A PARAFAC-based Channel Estimation Algorithm for
Multi-user MIMO Two-way Relay Systems
Siyu Ye and Jianhe Du
Communication University of China
School of Information and Engineering
Communication University of China
Beijing 100024
dujianhe1@gmail.com
Ruyi Deng and Rui Chang
Communication University of China
School of Information and Engineering
Communication University of China
Beijing 100024
ABSTRACT
In this paper, the authors present a novel channel estimation
method for multi-user multiple-input multiple-output (MIMO)
two-way relay systems using parallel factor (PARAFAC) model.
The proposed method transmits interactive orthogonal channel
training sequences at each user end, the relay uses different
amplifying factors to amplify the received signals, and forward
the amplified signals to users. Finally, the PARAFAC model is
constructed at each user end and this PARAFAC model is fitted to
estimate all the channel matrices. The proposed method has higher
channel estimation accuracy. Moreover, the method can estimate
all the channel matrices at each user. Numerical examples are
shown to demonstrate the effectiveness of the PARAFAC-based
channel estimation algorithm.
CCS Concepts
• Theory of computation ➝Design and analysis of algorithms
Keywords
Channel estimation; two-way relay; PARAFAC; estimation
accuracy.
1. INTRODUCTION
In recent years, multi-input multi-output(MIMO) relay
communication systems have attracted a lot of research interests
due to its capability in reducing the path loss, extending network
coverage and improving energy efficiency [1].The optimal relay
amplifying matrix is derived in [2-4]to maximize the mutual
information between the source and the destination nodes.
Evidently, the above-mentioned MIMO relay system is dominant
in any case if the channel state information (CSI) of all the
involved links is already known.
In many previous studies, channel estimation was often neglected.
It can be found in [5-8] that the knowledge of the instantaneous
channel state information (CSI) should be considered at the
destination node to retrieve the information transmitted by the
source node in a MIMO relay system. But in practice, the CSI is
unknown, so it needs to be estimated. In [9], the authors obtain
sufficient and necessary conditions for the relay amplifying matrix
to ensure that the relay channel is estimated viably. In [10], the
authors proposed a least-squares (LS) fitting channel estimation
algorithm for a two-hop MIMO relay system.
In the study [11] by Shannon, two-way relay systems are
emphasized because of their higher spectral efficiency than one-
way relaying systems. The main difficulty in channel estimation
for two-way MIMO relay system is to obtain instantaneous CSI of
the first-hop and second-hop links by means of a small amount of
signal processing. The multi-pair MIMO two-way relay system
consisting of multiple user nodes and one relay has been studied
in recent years [12]. In this relay system, each node has multiple
antennas, and the user nodes are divided into multiple pairs and
each user only exchanges data with the same pair of users.
Recently tensor analysis has been found to be an efficient method
for estimating channels in two-hop MIMO relay system [13-15].
In [13], a channel estimation algorithm for two-hop MIMO relay
systems is developed by adopting parallel factor (PARAFAC)
analysis. Enlightened by [13] of its channel estimation algorithm,
a low complexity PARAFAC-based channel estimation algorithm
is proposed in [14] for two-hop non-regenerative MIMO relay
systems.
In this study, we consider a two-hop AF MIMO relay system
consisting of four users and one relay. A new method of channel
estimation algorithm for (MIMO) relay systems is proposed by
using PARAFAC model. The PARAFAC model is constructed at
each user end and it is fitted to estimate all the channel matrices.
The proposed method has higher accuracy for channel estimation.
The rest of this paper is organized as follows. The system model
of two-way MIMO relay system is presented in Section 2. The
uniqueness conditions are also discussed. The BALS fitting
algorithm is developed in Section 3. Section 4 shows numerical
examples to demonstrate the performance of the proposed
algorithms. Finally, conclusions are drawn in Section 5.
Notations: Scalars, vectors, matrices and tensors are denoted by
lower-case letters
, lower-case boldface letters
,
boldface capitals
, and underlined boldface capitals
, respectively.
,
and
stand for transpose,
conjugate transpose and pseudo-inverse of the matrix
,
respectively.
is the Frobenius norm of
.
is the
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ICCIS 2017, November 7-9, 2017, Wuhan, China
© 2017 Association for Computing Machinery.
ACM ISBN 978-1-4503-5348-9/17/11…$15.00
DOI: https://doi.org/10.1145/ 3158233.3159333