Multiple Access Relay Network


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We consider a multiple access relay network where each
source transmit channel coded packets, relay decode the transmitted
packet, generate network coded parity symbol, and retransmit
it. We assume the relay has multiple antennas, so
relay to destination link is MIMO channel. We consider two
MIMO transmission mode at the relay, spatial multiplexing
(SM) and beamforming as transmit diversity (TD), and assume
that the relay use different network coding scheme depending
on the MIMO transmission mode. In other words, we consider
a network with three types of linear combination; channel
coding at the source, network coding at the relay, and mixing
over the air with MIMO channel. The main objective of the
paper is to propose a transmission mode selection scheme
at the relay which optimize these three linear combinations
concurrently.
There are numerous work that optimize either the network
coding, MIMO transmission mode, or data rate over multiple
access relay channel. Network coding techniques for single
antenna relay network has been addressed in [1] - [4]. Authors
in [1] investigated the cooperative diversity gain offered by the
network coding. Authors in [2] proposed a network coding
scheme based on low-density parity-check (LDPC) codes that
accounts for the lossy nature of wireless networks and showed
that a significant coding/diversity gain can be achieved. Author
in [3] investigated the tradeoff between reliability and rate
as a function of node density and SNR, and showed how
the energy and node density can be traded in achieving a
given reliability-rate pair in single antenna case. Authors in
[4] analyzed an network coded cooperation which adaptively
match networks-on-graphs to the well-known class of codeson-
graphs such as LDPC codes. This approach enables realtime
adaptation of network codes to variant link states and
changing network topologies. Network coding for multiple antennas
have been studied for special network geometry in [5],
[6]. Authors in [5] proposed a cross-layer design employing
multiple antenna techniques and network coding called MIMO
two-way relay for one dimensional mesh network and authors
in [6] investigated the performance of MIMO network coding
in bi-directional relay network. Adaptive relay protocol has
been proposed for a network with single antenna relays in [7]
- [9] and for a network with multiple antennas using amplify
and forward protocol in [10], [11]. Authors in [11] proposed
an adaptive antenna selection scheme at both the relay and the
source for half-duplex MIMO amplify and forward relay protocol.
Rate optimization for relay network has been addressed
in [12], [13]. Authors in [12] proposed throughput optimal
control policy for a parallel relay network with decode and
forward protocol. Authors in [13] analyzed the performance
of variable-rate two phase collaborative diversity protocols and
optimized the transmission rate based on the node location.

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These previous work solve optimization problem for a
specific linear combination. They either optimize the network
coding and MIMO, adapt the relay protocol for different
network model, or optimize network coding and channel
coding. However, if multiple linear combinations coexist in
the network, these approach provides a suboptimal solution.
With this motivation, we analyze a multiple access relay
network where three types of linear combination coexist and
optimize these combinations concurrently. To that end, we
derive the outage probability with the maximum likelihood
decoding at the destination and investigate the effect of MIMO
transmission mode at the relay, coding rate from each source,
relay locations, and different network coding schemes on the
outage probability. Throughout the outage probability analysis,
we propose an optimal MIMO mode selection scheme which
depends on channel coding from the source, network coding at
the relay, and MIMO transmission mode. This mode selection
scheme serve as a design guideline for an optimal relay
network.
The remainder part of this paper is organized as follows.
System model is described in Section II and the outage
probability is derived in Section III and Section IV presents
optimum MIMO mode selection scheme. Section V provide
numerical results and Section VI concludes the paper.


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