Outage-optimal opportunistic scheduling with analog network coding in multiuser two-way relay networks
Prabhat K Upadhyay
0
Shankar Prakriya
0
0
Department of Electrical Engineering, Indian Institute of Technology Delhi
, New Delhi, 110016,
India
This paper investigates the performance of an outage-optimal opportunistic scheduling scheme for a multiuser two-way relay network, wherein an analog network coding-based relay serves multiple pairs of users. Under a Rayleigh flat-fading environment, we derive an exact expression for cumulative distribution function (CDF) of the minimum of the two end-to-end instantaneous signal-to-noise ratios (SNRs) and utilize this to obtain an exact expression for the outage probability of such a greedy scheduling scheme. We then develop a modified scheduler that ensures fairness among user pairs of the considered system. By using a high SNR approximation of derived CDF, we present a simple closed-form expression for outage probability of the overall system and establish that a multiuser diversity of order equal to the number of user pairs is harnessed by the scheme. We also present an efficient power allocation strategy between sources and relay, subject to a total power constraint, that minimizes the outage probability of the overall system. Further, by deriving both upper and lower bound expressions for the average sum-rate of the proposed scheme, we demonstrate that an average sum-rate gain can also be achieved by increasing the number of user pairs in the system. Numerical and simulation results are presented to validate the performance of the proposed scheme.
1 Introduction
Cooperative relaying techniques have recently gained
great research interest because of their potential in
enhancing the throughput or reliability of wireless
networks. Several schemes have been extensively studied in
literature to achieve cooperative diversity utilizing the
one-way relaying protocol [1]. However, the half-duplex
constraint at the relays incurs a spectral efficiency loss
in such schemes. Recent research has shown that such a
loss can be effectively mitigated by exploiting the idea of
network coding [2] in bidirectional communication
scenarios [3-7]. Bidirectional cooperative relaying strategies
facilitate information exchange between two users in
either four, three, or two time phases via a half-duplex
relay. The four-phase protocol follows the conventional
approach by requiring two separate time phases for data
flow in each direction and hence is spectrally inefficient.
However, the bidirectional communication has been
shown to be accomplished in even three phases in [3-7].
In the three-phase protocol (called physical layer
network coding (PNC) [6] or time division broadcast
(TDBC) [7]), the two users transmit successively in first
and second phases, the relay then decodes both the
data, applies network coding, and forwards the
combined data to both users in the third phase. After
canceling the self-interferences (as they are known by the
respective users), the intended message can be received
at each of the user terminals. Recently, a two-way
relaying protocol [8,9] has emerged as a promising technique
to mitigate the spectral efficiency loss of conventional
half-duplex relaying systems. In this scheme, the two
users communicate bidirectionally (in the absence of a
reliable direct link) in just two time phases, namely the
multiple access channel (MAC) phase and the broadcast
Table 1 Selected values of channel variances over the
two hops for i.ni.d. user pairs
a2,k kK=1
0.2
0.8
0.4
0.9
0.4
0.2
0.9
0.1
0.7
0.2
0.3
0.6
0.8
0.5
0.2
0.4
channel (BC) phase. In the first phase (MAC), both
users transmit their data simultaneously to the relay,
and the relay broadcasts the processed signal to both
users in the second phase (BC). When an
amplify-andforward (AF) processing is applied on the superimposed
signal received during the MAC phase at the relay, such
a scheme is usually termed as analog network coding
(ANC) [10-13].
The two-phase two-way relaying protocol has also
been generalized to a multiuser scenario in which
multiple pairs of users communicate bidirection-ally via one
or more relays [8,14-18]. The authors in [8,14]
considered several relays or antennas that orthogonalize
multiple pairs by a distributed zero-forcing technique. A
spread spectrum based interference management
scheme wherein each pair shares a common spreading
signature, and the relay uses a jointly
demodulate-andXOR forward strategy is proposed in [15]. The
information theoretic capacity for such a scheme is studied in
[16] and [17] by considering a deterministic channel
model and a Gaussian two-pair two-way full-duplex
relay network, respectively. To combat interference at
each user of such a system, the authors in [18] proposed
different beamforming schemes with
amplify-and-forward (AF) and quantize-and-forward (QF) strategies at
the relay. However, to the best of our knowledge, a
performance analysis exploiting multiuser diversity for this
system has not been reported so far. Although the
twophase two-way relay (...truncated)