Effect of comm.RayleighChannel on constellation map

Hi,

I have a question about the effect of the path delay on the comm.RayleighChannel propagation model because path delays become very sensitive to my inputs.

I noticed that my constellation map looks fine after EQ if I apply 'PathDelays',[0 1.1184e-05]. In Figure rayleigh1 you can see that the EQ works well. However if I apply the almost same value 'PathDelays',[0 1183999999999e-05]. the result differs extremly as seen in Figure rayleigh2. I assume that a condition between the lowest possible path delay and the sampling rate fs migh exists.

Does someone know how comm.RayleighChannel computes the channel response in detail?

Thanks

fs = 1/1.6e-6;
rayleighchan = comm.RayleighChannel( ...
    'SampleRate',fs, ...
    'PathDelays',[0 1.1183999999999e-05], ... %select 1183999999999e-05 or 1.1184e-05
    'AveragePathGains',[0 -60], ...
    'NormalizePathGains',true, ...
    'MaximumDopplerShift',40, ...
    'RandomStream','mt19937ar with seed', ...
    'Seed',22, ...
    'PathGainsOutputPort',true);
    
[channelResponse,channelGain] = rayleighchan(ofdmSymbols);

Answer 1

[Sudarsanan A K]

Hello Sergio,

I understand that you are curious about the effect of path delays in the channel response computation and trying to find the relationship between path delays and sampling rate in the simulation of "comm.RayleighChannel" propagation model.

Internally, the "comm.RayleighChannel" object computes the channel response by applying a filter that represents the multipath effect. The filter taps are derived from the path delays and average path gains. The taps are complex-valued to represent both the amplitude and phase changes introduced by the channel.

The path gains occur at time instances that correspond to the specified path delays and might not align with the input sampling time as in your case. The implementations interpolate the channel filter coefficients from the actual path gains, use the coefficients to model the channel, and align the coefficients with the input sampling time. Small differences in the path delays can result in different interpolation results, which might significantly affect the channel response and, consequently, the constellation map after equalization.

To delve into the details of fading channel simulation model and channel visualization, you can refer to the following documentations:

• Methodology for Simulating Multipath Fading Channels: https://mathworks.com/help/comm/ug/fading-channels.html#bq5zk36
• Channel Visualization: https://mathworks.com/help/comm/ug/channel-visualization.html

I hope this helps!