Physical Layer Security of Buffer-Aided Hybrid Virtual
Full-Duplex and Half-Duplex Relay Selection
Gan Srirutchataboon and Shinya Sugiura∗
Institute of Industrial Science, The University of Tokyo, Japan
Email: {gan, sugiura}@iis.u-tokyo.ac.jp

Abstract—In this paper, we propose a novel secure bufferaided relay selection that is capable of operating both virtual
full-duplex (VFD) and half-duplex (HD) transmissions in a hybridmanner. The proposed scheme consists of five modes: two unicast
modes, a broadcast mode, cooperative beamforming, and a VFD
mode. Since the VFD mode has the potential of achieving ahigher secrecy capacity than the other four HD modes, theproposed relay selection algorithm gives the highest priority toactivating the VFD mode. Our performance results demonstratethat the proposed secure relay selection scheme outperforms thebenchmarks in terms of the secrecy outage probability.

I. I NTRODUCTION
Physical layer (PHY) security [1, 2] has been developed tobest serve confidential information in wireless communication
systems. The use of signal processing techniques, such as relay
selection, cooperative beamforming, and jamming, allows us toachieve an increased secrecy capacity [3, 4]. The secure relay
selection techniques were presented in [5–7], which decreasean outage probability by selecting a link having the highest
channel capacity.
Buffer-aided relay selection [8–11] is an extended versionof relay selection, which increases the design degree of
freedom compared with conventional relaying scheme [12].
More recently, non-orthogonal multiple access (NOMA) and
full-duplex (FD) are exploited in the context of buffer-aided
relay selection [13–16]. In [17], secure buffer-aided relay
selection was considered while assuming that an eavesdropper
intercepts information from only a relay node. Also, themax-min ratio scheme was proposed for secure buffer-aided
relay selection [18], where a single link having the maximum
secrecy capacity is selected from all the source-to-relay (SR)and relay-to-destination (RD) links in each time slot under
the assumption that an eavesdropper is capable of intercepting
information from both source and relay nodes. In [6], Chen etPreprint (accepted version) for publication in 2022 IEEE 95th Vehicular
c 2022 IEEE. Personal use ofTechnology Conference (VTC2022-Spring). ⃝this material is permitted. Permission from IEEE must be obtained for allother uses, in any current or future media, including reprinting/republishing
this material for advertising or promotional purposes, creating new collective
works, for resale or redistribution to servers or lists, or reuse of any
copyrighted component of this work in other works. This work was supported
in part by the Japan Society for the Promotion of Science (JSPS) KAKENHI(Grant Number 17H03259) and in part by the Japan Science and Technology
Agency (JST) Precursory Research for Embryonic Science and Technology(PRESTO) (Grant Number JPMJPR1933). Also, this work was partiallyconducted as the research commissioned by National Institute of Information
and Communications Technology (NICT), JAPAN.

al. proposed the max-ratio relay selection with the knowledgeof transmitter-to-eavesdropper links, which outperforms the
max-min ratio counterpart in terms of the secrecy outage
performance. In [7], the secure buffer-state-based (BSB) maxratio relay selection was proposed to avoid the empty buffer
states and buffer overflow, and the concept of cooperative jamming was exploited to minimize the possibility of interception
by the eavesdropper.
In full-duplex (FD) transmission [19], transmission andreception are carried out simultaneously with the aid of selfinterference (SI) cancellation techniques, and it may provide
a doubled secrecy rate compared to the conventional halfduplex (HD) transmission. FD transmission is utilized in PHY
security [20] to degrade the signal-to-interference and noise
ratio (SINR) at an eavesdropper, where the receiver receives
source information while transmitting an artificial noise to theeavesdropper. In [21], a source and an FD relay simultaneouslytransmit artificial noises to the eavesdropper while sending andrelaying information, respectively. However, the performance
suffers from the strong SI.
In [22, 23], the concept of virtual full-duplex (VFD) transmission was introduced to overcome the limitation of SI.
More specifically, in the VFD transmission, the transmission
and reception of packets are carried out by different nodes
simultaneously, i.e., a source node transmits a packet toa relay node, while another relay node transmits a packet
to a destination node. Furthermore, in [24, 25], interference
between transmitting and receiving relay nodes, referred toas inter-relay interference (IRI), is eliminated with the aid of
multiple antennas equipped at the relay nodes. Most recently,
in [11], the hybrid use of HD and VFD transmission in bufferaided relay selection was proposed.
Motivated by [11], this paper proposes a secure buffer-aided
relay selection based on the hybrid HD and VFD transmission.
The proposed scheme supports five transmission modes, i.e.,
one VFD mode and four HD modes. The VFD mode is given
priority to be activated over the other four modes since the
VFD mode has the potential of achieving a higher secrecy rate
and a higher interference to the eavesdropper.1 Owing to thebenefits of the broadcast mode, the multiple relay nodes havea chance to share an information packet in their buffers in a
1 Note that in [11], capacity, rather than secrecy capacity, is employed as a
metric to activate one out of transmission modes, implying that the presenceof eavesdroppers is not taken into account.

seamless manner. Thus, it is possible to resolve the influence of
IRI with the aid of successive interference cancellation (SIC).

II. S YSTEM M ODEL
We consider a two-hop cooperative relay network thatconsists of one source node (Alice), one destination node(Bob), one eavesdropper (Eve), and K decode-and-forward(DF) relays nodes. Each node is equipped with a single
antenna operated in HD transmission. The kth relay is denoted
as Rk (k ∈ {1, · · · , K}). We assume that Alice needs theassistance of a relay node to communicate with Bob due tothe presence of an obstacle between Alice and Bob. Eve tries tointercept information transmitted from Alice to the relay nodes
as well as that from the relay nodes and Bob. Additionally,each relay node has a data buffer of size L, and the numberof packets stored at the kth relay node’s buffer is denoted asψk (0 ≤ ψk ≤ L).
The channel coefficients of the ith SR link, the jth RD
link, the relay-to-relay (RR) link between of the ith and jth
relay nodes, the source-to-eavesdropper (SE) link, and therelay-to-eavesdropper (RE) link between the jth relay nodeand the eavesdropper denote hSRi , hREj , hRRji , hSEi , hREj ,respectively. We assume each of the 2K + 2 links is modeledby an independent and identically distributed (IID) frequencyflat Rayleigh fading channel, and each channel coefficient isgenerated as a random variable, following complex-valued
Gaussian distribution with a zero mean and unit variance.
Similar to [11], Bob acts as a central coordinator to gather all
channel state information (CSI) and buffer state information(BSI). More specifically, Alice periodically broadcasts a pilot
signal to the K relay nodes, and each relay node acquires
CSI based on the received pilot signal. Then, each relay node
relays the estimated SR CSI, its BSI, and a pilot signal to Bob.
Finally, in each time slot, Bob sends a control packet to eachnode to collect CSI and BSI, and decides the transmission
mode based on the collected CSI and BSI. After Bob successfully receives the packet, Bob sends back an acknowledgment
packet through a low-rate feedback channel to the relay nodes.
Then, the associated relay nodes delete the packet from theirbuffer.
In the proposed scheme, we have five transmission modes,
i.e., a unicast mode for SR transmission, the unicast mode for
RD transmission, the broadcast mode for SR transmission, thecooperative beamforming mode for RD transmission, and the
VFD mode. One out of the five transmission modes is activatedbased on CSI and BSI, which have to be successfully collected
at the coordinator under the assumption of the use of powerfulchannel coding.

A. Unicast Mode for SR Transmission
In the unicast mode for SR transmission, Alice transmits
an information packet to a single selected relay node. Here,the channel capacities of the ith SR link and the SE link are
given, respectively, by
(
)
1
(1)
CSRi = log2 1 + γSRi |hSRi |2 ,2()
1
CSE = log2 1 + γSE |hSE |2 .
(2)
2
The secrecy capacity of the ith SR link, where Eve is not able
to intercept information, is given by [7]secure= CSRi − CSE ,
CSR
i
)
(
1
1 + γSR |hSRi |2= log2,2
1 + γSE |hSE |2(3)

and γSRi and γSE are the average signal-to-noise ratio (SNR)of the ith SR link and the SE link, respectively. The unicast
SR transmission from Alice to the ith relay node is successful,
if the buffer of the ith relay node is not full and if we havesecureCSR> rsc , where rsc is a target secrecy rate.
i
B. Unicast Mode for RD Transmission
In the unicast mode for RD transmission, the jth relay
node relays a packet stored in the buffer to Bob. The channel
capacity of the jth RD link and the jth RE link are given,
respectively, by()
1
CRDj = log2 1 + γRDj |hRDj |2 ,
(4)
2
(
)
1
CREj = log2 1 + γREj |hREj |2 .
(5)
2
Similar to (3), the secrecy capacity of the jth RD link isformulated by
secureCRD= CRDj − CREj ,j()
1 + γRDj |hRDj |2
1= log2,2
1 + γREj |hREj |2(6)where γREj and γREj are the average SNRs of the jth RD
link and the jth RE link, respectively. The secure unicast
transmission of the jth RD link is successful, if the buffer
secureof the jth relay node is not empty and if CRD> rsc .
j
C. Broadcast Mode for SR Transmission
In the broadcast mode for SR transmission, Alice broadcasts
an information packet to multiple relay nodes. Hence, theSR links, which satisfy (3) and the buffers of the related
relay nodes are not full, are activated. In this mode, aninformation packet can be shared among the relay nodes
corresponding to the activated SR links, which allows us
to perform single-antenna-based SIC in the VFD mode andcooperative beamforming. Let us define I as the subset of the
SR links, which are activated in the broadcast mode. Note that
if there is only a single activated SR link, i.e., |I| = 1, thismode becomes equivalent to the unicast mode.
D. Cooperative Beamforming Mode for RD Transmission
In the cooperative beamforming mode for RD transmission,
multiple relay nodes cooperatively transmit a common packet
to Bob. Here, J denotes the subset of the RD links, which areavailable for cooperative beamforming, where the related relay
nodes share a common packet in their buffers. Then, let us
introduce the RD channel coefficients associated with cooperative beamforming as g = [g1 , · · · , gQ ]T ∈ J , where |J | = Q.
According to [7], each activated relay node’s beamforming
weight is given by the conjugate of the associated RD link,normalized by ∥g∥. Hence, the capacity of the cooperative
beamforming mode is given by1
2
log2 (1 + γRD ∥g∥ ),(7)2
under the assumption that the average SNRs of all the RD
links are identical as γRD1 = · · · = γRDK = γRD . Similarly, when considering the channel coefficients of the Q
RE links, associated with those of the RD links g, to be′ T] , we arrive at the secrecy capacity of theg′ = [g1′ , · · · , gQ
cooperative beamforming mode as follows:()
2
1
1 + γRD ∥g∥secureCBeam = log2
(8)2
1 + γRE (|gH g′ |/ ∥g∥)2
CBeam =

where we assume the identical average SNR of RE links, i.e.,
γRE1 = · · · = γREK = γRE . Finally, if the secrecy capacity (8)secureis higher than the target secrecy rate, i.e., CBeam> rsc , thetransmission is successful.

E. VFD Mode for SR and RD Transmission
In the VFD mode for SR and RD transmission, Alicetransmits an information packet to a single receiving relay
node, while a single activated transmitting relay node relays apacket to Bob. We assume the ith relay node is the receiving
relay node, and the jth relay node is the transmitting relay
node. Here, the received signals at the ith relay node, Bob,
and Eve are given, respectively, by
yRi = hSRi xA + hRRji xj + ni

(9)yB = hRDj xj + nB ,(10)

yE = hSE xA + hREj xj + nE

(11)the central coordinator (Bob).2 Hence, the capacity of thereceiving relay node and that of Bob are represented by (1)and (4), respectively.
Furthermore, since each mode of our protocol is designed
to be information-theoretically secure, Eve does not have any
chance to intercept a packet xj stored in the jth relay node’s
buffer. In the VFD mode, the Eve’s capacity for the SE link
and that for the RE link between the jth relay node and Eve
are formulated, respectively, by()
1
γSE |hSE |2
CVFD,SE = log2 1 +(14)
2
1 + γREj |hREj |2()
γREj |hREj |2
1
CVFD,REj = log2 1 +(15).
2
1 + γSE |hSE |2
Hence, our VFD mode has the benefits of imposing increased
interference on signals received at Eve. From (1) and (14), thesecrecy capacity of the link between Alice and the receiving
relay node in the VFD mode is given by2
1
1 + γSRi |hSRi | 
secure
CVFD,SR= log2 
.
(16)
2
i
2
1 + γSE |hSE | 2
1+γREj |hREj |Similarly, from (4) and (15), the secrecy capacity of the link
between the transmitting relay node and Bob in the VFD modeis expressed by


2
1
+
|h
|
γ
1
RDj RDj
secure.
CVFD,RD= log2 (17)γREj |hREj |2j2
1+
1+γSE |hSE |2

Finally, our VFD mode is successful if the following relationship is satisfied:securesecuremin{CVFD,SR, CVFD,RD} > rsc .
i
j

(18)

Since the VFD mode is capable of achieving a doubled
transmission rate compared to the HD modes, the VFD modeis given the highest priority to be activated in our selection
algorithm.
Note that the average power consumption in each SR or
RD transmission of our scheme is maintained constant, whichis the same as that of the conventional relaying schemes that
dispense with buffering or beamforming.

where xA and xj are the packet transmitted from Alice andthat from the jth relay node, respectively. The associatedcomplex-valued Additive white Gaussian noises (AWGNs) at
III. P ROPOSED S ELECTION A LGORITHM
the ith relay node, Bob, and Eve are represented by ni , nB
As mentioned above, the VFD mode is put the highest
and nE , respectively.
priority among the five modes since the VFD mode achieves
In our VFD mode, the receiving and the transmitting relay
the doubled transmission rate. The three conditions that havenodes are selected under the assumption that both the relay
to be satisfied in our VFD mode are summarized as follows:
nodes share a common packet in their buffers. Thus, the(A1)
The receiving relay node and the transmitting relay node
receiving relay node can calculate hRRji xj in (9) to eliminate
have to be different. This corresponds to the VFD conIRI via using SIC as follows:ȳRi = yRi − hRRji xj(12)= hSRi xA + ni .

(13)Here, we assume that the receiving relay node has theknowledge of the RR channel of hRRji by overhearing thepilot signal transmitted from the transmitting relay node to

2 In the proposed scheme, a packet used in SIC, i.e., x of (12), is sucj
cessfully shared among the relay nodes through the broadcast and full-duplex
modes, hence free from any error propagation, while SIC in conventional
MIMO and NOMA systems typically suffer from the detrimental effectsof such error propagation due to mis-demodulation of xj . Furthermore, thepotential channel estimation errors of the RR channel may induce a residual
SIC error in (12). However, even when the SNR of the RR channel is low,
the associated effects may not be high owing to low IRI.

cept [11, 22, 23] that there is one relay node to receive apacket while another relay node transmits another packet
simultaneously.
(A2) The receiving relay node and the transmitting relay node
have to share a packet in their buffers. Owing to this, oursingle-antenna-based SIC of (12) becomes realistic.
(A3) Both the secure transmissions from Alice and the transmitting relay have to be successful, i.e., the inequality of(18) has to be satisfied.
Here, let us denote L as the set of relay pairs (i, j) that satisfy(A1)–(A3).
A. Case of L ̸= ∅In this case, the VFD mode is activated. Among all the relay
pairs in L, the relay node that stores the highest number ofpackets in its buffer is selected as the transmitting relay node.
If multiple candidates of the transmitting relay node exist, thesecurerelay node that achieves a higher secrecy capacity CVFD,RDjof (17) is selected as the transmitting relay node. Let us denotethe index of the selected transmitting relay node as ĵ.
Then, the index î of the receiving relay node is selectedfrom the subset (î, ĵ) ∈ L, such that the secrecy capacity of
the VFD mode is maximized.

Fig. 1. Secrecy outage probabilities of the proposed scheme with and without
the VFD mode, the conventional max-ratio, and the BSB max-ratio scheme,
where we considered the system parameters of (K, L) = (3, 5), and thetarget secrecy rate was varied from rsc = 0.1 to 3.0 bps/Hz.

B. Case of L = ∅of ξSR = γSR /γSE , and ξRD = γRD /γRE . Additionally, theinitial buffer state is set to empty one in each Monte Carlosimulation. Also, we assumed the symmetric channel scenario
of γSR = γRD = 40 dB, and the ratios of ξSR = ξRD = 5.3

If there is no relay pair to activate the VFD mode, i.e.,
L = ∅, one out of the four HD modes is activated basedon CSI and BSI. Here, we introduce a parameter ω, which isused for characterizing our algorithm to select one out of thefour HD modes, where 0 ≤ ω ≤ L. For example, when ω ishigh, i.e., ω > 0.5L, the average packet delay tends to be low
at the cost of the increased secrecy outage probability. Morespecifically, to avoid the detrimental of the buffer overflow
and empty buffer state, we classify our algorithm based on
BSI and ω into three as follows.
1) max{L − ψi } > max {ω + ψj }: In this case, either theFirst, we investigated the effects of ω on the performance of the proposed scheme, where we considered ω =0, 0.50L, 0.75L. Fig. 1 compares the secrecy outage probabilities of the proposed scheme with and without the VFD
mode, where the target secrecy rate was varied from rsc = 0.1
to 3.0 bps/Hz. As seen in Fig. 1, the proposed scheme with
the VFD mode (ω = 0) achieved the lowest secrecy outage
probability, which is achieved at the cost of a higher delay, as
shown later. Upon increasing ω in the proposed scheme with
the VFD mode, the secrecy outage probability monotonicallyincreased.

unicast mode for SR transmission or the broadcast modes is
activated. More specifically, the broadcast mode is activated if
multiple SR links are available. Otherwise, the unicast modeis activated for SR transmission.
2) max {ω + ψj } ≥ max{L − ψi }: In this case, either the

Furthermore, in Figs. 2(a) and 2(b), we investigated theeffects of the number of the relay nodes K and the buffer
size L on the secrecy outage probabilities, respectively. In
Fig. 2(a), the number of buffer size was fixed to L = 5 while
the number of relay nodes was varied from K = 4 to 10. As
seen in Fig. 2(a), the proposed scheme with the VFD mode(ω = 0) achieved the lowest secrecy outage probability formost of K values, which was followed by the proposed schemewith the VFD mode (ω = 50L). Also, the proposed schemewith the VFD mode (ω = 0.75L) exhibited a lower secrecy
outage probability than the conventional max-ratio scheme. In
Fig. 2(b), the number of relay nodes was given by K = 5 while
the buffer size was varied from L = 5 to 100. From Fig. 2(b),it was found that the proposed scheme with the VFD mode(ω = 0) exhibited the best performance in the entire L range.

∀i∈I

∀j∈J

∀j∈J

∀i∈I

unicast mode for RD transmission or the cooperative beamforming mode is activated. If multiple RD links are available
in an outage and their buffers contain a common packet,
the cooperative beamforming mode is activated. Otherwise,a single strongest RD link is selected, which corresponds tothe unicast mode for RD transmission.
3) I = J = ∅: In this case, there is neither available
SR nor RD link, and hence the transmission is counted as an
outage event.
IV. P ERFORMANCE R ESULTS
In this section, the achievable performance of the proposed
scheme is compared with those of the existing benchmark
schemes, i.e., the BSB max-ratio scheme [7] and the conventional max-ratio scheme [6]. Let us introduce the SNRs

3 In this paper, we considered the high SNR (i.e., γ
SR = γRD = 40 dB)
scenarios to confirm the ideal achievable performance limit. The investigationsof further realistic scenarios, such as the low SNRs or the asymmetricchannels, are left for future studies.

(a)

(b)
Fig. 2. Secrecy outage probabilities of the proposed scheme with and without
the VFD mode, the conventional max-ratio, and the BSB max-ratio scheme
for the target secrecy rate of rsc = 1.0 bps/Hz; (a) L = 5 and (b) K = 5.

V. C ONCLUSIONSIn this paper, we proposed the novel secure buffer-aided
relay selection scheme with the aid of hybrid HD and VFD
transmissions. The presence of our VFD mode contributes toimposing interference on Eve, hence increasing secrecy capacity. Our simulation results demonstrated that the proposed
scheme exhibited a better secrecy outage probability comparedto the benchmark schemes.
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