J. Shanghai Jiao Tong Univ. (Sci.), 2019
https://doi.org/10.1007/s12204-019-2077-3
Tensor-Based Joint Channel Estimation and Symbol Detection
for AF MIMO Relay Networks
LIN Heyun
2
(
), YUAN Chaowei
2
(
), DU Jianhe
1∗
(
), HU Zhongwei
2
(
)
(1. School of Information and Communication Engineering, Communication University of China, Beijing 100024, China;
2. School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing
100876, China)
© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract: A study on the joint channel and symbol estimation issue is provided for two hop relay networks which
employ the amplify-and-forward (AF) relaying approach. The encoding scheme at the source node introduces
the time-domain spreading with a time-varying linear constellation precoding. Then, a set of amplifying factors
matrices is utilized by the relays to amplify and forward the received data to the destination. The received signal
at the destination can be constructed as a fourth-order tensor model, which is referred to as the nested parallel
factor (PARAFAC) model. And then, we present a novel Levenberg-Marquardt (LM) algorithm based on this
tensor model. The proposed method does not require complex signal processing at the relay, which effectively
reduces the burden of relay. As a semi-blind method, which does not require the pilot signal, the proposed receiver
can jointly recover the channels and information symbols. Moreover, the proposed semi-blind receiver is robust
as it can work in different wireless channel scenarios. Simulations are conducted to demonstrate the efficiency of
the proposed semi-blind approach.
Key words: fourth-order tensor, semi-blind receiver, Levenberg-Marquardt algorithm, nested parallel factor
model, amplify-and-forward
CLC number: TN 929.53 Document code: A
0 Introduction
As a promising solution to improving the link re-
liability and providing broader coverage, multiple-
input-multiple-output (MIMO) relay communication
networks have attracted much attention of some re-
searchers in recent years
[1-3]
. Among different relaying
strategies, the amplify-and-forward (AF) approach has
drawn a great attention for its simplicity and mathe-
matical tractability. In this context, there have been
a number of research efforts on AF MIMO relay net-
works over the past years
[4-6]
. For MIMO relay net-
works discussed in Refs. [4-6], an accurate channel state
information (CSI) is required to solve the optimization
problem. Unfortunately, in practice, the accurate CSI
cannot be known at all nodes in the MIMO relay net-
work. Therefore, the estimation for CSI at the destina-
Received date: 2018-05-04
Foundation item: the National Natural Science Founda-
tion of China (Nos. 61601414 and 61701448), the
National Key Research and Development Program
of China (No. 2016YFB0502001), and the Funda-
mental Research Fund for the Central Universities
(Nos. 2018CUCTJ082 and CUC18A007)
∗E-mail: dujianhe1@gmail.com
tion is needed. To estimate the CSI of both two hops,
a two-stage training (TST) scheme has been proposed
in Ref. [7]. The main drawback in Ref. [7] is its incom-
patibility with the two-stage signal transmission.
It has been shown that multidimensional signaling
methods utilize different dimensions of signal, which
have great potential to improve the transmission rate
and to enhance the reliability of the communication
[8]
.
Consequently, solid researches on the tensor model for
MIMO communication systems have appeared in many
literatures
[9-11]
. The authors in Ref. [9] have provided a
Khatri-Rao space-time coding (KRSTC) method which
relies on the three way parallel factor (PARAFAC)
model. In Ref. [10], a semi-blind receiver is presented
for MIMO orthogonal frequency division multiplexing
(OFDM) systems via applying the Khatri-Rao space-
frequency coding. Furthermore, a new coding approach
named double Khatri-Rao space-time-frequency cod-
ing, which can be seen as an extension of the idea
of KRSTC in Ref. [9], is proposed in Ref. [11]. How-
ever, the above tensor-based receivers cannot be ap-
plied to two-hop MIMO relay networks to estimate the
individual channel matrices of both two hops. Re-
cently, several receivers based on tensor model have
been proposed to estimate the CSI and/or the symbols