Optimal Pilot Symbols Ratio in terms of Spectrum
and Energy Efficiency in Uplink CoMP Networks
Yuhao Zhang, Qimei Cui, and Ning Wang
School of Information and Communication Engineering,
Beijing University of Posts and Telecommunications, Beijing, 100876, China
Email: cuiqimei@bupt.edu.cn
Abstract—In wireless networks, Spectrum Efficiency (SE) and
Energy Efficiency (EE) can be affected by the channel estimation
that needs to be well designed in practice. In this paper,
considering channel estimation error and non-ideal backhaul
links, we optimize the pilot symbols ratio in terms of SE and EE
in uplink Coordinated Multi-point (CoMP) networks. Modeling
the channel estimation error, we formulate the SE and EE
maximization problems by analyzing the system capacity with
imperfect channel estimation. The maximal system capacity in SE
optimization and the minimal transmit power in EE optimization,
which both have the closed-form expressions, are derived by
some reasonable approximations to reduce the complexity of
solving complicated equations. Simulations are carried out to
validate the superiority of our scheme, verify the accuracy of
our approximation, and show the effect of pilot symbols ratio.
Index Terms—Spectrum efficiency, Energy efficiency, Coordi-
nated multi-point, Channel estimation error, Pilot symbols ratio.
I. INTRODUCTION
In Coordinated Multi-point (CoMP) networks, Spectrum
Efficiency (SE) and Energy Efficiency (EE), the important
indexes in wireless networks [1], [2], can be both improved
by the provided cooperative diversity gains [3], [4]. For uplink
transmission, Joint Reception CoMP (JR-CoMP), the efficient
uplink CoMP scheme, is characterized by simultaneous recep-
tion at multiple cooperative nodes with fully data and control
information exchange [5]. It is known that the closed-form
approximation for EE-SE trade-off is derived with idealistic
and realistic accuracy demonstration on the assumption that
the backhaul links are prefect [3]. However, ideal backhaul
links and perfect Channel State Information (CSI) are lim-
ited and impossible in practical networks [6]. Therefore, we
mainly study the SE and EE maximization based on non-ideal
backhaul links and imperfect CSI.
In practice, only imperfect and non-real-time (long-term)
CSI can be obtained and exchanged in the networks due to
the channel estimation error and the capacity limited backhaul
links. These limitations need to be well considered and have
already catched much research attentions. In [7], considering
the backhaul link constraint, different theoretical uplink CoMP
concepts are analyzed. And the framework incorporating these
concepts is provided with practical CoMP algorithms. In [8],
the optimal clustering and rate allocation scheme for JR-CoMP
networks with delayed CSI feedback is proposed by taking
a stochastic decision approach. However, these works only
assume non-ideal backhaul links and imperfect CSI sharing
but without the consideration of channel estimation error.
It is known that the channel estimation is usually carried
out by periodic pilot or training symbols transmission, where
the estimation error occurs inevitably [9]–[11]. It is straight-
forward that too much and too less pilot symbols in channel
estimation will both affect the system performance, so its
suitable ratio needs to be determined rationally. In terms of SE
and EE, decreasing transmit power and reducing pilot symbols
will overcome system throughput deterioration, which unfortu-
nately leads to the degradation of Bit Error Probability (BEP)
performance [9]. In order to find the optimal trade-off, the
power and spacing of the pilot symbols are optimized to
maximize SE in adaptive modulation OFDM networks with the
imperfect CSI [10]. And in [11], closed-form BEP expression
is derived for Filter Bank Multicarrier (FBM) networks, based
on which the optimal power allocation between pilot and
data symbols is proposed to minimize BEP. In uplink CoMP
networks with perfect backhaul links, the channel estimation
error is modeled and the system-level computer simulation
is conducted to investigate system and user throughput [12].
However, to the best of our knowledge, the pilot symbols
assignment for optimal SE and EE in JR-CoMP networks with
non-ideal backhaul links has never been discussed so far.
In this paper, we investigate optimal pilot symbols ratio for
channel estimation to maximize SE and EE in uplink CoMP
networks with non-ideal and limited backhaul links. Modeling
the channel estimation error, we first formulate the SE and
EE maximization problems by deriving the system capacity.
Utilizing the optimal derivative conditions in SE maximization
and the Lagrange multiplier method in SE maximization, the
optimal pilot symbols ratio at every cooperative node are
derived, based on which the maximal system capacity in SE
optimization and the minimal transmit power in EE optimiza-
tion are obtained consequently. To avoid solving complicated
equations, we introduce some reasonable approximate rela-
tionships to get the closed-form expressions of these results.
Finally, numerical simulations validate t he superiority of our
scheme and the accuracy of our approximation, and reveal that
with the increase of pilot symbols ratio, SE and EE first rise
rapidly in channel estimation limited region, and then decrease
slowly in useful information limited region.
The rest of the paper is organized as follows. System
model is described in Section II. SE and EE optimizations
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