This paper described a spatial correlation and eigenvalue in a multipleinput multipleoutput (MIMO) channel. A MIMO channel model with a multipath propagation mechanism was proposed and showed the channel matrix. The spatial correlation coefficient formula
To support realtime multimedia communication, future mobile communications will require a highbitrate transmission system with high utilization of the frequency spectrum in multipath channels with lineofsight (LOS) and nonlineofsight (NLOS) paths [
With this in mind, we proposed a MIMO channel model with a propagation mechanism composed of multipath propagation and mobile and basesite antenna configurations and created the channel matrix on the basis of the model. The channel matrix is allowed to consist of matrix elements with a given fixed theoretical correlation between antenna elements at the mobile and base sites because the propagation mechanism is known and we can calculate the correlation. Therefore, the matrix requires a formula for estimating the correlation between each pair of antenna elements at one side and at both sides under various multipath conditions and base and mobilesite situations. So we derived the correlation formulas by using the matrix for indoors, outdoors, and so forth. Using the matrix, we could also calculate the matrix eigenvalue and we clarified its properties by simulation; moreover, it was possible to study the relation between the correlation and eigenvalue.
This paper is organized as follows. Section
MIMO systems will be used in various areas: the cells are called pico, micro, and macro cells. The MIMO channel model, which consists of a delay profile measured around the base and mobilesite origins and the antenna configurations with coordinate systems common to the profile’s angle, is shown in Figure
The number of arriving waves is
The waves have excess delay time
The amplitude is
Whether a wave’s arriving angle at the mobile or base is also the incident angle to multipath scattering from the mobile or base site depends on whether the site is receiving or transmitting. Here, the mobilesite angle is denoted by
MIMO channel model.
On the other hand, assuming that all the antennas used have the same pattern with omnidirectionality and no mutual coupling, the antenna coordinates use a polar coordinate system centered at each site’s origin, as shown in Figure
In this paper, we also assume that all antenna elements of each station have the same values of
Angle difference
Under the conditions described above and assuming a narrowband system such as OFDM, the MIMO channel, which is composed of the
When the number of antenna elements at each station is
We start by studying the general spatial correlation between MIMO
The first and second terms in (
The
We first calculate
Next, we calculate
A computer simulation was performed to verify (
Simulation parameters.
Correlation  Eigenvalue  
MIMO channel  Oneside channel  Bothside channel  Bothside channel  
Environment  Indoors  Outdoors  Indoors  Outdoors  Indoors  Outdoors  
 
Incident/arriving angle  Distribution  Uniform  Gaussian  Uniformuniform  UniformGaussian  Uniformuniform  UniformGaussian 

0, 0 
— 
0 
0 

0 
0 


— 


0, 

 
Delay profile 

10 waves  

Exponential distribution (effective amplitude greater than −25 dB)  






 
Antenna 

0~5 
—  0~5, 
0~20 



—  0~20 
0~5 
0~20 



Components 





Figure
Correlation of oneside channel. (a) NLOS indoors (uniform distribution). (b) LOS indoors (uniform distribution). (c) NLOS outdoors (Gaussian distribution).
Figure
Correlation of dependence on arrival angle for oneside channel. (a) Uniform distribution. (b) Gaussian distribution.
Figure
Correlation of bothside channel (uniformuniform distribution). (a)
Figure
Correlation of bothside channel (uniformGaussian distribution). (a)
All of the eigenvalues were simulated by a MIMO antenna with a
Figure
Example of eigenvalue variation with movement (
Figure
Dependence of eigenvalue on correlation (
Figure
Dependence of eigenvalue on Gaussian distribution (
To study MIMO channel properties, we proposed a MIMO channel model with a propagating mechanism composed of multipath propagation and antenna configurations and then showed the MIMO channel matrix. Under this model, the spatial correlation formula
Assuming that
The
Furthermore, by continuously analyzing
We expand the real and imaginary parts for
The real and imaginary parts of
The real and imaginary parts for
Putting