6104 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 8, AUGUST 2016
1) FD Relay Transmission Mode: In both odd and even time
slots, the BS transmits downlink signals containing independent
messages to the relays while the relays decode and retransmit
the signals, which are received from the BS in the p revious time
slot, to different users. For the same user, the BS and the relay
transmit their signals over the same subcarrier in both odd and
even time slots, i.e., k
1
= k
2
= k.
In this paper, we treat the signals from the BS as the inter-
ference to the links between the relays and users.
4
Hence, the
transmission rate for U
n
through R
m
within one frame in FDRT
mode is expressed as
R
k
1
,k
2
,1
n,m
=
1
2
min
log (1 + p
b,n,k
2
α
b,m,k
2
)
log
1 +
p
m,n,k
1
α
m,n,k
1
p
b,n,k
1
α
b,n,k
1
+ 1
+
1
2
min
log (1 + p
b,n,k
1
α
b,m,k
1
)
log
1 +
p
mn,k
2
α
m,n,k
2
p
b,n,k
2
α
b,n,k
2
+ 1
(1)
where k
1
= k
2
.
Note that we do not consider subcarrier pairing in FDRT
mode. In other words, we do not consider the case where k
1
=
k
2
. Hence, the transmission rate for U
n
through R
m
within one
frame in FDRT mode is given by
R
k
1
,k
2
,1
n,m
= 0, if k
1
= k
2
. (2)
2) HD Relay Cooperative Transmission Mode: In an odd
time slot, the BS transmits the downlink signals containing
independent messages for different users, whereas all the users
and the HD relays keep silent. In a n even time slot, the HD
relays forward the signals received in the odd time slot to the
users operating in the HDRCT mode. At the same time, the
BS transmits the same information as the re lay to the target
user. The users then combine the signals 1) received from the
BS in the odd time slot and 2) received from the BS and the
relay in the even time slot using the maximal ratio combining
technique. The subcarrier used in the link between BS and relay
can be different from the subcarrier used in the link between the
relay and the user. The pairing of the subcarriers is the so-called
subcarrier pairing. More explicitly, subcarrier pa iring means
that the signals received by the relay on subcarrier k
1
will be
forwarded on subcarrier k
2
to the destined user, where k
1
and
k
2
are not necessarily the same and they form a subcarrier
pair denoted (k
1
,k
2
). When the decode-and forward relaying
4
If the signal from the relay is considered interference, FDRT becomes
meaningless. Note that there are advanced encoding strategies, namely, block
Markov encoding, which enable the direct link to help rather than to interfere
with the relay link [1], [38]. Ho wever, the block Markov encoding needs
some adv a nced decoding algorithms, such as joint decoding [1], successive
decoding, sliding-windo w decoding, and backward decoding [39]. Ho wever,
joint decoding has much higher computation complexity, and decoding delay
and successive decoding/sliding-window decoding/backward decoding could
increase the probability of error propagation in practical systems. Thus, we do
not consider block Markov encoding strategies in this paper .
strategy is used, the transmission rate for U
n
through R
m
within
one frame is given by
R
k
1
,k
2
,2
n,m
=
1
2
min
log (1 + p
b,n,k
1
α
b,m,k
1
)
log
1 + p
b,n,k
1
α
b,n,k
1
+
√
p
b,n,k
2
α
b,n,k
2
+
√
p
m,n,k
2
α
m,n,k
2
2
.
(3)
3) Direct Transmission Mode: In both odd and even time
slots, the BS transmits downlink signals containing independent
messages for different users, whereas no relay transmits signals.
The BS can use two different subcarriers in the odd and even
time slots: subcarrier k
1
is for the transmission in the odd time
slots, and k
2
is for the transmission in the even time slots. Then,
the achievable rates of user U
n
over subcarrier k
1
and k
2
for DT
mode within one frame are given, respectively, as follows:
R
k
1
n
=
1
2
log (1 + p
b,n,k
1
α
b,n,k
1
) (4)
R
k
2
n
=
1
2
log (1 + p
b,n,k
2
α
b,n,k
2
) . (5)
Remark 1: In HDRCT mode, the subcarrier in the first hop
can be different from the subcarrier in the second hop. In
addition, in DT mode, the subcarriers in the first and second
hops are not necessarily the same. However, in FDRT mode, we
restrict that the subcarriers assigned in the first and second hops
are the same, i.e., k
1
= k
2
= k. The reason is that if subcarriers
in the first and second hops are not assigned to the same relay,
interrelay interference will appear. For example, we suppose
the subcarrier k is assigned in the first hop to relay R
1
and
also assigned in the second hop to relay R
2
. Although R
1
is
receiving signals from the BS, it will be interfered with by R
2
over subcarrier k.
Remark 2: In summary, each given relay decodes signals
from subcarriers selected for FDRT or HDRCT mode during
the odd time slots and retransmit them in the even time slots.
Similarly, the relay decodes signals from subcarriers only se-
lected for FDRT during the even time slots and retransmit them
in the odd time slots. Thus, once the subcarriers selected for FD
or HD relay transmission are known, the relay can perform the
decoding and retransmission accordingly. Hence, our system
model can be implemented in practice.
B. Subcarrier and Power Constraints
1) Subcarrier Constraints: We now introduce four sets of
binary assignment variables for subcarriers as follows.
• ρ
k
1
,1
n
indicates whether subcarrier k
1
in the odd (first)
time slot is assigned to user U
n
in DT mode.
• ρ
k
2
,2
n
indicates whether subcarrier k
2
in the even (second)
time slot is assigned to user U
n
in DT mode.