Pilot Optimization in Multicell Massive MIMO
M. A. Teeti and Rui Wang
Dept. of Electrical and Electronic Engineering,
Southern University of
Science and Technology of China,
Shenzhen, Guangdong, China
Email: teeti.moh@gmail.com,
wang.r@sustc.edu.cn
Yingzhuang Liu
School of Electronic Information
and Communications,
Huazhong University of
Science and Technology,
Wuhan, Hubei, China,
Email: liuyz@hust.edu.cn
Qiang Ni
School of Computing
and Communications,
Lancaster University,
Lancaster, Lancashire, UK,
Email: q.ni@lancaster.ac.uk
Abstract—In this paper we consider pilot contamination prob-
lem in the uplink of a multi-cell massive MIMO. Each base station
(BS) is equipped with M (unlimited) antennas serving K (large
but finite) users. Further, we let τ (pilot length) be an arbitrary
but small value. As such, pilot optimization is formulated as
a multi-objective optimization problem (MOP). It is shown that,
when power control is enabled, maximally spaced sequences solve
a worst-case signal-to-interference (SIR) problem only under a
special channel case, whereas the general channel case doesn’t
admit a simple solution. Motivated by the epsilon-constraint
technique in MOP, we propose a low-complexity algorithm for
optimizing pilots of different users from a fixed orthonormal basis
in an iterative manner. For only a few iterations, the algorithm
shows good convergence property, which is supposed to converge
to a Pareto-optimal solution. The numerical results show that
the algorithm gives rise to a significant improvement of the cell
throughput as well as the per-user mean SIR and per-user mean
rate.
Index Terms—pilot contamination, massive MIMO, multi-
objective optimization, epsilon-constraint technique.
I. INTRODUCTION
In massive MIMO the main challenge for acquiring a
reliable CSI is the so-called pilot contamination problem [1],
resulting from pilot reuse in neighboring cells. In massive
MIMO, the uncorrelated noise and small-scale fading vanish
due the law of large numbers (LLN). Despite the increase in
the number of antennas M, the large-scale fading (i.e., due to
distance and shadowing effect) does’t vanish, and hence plays
a significant role in performance.
Recently, a growing body of research has studied different
techniques for tackling pilot contamination problem. In [2] a
precoding technique is introduced exploiting the large-scale
fading coefficients which are typically tractable due to their
slow rate of change over a large time interval. In [3], [4]
subspace-based method is investigated as a possible means of
avoiding pilot contamination problem for both the canonical
and physical channel models. Different transmission tech-
niques are also studied such as time-shifted pilots method [5]
and similar techniques can be also found in the literature.
More recently, there has been some interest in pilot design.
In [6], authors assume a single-cell scenario where it is
assumed that pilot contamination problem occurs within the
same cell as long as τ<K, thereby the maximum number
of users, K that can be accommodated in the systems is
studied when a set of quality of services (QoS) is needed
to be simultaneously met for all users in the forward link.
In [6] it was found that the generalized Welch bound equality
(GWBE) sequences [7] are optimal. This result is similar to
optimality established in [8] for signatures in CDMA systems,
due to the analogy between the role of pilots and signatures
in massive MIMO and CDMA systems, respectively. Other
works can also be found in [9] where the authors suggest
that optimal pilots should be equally spaced on Grassmannian
manifold. Other pilot design is based on the received signal-
to-interference (SIR) is proposed in [10].
In this work we focus on pilot optimization in the uplink
of a multicell massive MIMO system, where the problem is
formulated as a MOP. We show that the problem admits a
simple solution (max-min problem) only under special channel
situation, where maximally spaced sequences are optimal. For
a more general channel, the solution for the MOP is chal-
lenging. Thus a low complexity algorithm for pilot update is
proposed, which’s motivated by the epsilon-constraint method
which is well-known in MOP. Due to lack of works on pilot
optimizations in literature, it is difficult to compare it with
other algorithms on equal footing. Thus, in our simulation
part, the algorithm is compared against the randomly pilot
assignment technique. The numerical results show a significant
improvement on the sum rate (performance metric) as well as
mean per-user rate.
The rest of this paper is organized as follows. In Sec. II
the channel model and problem formulation are presented.
In Sec. III a max-min solution of SIR under special channel
situation is derived, and the proposed algorithm is discussed
afterwards. The numerical results are presented in Sec. IV and
Sec. V concludes this paper.
II. C
HANNEL MODEL AND PROBLEM FORMULATION
A. Channel Model
We consider the uplink in a synchronous multicell multiuser
massive MIMO system with L cells. Each BS is equipped
with M (grows unboundedly) antennas, serving K (large
but finite) users in the same time-frequency resource. For
small-scale fading, we adopt a flat Rayleigh block-fading
model [11]. In our model, we also account for large-scale
fading (due to path-loss and shadowing) which is assumed
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