In this
paper, we consider a general bi-directional relay network with two sources and
N relays when neither the source nodes nor the relays know the channel state
information (CSI). A joint relay selection and analog network coding using
differential modulation (RS-ANC-DM) is proposed. In the proposed scheme, the
two sources employ differential modulations and transmit the differential modulated
symbols to all relays at the same time.
All these problems present a great challenge for
designing differential modulation schemes in two-way relay channels. To solve
this problem, in [13], a non-coherent receiver for two-way relaying was
proposed for ANC based bi-directional relay networks. However, the schemes
result in more than 3 dB performance loss compared to the coherent detection.
To further improve the system performance, a differential ANC scheme was
proposed in [14] and a simple linear detector was developed to recover the
transmitted signals at two source nodes.
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The signals
received at the relay are a superposition of two transmitted symbols, which we
call the analog network coded symbols. Then a single relay which has minimum
sum SER is selected out of N relays to forward the ANC signals to both sources.
To facilitate the selection process, in this paper we also propose a simple
sub-optimal Min-Max criterion for relay selection, where a single relay which
minimizes the maximum SER of two source nodes is selected.
Simulation
results show that the proposed Min-Max selection has almost the same
performance as the optimal selection, but is much simpler. The performance of
the proposed RS-ANC-DM scheme is analyzed, and a simple asymptotic SER
expression is derived. The analytical results are verified through simulations.
In a
bi-directional relay network, two source nodes exchange their messages through
the aid of one or multiple relays. The transmission in bi-directional relay
network can take place over four, three or two time slots. In the four time
slots transmission strategy, the relay helps to forward source S1’s message to
source S2 in the first two time slots and source S2’s message to source S1 in
the next two time slots. Four time slots transmission has been shown to be very
inefficient.
When the
relay receives two sources’ messages, it combines them before forwarding to the
destination, which will save one time slot transmission. This three time slots
transmission scheme is usually referred to as the digital network coding [1]– [3].
In this method, two source nodes transmit to the relay, separately. The relay
decodes the received signals, performs binary network coding, and then broadcasts
it back to both source nodes.
To further
improve the spectral efficiency, the message exchange between two source nodes can
actually take place in two time slots. In the first time slot, both source nodes
transmit at the same time so that the relay receives a superimposed signal. The
relay then amplifies the received signal and broadcasts it to both source nodes
in the second time slots. This scheme is referred to as the analog network
coding (ANC) [4]–[6]. Various transmission schemes and wireless network coding
schemes in bi directional relay networks have been analyzed and compared in
[7]–[12].
Most of
existing works in bi-directional relay communications consider the coherent
detection at the destination and assume that perfect channel state information
(CSI) are available at the sources and relays [1]–[12]. In some scenarios, e.g.
the fast fading environment, the acquisition of accurate CSI may become
difficult. In this case, the non-coherent or differential modulation would be a
practical solution. In a differential bi-directional relay network, each source
receives a superposition of differentially encoded signals from the other
source, and it has no knowledge of CSI of both channels.
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