In order to address an explosive increase in data traffic generated by various wireless devices (e.g., smart phones, tablets and laptops) , , heterogeneous networks (HetNets) are emerging as an effective paradigm to enhance the system capacity and coverage for guaranteeing the quality-of-service (QoS) of subscribers -. HetNets are usually composed of various macro cells, small cells (e.g., pico cells and femto cells), and relay stations, where low-power small cells (ranging from 250mW to 2W) are underlaid in higher-power macro cells (5W-40W) . Typically, macro base stations (MBSs) and small base stations (SBSs) are permitted to simultaneously transmit their respective confidential messages over the same spectrum band. As a result, the spectral efficiency can be significantly improved along with an increased network capacity , . However, mutual interference may exist among the macro cells and small cells, as the same spectrum band is simultaneously accessed in an underlay manner. In order to alleviate the mutual interference problem, an interference-aware muting scheme was proposed in  to reduce the interference level below a tolerable threshold. In , the authors proposed an interference cancelation scheme at MBS to cancel out the cross-tier interference received at a small-cell subscriber and derived a closed-form outage probability expression of HetNets. In -, the authors explored interference management for the sake of improving the network coverage of HetNets.
However, due to the broadcast nature of wireless communications  and the open system architecture of HetNets , confidential messages transmitted to legitimate users are extremely vulnerable to eavesdropping attacks. Thus, it is of importance to investigate the transmission confidentiality of HetNets against eavesdropping. Traditionally, key-based cryptographic methods were employed to guarantee the confidentiality of wireless transmissions. However, with the fast development of computing technology, the eavesdropper may have a sufficiently high computing power to crack the secret key. Since the first physical-layer security work carried out by Wyner in , where the secrecy capacity was given as the difference between the capacity of main channel and that of wiretap channel, an increasing research attention has been paid to this research field, which is considered as a promising means of achieving a perfect secrecy against eavesdropping. During the past decades, cooperative relay -, beamforming -, and multiuser scheduling - were proposed to strengthen the physical-layer security for different wireless network scenarios. Moreover, distributed multiple-input multiple-output (MIMO) systems were also investigated from the physical-layer security perspective in  and .
To the best of our knowledge, most of existing research efforts have been focused on the network coverage , , energy efficiency , , and spectral efficiency ,  of HetNets. Besides, there also exits some research work on physical-layer security for spectrum-sharing HetNets -. Typically, cognitive radio (CR) networks can be envisioned as one type of spectrum-sharing HetNets. In CR systems, an unlicensed secondary user is allowed to access the licensed spectrum that is not used by a primary user, where the primary user has a higher priority than the secondary user in accessing the spectrum. Moreover, the primary user and secondary user belong to two different networks, which are typically separated and independent from each other. In  and , the authors investigated physical-layer security of secondary transmissions without affecting the QoS of primary transmissions for CR networks. In , the authors studied the secrecy-optimized resource allocation for device-to-device communication systems. In , a secrecy coverage probability was derived in downlink MIMO multi-hop HetNets. It is noted that mutual interference between the macro cells and small cells is critical in underlay HetNets, which was intelligently exploited in  to defend against eavesdropping for spectrum-sharing HetNets. In , an interference-canceled underlay spectrum sharing (IC-USS) scheme was proposed for canceling out the interference received at a macro user (MU) while interfering with an unintended eavesdropper.
Differing from the system model with a single antenna as studied in , we consider multiple distributed antennas available in the macro cell of heterogeneous cellular networks to guarantee the QoS of far-off subscribers , . Both MBS and SBS are connected to a core network via fiber cables, e.g., a mobile switch center (MSC) in the global system for mobile communication (GSM) and a mobility management entity (MME) in the long term evolution (LTE) , which ensures the real-time interaction between MBS and SBS. The main contributions of this paper are summarized as follows. First, combining the interference cancelation of  and opportunistic antenna selection (OAS) techniques, we propose an interference-canceled OAS (IC-OAS) scheme for the sake of improving the security-reliability tradeoff (SRT) performance of heterogeneous cellular networks. The proposed IC-OAS is different from the zero-forcing beamforming of , where multiple transmit antennas are employed to emit a source signal simultaneously with a beamforming vector, which requires complex symbol-level synchronization between the multiple antennas for avoiding severe inter-symbol interference. By contrast, in our IC-OAS scheme, only a single distributed antenna is chosen to transmit the source signal, which reduces the complexity of distributed antenna synchronization. Second, we derive closed-form expressions of intercept probability and outage probability for the proposed IC-OAS as well as conventional interference-limited OAS (IL-OAS) schemes. Numerical results show that the proposed IC-OAS scheme is capable of improving the SRTs of both the macro cell and small cell, as compared to the conventional IL-OAS approach. Additionally, a normalized sum of intercept probability and outage probability (denoted IOP for short) of both the macro cell and small cell versus a ratio of the transmit power of SBS to that of MBS, referred to as the small-to-macro ratio (SMR), is evaluated for the IL-OAS and IC-OAS schemes. It is demonstrated that the normalized sum IOP of our IC-OAS scheme can be further optimized with regard to the SMR and the optimized sum IOP of proposed IC-OAS is much better than that of conventional IL-OAS.
The reminder of this paper is organized as follows. In Section II, we present the system model of a spectrum-sharing heterogeneous cellular network and propose the IC-OAS scheme. For comparison purposes, the conventional IL-OAS scheme is also presented. In Section III, we characterize the SRT for both IC-OAS and IL-OAS in terms of deriving their closed-form expressions of intercept probability and outage probability. Next, numerical SRT results and discussions are provided in Section IV. Finally, some concluding remarks are given in Section V.
Ii Spectrum-sharing Heterogeneous Cellular Networks
In this section, we first present the system model of a heterogeneous cellular network, where a macro cell coexists with a small cell and an eavesdropper is assumed to tap legitimate transmissions of both the macro cell and small cell. Next, an underlay spectrum sharing (USS) mechanism  is considered for the heterogeneous cellular network.
Ii-a System Model
Fig. 1 shows a heterogeneous cellular network composed of a macro cell and a small cell. Differing from the separated independent primary and secondary networks in CR systems, the macro cell and small cell are coordinated via the core network in heterogeneous cellular networks, through which the reliable information exchange can be achieved between MBS and SBS. This guarantees that a specially-designed signal becomes possible at MBS, since the design of such a special signal requires the reliable exchange of some system information between MBS and SBS , e.g., the channel state information (CSI), transmit power, and so on. Moreover, although only a single small cell is taken into account in this paper, a possible extension can be considered for a large-scale heterogeneous network consisting of massive small cells with the help of stochastic geometry  and user scheduling . Additionally, if more than one SBS is available, the given spectrum may be divided into multiple orthogonal sub-bands which are then allocated to different SBSs. In this way, only one SBS is assigned to simultaneously access an orthogonal sub-band with MBS for the sake of alleviating the complex synchronization among spatially-distributed SBSs.
In the macro cell, MBS first sends its confidential message to distributed antennas (), where is the number of distributed antennas. Then, a single antenna is opportunistically selected to transmit the confidential message of MBS to MU. Meanwhile, in the small cell, SBS transmits its signal to a small user (SU) over the same spectrum used by MBS. Moreover, a passive eavesdropper is assumed to tap -MU and SBS-SU transmissions. To improve the spectrum utilization, we consider an USS mechanism for the heterogeneous cellular network throughout this paper. Specifically, in the USS mechanism, MBS and SBS are permitted to simultaneously transmit their respective confidential messages over the same spectrum band. However, in order to guarantee the QoS of heterogeneous cellular networks, the transmit powers of MBS and SBS should be controlled to limit mutual interference. For notational convenience, let and
denote the transmit powers of MBS and SBS, respectively. Moreover, an additive white Gaussian noise (AWGN) is encountered at any receiver of Fig. 1 with a zero mean and a variance of.
Ii-B Conventional IL-OAS
In this section, we present the conventional IL-OAS scheme as a baseline, where MBS and SBS are allowed to simultaneously access the same spectrum band. In order to guarantee the QoS of macro cell, the transmit power of SBS is controlled for limiting the interference to macro cell . For the macro cell, MBS first transmits its confidential message () to through a fiber-optic cable. Then, a single antenna is opportunistically selected to forward its received messages to MU at a power of . By contrast, in the small cell, SBS directly transmits its message () to SU over the same spectrum used by MBS at a power of . The aforementioned transmission process leads to the fact that a mixed signal of and is received at MU and SU. For notational convenience, let represent the set of distributed antennas.
For the macro cell, if a distributed antenna is selected to transmit the signal , the received signal at MU can be expressed as
where , , and represent the small-scale fading gains of -MU and SBS-MU channels, respectively, and are the distances of -MU and SBS-MU transmissions, and are path loss factors of the -MU and SBS-MU channels, respectively, and is the AWGN encountered at MU. According to Shannon’s capacity formula, we can obtain the channel capacity of -MU from (1) as
where and are the signal-to-noise ratios (SNRs) of MBS and SBS, respectively. Typically, the antenna with the highest instantaneous channel capacity of is selected to assist the MBS-MU transmission. Thus, from (2), an opportunistic antenna selection criterion is given by
which shows that the CSI is used to perform the opportunistic antenna selection. According to (3), the channel capacity of MBS-MU is obtained as
where subscript denotes the distributed antenna selected. Also, for the small cell, the received signal at SU can be similarly expressed as
where , , and denote the small-scale fading gains of SBS-SU and -SU channels, respectively, and are the distances of SBS-SU and -SU transmissions, and are path loss factors of the SBS-SU and -SU channels, respectively, and is the AWGN encountered at SU. Similarly, the channel capacity of SBS-SU is obtained from (5) as
Meanwhile, the eavesdropper may overhear both the MBS-MU and SBS-SU transmissions. As a result, the corresponding received signal at the eavesdropper can be written as
where , , and represent the small-scale fading gains of -E and SBS-E channels, respectively, and are the distances of -E and SBS-E transmissions, and are path loss factors of the -E and SBS-E channels, respectively, and is the AWGN encountered at the eavesdropper. For simplicity, we here assume that the eavesdropper decodes and separately without the help of successive interference cancelation. Based on the Shannon’s capacity formula, the channel capacity of MBS-E and that of SBS-E are given by
Ii-C Proposed IC-OAS
In this section, we propose an IC-OAS scheme, where MBS and SBS are also permitted to access the same spectrum simultaneously, leading to an existence of mutual interference between the macro cell and small cell, as aforementioned. For the sake of canceling out the interference received at MU from SBS, a special signal denoted by is designed and emitted through a selected antenna at MBS. When a mixed signal of and is transmitted at MBS, a weight coefficient is utilized at SBS for transmitting its signal at a power of . The instantaneous and average transmit powers of are represented by and , respectively. For a fair comparison with the IL-OAS scheme, the total average transmit power of and is constrained to at MBS. In this sense, the transmit power of is given by . Obviously, the average transmit power of should satisfy the following inequality
Considering that a distributed antenna is selected to transmit the mixed signal of and , we can express the received signal at MU as
where represents a fading coefficient of the channel from the distributed antenna to MU. For the sake of neutralizing the interference term of (11), the following equality should be satisfied
from which various solutions of can be found for the interference neutralization. Throughout this paper, a solution of to the preceding equation is given by
where represents the variance of the channel from the distributed antenna to MU, and denote the phase of the channel from the distributed antenna to MU and that from SBS to MU, respectively. It can be observed from (12) that the design of requires the knowledge of , , , and at MBS and SBS. Typically, the CSIs of and
are usually estimated at MU and then fed back to MBS and SBS . The statistical CSI ofcan be readily obtained by exploiting the accumulated knowledge of instantaneous CSIs of . Moreover, the information of and may be acquired at MBS through the core network. It is worth mentioning that the message is not generated at SBS, which is typically initiated by another user terminal of cellular networks and sent via the core network first to SBS that then forwards to SU through its air interface in the subsequent stage. Thus, when the core network sends the message to SBS in the first stage, the same copy of can be received and stored at MBS simultaneously. This guarantees that no significant amount of extra time delay is incurred at MBS in obtaining as compared to SBS, regardless of the latency of the core network. Additionally, a small cell is generally deployed for various indoor scenarios with narrow coverage, where user terminals often stay stationary or move at a very low speed (-km/h) . In this case, the transmission distance of SBS-SU is normally stationary along with a quasi-static path loss and thus the transmit power of SBS is stable, which can be pre-determined before the information transmission and sent to MBS in advance. Therefore, the information of both and can be pre-acquired at MBS before starting the transmission of and , implying that our interference cancelation mechanism is nonsensitive to the time delay of the core network. It is of particular interest to examine the impact of channel estimation errors and feedback delay on the SRT performance of our IC-OAS scheme, which is considered for further work. From (12), the instantaneous and average transmit powers of are given by
where and are the means of and , respectively. Combining (10) and (13), we obtain
which indicates that the interference received at MU from SBS can be perfectly canceled out when the average received signal strength from MBS is stronger than the one from SBS. It needs to be pointed that there may exist an optimal solution of in terms of maximizing the secrecy performance of MBS-MU transmissions, which is out of the scope and may be considered for future work. Substituting (12) into (11) yields
from which the capacity of the channel from a distributed antenna to MU is given by
Typically, the distributed antenna with the highest instantaneous channel capacity of is selected to transmit the MBS’ signal. Thus, from (16), an opportunistic antenna selection criterion is expressed as
where the subscript ‘’ denotes the distributed antenna selected. Moreover, when the channel fading coefficients for different distributed antennas are considered to be independent identically distributed (i.i.d.), the aforementioned antenna selection criterion of (17) becomes the same as the conventional one of (3). Hence, the channel capacity of MBS-MU relying on the opportunistic antenna selection of (17) is obtained as
Also, for the small cell, the received signal at SU can be similarly written as
where represents a fading coefficient of the channel from the selected antenna to SU, denotes the specially-designed signal emitted at the selected antenna and is the average transmit power of . It can be observed from (19) that although the term contains the SBS’ signal as implied from (12), it is not aligned and thus interfered with , since the signal is designed to be neutralized with the interference received at MU. Moreover, an advanced signal processing technique e.g. selection diversity combining (SDC) may be employed at the SU receiver by jointly exploiting the terms and for decoding , which can be also adopted by the eavesdropper, thus no improvement is expected for the small cell from an SRT perspective. For simplicity, the signal is treated as an interference at both the SU and eavesdropper in decoding . Hence, the capacity of SBS-SU channel can be obtained from (12) and (19) as
where . Meanwhile, the eavesdropper is considered to tap both the MBS-MU and SBS-SU transmissions. As a result, the corresponding received signal at the eavesdropper can be written as
where represents a fading coefficient of the channel from the selected antenna to the eavesdropper. Again, considering that the eavesdropper decodes and separately without successive interference cancelation as well as using (12) and (13), we can obtain the channel capacity of MBS-E and that of SBS-SU as
Iii Security and Reliability Performance Analysis
In this section, we characterize the SRT of proposed IC-OAS and conventional IL-OAS schemes in terms of deriving their closed-form expressions of intercept probability and outage probability over Rayleigh fading channels. Following  and , an outage probability of legitimate transmissions is given by
where denotes the channel capacity of legitimate transmissions and is an overall transmission rate. Moreover, an intercept probability can be written as
where represents the wiretap channel capacity and is a secrecy rate. It can be observed from (25) that when the wiretap channel capacity becomes higher than the rate difference of , a prefect secrecy is impossible and an intercept event happens in this case.
Iii-a Conventional IL-OAS
In this subsection, we analyze the outage probability and intercept probability of the macro-cell and small-cell transmissions relying on the conventional IL-OAS scheme. From (24), an outage probability of the MBS-MU transmission is written as
where is an overall data rate of MBS-MU transmission. Substituting from (4) into (26) yields
where . Proceeding as in Appendix A, we can obtain as
where represents the -th non-empty subset of the antenna set . Similarly, by using (6) and (24), the outage probability of SBS-SU transmission is expressed as
where is the overall data rate of SBS-SU transmission. Substituting from (6) into (29) yields
where . Since , and, and , we can further obtain as
where the terms and are given by
where represents the -th non-empty subset of and ‘’ represents the set difference.
Moreover, combining (8) and (25), an intercept probability of the MBS-E transmission is obtained as
where is a secrecy rate of the macro-cell transmission. Substituting from (8) into (34) yields
where . Noting that all the random variables , and of (35) are independent exponentially distributed random variables with respective means of , and , we can obtain as
where is given by (33) and can be readily computed as
Similarly, combining (9) and (25), an intercept probability of the SBS-E transmission is given by
where is a secrecy rate of the small-cell transmission. Substituting from (9) into (38) yields
where is given by (33) and the term is obtained as
Iii-B Proposed IC-OAS
This subsection presents the outage probability and intercept probability analysis of macro-cell and small-cell transmissions for the proposed IC-OAS scheme. From (18) and (24), an outage probability of the MBS-MU transmission relying on our IC-OAS scheme is given by
Substituting from (18) into (41) yields
where . Similarly, by using (20) and (24), an outage probability of the SBS-SU transmission for IC-OAS scheme is expressed as
where is an overall data rate of the SBS-SU transmission. Substituting from (20) into (43) and denoting , we have
where . It is very challenging to obtain an exact closed-form expression of . Following the existing literature on multi-antenna systems -, we assume that the channel fading coefficients for different distributed antennas are i.i.d. with the same mean of . Also, the fading coefficients of are assumed to be i.i.d. for different distributed antennas, leading to the fact that of (44) follows an exponentially distributed random variable with a mean of , regardless of the selected antenna . Moreover, we consider an asymptotic case of , for which the equality of holds with the probability of one, since both the mean and variance of random variable approach to zero for . Hence, using (17) and considering the i.i.d. case, we can rewrite (44) as
for . Letting and using Appendix B, we obtain from (45) as
where is the number of distributed antennas. Moreover, denoting and using (B.9) of Appendix B, we can obtain an asymptotic outage probability of in the high SNR region as
for , wherein . In addition, combining (22) and (25), an intercept probability of the MBS-E transmission for IC-OAS scheme is obtained as
Substituting from (22) into (48) yields
where and . Assuming that the fading coefficients of are i.i.d. exponentially distributed random variables for different distributed antennas, we can obtain that of (49) is exponentially distributed with a mean of . Thus, combining (17) and (49) yields
where . Similarly to (45), we also consider an asymptotic case of , for which the random variable of approaches to with the probability of one, leading to . Noting that and are independent exponentially distributed random variables with respective means of and , we arrive at