The MIMO channel does not depend on the routing of data and there is no obligation to use clusters of antennas. This channel depends on the system fraquency bandwidth, the type of antennas, their number and location and their orientation.
For narrowband MIMO systems, the MIMO channel is characterized by its matrix H of size NxM, where N is the number of transmit antennas and M is the number of receive antennas. This can be the case of MIMO systems using Orthogonal Frequency Division Modulation (OFDM) where each sub-channel can be considered as a SISO (Single Input Single Output) flat channel (frequency not-selective channel). For time-varying MIMO channels, the coefficients of the channel matrix H are random variables, for example Rayleigh variables. When using a base-band representation of MIMO systems, the channel coefficients are complex Gaussian variables with zero mean and equal variance. These coefficients can be independent identical variables but other MIMO channels models can introduce correlations between these variables, as in
B. Habib, G. Zaharia, H. Farhat, G. El Zein Outdoor-to-Indoor MIMO Hardware Simulator with Channel Sounding at 3.5 GHz, Proc. of VTC-Spring, 2013
For wideband MIMO systems, each coefficient hmn(t) of the channel matrix H is the impulse response of the SISO multipath propagation channel between the transmit antenna m and the receive antenna n. These coefficients are random functions. They can be consideres independent or dependent, depending on the used MIMO channel.
Thanks all. In almost all papers on massive MIMO, Ray Leigh block fading model is used.
Sir, G. Zaharia, thanks for your valuable answer. Can you please let me know, what will be the coefficients of channel matrix H for Massive MIMO? Should I consider independent Guassian random variables?
So far there are only a few channel measurements reported for massive MIMO so it is hard to say what kind of channel model that is most appropriate in different scenarios. Models for small-scale MIMO is a good starting point, but needs to be revised to handle shadowing variations of the array, spherical wavefronts in the near-field, etc.
Most analytical papers consider simple Rayleigh fading channels since it simplifies the analysis. Measurements have shown similar performance results even if the channel models are not the same.
For the coefficients of the MIMO channel matrix it is possible de consider independent Gaussian random variables. This depends on the accuracy of the results you wish to obtain. Some correlation between these coefficients can be introduced, as in the indicated paper. There is no much difference between the MIMO propagation channel and the massive MIMO propagation channel. Only the size of the channel matrix is increased for massive MIMO. The main difference is the manner to use the propagation channel by the massive MIMO systems.
Thanks all for the valuable answers. Small scale fading channel can be considered when the antennas are well separated. Is it okay to consider the channel coefficients as the product of small scale fading coefficients and the path loss attenuation? Please correct me if I am wrong?
Yes, the channel coefficients are usually modeled as product between small-scale fading (= variations caused by multi path propagation) and large-scale fading (= distant dependent path loss attenuation and location-dependent shadowing).
Thank you sir Emil. Can you also please tell me that, while using rayleigh fading channel in MATLAB, should I consider the channel matrix as the element of Tx antenna of BS and the number of users? Is there example of any MATLAB code for this channel model?
At each moment t, the element h_nm of the channel matrix H represents the path loss between the transmit antenna m (M transmit antennas) and the receive antenna n (N receive antennas). the value h_nm at the instant t depends on the distance between the transmitter and the receiver, the type of antennas (Tx ans Rx) and the propagation environment. The matrix H does not depend on the number of users.
Try :
L Schumacher, WLAN MIMO channel matlab program (http://www), . info.fundp.ac.be/~lsc/Research/IEEE_80211_HTSG_CMSC/distribution_terms.html webcite
Why we prefer i.i.d Rayleigh Fading over Correlated Rayleigh Fading in Massive MIMO? What are the bnefits of i.i.d Rayleigh Fading? Please answer of my question and a special request to Emil Björnson for reply.