Optimal Pilot Design for Space-Time Coded
Multi-user MIMO OFDM/SDMA Systems
Zhe Zhang
†
, Jiankang Zhang
†∗
, Shuangzhi Li
†
, Xiaomin Mu
†
†School of Information Engineering, Zhengzhou University, Zhengzhou, China
∗
National Mobile Communications Research Laboratory, Southeast University, Nanjing, China
Email: zhangzheie@qq.com, iejkzhang@zzu.edu.cn, 1142240382@qq.com, iexmmu@zzu.edu.cn
Abstract—In this paper, we propose an optimal pilot de-
sign scheme for multi-user Multiple-Input Multiple-Output (MI-
MO) Orthogonal Frequency Division Multiplexing/Space Division
Multiple Access (OFDM/SDMA) systems. We derive the optimal
pilot design criterion with regard to the computational complexity
and the Mean Square Error (MSE) of the Least Square (LS)
estimator. Furthermore, we propose a binary-tree based search
scheme in order to find the optimal position for placement the
Space-Time Coded pilot symbols. Through our analysis and
simulations, it is shown that the pilot design complied with the
our proposed placement criteria could obtain the lowest com-
putational complexity and the optimum estimate performance.
Index Terms—Orthogonal Frequency Division Multiplex-
ing/Space Division Multiple Access, channel estimation, pilot
design, space-time code.
I. INTRODUCTION
Multi-user Multiple-Input-Multiple-Output (MIMO) Or-
thogonal Frequency Division Multiplexing (OFDM) / Space
Division Multiple Access (SDMA) systems have recently
attracted substantial research interest, since they beneficially
combine the advantages of OFDM and SDMA [1, 2]. More
specifically, the transmitted uplink signals of U simultaneous
Mobile Stations (MS), each of which employs a single transmit
antenna, are received by an array of antennas at the Base
Station (BS), where the superimposed signals are differentiated
with the aid of their unique, user-specific Channel Impulse
Responses (CIRs). Hence, the performance of these MIMO
SDMA/OFDM systems is critically dependent on the accuracy
of the estimated channel knowledge, since the separation of
the signals received from the spatially multiplexed users relies
precisely on this channel knowledge.
Channel estimation is typically based on training sequences
that are known a priori at the receiver [3], albeit blind
estimation may also used, which purely relies on exploiting the
statistical properties of both the transmitted and received signal
[4, 5]. Channel estimation based on training symbols has been
shown to strike an attractive design compromise compared to
blind channel estimation, since the latter suffers from a long
processing delay and high computational complexity.
There are three main aspects that have to be considered in
the context of pilot based channel estimation, namely (1) how
Acknowledgments: The financial support of the National Natural Science
Foundation of China under Grants 61571401, 61301150 and 61271421 as
well as the open research fund of National Mobile Communications Research
Laboratory, Southeast University(No.2016D02) are gratefully acknowledged.
to design the pilot sequences and how to incorporate them? (2)
How to extract the Channel State Information (CSI) based on
different estimation criteria? (3) How to reconstruct the CSI on
the position of all data-bearing OFDM subcarrier? Naturally,
the specific design and placement of the pilot sequences is
of prime importance. Hence, in this treatise we restrict our
attention to the optimal design and placement of the pilot
sequences.
The amount of pilot symbols, the power allocation for
pilot symbols and the location of these pilots inserted in the
transmitted data stream all affect the system performance with
regard to the reliable transmission rate, Bit Error Ratio (BER),
Mean Square Error (MSE) and/or the computational complex-
ity of the estimator [6]. The optimal placement of the pilot
tones was first proposed in [7] with the regard to the MSE of
the Least Squares (LS) estimator for the Single-Input Single-
Output (SISO) OFDM systems. Orthogonal Walsh code was
introduced in [8] as pilot symbols for estimating the channel
parameters, which allowed channel parameter estimation on
an OFDM symbol-by-symbol basis. The authors of [9, 10]
discussed the optimal placement and power allocation of the
pilot symbols for the uncorrelated fading MIMO channels with
regard to the MSE of the LS estimator. [11, 12] proposed the
design criterion of the training sequences for spacial correlated
fading MIMO channels, which also minimized the MSE of
the estimator. Space-Frequency Code (SFC) was used as pilot
symbols in [13, 14] inorder to simplify the channel estimation
of the fast time-varying and frequency-selective fading channel
for MIMO-OFDM systems.
In this paper, we analyze the MSE of the LS channel estima-
tor and then we derive the sufficient and necessary conditions
of design of the optimal pilots and the optimal placement of
these pilot symbols. Furthermore the novel contribution of
this paper is that we develop a training design schemes
using Space-Time Code (STC) and propose an binary-tree
based search scheme to search the “optimal placement“ of
these pilot symbols, which makes the LS estimator arrive at
the minimum MSE with lowest computational complexity
(free of matrix inversion) using lower pilot overhead.
The rest of the paper is organized as follows. In Section
II, a classic multi-user MIMO OFDM/SDMA system model
is described. Section III discusses the optimal pilot design
criterion. Tree-search algorithm for the optimal placement
of the STC-based pilot symbols is given in Section IV. In
Section V, the performance of the proposed optimal pilot
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