Approximate closed-form power allocation
scheme for multiple-input–multiple-output
hybrid automatic repeat request protocols
over Rayleigh block fading channels
ISSN 1751-8628
Received on 29th December 2014
Revised on 9th May 2015
Accepted on 17th July 2015
doi: 10.1049/iet-com.2014.1263
www.ietdl.org
Songhu Ge
✉
, Yong Xi, Shengchun Huang, Yue Ma, Jibo Wei
School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, Hunan, People’s Republic of
China
✉ E-mail: gesonghu@126.com
Abstract: In this study, the outage-limited optimal power allocation problem for hybrid automatic repeat request (HARQ)
protocol over multiple-input–multiple-output (MIMO) block Rayl eigh fading channels is addressed. Considering three
typical HARQ protocols, the authors first derive the approximate outage probabilities of the MIMO HARQ proto cols at
the high signal-to-noise ratio region. On the basis of th e appro ximations, they then formulate an optimisation problem
of minimising the average total power usage with the constraints of the targeted outage probability and the maximum
number of transmission rounds. A closed-form optimal power sequence is obtained by solving the outage-limited
optimisation problem. Applying the solutions, the monotonicity of the optim al power sequence is further investigated.
It is found that the optimal power sequence is monotonically increasing when the targeted outage probability is
smaller than a threshold. They also study the impacts of the system parameter s on the optimal power sequence and
the power allocation gain under various conditions. Finally, the numerical and simulation results are presented to
verify the theoretical derivation.
1 Introduction
As a key technology to improve the spectral efficiency in modern
wireless communications, multiple-input–multiple-output (MIMO)
has been adopted in various communication standards, such as
IEEE 802.11 [1], IEEE 802.16 [2] and 3GPP LTE [3]. On the
other hand, hybrid automatic repeat request (HARQ) protocol [4]
is also the indispensable approach to increase the data transmission
reliability in those standards. Therefore, the HARQ protocols over
MIMO channels are widely studied in the literature to improve the
system performance. By far, the MIMO HARQ related works can
be roughly categorised into three major classes. One class focused
on the performance tradeoff in MIMO HARQ systems. Following
Zheng and Tse’s work in [5], the diversity–multiplexing–delay
tradeoff [6], throughput–diversity–delay tradeoff [7] and rate–
diversity–delay tradeoff [8] for MIMO HARQ were investigated.
The second class studied the system design of MIMO HARQ, for
example, precoder design [9] and detection algorithm design [10].
The last class treated the performance analysis of MIMO HARQ,
for example, outage analysis with multibit feedback [11], transition
control protocol (TCP) performance analysis with packet
combining [12].
Besides those research issues, the energy efficiency is also an
important metric for the HARQ protocols in the energy-limited
networks. Recently, for different kinds of HARQ protocols in
single-input–single-output (SISO) systems, extensive studies have
shown that the power allocation schemes among different
transmission rounds bring significant energy efficiency
improvement. First, for basic HARQ, the optimal power allocation
(OPA) schemes in single- and multi-hop wireless links were
exploited to improve the energy efficiency in [13]. Second, for
chase combining-based HARQ (CC-HARQ), the OPA scheme of
minimising the average total transmission power consumption over
quasi-static Rayleigh fading channels and block Rayleigh fading
channels [In HARQ protocols, the quasi-static fading channel is
commonly defined as the model in which all the transmission
rounds experience the same channel gain, whereas the channel
gains between different transmission rounds are independent for
the block fading channel model.] were investigated in [14, 15],
respectively, while satisfying the given outage probability
constraint. Furthermore, considering the metric of the packet error
rate, Ge et al. [16] further developed a closed-form solution to the
optimisation problem considered in [15
]. At last, for incremental
redundancy HARQ (IR-HARQ), Chaitanya and Larsson [17]
studied the OPA scheme that minimises the packet drop
probability under the average transmit power constraint, and gave
a closed-form solution to the special case of L = 2. Recently in
[18], aiming at minimising the outage-limited average transmission
power, the OPA schemes were obtained under both continuous
and bursting communication models for both CC-HARQ and
IR-HARQ protocols.
Although the power allocation schemes for the HARQ protocols
in SISO systems have been well studied, the results for MIMO
HARQ protocols are limited. Recently in [19], the effects of the
power allocation scheme on the MIMO HARQ system were
discussed and in [20] the energy-limited OPA was studied. It was
shown in [19] that the throughput of the MIMO HARQ system
can be improved by both the temporal power allocation (power
allocation among different transmission rounds) and the spatial
power allocation (power allocation among different antennas), and
it was revealed in [20] that the OPA increases the diversity gain of
the MIMO automatic repeat request (ARQ) remarkably. The
optimisation objects are throughput and outage probability in [19,
20], respectively, instead of the power usage. More importantly,
the solutions of the optimal power sequences were obtained by a
search algorithm in [19] and for the special case of L = 2 in [20],
which are inconvenient to investigate the properties of the optimal
power sequence.
In this paper, we consider the outage-limited OPA problem for
MIMO HARQ protocols over block fading channels, which extend
our prior work in [16] to MIMO systems and three typical HARQ
protocols. Our goal is to find the optimal power sequence that
IET Communications
Research Article
IET Commun., 2015, Vol. 9, Iss. 16, pp. 2023–2032
2023
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The Institution of Engineering and Technology 2015
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