Channel Estimation in Full-dimensional Massive
MIMO System Using One Training Symbol
Lei Cheng
∗
, Yik-Chung Wu
∗
, Shaodan Ma
†
, Jianzhong (Charlie) Zhang
♯
and Lingjia Liu
‡
∗ Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong
† Department of Electrical and Computer Engineering, University of Macau, Macao
♯ Standards and Mobility Lab., Samsung Research America, Richardson, TX, USA
‡ Department of Electrical Engineering and Computer Science, The University of Kansas, Lawrence, KS, USA
Abstract—In this paper, an algorithm is proposed to esti-
mate thousands of channel parameters in massive multiple-
input multiple-output (MIMO) systems with a three-dimensional
antenna array, using only one training symbol while assuming
no knowledge of path number, noise power, path gain and
direction-of-arrival (DOA) statistics. Furthermore, the received
data structure is exploited to give a low-complexity DOA acqui-
sition scheme with closed-form computations. Simulation results
show excellent performance of the proposed algorithm in both
channel estimation and DOA acquisition.
I. INTRODUCTION
Massive multiple-input multiple-output (MIMO) system, an
enabling technology to meet the future spectral efficiency
demand, has created much interest in both academia and
industry [1]. With the help of a large number of antennas,
extensive spatial freedoms can be exploited to significantly
save the time and frequency resources, and thus the long-
standing bandwidth limitation in wireless communications
is circumvented. However, the realization of the benefit in
massive MIMO system relies on the accurate channel state
information (CSI) obtained at the base station (BS), which
is critical for functionalities such as data detection, downlink
beamforming and transmitter precoding.
To acquire accurate CSI, a long training sequence might
be required. Transmitting a training sequence not only costs
much energy at user terminal, but also occupies scarce spectral
resources. Fortunately, this can be remedied by exploiting
the underlying structure of wireless channels. In particular,
parametric channel model, which has been validated by real-
world measurements [1] and has been widely adopted in
recent massive MIMO [2]–[4] and millimeter wave MIMO
[5] systems, is determined by direction-of-arrival (DOA) and
fading parameters of different propagation paths. This model
reduces the parameters to be estimated significantly, offering
the possibility of accurate channel estimation using one train-
ing symbol only.
With large number of antennas employed at BS, massive
MIMO systems would very likely employ three-dimensional
(3D) arrays to accommodate the vast amount of antennas,
giving rise to the so-called full-dimensional (FD) MIMO
systems [1]. Although techniques developed for 1D arrays [2]
or 2D arrays [4] can be applied to estimate the channel in
3D arrays, they fail to fully exploits the 3D channel structure,
leading to degraded performance. In contrast, based on the
low-rank structure of the 3D channel, this paper reformulates
the channel estimation problem as a tensor decomposition
problem. Using the probabilistic inference framework, the
channel tensor can be recovered even without the knowledge
of the number of signal propagation paths. Furthermore, by
exploiting the uniqueness property of the 3D tensor decom-
position, closed-form signal DOA estimates can be obtained,
which is essential in many massive MIMO tasks such as
interference mitigation [2], optimal pilot beam pattern design
[6] and user scheduling [7].
II. S
YSTEM MODEL
Consider a massive MIMO system where antennas at the
BS are arranged in a 3D uniform cuboid array, and user
mobile terminal is equipped with one antenna, as shown in
Figure 1. The number of BS antennas in the x-direction, y-
direction and z-direction are 𝑀
𝑥
, 𝑀
𝑦
and 𝑀
𝑧
respectively,
with corresponding inter-antenna spacing being 𝑑
𝑥
, 𝑑
𝑦
and
𝑑
𝑧
. For the uplink transmission, one pilot symbol 𝑠(𝑛) at
𝑛
𝑡ℎ
snapshot goes through a channel with channel state
information (CSI) ℎ
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛). The discrete-time complex
baseband signal received by the (𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
)
𝑡ℎ
antenna at
BS is
𝑦
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛)=𝑠(𝑛)ℎ
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛)+𝑤
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛), (1)
where the additive noise 𝑤
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛) ∼
𝒞𝒩
(
𝑤
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛) ∣ 0,𝛽
−1
)
is spatially and temporally
independent.
A simple method to acquire the CSI ℎ
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛) is the
least-squares (LS) based estimator
ℎ
LS
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛)=𝑦
𝑚
𝑥
,𝑚
𝑦
,𝑚
𝑧
(𝑛)/𝑠(𝑛). (2)
However, as there is only one pilot symbol and (2) estimates
each channel parameter independently, this estimator would
give poor estimation performance. To improve the accuracy,
one way is to collect more training symbols. This not only
costs more resources, but the estimation accuracy is still
limited by the channel coherent time. An alternative is to
explore the underlying structure of the channel. In particular,
in this paper, we consider the parametric channel model
2017 IEEE 18th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
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