Documentation 
The MIMO Channel block filters an input signal using a multipleinput multipleoutput (MIMO) multipath fading channel.
This block accepts up to four input ports. When you set the Antenna selection parameter to Tx, there is one additional input port. When you set the Antenna selection parameter to Rx, there is one additional input port. When you set the Antenna selection parameter to Tx and Rx, there are two additional input ports. Independent of the input ports resulting from the antenna selection parameters, when you set the Technique for generating fading samples parameter to Sum of sinusoids and the Initial time source parameter to Input port, an additional input port is created. When you check the Output channel path gains check box, there is an additional output port for the channel path gains of the underlying fading process.
The fading processing per link is described in Methodology for Simulating Multipath Fading Channels section and assumes the same parameters for all links of the MIMO channel.
Antenna Selection Parameter  Signal Input  Transmit Selection Input  Receive Selection Input  Signal Output  Optional Channel Gain Output 

Off  N_{s}byN_{t}  N/A  N/A  N_{s}byN_{r}  N_{s}byN_{p}byN_{t}byN_{r} 
Tx  N_{s}byN_{st}  1byN_{t}  N/A  N_{s}byN_{r}  N_{s}byN_{p}byN_{t}byN_{r} 
Rx  N_{s}byN_{t}  N/A  1byN_{r}  N_{s}byN_{sr}  N_{s}byN_{p}byN_{t}byN_{r} 
Tx and Rx  N_{s}byN_{st}  1byN_{t}  1byN_{r}  N_{s}byN_{sr}  N_{s}byN_{p}byN_{t}byN_{r} 
where
N_{s} represents the number of samples
N_{t} represents the number of transmit antennas determined by the Transmit spatial correlation or Number of transmit antennas
N_{r} represents the number of receive antennas determined by the Receive spatial correlation or Number of receive antennas
N_{p} represents the number of paths determined by the Discrete path delays or Average path gains
N_{st} represents the number of selected transmit antennas determined by the number of ones in the Transmit Selection Input
N_{rt} represents the number of selected receive antennas determined by the number of ones in the Receive Selection Input
Specify the sample rate of the input signal in hertz as a doubleprecision, real, positive scalar. The default value of this parameter is 1 Hz. To match the model settings, set the value of this parameter so it equals number of rows of the signal input divided by the model sample time.
Specify the delays of the discrete paths in seconds as a doubleprecision, real, scalar or row vector. The default value of this parameter is 0. When you set Discrete path delays to a scalar, the MIMO channel is frequency flat. When you set Discrete path delays to a vector, the MIMO channel is frequency selective.
Specify the average gains of the discrete paths in decibels as a doubleprecision, real, scalar or row vector. The default value of this parameter is 0. Average path gains must have the same size as Discrete path delays.
Select this check box to normalize the fading processes so that the total power of the path gains, averaged over time, is 0 dB.
Specify the fading distribution of the channel as Rayleigh or Rician. The default selection is Rayleigh.
Specify the K factor of a Rician fading channel. This parameter accepts a doubleprecision, real, positive scalar or nonnegative, nonzero row vector with the same length as Discrete path delays. The default value of this parameter is 3. This parameter applies when you set Fading distribution to Rician.
If you set Kfactors to a scalar, the first discrete path is a Rician fading process with a Rician Kfactor of Kfactors. Any remaining discrete paths are independent Rayleigh fading processes.
If you set Kfactors to a row vector, the discrete path corresponding to a positive element of the Kfactors vector is a Rician fading process with a Rician Kfactor specified by that element. The discrete path corresponding to a zerovalued element of the Kfactors vector is a Rayleigh fading process.
Specify the Doppler shift(s) for the lineofsight component(s) of the Rician fading channel in hertz. This parameter accepts a doubleprecision, real scalar or row vector. This parameter appears when you set Fading distribution to Rician. The default value of this parameter is 0. This parameter must have the same size as Kfactors.
If you set LOS path Doppler shift to a scalar, it represents the lineofsight component Doppler shift of the first discrete path that is a Rician fading process.
If you set LOS path Doppler shift to a row vector, the discrete path that is a Rician fading process indicated by a positive element of the Kfactors vector has its lineofsight component Doppler shift specified by the corresponding element of LOS path Doppler shift.
Specify the initial phase(s) of the lineofsight component(s) of a Rician fading channel in radians. This parameter accepts a doubleprecision, real scalar or row vector. This parameter appears when you set Fading distribution to Rician. The default value of this parameter is 0.
LOS path initial phase must have the same size as Kfactors.
If you set LOS path initial phase to a scalar, it is the lineofsight component initial phase of the first discrete path that is a Rician fading process.
If you set LOS path initial phase to a row vector, the discrete path that is a Rician fading process indicated by a positive element of the Kfactors vector has its lineofsight component initial phase specified by the corresponding element of LOS path initial phase.
Specify the maximum Doppler shift for all channel paths in hertz as a doubleprecision, real, nonnegative scalar. The default value of this parameter is 0.001 Hz.
The Doppler shift applies to all the paths of the channel. When you set this parameter to 0, the channel remains static for the entire input.
For a Doppler spectrum type other than Gaussian and biGaussian, the value of fc is 1. For these two Doppler spectrum types, fc is dependent on the Doppler spectrum structure fields. See the algorithm section for comm.MIMOChannel for more details on how the cutoff frequency is defined.
Specify the Doppler spectrum shape for all channel paths as a single Doppler spectrum structure returned from the doppler function, or a 1byN cell array of such structures. The default value of this parameter is Jakes Doppler spectrum. This parameter applies when Maximum Doppler shift is greater than zero.
If you assign a single Doppler spectrum structure, all paths have the same specified Doppler spectrum. If the Technique for generating fading samples parameter is set to Sum of sinusoids, Doppler spectrum must be doppler('Jakes'); otherwise, select from the following:
doppler('Jakes')
doppler('Flat')
doppler('Rounded', ...)
doppler('Bell', ...)
doppler('Asymmetric Jakes', ...)
doppler('Restricted Jakes', ...)
doppler('Gaussian', ...)
doppler('BiGaussian', ...)
You can assign a 1byN cell array of Doppler spectrum structures, chosen from any items in the previous list. Each path has the Doppler spectrum specified by the corresponding Doppler spectrum structure in the array. In this case, the length of the cell array must be equal to the length of Discrete path delays.
If you run a model that contains this block in any mode except normal mode or you set Simulate using of this block to Code generation, you must specify Doppler spectrum to a single Doppler spectrum structure across different paths.
Select this check box to specify the transmit and receive spatial correlation matrices from which the number of transmit and receive antennas can be derived.
Clear this check box to specify the number of transmit and receive antennas using block parameters. In this case, the transmit and receive spatial correlation matrices are both identity matrices.
Specify the number of transmit antennas. You can specify up to eight antennas. This parameter appears when you clear the Spatially correlated antennas check box.
Specify the number of receive antennas. You can specify up to eight antennas. This parameter appears when you clear the Spatially correlated antennas check box.
Specify the spatial correlation of the transmitter as a doubleprecision, real or complex, 2D matrix or 3D array. This parameter only appears when you select the Spatially correlated antennas check box. The default value of this parameter is [1 0;0 1].
The first dimension determines the number of transmit antennas, N_{t}, that must be between 1 and 8, inclusive. If the channel is frequencyflat, i.e., Discrete path delays is a scalar, Transmit spatial correlation is a 2D Hermitian matrix of size N_{t}–by–N_{t}. The main diagonal elements must be all ones, while the offdiagonal elements must be real or complex numbers with a magnitude smaller than or equal to one. If the channel is frequencyselective, i.e., Discrete path delays is a row vector of length N_{p}. You can specify Transmit spatial correlation as a 2D matrix, in which case each path has the same transmit spatial correlation matrix. Alternatively, it can be specified as a 3D array of size N_{t}–by–N_{t}–by–N_{p}, in which case each path can have its own different transmit spatial correlation matrix.
Specify the spatial correlation of the receiver as a doubleprecision, real or complex, 2D matrix or 3D array. This parameter only appears when you select the Spatially correlated antennas check box. The default value of this parameter is [1 0;0 1].
The first dimension determines the number of receive antennas, N_{r}, that must be between 1 and 8, inclusive. If the channel is frequencyflat, i.e., Discrete path delays is a scalar, Receive spatial correlation is a 2D Hermitian matrix of size N_{r}–by–N_{r}. The main diagonal elements must be all ones, while the offdiagonal elements must be real or complex numbers with a magnitude smaller than or equal to one. If the channel is frequencyselective, i.e., Discrete path delays is a row vector of length N_{p}, you can specify Receive spatial correlation as a 2D matrix, in which case each path has the same receive spatial correlation matrix. Alternatively, you can specify Receive spatial correlation as a 3D array of size N_{r}–by–N_{r}–by–N_{p}, in which case each path can have its own different receive spatial correlation matrix.
Define the antenna selection mode as one of Off, Tx, Rx, or Tx and Rx. The default selection is Off.
Antenna Selected  Input Ports Added 

Off  None 
Tx  Tx Sel 
Rx  Rx Sel 
Tx and Rx  Tx Sel, Rx Sel 
Select this check box to normalize the channel outputs by the number of receive antennas.
Specify the channel modeling technique as either Filtered Gaussian noise or Sum of sinusoids . The default selection is Filtered Gaussian noise.
Specify the number of oscillators used in modeling the fading process as a positive integer. This parameter is available when Technique for generating fading samples is set to Sum of sinusoids. The default value is 48.
Specify the source of the fading model's initial time offset as either Property or Input port. This parameter is available when Technique for generating fading samples is set to Sum of sinusoids. The default selection is Property.
Specify the time at which the fading process begins as a real, nonnegative scalar measured in seconds. This parameter is available when Technique for generating fading samples is set to Sum of sinusoids and Initial time source is set to Property. The default value is 0.
Specify the initial seed of the random number generator for this block as a doubleprecision, real, nonnegative integer scalar. The default setting for this parameter is 73.
Select this check box to output the channel path gains of the underlying fading process using a secondary block output port.
Select either Code generation or Interpreted execution. The default selection is Interpreted execution.
If you run a model that contains this block in any mode except normal mode or you set Simulate using to Code generation, you must specify Doppler spectrum to a single Doppler spectrum structure across different paths.
Select among Off  Impulse response  Frequency response  Doppler spectrum  Impulse and frequency responses to set the channel visualization option. Visualization is available only when the Technique for generating fading samples parameter is set to Filtered Gaussian noise. The default selection is Off.
Select the transmitreceive antenna pair to display. This parameter is available when Channel visualization is not Off. The default value is [1, 1].
Select the percentage of samples to display from among 10%  25%  50%  100%. Increasing the percentage improves display accuracy at the expense of simulation speed. This selection is available when Channel visualization is set to Impulse response, Frequency response, or Impulse and frequency responses. The default value is 25%.
Select the path for which the Doppler spectrum is displayed. The path number is a positive integer scalar with maximum value equal to the number of discrete paths. The default value is 1.
Port  Supported Data Types 

Signal input 

Optional transmit selection input 

Optional receive selection input 

Signal output 

Optional path gain output 

[1] Oestges, C., and B. Clerckx. MIMO Wireless Communications: From RealWorld Propagation to SpaceTime Code Design, Academic Press, 2007.
[2] Correira, L. M. Mobile Broadband Multimedia Networks: Techniques, Models and Tools for 4G, Academic Press, 2006.
[3] Kermoal, J. P., L. Schumacher, K. I. Pedersen, P. E. Mogensen, and F. Frederiksen. "A stochastic MIMO radio channel model with experimental validation." IEEE Journal on Selected Areas of Communications. Vol. 20, Number 6, 2002, pp. 1211–1226.
[4] Jeruchim, M., P. Balaban, and K. S. Shanmugan. Simulation of Communication Systems, Second Edition, New York, Kluwer Academic/Plenum, 2000.
[5] Pätzold, Matthias, ChengXiang Wang, and Bjorn Olav Hogstand. "Two New SumofSinusoidsBased Methods for the Efficient Generation of Multiple Uncorrelated Rayleigh Fading Waveforms." IEEE Transactions on Wireless Communications. Vol. 8, Number 6, 2009, pp. 3122–3131.