# General Questions MIMO Communication theory

The following are questions regarding MIMO communication theory. I have come across a MATLAB implementation of MIMO channel. My questions are not regarding the implementation, but rather regarding the theory itself. In MATLAB there is comm.MIMOChannel that creates a MIMO channel. The following are the properties which one can play with

 MIMOChannel properties:
%
%   SampleRate                  - Input signal sample rate (Hz)
%   PathDelays                  - Discrete path delay vector (s)
%   AveragePathGains            - Average path gain vector (dB)
%   NormalizePathGains          - Normalize path gains (logical)
%   KFactor                     - Rician K-factor scalar or vector (linear scale)
%   DirectPathDopplerShift      - Doppler shift(s) of line-of-sight component(s) (Hz)
%   DirectPathInitialPhase      - Initial phase(s) of line-of-sight component(s) (rad)
%   MaximumDopplerShift         - Maximum Doppler shift (Hz)
%   DopplerSpectrum             - Doppler spectrum
%   SpatialCorrelation          - Spatially correlated
%   NumTransmitAntennas         - Number of transmit antennas
%   TransmitCorrelationMatrix   - Transmit correlation matrix (or 3-D array)
%   AntennaSelection            - Optional transmit and/or receive antenna selection
%   NormalizeChannelOutputs     - Normalize channel outputs (logical)
%   RandomStream                - Source of random number stream
%   Seed                        - Initial seed of mt19937ar random number stream
%   PathGainsOutputPort         - Enable path gain output (logical)


I have the following questions: ( I really hope I can get some help)

1. Does the sample rate mean the actual symbol rate of the input? Is it related to the modulation we use?

2. Do path delays dictate whether we have a frequency selective or frequency flat fading channel?

3. The channel above gives the option of having either Rayleigh or Ricean fading channel gains, I know that Rayleigh is good approximation because of the central limit theorem (i.e large number of random paths), if one specifies that the distribution is Rayleigh, does that mean that the Path Delays should be infinite? Or does this distribution mean a distribution of the path itself.

4. Why would a Direct PATH (LOS) have a doppler shift different that the maximum doppler shift? Then which one dictates the coherence time?

Thank you for any advice or answers on any of the above questions

1. As it says in the documentation, SampleRate is the signal's sampling rate, not the symbol rate.

2. The path delays together with your symbol rate determine whether the channel is flat or frequency-selective.

3. You should choose Rayleigh if there is no line-of-sight component in the received signal, and Rice otherwise. Regarding the path delays: the model is that the gain you observe at each sampling instant is the result of many paths, whose arrival times are so close that you can't resolve them. So, in your model, you always have a finite number of paths, each of which has random Gaussian gain.

4. Each path has a different length and arrival angle, so it can have a different Doppler.

As a side note, and expressing only my opinion, it is more educational to try to create your own models of the fading channel than using a Matlab toolbox. Toolboxes are created to increase an expert's productivity, not for learning.

• Thank you @MBaz, for taking the time to answer. Regarding 1) how is the sample rate related to the symbol rate? 2) I understand that the max delay spread compared to symbol rate dictates whether you have flat or frequency selective, does the sample rate also affect this choice? 3)as i understand from your answer, fading is describing the path itself which is a result of many paths? 4) Which one is related to coherence time and thus dictates whether we have slow or fast fading? Thanks. Apr 20, 2015 at 16:44
• I also agree with your side note, I am trying to implement my own MIMO fading channel, but have looked at the toolbox first. Apr 20, 2015 at 16:45
• 1) No relation, except that you need to meet the sampling theorem ($f_s>2B$ where $B$ is your bandwidth). 2) No, the sampling rate is independent of whether the channel is flat or F.S. However, a higher sampling rate allows you to resolve more individual paths. 3) Yes; the model is that paths whose arrival time is too close are not resolvable, their effect is the same as having a Gaussian gain. 4) Coherence time is just the time difference between the first and the last reflections arrive at the receiver. Whether the channel is slow or fast depends also on your symbol rate.
– MBaz
Apr 20, 2015 at 17:01
• I thought the coherence time is the inverse of the maximum dopppler shift, is that what you mean by 4? While the difference between the first and last reflections is the delay spread?@MBaz Apr 20, 2015 at 17:02
• Also, what property above specifies whether I have LOS or NLOS? is it the path delay? And so how can one distinguish if a LOS is Ricean and NLOS is Rayeligh, Thanks in advance and sorry for asking alot. These are my last questions @MBaz Apr 20, 2015 at 17:20