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inclusion of new signalling packets (for example for
establishing the relation of cooperation and for
requesting frame copies). The ML-FC operation
requires that each node knows the average SNR
during frame reception. This information is readily
available, with different levels of accuracy, from
many of the wireless NICs used in current networks.
Previous studies on C-ARQ (e.g. (Miu, 2005),
(Monti, 2005), (Zhao, 2005)) report significant
improvements in terms of transmission power,
transmission range or throughput. Reference
(Morillo, 2005) studies a majority voting frame
combiner for AWGN and Rayleigh channels. An
ARQ variant (that the authors call Memory ARQ)
that uses frame combining of erroneous frames was
previously introduced in (Lau, 1986). This work,
however, is not in the framework of cooperative
ARQ, as all the copies come from the original
transmitter. Moreover, (Lau, 1986) analyzes the
performance of such system in an AWGN channel
while our work is focused on Rayleigh fading
channels. The work reported in (Eaves, 1977),
studies the probability of block error (i.e. FER) for
slow Rayleigh fading channels. Although it is not a
work on cooperative techniques nor on ARQ
protocol, it gives to us a good base line scenario to
compare with our proposal.
Next, Section II gives a brief description of the
C-ARQ variant that is studied in this paper. Section
III presents the Maximum-Likelihood (ML) frame
combiner (FC) integrated in the studied C-ARQ
scheme. Section IV presents the evaluation of the
FER for such kind of system.
2 COOPERATIVE ARQ
In this section we give a brief description of the C-
ARQ variant studied in this paper: Let us assume a
wireless ad-hoc network. For a given node x of the
network, we define R
x
as the set of nodes which
receive the signal from x with some minimal quality
parameters. Let y be a node of R
x
, to which node x
wants to send a frame, and let d be the distance
between x and y. From the set R
y
, we form a subset
of cooperating nodes, that we call C
y
, which
includes all nodes from that y receives signals with
an excellent quality (including y itself), and that are
willing to cooperate with y. We assume a perfect
channel between y and nodes in C
y
, due to this
excellent signal quality. Although this is a strong
assumption, it can be justified by the proximity
between y and nodes in C
y
. In the rest of the paper
we assume |C
y
| = M. Usually, we will have that
distance between y and nodes of C
y
will be bounded
to d’, with d’<<d. We can thus approximate the
distance between x and nodes of C
y
to the value d.
We assume that when x transmits a frame
addressed to y, nodes of C
y
observe different values
of SNR, following a Rayleigh distribution:
0
*
1
)(
*
≥=
−
γ
γ
γ
γ
γ
ef
where the average SNR, γ*, is the same for all nodes
and constant with time. We also assume that for
each node, the SNR value is constant during a frame
reception, but it can be different for each frame.
Let x transmit a frame to y, which is received by
nodes of C
y
. We assume that these nodes can
identify that the final destination of the frame is y
even in presence of transmission errors (e.g. using a
strong error correction code for the corresponding
header fields). After receiving the frame, every node
checks for its correctness using for instance a CRC.
For simplicity, it is assumed throughout this paper
that the error detection code used will detect all
errors introduced by the channel. In practice, this is a
reasonable assumption since the probability of an
undetected error can be made very small.
In a C-ARQ system without frame combining,
nodes in C
y
that correctly receive the frame will
keep a copy of it. If node y detects that its reception
is erroneous, it will ask one of these nodes for a
retransmission of a correct copy. Only in the case
that any node in C
y
has correctly received the frame,
y would ask for a retransmission to node x.
In a C-ARQ with FC, in contrast, even if the
frame was received with errors, nodes in C
y
will
keep a temporary copy of it. In case node y finds
that the frame has suffered errors, it will request
their cooperators for a correct copy of the frame. In
case there is no correct frame received by any
cooperator, it will send a signaling packet to its
cooperators requesting a retransmission of their
erroneous frame copies (Figure 1). Cooperators of y
will send, in turns, their copies of the frame,
attaching the measured value of SNR during the
frame reception, γ
i
, until y is able to correctly decode
the frame by performing the frame combining.
Recall that we assume a slow fading channel and,
therefore, that γ
i
is constant during frame reception,
but in general different for each cooperator. At each
reception of the information sent by each cooperator
- and assuming that this received copy of the frame
has not a correct CRC-, terminal y uses a Maximum-
Likelihood (ML) decision rule for constructing a
“hypothetically correct” received frame (Figure 1).
That is, y uses a statistically optimal fusion rule in
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