A Signal Perturbation Free Semi-Blind MRT
MIMO Channel Estimation Approach
Chung Chen
∗
, Wei-Ping Zhu
†∗
, Qingmin Meng
∗
,
∗
Institute of Signal Processing and Transmission
Nanjing University of Posts and Telecommunications, Nanjing, China 210003
Center for Signal Processing and Communications
Dept. of Electrical and Computer Engineering, Concordia University, Montreal, Quebec, Canada H3G 1M8
Abstract— In this paper, an efficient signal-perturbation-free
semi-blind approach is proposed for flat-fading channel esti-
mation of multiple-input multiple-output (MIMO) systems with
maximum ratio transmission (MRT). A novel transmit scheme
is developed based on the eigenvalue decomposition of the
correlation matrix of the transmitted signal. The new scheme
is to send a small volume of data bearing the information of
the correlation matrix to the receiver for the cancellation of
the signal perturbation error. Computer simulations show that
the proposed approach significantly outperforms the closed-form
semiblind estimation method (CFSB) in terms of the MSE of the
beamforming vector estimate.
I. INTRODUCTION
In recent years, multiple-input multiple-output (MIMO)
communication has received much attention due to its pro-
vision of a capacity gain from spatial multiplexing as well as
a diversity gain to against signal fading. In order to achieve
these performance improvements, accurate estimation of the
MIMO channels is necessary. Channel estimation techniques
are commonly divided into three categories: training-based,
semi-blind, and blind. The training-based estimation is entirely
based on transmission of training sequences (known a priori
to the receiver). The blind estimation only exploits some
known structure of the received data. The combination of these
techniques is called semi-blind estimation.
The beamforming strategy uses the precoding and shaping
matrices that are the right and left dominant singular vectors
of H, v
1
and u
1
, respectively, where H is the N
r
×N
t
channel
transfer matrix [1]. The performance gain depends on whether
or not the channel is known at the transmitter. Training-based
and semiblind channel estimation has been intensively studied
for frequency-flat MIMO channel estimation, recently. The
training-based conventional least-squares estimation (CLSE)
algorithm, and a closed-form semiblind (CFSB) algorithm that
estimates u
1
from data using a blind algorithm and estimates
v
1
from the training, have been described in [2]-[4]. However,
these algorithms are subject to signal perturbation [5][6].
In [7]-[8], a perturbation-free channel estimation scheme
is proposed. It offsets the perturbation error derived from
the whitening-rotation algorithm. This paper adopts the novel
∗
This work was jointly supported by National Natural Science Foundation
of China (No. 60872104), Natural Sciences Fundamental Research Program of
Jiangsu Universities (No. 08KJD510001), and Doctoral Program Foundation
of Ministry of Education (No. 20080293004).
scheme overcome the perturbation error of CFSB in order
to improve the channel estimation performance. By utilizing
the eigenvalue decomposition (EVD) of the transmit signal
perturbation matrix, an efficient transmit structure is designed
for the elimination of the signal perturbation error in the re-
ceiver, leading to a signal-perturbation-free CFSB approach. It
is shown that the new approach provides a better performance
than the original CFSB method.
II. BRIEF OVERVIEW OF TRAINING-BASED AND
SEMIBLIND CHANNEL ESTIMATION
Consider a (N
r
, N
t
) MIMO system, where the channel
experiences slow and frequency non-selective Rayleigh fading,
and is characterized by an N
r
×N
t
matrix H = [h
ij
] whose el-
ements are independent identically distributed (i.i.d.) complex
Gaussian random variables (CGRVs) with zero-mean and unit
variance, i.e., E(|h
ij
|
2
) = 1. Here, h
ij
denotes the channel
gain from the j-th transmit antenna to the i-th receive antenna.
Given the transmitted signal vector s(n)
∆
= [s
1
(n), ...s
N
t
(n)]
T
whose elements are i.i.d. Gaussian random variables with zero
mean and unit variance δ
2
s
= 1, the received signal vector
x(n)
∆
= [x
1
(n), ...x
N
r
(n)]
T
can be written as
x(n) = Hs(n) + w(n) (1)
where the noise vector w(n)
∆
= [w
1
(n), ...w
N
r
(n)]
T
is spa-
tially and temporally uncorrelated with variance δ
2
w
.
In each block, the first L
p
slots are used for training purpose.
Let L
d
denote the number of spatially-white data symbols
transmitted, that is, a total of L
p
+ L
d
= N vectors are
transmitted prior to transmitting the beamformed-data. Note
that the L
d
white data symbols carry infomation bits, and thus
making an efficient use of available bandwidth.
We now briefly review the Maximum ratio transmission
communication system and the MIMO channel estimation
algorithms for beamforming.
Fig. 1 shows the MRT MIMO system model with beam-
forming at the transmitter and the receiver. We perform the
singular value decomposition (SVD) of H, i.e. H = UΣV
H
,
where Σ ∈ R
N
r
×N
t
contains the singular values σ
1
≥ σ
2
≥
... ≥ σ
m
> 0, as its diagonal elements, m = rank(H). Let v
1
and u
1
denote the first columns of V and U , respectively. The
transmitter employs MRT to send data, that is, the data stream