Sparse Channel Estimation in Millimeter Wave
Communications: Exploiting Joint AoD-AoA Angular Spread
Pu Wang, Milutin Pajovic, Philip V. Orlik,
Toshiaki Koike-Akino, and Kyeong Jin Kim
Mitsubishi Electric Research Laboratories
201 Broadway, Cambridge, MA 02139, USA
Emails: {pwang, pajovic, porlik, koike, kkim}@merl.com
Jun Fang
National Key Laboratory on Communications
University of Electronic Science and Technology of China
Chengdu 611731, China
Email: junfang@uestc.edu.cn
Abstract—In this paper, channel estimation in millimeter wave
(mmWave) communication systems is considered. In contrast to
prevailing mmWave channel estimation methods exploiting the
sparsity nature of the channel, we move one step further by
exploiting the joint AoD-AoA angular spread. By formulating
the channel estimation as a block-sparse signal recovery with
an underlying two-dimensional cluster feature, we propose a
two-dimensional sparse Bayesian learning method without a
priori knowledge of two-dimensional angular spread patterns. It
essentially couples the channel path power at one angular direc-
tion with its two-dimensional AoD-AoA neighboring directions.
Compared with existing sparse mmWave channel estimation
methods, the proposed method is numerically verified to reduce
the training overhead and channel estimation error.
I. INTRODUCTION
Millimeter wave (mmWave) communication is a promising
technology for future fifth generation (5G) cellular networks.
It has the potential to offer gigabit-per-second data rates by
exploiting the large bandwidth available at mmWave frequen-
cies [1], [2]. However, communication at such high frequen-
cies suffers from high attenuation and signal absorption. To
compensate for the significant path loss, large antenna arrays
can be used at the base station (BS) and mobile station
(MS) to exploit beam steering to increase the link gain. On
one hand, directional precoding and beamforming provide
sufficient beamforming gain for mmWave communications.
On the other hand, the precoding design requires reliable
channel state information (CSI) which is challenging to obtain
due to the large number of antennas and rapidly varying
channel statistics.
The sparse scattering nature of the mmWave channel has
been utilized in [3] and [4] to reduce the training overhead
for mmWave channel estimation. [3] presented a new multi-
resolution beamforming codebook and an adaptive compressed
channel sensing method for the mmWave channel estimation.
The compressed channel sensing scheme divides the training
process into several phases, in which the precoding design
uses the information from previous phases. However, the
requirement of a feedback channel may not be favorable
in certain scenarios. On the other hand, [4] focused on the
compressed channel sensing scheme with significantly less
training signals by taking into account the sparse nature of
the mmWave channel.
In this paper, we are still interested in the mmWave channel
estimation and move one step further to exploit, in addition
to the sparse channel scattering, the joint angular spread of
path clusters in the angle-of-departure (AoD) and angle-of-
arrival (AoA) domain. The joint angular spread induces a
two-dimensional block sparse pattern in the resulting complex
channel gain matrix, which has been shown in real-world
measurements in urban environments [5]–[7]. Specifically, we
propose a two-dimensional coupled sparse Bayesian learning
(SBL) algorithm to exploit the joint AoD-AoA angular spread.
The coupled SBL algorithm treats the channel gain of each
path as a random variable and imposes a two-dimensional
statistical dependence across the channel path power to favor
block-sparse solutions without knowing the block pattern a
priori. The proposed algorithm encompasses two steps and
iterates between them: the Bayesian estimation of the chan-
nel gain matrix followed by iteratively updating the prior
variance (or, equivalently, the channel path power) by using
the expectation-maximization (EM) algorithm. Compared with
several existing sparse channel estimation methods, the pro-
posed algorithm shows numerical advantages such as reduced
training overhead and lower estimation errors for the mmWave
channel estimation.
The rest of the paper is organized as follows. Section II
introduces the system model and a sparse representation of
the mmWave channel. Section III provides motivations to
exploit the joint AoD-AoD spread and formulates the problem
in a block-sparse signal recovery framework. In Section IV,
we provide the details on deriving the proposed algorithm.
Numerical results are provided in Section V, followed by
concluding remarks in Section VI.
II. S
PARSE MMWAV E CHANNEL MODEL
Consider a mmWave communication system with N
T
trans-
mitters at the BS and N
R
receivers at MS. At time instant k,
the BS applies a precoder/beamformer p
k
to transmit a symbol
s. Without loss of generality, s =1. Correspondingly, the MS
applies a combiner q
k
to generate the received signal y
k
:
y
k
=
√
ρq
H
k
Hp
k
s + q
H
k
v,k=1, 2, ···,K, (1)
where ρ is the average transmitted power, H ∈C
N
T
×N
R
is
the channel matrix, and v is the white Gaussian noise with an
IEEE ICC 2017 Signal Processing for Communications Symposium
978-1-4673-8999-0/17/$31.00 ©2017 IEEE
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