THE JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOMMUNICATIONS
Volume 14, Issue 4, December 2007
ZHANG Hui-ping, WU Ping, LIU Ai-jun
Ergodic channel capacity of the spatial correlated rayleigh
MIMO channel
CLC number TN911 Document A Article ID 1005-8885 (2007) 04-0032-04
Abstract The theoretical capacity of the spatial correlated
Rayleigh multiple input multiple output (MIMO) channel is an
important issue in MIMO technology. In this article, an ergodic
channel capacity formula of the spatial correlated rayleigh
MIMO channel is provided, which is deduced when two
antennas exist at either the transmitter or the receiver. The
multi-dimensional least-squares fit algorithm is employed to
narrow the difference between the theoretical formula capacity
and the practical capacity. Simulation results show that the
theoretical capacity approaches the practical one closely.
Keywords MIMO, rayleigh fading channel, shannon capacity
1 Introduction
The MIMO system is considered as a key technology owing
to the considerable capacity or spectrum efficiency [13].
Channel capacity is an important issue in the MIMO system. A
great deal of study has been carried out in this filed, e.g. the
theoretical capacity of the uncorrelated rayleigh MIMO
channel has been studied sufficiently [47]. However, in the
MIMO system, when the antennas are not separated
sufficiently and/or there is lack of scattering, spatial
correlation will exist. The research of the correlated MIMO
channel capacity has traditionally been considered as a
difficult problem [810]. Semi-correlated channel capacity
has been studied in Ref. [9]. The distribution of the correlated
channel capacity has been discussed in Ref. [11], and some
capacity bounds of the correlated channel have been provided
in Ref. [12]. However, a close-form formula of the correlated
MIMO capacity has not been proposed.
Received date: 2007-04-17
ZHANG Hui-ping, LIU Ai-jun
School of Languages, Beijing University of Posts and Telecommunications,
Beijing 100876, China
WU Ping ( )
Key Laboratory of Universal Wireless Communications (Beijing University of
Posts and Telecommunications) Ministry of Education, Wireless Technology
Innovation Institute, Beijing 100876, China
E-mail: wuping1983@gmail.com
The main contribution of this article is that it provides a
close-form formula of the ergodic channel capacity for the
spatial correlated rayleigh MIMO channel, which has two
antennas at either the transmitter or the receiver. The proposed
formula can be used for MIMO theoretical analysis and
engineering application conveniently. Simulations show that
the capacity calculated by the formula and the capacity
obtained by monte carlo simulation coincide perfectly.
This article is organized as follows: Section 2 introduces the
Kronecker spatial correlated MIMO channel model. Sections
3 and 4 provide the capacity formula. Section 5 provides the
simulation results. Finally, Section 6 concludes the article.
2 Spatial correlated channel model
We consider that the MIMO system has
transmitting
antennas and
receiving antennas, and the channel matrix
is H.
The Kronecker spatial correlated MIMO channel can be
modeled as [1013]:
1/ 2 1/ 2
rt
w
y Hs n R H R s n
(1)
where [
•
]
1/2
represents the matrix square root;
is a
complex matrix, whose elements are independently
identically distributed (i.i.d.) complex Gaussian random
variables with zero mean and unit variance; and
,
, and
represent the transmitting, the receiving, and the noise
vector, respectively. We assume that the spatial correlation at
the transmitter is independent of the correlation at the receiver.
is
transmitting correlation matrix and
is
receiving correlation matrix.
,
are written as:
22
rr
2
r
2
r
22
rr
( ) ( 1)
()
r
()
( 1) ( )
1 ... ...
1 ... ... ...
... ... ... ...
... ... ... ... ...
... ... ... 1
... ... 1
N i N
Nl
Nk
N N j
r r r
r
r
r
r
r r r
R