Secrecy Outage and Diversity Analysis of Spectrum-Sharing Heterogeneous Wireless Systems

01/29/2019 ∙ by Xiaojin Ding, et al. ∙ University of Southampton 0

We study the physical-layer security of a spectrum-sharing heterogeneous wireless network in the face of an eavesdropper, which is composed of multiple source-destination (SD) pairs, where an eavesdropper intends to wiretap the signal transmitted by the SD pairs. In order to protect the wireless transmission against eavesdropping, we propose a heterogeneous cooperation framework relying on two stages. Specifically, an SD pair is selected to access the shared spectrum using an appropriately designed scheme at the beginning of the first stage. The other source nodes (SNs) transmit their data to the SN of the above-mentioned SD pair through a reliable short-range wireless interface during the first stage. Then, the SN of the chosen SD pair transmits the data packets containing its own messages and the other SNs' messages to its dedicated destination node (DN) in the second stage, which in turn will forward all the other DNs' data to the corresponding DNs via the backhaul. We conceive two specific SD pair selection schemes, termed as space-time coding aided source-destination pair selection (STC-SDPS), and the transmit antenna selection aided source-destination pair selection (TAS-SDPS), respectively. We derive the secrecy outage probability (SOP) expressions for both the STC-SDPS and for the TAS-SDPS schemes. Furthermore, we carry out the secrecy diversity gain analysis in the high main-to-eavesdropper ratio (MER) region, showing that both the STC-SDPS and TAS-SDPS schemes are capable of achieving the maximum attainable secrecy diversity order. Additionally, increasing the number of the heterogeneous transmission pairs will reduce the SOP, whilst increasing the secrecy diversity order of the STC-SDPS and TAS-SDPS schemes.

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I Introduction

Heterogeneous wireless networks can access the same spectrum resource dynamically with the aid of spectrum sharing techniques [1], [2], which are capable of increasing the system’s efficiency and flexibility, whilst reducing their deployment cost. Recently, the spectrum sharing concept has also been extended to the fifth-generation (5G) systems [3], [4], wherein the licensed and unlicensed spectrum can be flexibly utilized to improve the quality of experience. However, heterogeneous wireless systems may be vulnerable to both internal as well as to external attackers, when they operate independently in non-cooperative scenarios. For example, a hostile attacker may contaminate the legitimate transmission, thus degrading the quality of service (QoS). Furthermore, owing to the broadcast nature of radio propagation, the confidential messages may be overheard by malicious eavesdroppers. Hence, we have to protect the heterogeneous wireless networks against malicious eavesdropping.

Physical-layer security [5]-[7] emerges as an effective method of guarding against wiretapping by exploiting the physical characteristics of wireless channels. Single-input multiple-output (SIMO) and multiple-input multiple-output (MIMO) schemes were conceived in [8], [9] for reducing the secrecy outage probability. Similarly, beamforming techniques were also invoked for improving the secrecy of wireless transmissions [10] and [11]. Moreover, the concept of cognitive jamming was explored in [12], while specially designed artificial noise was used for preventing eavesdropping in [13]. Furthermore, the authors of [14] and [15] explored opportunistic user scheduling conceived with cooperative jamming. More specifically, in [15], the non-scheduled users of the proposed user scheduling scheme were invoked for generating artificial noise in order to improve security in a multiuser wiretap network. Both one-way [16], [17] and two-way [18], [19] relying schemes were conceived for guarding against eavesdropping, demonstrating that relay selection schemes are capable of improving the physical-layer security. This is indeed expected, because they improve the quality of the desired link.

As a further development, physical-layer security has also been designed for heterogeneous wireless networks, supporting a multiplicity of diverse devices. Hence, more efforts should be invested in enhancing the physical-layer security of heterogeneous wireless networks. The secrecy beamforming concept has been proposed by Lv et al. [20] for improving the physical-layer security of heterogeneous networks. Moreover, jamming schemes have been investigated in [21] and [22]. To be specific, in [21], the jammers were selected to transmit jamming signals for contaminating the wiretapping reception of the eavesdroppers. Meanwhile, the interfering power imposed on the scheduled users was assumed to be below a threshold. A comprehensive performance analysis of artificial-noise aided secure multi-antenna transmission relying on a stochastic geometry framework was provided in [22] for -tier heterogeneous cellar networks. In [23], antenna selection was used for improving the security of source-destination transmissions in a multiple antenna aided MIMO system consisting of one source, one destination and one eavesdropper. Furthermore, the co-existence of a macro cell and a small cell constituting a simple heterogeneous cellular network was investigated by Zou [24]. Specifically, the overlay and underlay spectrum sharing schemes have been invoked for a macro cell and a small cell, respectively. Moreover, an interference-cancelation scheme was proposed for mitigating the interference in the underlay spectrum sharing case. In [25], Tolossa et al. investigated the base-station-user association scenarios suitable for protecting the ongoing transmission between the base-station and the intended user against eavesdropping. Additionally, the achievable average secrecy rate was analyzed by exploiting the association both with the “best” and with the th best base-stations.

Against this backdrop, in this paper, we explore the physical-layer security of a heterogeneous wireless network comprised of multiple source-destination (SD) pairs in the presence of an eavesdropper. In contrast to [20]-[25], we investigate the cooperation between different SD pairs for safeguarding against malicious eavesdropping with the aid of a specifically designed cooperative framework, and the main differences between this paper and [20]-[25] are summarized in table 1. Moreover, we propose a pair of cooperation schemes based on source-destination (SD) pair scheduling. More explicitly, against this background, the main contributions of this paper are summarized as follows.

  1. Firstly, we propose a heterogeneous cooperative framework relying on two stages for protecting wireless transmissions against eavesdropping, Specifically, in the first stage, an SD pair will be chosen at the beginning of the transmission slot. Then, other source nodes (SNs) will confidentially transmit their data to the chosen SN via a high-reliablility low-power auxiliary sub-system. In the second stage, the specifically chosen SN transmits the repacked data to its destination node (DN), which will forward the received packets to the DNs of the other SNs via the secure backhaul.

  2. Secondly, we present two specific transmission selection schemes. The first one is termed as the space-time coding aided source-destination pair scheduling (STC-SDPS), while the second one is referred to as the transmit antenna selection aided source-destination pair scheduling (TAS-SDPS). To be specific, an SD pair having the maximal channel capacity will be regarded as the transmission pair with the aid of the shared spectrum in the STC-SDPS scheme. By contrast, in the TAS-SDPS scheme, the “best” antenna of a chosen SD pair will be selected to transmit the repacked data relying on the shared spectrum.

  3. Thirdly, we analyze the secrecy outage probability (SOP) of the proposed STC-SDPS and TAS-SDPS schemes for transmission over Rayleigh fading channels. We also evaluate the SOP of the traditional round-robin transmission pair scheduling (RSDPS) scheme for comparison. Moreover, we evaluate the secrecy diversity gains of both the STC-SDPS and TAS-SDPS schemes as well as the RSDPS scheme, demonstrating that the STC-SDPS and TAS-SDPS schemes are capable of achieving the full secrecy diversity gain.

  4. Finally, it is shown that the SOPs of the STC-SDPS and TAS-SDPS schemes will be beneficially reduced by increasing the number of SD transmission pairs. Furthermore, the STC-SDPS and TAS-SDPS schemes outperform the RSDPS scheme in terms of both the SOP and the secrecy diversity gain attained, demonstrating that the advantages of the proposed heterogeneous cooperative framework improves the security of wireless communications.

The organization of this paper is as follows. In Section II, we briefly characterize the physical-layer security of a heterogeneous wireless network. In Section III, we carry out the SOP analysis of the RSDPS, STC-SDPS and TAS-SDPS schemes communicating over a Rayleigh channel. In Section IV we evaluate the secrecy diversity gain of the proposed STC-SDPS and TAS-SDPS schemes as well as of the RSDPS scheme. Our performance evaluations are detailed in Section VI. Finally, in Section V we conclude the paper.

Ii System Model and SD Pairs Scheduling

Fig. 1: A heterogeneous wireless network consisting of multiple source-destination pairs in the presence of an eavesdropper E.
Fig. 2: Two stages of the proposed cooperation framework for a heterogeneous wireless network.

Ii-a System Model

As shown in Fig. 1, we consider source-destination (SD) pairs in the presence of an eavesdropper, where an SD is denoted by . This source node (SN) communicates with its corresponding destination node (DN) via the dynamically shared spectrum, , as well as with the other SNs via a reliable short-range interface (e.g., Zigbee, Bluetooth, etc.), since we assume that the distance between any two SNs is short. For notational convenience, we let represent the set of the SD pairs. The eavesdropper is denoted by E, which intends to wiretap the legitimate SD pairs with the aid of a wide-band receiver. All nodes are assumed to be equipped with multiple antennas. All DNs are connected via a backhaul [26], which has the ability of exchanging the signals received from the DNs. Moreover, both the main and the wiretap links are modeled by Rayleigh fading [17], where the channel gains of the main links (spanning from the legitimate transmitter to its legitimate receiver) and the wiretap links (spanning from the legitimate transmitter to the eavesdropper) are denoted by , and , , , , , respectively, where , , and denote the number of transmit antennas of , , and E, respectively.

The heterogeneous cooperative framework relies on two stages, as illustrated in Fig. 2. To be specific, an SD pair will be chosen to dynamically access the shared spectrum according to two specific SD scheduling schemes at the beginning of the first stage, where the SD scheduling schemes only consider the links transmitting between the SNs and DNs, without considering the transmitting links between SNs. This is due to the fact that the SNs communicate with each other with the aid of a high-reliability low-power system, hence the outage probability of the links between a pair of SNs is lower than that of the SNs-DNs links. Moreover, in order to help other pairs transmit their data, the chosen SD pair will receive the data of the other nodes through a high-reliability short-range system, and repack the successfully decoded data and its own data. As illustrated in Fig. 2, the sub-packet of a pair is comprised of three parts, which include the index of the SD pair, the length of the repacked data, and the repacked data. In the second stage, the specifically selected SN transmits the packet to its DN. After decoding the packet, the DN forwards the sub-packets to the other DNs relying on the index of the pair in the sub-packet via a high-speed backhaul.

Ii-B Signal Model

In the first stage, let us assume that the SN is selected as the transmitting node. As mentioned above, other SNs will transmit their signal to via a high-reliability low-power system with the aid of a single antenna. Thus, the signal received at transmitted by , , is given by:

(1)

where , , and denotes the transmitted power of relying on a high-reliability low-power system, the transmitted signal of , the channel gain of the

link having zero mean and variance of

, and the thermal noise received at the , respectively.

In the meantime, the signal transmitted by will be overheard by E, which can be expressed as

(2)

where represents the thermal noise received at E.

From (1) and (2), the channel capacity of the and links can be expressed as

(3)

and

(4)

respectively, where , , and denotes the channel bandwidth.

In the second stage, transmits the packet . Thus, the signal received at can be formulated as

(5)

where and denote the transmitted power of , and the thermal noise received at the , respectively. In the space-time coding (STC) case, for simplicity, we assume that the transmitted power of each antenna of is equal, thus, , where represents the available transmit power of each SN. By contrast, we have in the transmit antenna selection (TAS) case.

Similarly to (3), the signal transmitted by will be overheard by E, which can be written as

(6)

Relying on (5), the instantaneous channel capacity of the and of the links in the STC and TAS cases can be formulated as

(7)

and

(8)

respectively, where , , and denotes the variance of thermal noise and .

Using (6), the instantaneous channel capacity of the links can be expressed as

(9)

where in the STC case, and in the TAS case.

Using (4) and (9), the overall capacity of the link spanning from , , the wiretap channel from and can be obtained by using the maximum of the individual channel capacity of these two links in the first and second stages, i.e.

(10)

As mentioned above, given the chosen transmission pair, the signal of the chosen SD will only be transmitted during the second stage. By contrast, the signal of other SDs will be transmitted both during the first state and be forwarded in the second stage. Hence, the signal of the other SDs that are being overheard in the two stages has been given in (3) and (5), respectively. Noting that although only selection combining (SC) is considered, here similar results can be achieved with the aid of maximal ratio combining (MRC). Moreover, as discussed in [16], when independent and different codewords are used in the two stages, MRC becomes inapplicable, whereas SC is still suitable for the E.

Ii-C Space-Time Coding Aided SD Scheduling

In this subsection, we propose a space-time coding aided source-destination scheduling (STC-SDPS) scheme for the sake of improving the security of the SDs’s wireless transmissions, wherein an SD pair having the instantaneous channel capacity will be selected, yielding

(11)

where denotes the index of the selected pair in the proposed STC-SDPS scheme. Hence, the secrecy capacity of the and links in the STC-SDPS scheme is given by and , respectively.

Ii-D Transmit Antenna Selection Aided SD Pair Scheduling

This subsection proposes a transmit antenna selection aided source-destination pair scheduling (TAS-SDPS) scheme. In the TAS-SDPS scheme, the “best” antenna having the maximal channel capacity of all SDs in the set will be chosen to access the shared spectrum for the sake of improving the security of the SDs’ wireless transmissions. Therefore, based on (7), the SD pair scheduling scheme in the TAS-SDPS can be formulated as

(12)

where represents the index of the selected pair in the TAS-SDPS scheme, and denotes the index of the chosen antenna of , yielding:

(13)

Therefore, the secrecy capacity of and in the TAS-SDPS scheme can be formulated as and , respectively.

Iii Secrecy outage analysis over Rayleigh Fading Channels

In this section, we present our performance analysis for the RSDPS, STC-SDPS and TAS-SDPS schemes for transmission over Rayleigh fading channels. The secrecy outage probability (SOP) expressions of the RSDPS scheduling as well as of the STC-SDPS and TAS-SDPS scheduling are derived.

Iii-a Conventional RSDPS Scheme

This subsection provides the SOP analysis of the traditional RSDPS scheme used as a benchmarking scheme. In the conventional RSDPS scheme, each SD pair in the set will be chosen to transmit with an equal probability. Therefore, according to the definition of SOP [7], we can obtain the SOP of the signal arriving from and in the first as well as second stage for the RSDPS scheme relying on the pair formulated as

(14)

and

(15)

respectively, where is a predefined secrecy rate. Upon combining (7), (9) and (10), we arrive at

(16)

and

(17)

respectively, where we have , and

. Furthermore, performing SD pair selection in the RSDPS scheme is independent of the random variables (RVs)

and . For simplicity, given the SD transmission pair , we assume that the fading coefficients for , , of all main channels are independent and identically distributed (i.i.d.) RVs with the same mean, denoted by . Moreover, we also assume that the fading coefficients for , , of all wiretap links are i.i.d RVs having the same average channel gain denoted by , which is a common assumption widely used in the cooperative communication literature. Hence, according to (A.6) and (A.7), (16) and (17) can be obtained.

Hence, the SOP of the system investigated relying on can be defined as

(18)

where , and is the data rate of a pair of SNs links.

As mentioned above, in the RSDPS scheme, each SD pair has an equal probability to be chosen. Furthermore, using the law of total probability [29], we can obtain the SOP for the RSDPS scheme as

(19)

Iii-B Proposed STC-SDPS Scheme

Let us now analyze the SOP of the STC-SDPS scheme in this subsection. In the STC-SDPS scheme, an SD pair having the maximal channel capacity will be selected to participate in transmitting the messages from the source to the destination. As discussed in (11), the index of the chosen pair associated with the STC-SDPS scheme is denoted by . Hence, the SOP of the signal arriving from and under the STC-SDPS scheme with the aid of the pair can be shown to be

(20)

and

(21)

respectively.

Substituting and from (7), (9)-(10) into (20) and (21) yields

(22)

and

(23)

respectively.

In the spirit of [27], it is shown that performing the optimal user selection for the SD pairs can be viewed as being equivalent to the random pair selection for the E. Thus, using (11), both (22) and (23) can be expanded as

(24)

and

(25)

respectively.

Using (A.10) and (A.11), both (24) and (25) can be obtained. Similarly to (18), the SOP of the STC-SDPS scheme may be formulated as

(26)

where is given by , since for simplicity, we assume that the channel gains of each pair of SNs are independent and identically distributed (i.i.d).

Iii-C Proposed TAS-SDPS Scheme

In this subsection, we present the SOP analysis of the TAS-SDPS scheme. As shown in (12), let denote the index of the chosen antenna of an SD pair under the TAS-SDPS scheme. Thus, we can formulate the SOP of the signal impinging from and under the TAS-SDPS scheme with the aid of the pair as

(27)

and

(28)

respectively.

Using (8)-(10), both (27) and (28) can be rewritten as

(29)

and

(30)

respectively, where we have , and . Similarly to (24) and (25), based on (13), we arrive at:

(31)

and

(32)

respectively.

Finally, using (A.17) and (A.18), both (31) and (32) can be obtained. Moreover, relying on the definition in (18), the SOP of the investigated system relying on the proposed TAS-SDPS scheme can be expressed as:

(33)

Iv Secrecy Diversity Gain Analysis

In this section, we present the secrecy diversity analysis of the RSDPS, STC-SDPS, and TAS-SDPS schemes in the high MER region for the sake of providing further insights from (16), (17), (24), (25), (31) and (32) conceiving both the conventional RSDPS as well as the proposed STC-SDPS and TAS-SDPS schemes.

Iv-a Traditional RSDPS Scheme

This subsection analyzes the asymptotic SOP of the conventional RSDPS scheme. In the spirit of [28], the traditional diversity gain is defined as

(34)

which is used for characterizing the reliability of wireless communications, where and denote the signal-to-noise ratio (SNR) of the destination node and the bit error ratio (BER), respectively. However, we can observe that the SOPs of the RSDPS, STC-SDPS, and TAS-SDPS schemes are independent of the SNR, hence the definition of the traditional diversity gain may not perfectly suit our SOP analysis. Moreover, as shown in (16), (17), (24), (25), (31) and (32), the SOP of the RSDPS scheme is related to the main channel as well as to the eavesdropping channels and . For notational convenience again, let denote the MER. In spirit of the above observation, we define the secrecy diversity gain as the asymptotic ratio of the logarithmic SOP to the logarithmic MER as , which is mathematically formulated as

(35)

Meanwhile, in (35), the SOP behaves as in the high MER region, which means that upon increasing the diversity gain , decreases faster in the high MER region.

Using (35), the secrecy diversity gain of the RSDPS scheme can be expressed as

(36)

Moreover, using the inequality , , and
into (16), we have

(37)

Based on (B.12) and (B.13), (37) can be reformulated as (38) shown at the top of the following page.

(38)

 

Combining (36) and (38) yields

(39)

Furthermore, in the high-SNR region we can observe from (17) that as the transmit power tends to infinity, approaches zero. Substituting the inequality , , and into (18) yields

(40)

Similarly to (37), (40) can be reformulated as (41) shown at the top of the following page, where , ,