measurement of such algorithms in the future.
The graph implementing this simulation and a still from it are shown below …
Finally, running the simulation, we put together a short video clip to show flat white noise through a Rayleigh/NLOS channel simulation.