Optimal Asymmetric Resource Allocation for
Dual-Hop Multi-Relay LTE-Advanced Systems in
the Downlink
Linhao Dong
1
, Xu Zhu, Yi Huang
Department of Electrical Engineering
and Electronics
The University of Liverpool
Liverpool, L69 3GJ, UK
Emails: {Linhao.Dong, xuzhu, huangyi}@liv.ac.uk
Abstract—We propose an optimal asymmetric resource allo-
cation (ARA) algorithm for the decode-and-forward (DF) dual-
hop multi-relay Long Term Evolution Advanced (LTE-Advanced)
system in the downlink, with orthogonal frequency division
multiplexing (OFDM) transmission. Our work is different in that
the time slots for the two hops via each of the relays are designed
to be asymmetric, i.e., with K relays in the cell, a total of 2K
time slots may be of different durations, which enhances the
degree of freedom over the previous work. Also, a destination
may be served by multiple relays at the same time to enhance the
transmission diversity. Moreover, closed-form results for optimal
allocation are derived, which requires only limited feedback
information. Simulation results show that, thanks to the multi-
relay, multi-user and time diversities, the proposed ARA scheme
can provide a much better performance than the scheme with
symmetric time allocation, as well as the scheme with asymmetric
time allocation for a system composed of independent single-relay
sub-systems, especially when the relays are close to the source.
Index Terms—Relay, resource allocation, OFDM, LTE-
Advanced, multi-relay diversity, multi-user diversity
I. INTRODUCTION
Recently, relay technologies, including amplify-and-forward
(AF) [1] and decode-and-forward (DF) [2] modes, have been
considered as a promising and achievable solution for the
fourth-generation (4G) mobile communication systems such
as Long Term Evolution Advanced (LTE-Advanced) systems
[4].
Adaptive resource allocation (RA) [5] plays an essential
part in relay systems. In [6], subcarrier pairing and power
allocation were conducted successively in a single-relay sys-
tem for both AF and DF modes to maximise the system
capacity. In [7], the optimal joint subcarrier matching and
power allocation were proposed for DF relay systems with
single destination. However, it requires the bits to be grouped
in relaying, moreover, the complexity of subcarrier pairing
is too high to guarantee that the channel state remains the
same during this process. In [8] an optimal RA algorithm
was proposed to maximise the bandwidth efficiency of the DF
1
This work was partially supported by the EPSRC Knowledge Exploitation
Laboratory Programme, UK.
relay system, however, it assumed fixed geometric locations
of the relays, which is merely practical in the real urban
environment. While in [9], the authors considered a multi-
relay system with random relay locations, and also proposed
an optimal RA algorithm. However, in most of previous works,
the time slots duration for the two hops were designed to
be symmetric. In [10], a two-way relay channel model was
investigated, and an asymmetric time allocation scheme was
proposed, where the two consecutive time slots duration are
designed to be asymmetric. However, it was only assumed
that a uniform power allocation was conducted across all
subcarriers, which was not efficient. In [12], an optimal ARA
scheme was proposed for an OFDM based multi-user DF
relay system, however, it can only be applied into a scenario
where a cell is divided into multiple independent single-relay
sub-systems and RA is conducted in each of individual sub-
systems. Each of destination is served by only one relay.
Hence, this ARA scheme is not readily extendable to a multi-
relay multi-destination system.
In this paper, we investigate an ARA scheme for DF dual-
hop multi-relay LTE-Advanced systems. Our work is different
in the following aspects. First, to the best of our knowledge,
this is the original work to apply asymmetric time allocation
to a general multi-relay and multi-destination system, where
the time slots for the two hops via each of the relays are
designed to be asymmetric, i.e., with K relays in the cell,
a total of 2K time slots may be of different durations. As
a result, it enhances the degree of freedom for transmission
over the previous symmetric RA (SRA) algorithm. Second,
an optimal algorithm is proposed to perform joint time,
power and subcarrier allocation to obtain the global optimal
results, with only limited feedback information from relays
and destinations. This is not an easy extension of [12], where
each destination is served by only one relay in an independent
sub-system. While the proposed work allows multiple relays
to serve a single destination, which increases the number of
degrees of freedom. Moreover, we demonstrate the impact
of the relays’ locations on the results of asymmetric time
allocation. Simulation results show that, thanks to the multi-
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