Reciprocally Benefited Spectrum Access Scheme With ... - IEEE Xplore

SPECIAL SECTION ON RECENT ADVANCES IN SOFTWARE DEFINED NETWORKING FOR 5G NETWORKS Received July 1, 2015, accepted July 20, 2015, date of publication August 3, 2015, date of current version August 11, 2015. Digital Object Identifier 10.1109/ACCESS.2015.2464081

Reciprocally Benefited Spectrum Access Scheme With Joint Power and Subcarrier Allocation in a Software-Defined Network DAWEI WANG, PINYI REN, QINGHE DU, AND LI SUN Department of Information and Communications Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Corresponding author: P. Ren ([email protected]). This work was supported by the National Natural Science Foundation of China under Grant No. 61461136001.

ABSTRACT Aiming at realizing ubiquitous spectrum access and improving the spectrum efficiency in a software-defined network, in this paper, we adopt the concept of cognitive radio and propose a joint subcarrier and power allocation (JSPA) scheme for reciprocally benefited spectrum access with secondary users (SUs) cooperating with primary users (PUs). In our proposed JSPA scheme, SUs adopt the decodeand-forward relaying protocol to help PUs in a two-stage way. Meanwhile, a fraction of unallocated licensed spectrum is allocated for the secondary transmission in every stage. However, if the two-stage cooperation still cannot satisfy the PUs’ outage quality-of-service (QoS) requirement, SUs then switch to the access mode and entirely capture the licensed spectrum. Our proposed scheme is to maximize the average transmission rate of SUs through joint optimal subcarriers and power allocation under the constraint of PUs’ outage QoS requirement. The closed-form expressions about the outage probability and average transmission of both PUs and SUs are derived, and we prove the optimality of our scheme. Simulation results show that, compared with the conventional cognitive cooperation scheme, the average transmission rate of SUs is improved. INDEX TERMS Software-defined network, cognitive radio, joint subcarrier and power allocation, reciprocally-benefited spectrum access, cooperative communication. I. INTRODUCTION

With the rapid proliferation of information and communication technologies, such as mobile, social, cloud and big data, ubiquitous accessibility, high bandwidth and dynamic management are crucial for the future computer network [1]. However, due the complexity of the tradition IP networks, the current Internet network hardly supports the demand for future communication which motivates the concept of software-defined networking (SDN) [2]. As a key feature of the 5G network, SDN breaks the vertical integration by separating the network’s control plane and data plane and makes the network switch simple and ubiquitous [3]–[7]. However, in the traditional wireless networks, as the traditional fixed radio spectrum allocation strategy causes network isolation among the current wireless communication networks such as LTE, Wi-Fi, and CDMA, it is hard to realize ubiquitous spectrum access. In addition, due to vast temporal and spatial variations in the usage of allocated spectrum, the traditional spectrum allocation strategy causes low spectrum utilization efficiency according to the US FCC report [8]. To efficiently utilize the scarce spectrum, the concept of 1248

cognitive radio was proposed in [9] which allocates SUs without licensed spectrum to opportunistically share the licensed spectrum with PUs. In SDN, we can employ the cognitive radio technique to realize the ubiquitous spectrum access in interweave, underlay or overlay modes [10]–[12]. For the interweave spectrum sharing mode, SUs detect unused licensed spectrum (known as white space) to access and avoid interference to PUs. For the underlay spectrum sharing scheme, SUs access the spectrum concurrently with the transmission of PUs under the interference temperature constraint of the primary system.1 For the overlay spectrum sharing mode, SUs actively relay PUs’ data packets in exchange for opportunities of spectrum access. Due to the inevitable sensing errors and undetermined interference threshold, it is hard for PUs to be not adversely affected by SUs in the interweave and underlay modes [13]. In addition, the poor direct channel quality further degrades the performance of the primary system and 1 Throughout the paper, we use ‘‘primary system’’ and ‘‘PUs’’ interchangeably and use ‘‘secondary system’’ and ‘‘SUs’’ interchangeably.

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VOLUME 3, 2015

D. Wang et al.: Reciprocally Benefited Spectrum Access Scheme With JSPA in an SDN

lowers the spectral efficiency simultaneously. Cooperative communication, which is considered as a promising spectrum sharing strategy [14], can support the QoS provisioning of PUs and provide spectrum opportunities for SUs in the overlay spectrum sharing mode [15]–[17]. Since better performance is expected for the primary system and the secondary transmission requirement can be satisfied, cooperative communication in the overlay spectrum sharing mode in SDN is a win-win scheme for both systems which will be investigated in this paper. Excellent reviews about cooperative communication for the spectrum sharing in cognitive radio networks of current literatures are given in [18]–[26]. References [18]–[20] study the cooperative communication between PUs and SUs in the time domain. In these schemes, the primary system accomplishes its transmission with the assistance of the secondary system. Due to the advantage of cooperation transmission, the outage performance of the primary system is ameliorated and the transmission time can be shortened. Then, as a reward, SUs can access the licensed spectrum in the remaining time for the secondary transmission. The frequency division multiple access model is considered in [21] where the whole frequency band is divided into two disjoint bands and one is used to assist the primary transmission and the other is used for the secondary transmission. In [22], a flexible channel cooperation scheme is proposed in both decentralized and centralized settings. In this scheme, SUs are allowed to freely optimize the utilization of channels for transmitting primary data along with their own. In [23], the ARQ control signal is used for spectrum sharing. In this strategy, SUs assist the primary system to accumulate credits which are utilized by the secondary system to gain spectrum opportunities of the retransmission slots of the primary system. In [24] and [25], the authors prove that the scaling law of the primary network can be improved when SUs are available to assist PUs. Owing to the flexibility in assigning transmission resources, orthogonal frequency division multiplexing (OFDM) is recognized as a potential technology for spectrum sharing. [26] learns the two-stage decode-and-forward (DF) spectrum sharing protocols which is denoted as LWLZ in OFDM-based cognitive networks. The secondary system decodes the signal which is received from PU in the first stage and utilizes a fraction of subcarriers to forward PUs’ information in the second stage. The remaining spectrum in the second stage is occupied by SUs for their own transmission. However, the resource allocation in the first phase is not considered in above schemes which results in low spectrum efficiency and motivates us to propose a spectrum sharing scheme to efficiently utilize the spectrum. In this paper, we propose a JSPA scheme which will realize ubiquitous spectrum access and improve the spectrum efficiency in SDN. Our scheme considers the power and subcarrier allocation in both two stages which is different from the above schemes. In our proposed scheme, the primary system predicts its achievable outage rate firstly to decide whether to seek cooperation with SUs or not. VOLUME 3, 2015

Once receiving the assistance requirement, SUs will estimate their ability to determine the operation mode. On one hand, if SUs can help PUs to avoid transmission outage, SUs will operate in the cooperation mode in a two-stage way. In the first stage, SUs receive and store PUs’ data. Moreover a fraction of licensed spectrum is allocated for SUs. In the second stage, SUs decode and forward PUs’ data packets. Meanwhile, a part of the unallocated spectrum is assigned to SUs under the constraint of PUs’ outage QoS requirement. On the other hand, if the primary outage is inevitable even with the assistance of SUs, SUs then work in the access mode and capture the licensed spectrum entirely. In our developed JSPA scheme, the joint subcarrier and power allocation problem is studied. With the target to maximize SUs’ transmission rate, we formulate the joint optimization problem. The closed-form expressions for the outage probability and average transmission rate of PUs and SUs are derived and we prove the optimality of our scheme. Simulation results show that compared with the conventional cognitive cooperation scheme, the average transmission rate of SUs improves. The rest of this paper is organized as follows. Section II describes the system model of our developed JSPA scheme. Section III interprets our proposed joint subcarrier and power allocation scheme particularly. The optimal resource allocation problem is formulated and solved in this section. The performance analysis is illustrated in section IV. We conduct extensive simulations in Section V, and Section VI concludes the paper. II. SYSTEM MODEL

We consider a overlay spectrum sharing system in SDN as shown in Fig. 1, where a primary system coexists with a secondary system. In this model, the primary system which includes one primary transmitter (PT) and receiver (PR) pair is delay-constrained. The secondary system which consists of one secondary transmitter (ST) and receiver (SR) pair can cooperate with PUs to relay their data. In our system, the primary system has the right to assign licensed spectrum to SUs while the secondary system does not have any licensed spectrum. This model can capture a SDN scenario, where the PU is a legacy mobile user that communicates with the macro base station over the licensed spectrum while SUs are the moving users with none licensed spectrum. PUs and SUs will exchange messages to control the transmission of both the primary and secondary data. The interference among different secondary systems significantly adds the complexity of the optimization problem, and shall be dealt with as a separate issue on its own right. In our model, ST adopts the DF relaying protocol to help the primary system in the cooperation mode when the direct transmission of PUs experiences outages (e.g., the direct transmission channel quality is serious due to large-scale fading or interference in the primary networks). The optimal cooperative SU selection strategy is not considered in our scheme which can refer to [27] and [28]. We assume 1249


¯ , G and G ¯ are the subcarrier FIGURE 1. The system model of the proposed scheme. (a) The system model of the cooperation mode ( G1 , G 1 2 2 allocation parameters and h1,k , h2,k , h3,k and h4,k are the channel coefficients). (b) The system model of the full access mode (K is the total subcarrier set).

1

that the secondary system is time synchronized with the primary system [29] and both systems experience independent and frequency-selective Rayleigh fading. There are K subcarriers in our system, which are denoted as set K. With OFDM modulated, the channel seen at each subcarrier is modeled as frequency-flat Rayleigh fading [26], [30] which means that the channel state remains invariant within an OFDM symbol and independently varies from one OFDM symbol to another. The knowledge of instantaneous channel state information (CSI) is available for both the primary and secondary systems in our scheme [29]. The channel coefficients of PT → PR and PT → ST links over kth (1 ≤ k ≤ K ) subcarrier are denoted as h1,k and h2,k , respectively. Similarly, the channel coefficients of ST → PR and ST → SR links are denoted as h3,k and h4,k , respectively. The channel power gains of PT → PR, PT → ST, ST → PR and ST → SR are 2 2 γ1,k , h1,k , γ2,k , h2,k , 2 2 γ3,k , h3,k , γ4,k , h4,k . (1)

where (x)+ = max(0, x), η is selected to satisfy PK p k=1 p,k = Pp and Pp is the transmit power budget of the primary system. The transmit power budget of the secondary system is Ps . The subcarriers which are used in the first and second stages are denoted as k and k 0 (1 ≤ k, k 0 ≤ K ), respectively. The power allocated by the secondary system can not exceed its total power budget and satisfies X X ps,k + ps,k 0 ≤ Ps , (4)

1 , 1, σ12 σ22

In our scheme, the primary system has right to allocate the licensed spectrum to the secondary system. We assume that the secondary system has codebooks of PUs to assist primary [31]. The operation mode of the secondary system depends on the primary direct channel quality. Through careful allocating subcarriers and power with the constraint of PUs’ outage QoS requirement, both the primary and secondary systems can benefit.

who follow exponential distributions with parameters 1 σ32

and

1 , σ42

respectively.

To easily analysis the performances of our developed scheme, we assume that all noise variables are cyclic symmetry complex Gaussian random variables with zero-mean and unit variance. The primary and secondary signals are denoted as xp,k and xs,k , respectively. xp,k and xs,k are defined as ( ∗ x } = 1, E{xp,k p,k (2) ∗ x } = 1. E{xs,k s,k The allocated power for each subcarrier by PUs is denoted as pp,k which is acquired by the optimal water-filling method as 1 1 + ) , (3) pp,k = ( − η γ1,k 1250

k0

k

where ps,k and ps,k 0 are PT’s transmit power on the kth and k 0 th subcarrier in the first and second stages, respectively. In our system, we consider the joint allocation of the sets of subcarriers for cooperation and power for each subcarrier in both two stages. To maximize the transmission rate of SUs, we formulate the optimization problem to optimally allocate the subcarrier and power. III. THE JOINT SUBCARRIER AND POWER ALLOCATION SCHEME

A. THE DESCRIPTION OF OUR DEVELOPED JSAP SCHEME

We assume that PR can acquire the CSI of its direct transmission link through feedback to predict its outage events. The instantaneous transmission rate (in one OFDM symbol) of the primary system is Rd , which is given by Rd =

K X

log2 (1 + γ1,k pp,k ).

(5)

k=1 VOLUME 3, 2015


Then the outage probability of PUs’ direct transmission can be calculated as n o d Pout (6) d = Pr R < Rp , where Rp represents the target transmission of the primary system.

system by RTC (Reject-to-Transmission) signal. The primary system then stops its transmission and the secondary system works in the full access mode and utilizes all the licensed spectrum and power for the secondary transmission. B. TRANSMISSION MODES

In this section, we will interpret our proposed two transmission modes of the JSPA scheme in detail. 1) THE FULL ACCESS MODE

FIGURE 2. The critical rate regions of our proposed scheme.

In Fig. 2, we demonstrate the outage region and the direct transmission region. When the direct channel quality of PUs is too serious to support PUs’ target transmission rate Rp , PUs will experience outage. The outage region is divided into two regions: the full access region and the cooperation region, which is shown in the lower part of Fig. 2. In the full access region, the primary system ceases its transmission and the second system employs all its power and all the licensed spectrum to transmit its own signals. In the cooperation region, the secondary system has the ability to guarantee the outage QoS requirement of PUs and a part of spectrum is allocated for the secondary transmission as a reward. Our scheme is implemented as below. When PUs predicts that their direct transmission experiences outage, They will exchange signals with SUs to acquire cooperation. Particularly, PR broadcasts a RTC (Require-to-Cooperate) signal to seek cooperation with the nearby SU. PT acknowledges with an ATC (Acknowledge-to-Cooperate) signal when it receives RTC signal. We assume that the power allocation parameters pp,k and the target rate Rp are embedded in ATC signal and the CSI knowledge between PT and PR is embedded in RTC signal. When ST receives RTC and ATC signals, it will estimate its ability to decide whether to help the primary system. With the CSI knowledge of PT → ST and ST → PR and its power budget constraint, PR achieves its maximum information rate Rmax when ST acts as a pure relay by employing all its power and all the licensed subcarriers for the primary transmission. If the maximum transmission rate of PUs can reach its target rate, PUs and SUs work in the cooperation mode and ST informs PUs by CTC (Confirm-to-Cooperation) signal. On the other hand, if the primary system still experiences outage even with the assistance of ST, ST informs the primary VOLUME 3, 2015

Once receiving the cooperation request, the secondary system will estimate the maximum transmission rate of the primary system with the assistance of ST to determinate the transmission mode. If the transmission rate of the primary system could not reach its target rate with the assistance of the secondary system, the primary system will cease its transmission and the secondary system will operate in the full access mode by occupying all subcarriers and devoting all its power for the secondary transmission. Otherwise, both the primary and secondary systems will work in the cooperation mode. When ST acts as a pure relay, the primary system will acquire its maximum transmission rate. The maximum transmission rate of PUs is calculated as below. In the first stage, PT broadcast its signal to PR and ST and the received signal at PR and ST is √ (7) ypp,k = pp,k xp,k h1,k + n1,k , and yps,k =

√ pp,k xp,k h2,k + n2,k ,

(8)

respectively, where xp,k is PT’ signal on kth subcarrier, n1,k and n2,k are the noise variables at PR and ST on kth subcarrier, respectively. The primary transmission rate Rmax at ST is 1 K

Rmax = 1

1X log2 (1 + γ2,k pp,k ), 2

(9)

k=1

In the second stage, the secondary system adopts the DF relaying protocol to relay PUs’ data. We use k 0 instead of k to denote the subcarrier used in the second stage. The received signal at PR is √ ysp,k 0 = psp,k 0 xsp,k 0 h3,k 0 + n3,k 0 , (10) where xsp,k 0 is the relaying signal, n3,k 0 is noise variable of the channel ST → PR on k 0 th subcarrier and psp,k 0 is ST’s power to relay the primary message. With the optimal MRC rule, the transmission rate of PR is given by Rmax = 2

K 1X log2 (1 + γ3,k 0 psp,k 0 + γ1,k 0 pp,k 0 ), 2 0

(11)

k =1

where psp,k 0 is the power allocated by ST through the optimal water-filling method. It can be calculated 1251


where the factor 1/2 is due to the two-stage transmission. The primary transmission rate at ST is 1 X log2 (1 + γ2,k pp,k ). (16) R1 = 2 k∈G1

¯ 1 ) subcarrier SR receives data from ST through kth (k ∈ G and the transmission rate of the secondary system is X log2 (1 + γ4,k pss,k ), (17) Rs1 =

FIGURE 3. Slot-subcarrier allocation for PUs and SUs.

k∈G¯1

by psp,k 0 =

( τ1

+ γ3,k 0 ) , where K P psp,k 0 = Ps . k=1

−

chosen to satisfy

1

1 (x)+ =

max(0, x) and τ is

The maximum transmission rate of the primary system with SUs’ assistance is max Rmax = min(Rmax 1 , R2 ).

(12)

When Rmax < Rp , the primary system still experiences outage. Then the primary system stops its transmission. At the same time, the secondary system works in the full access mode. Under this condition, the transmission rate of SUs is K X Rs = log2 (1 + γ4,k ps,k ), (13) k=1

where ps,k is the power allocated by the optimal water-filling method for the secondary transmission on kth subcarrier. 2) THE COOPERATION MODE

If the transmission rate of the primary system could reach its target rate with the assistance of the secondary system, both the primary and secondary systems work in the cooperation mode. The secondary system uses a fraction of power to help the primary system to guarantee its outage QoS requirement and ST is compensated by employing a fraction of subcarriers for the secondary transmission. The cooperative transmission is implemented in a twostage way as shown in Fig. 3. In the first stage, the primary system employs G1 subcarriers to transmit its own data and ¯ 1 subcarriers are allocated for SUs, where the remaining G ¯ 1 is the supplementary set of G1 . G1 ⊆ K and G In this stage, PT transmits its signals through subcarriers G1 and the received signals at PR and ST are given by (7) and (8), respectively where k ∈ G1 . Meanwhile, ¯ 1 to transmit its own ST accesses the remaining subcarriers G information which is given by √ (14) yss,k = pss,k xs,k h4,k + n4,k , where xp,k is ST’s signal, n4,k is noise variable at SR on kth subcarrier and pss,k is ST’s transmit power on ¯ 1. kth subcarrier. Here, k ∈ G The transmission rate of the primary system is 1 X Rd1 = log2 (1 + γ1,k pp,k ), (15) 2 k∈G1

1252

¯ 1 is used by The factor 1/2 is removed as the subcarriers in G the secondary system in both stages. In the second stage, the secondary system adopts the DF relaying protocol to relay PUs’ data. As the channel quality varies, a fraction of subcarriers of G1 which are denoted as G2 may guarantee PUs’ transmission requirement. Therefore, we use the set of subcarriers G2 to forward PUs’ data as (10) where k 0 ∈ G2 and G2 ⊆ G1 . The remaining subcarriers ¯ 2 are allocated for ST for in G1 which are denoted as G the secondary transmission to further improve the secondary performance. The signal received at SR is √ (18) yss,k 0 = pss,k 0 xs,k 0 h4,k 0 + n4,k 0 , ¯ 2 , xs,k 0 is the signal of the secondary system, where k 0 ∈ G 0 and pss,k is the power allocated by ST to transmit its own information. PR receives signals from the direct and relay links and adopting the optimal MRC rule, the achieved information rate at PR is 1 X R2 = log2 (1 + γ3,k 0 psp,k 0 + γ1,k 0 pp,k 0 ) 2 0 k ∈G2

1 X log2 (1 + γ1,k 0 pp,k 0 ), + 2 0

(19)

¯2 k ∈G

where the first item of right side is MRC result and the second item of right side is the primary transmission rate through ¯ 2 , the subcarriers G1 − G2 . By using the subcarriers in G secondary system can acquire instantaneous rate as 1 X Rs2 = log2 (1 + γ4,k 0 pss,k 0 ), (20) 2 0 ¯2 k ∈G

In order to satisfy the QoS requirement of the primary system, min(R1 , R2 ) must reach the target transmission rate ¯ 1 subcarof PUs. Meanwhile, the secondary system obtains G ¯ 2 subcarriers to use in the riers to use in both stages and G second stage. Regarding to the full access mode, we adopt the waterfilling method to easily allocate the transmission power for each subcarrier. However, it is hard to allocate the subcarriers and power in the cooperation mode which will be investigated in Section III-C. Specifically, we will jointly allocate the set of subcarriers used for cooperation and the power for each subcarrier to maximum the transmission rate of the secondary VOLUME 3, 2015


system, while assists the primary system, as a higher priority, to reach its target rate. The optimal problem will be formulated and solved in Subsection C. C. RESOURCE ALLOCATION

As it is easy to allocate resource for SUs in the full access mode, we put our emphasis on the subcarrier and power allocation in the cooperation mode. In this section, we will try to allocate subcarriers (eg. G1 and G2 ) and ST’s power (eg. psp,k 0 , pss,k and pss,k 0 ) in two stages to maximize the transmission rate of SUs with constraints of ST’s total power and PUs’ QoS provisioning. The joint power and subcarrier allocation problem can be formulated as max Rs1 + Rs2 G1 ,G2 ≥0,P0   R1 ≥ Rp ,    R ≥ R , 2 p s.t. P 1 X 1 X   Psp,k 0 + Pss,k + Pss,k 0 ≤ Ps ,   2 0 2 0 k∈G k ∈G2

1

k ∈G2

(21) where P , pss,k , psp,k0 , pss,k0 . The upper two constraints guarantee the QoS provisioning of the primary system and the remaining constraint is the total power constraint of SUs. To optimally allocate subcarriers and power, we need to solve a mixed integer programming problem. We can adopt the exhaustive search method to achieve the optimal result. However, it is computationally prohibitive since it involves K i P P total CKi ( CiM ) possibilities of subcarrier sets [32]. M =0

i=0

For example, when K = 32, there will be 1.8530e + 15 possibilities of subcarrier sets. Therefore, in this paper, we use the dual decomposition method to solve this problem in two computationally efficient steps in the following two subsections. The duality gap of JSPA in multi-subcarrier system is nearly zero if the number of subcarriers is large enough, such as K ≥ 32, and it is proved in Section IV. 1) THE DUAL PROBLEM

The Lagrange dual function of (21) can be written as g(βR1 , βR2 , βP ) = max L(G1 , G2 , P), G1 ,G2 ,P

(22)

where L(G1 , G2 , P) is the Lagrange function which is given by (23) at the bottom of this page and βR1 , βR2 ,and βP are Lagrange multipliers who are associated with subcarrier and power allocation variables. Then, the dual optimization problem can be defined as min

βR1 ,βR2 ,βP

g(βR1 , βR2 , βP ),

where βR1 , βR2 , βP ≥ 0. The dual problem is always convex, and we can solve it in the following steps. 2) THE OPTIMAL POWER AND SUBCARRIER ALLOCATION WITH GIVEN DUAL VARIABLES

The dual optimization problem can be computed in the following steps with given βR1 , βR2 and βP points. In the first step, we calculate the optimal vector pss,k , psp,k 0 , pss,k 0 with given sets G1 and G2 . In the second step, we can use the optimal power allocation parameters to figure out the optimal subcarrier sets G1 and G2 . a: THE OPTIMAL POWER ALLOCATION WITH GIVEN G1 AND G2

Supposing that subcarrier allocation parameters are given, we can use the partial derivatives of the Lagrange function (23) to derive the optimal power allocation. The partial derivatives are given by  βp βR2 γ3,k 0 ∂L   = √ − ,   0  ∂p 2 2 2 1 + γ1,k 0 pp,k 0 + γ3,k 0 psp,k 0 sp,k    ∂L βp γ4,k 0 = √ − , (25) ∂pss,k 0 2  2 2 1 + γ4,k 0 pss,k 0    ∂L γ4,k   =√  − βp .  ∂p 2 1 + γ4,k pss,k ss,k Applying the Karush-Kuhn-Tucker conditions, we can acquire the optimal power allocation parameters by setting the partial derivatives equal to zero. The power allocation parameters are obtained as !+   1 1  ∗  p = √ − ,   γ4,k  ss,k 2βp   !  +  1 1 ∗ (26) pss,k 0 = √ − ,  0 γ 2β  4,k p  !+    0 pp,k 0  1 + γ β 1,k R  2  − . p∗sp,k 0 = √ γ3,k 0 2βp

  X X X 1 X 1 1 log2 (1 + γ4,k 0 pss,k 0 ) + βP Ps − pss,k − psp,k 0 − pss,k 0  L(G1 , G2 , P) = 2 0 2 0 2 0 ¯2 ¯1 ¯2 k ∈G2 k ∈G k∈G k ∈G   X X 1 1 +βR2  log2 (1 + γ1,k 0 pp,k 0 + γ3,k 0 psp,k 0 ) + log2 (1 + γ1,k 0 pp,k 0 ) − RT  2 0 2 0 ¯2 k ∈G2 k ∈G   X X 1 + log2 (1 + γ4,k pss,k ) + βR1  log2 (1 + γ2,k pp,k ) − RT . 2 ¯1 k∈G

VOLUME 3, 2015

(24)

(23)

k∈G1

1253


  X X X 1 X 1 1 L(G1 , G2 , P) = log2 (1 + γ4,k 0 p∗ss,k 0 ) + βP Ps − p∗ss,k − p∗ss,k 0  p∗sp,k 0 − 2 0 2 0 2 0 ¯2 ¯1 ¯2 k ∈G2 k ∈G k∈G k ∈G   X X 1 1 +βR2  log2 (1 + γ1,k 0 pp,k 0 + γ3,k 0 p∗sp,k 0 ) + log2 (1 + γ1,k 0 pp,k 0 ) − RT  2 0 2 0 ¯2 k ∈G2 k ∈G   X X 1 log2 (1 + γ2,k pp,k ) − RT . + log2 (1 + γ4,k p∗ss,k ) + βR1  2

b: OPTIMAL SUBCARRIER ALLOCATION

Substituting the optimal power allocation parameters into (23), we can rewrite the Lagrangian function as (27) which is shown at the top of this page. With some mathematical manipulations, the Lagrange function can be rewritten as

−

K X

k 0 ∈G2

k=1

βP p∗ss,k + βp Ps − RT βR1 + βR2 .

(28)

k=1

where Tk1 =

1 1 βR1 log2 (1 + γ2,k pp,k ) + βR2 log2 (1 + γ1,k 0 pp,k 0 ) 2 2 1 ∗ − log2 (1 + γ4,k pss,k ) + log2 (1 + γ4,k 0 p∗ss,k 0 ) 2 1 ∗ ∗ +βP pss,k − pss,k 0 , (29) 2

and Tk20

1 1 = − log2 (1 + γ4,k 0 p∗ss,k 0 ) − βR2 log2 (1 + γ1,k 0 pp,k 0 ) 2 2 1 + βR2 log2 (1 + γ1,k 0 pp,k 0 + γ3,k 0 p∗sp,k 0 ) 2 1 ∗ 1 +βP pss,k 0 − p∗sp,k 0 . (30) 2 2

As only the first and second items on the right-side of (28) involve the subcarrier allocation parameters, we only need to maximize these two items to maximize the Lagrange function. The optimal subcarrier allocation problem is demonstrated as X X Tk1 + Tk20 ). (31) max ( G1 ,G2

k∈G1

k 0 ∈G2

As G2 ⊆ G1 , the k 0 th subcarrier which is in set G2 in the second stage will be in set G1 . As k 0 th is denoted as k in the first stage, therefore we only need to find set G1 that satisfies (Tk1 +Tk20 ) > 0 or (Tk1 +Tk20 ) ≤ 0, Tk1 > 0 in the first stage and set G2 that satisfies (Tk1 + Tk20 ) > 0 in the second stage. Then we can acquire the optimal subcarrier allocation parameters. 1254

As we have acquired the optimal power and subcarrier allocation parameters, then we only need to update the Lagrange multipliers to acquire optimal β = βR1 , βR2 , βP and update it as β t+1 = β t + α t 1β,

(32)

where step size α t

L(G1 , G2 , P) K X X X = Tk1 + log2 (1 + γ4,k p∗ss,k ) Tk20 + k∈G1

(27)

k∈G1

¯1 k∈G

follows a diminishing step-size policy [33], t is update time and subgradients of g(βR1 , βR2 , βp ) are shown as  1 X   1βR1 = log2 (1 + γ2,k pp,k ) − RT ,   2   k∈G 1    1 X   1βR2 = log2 (1 + γ1,k 0 pp,k 0 + γ3,k 0 psp,k 0 )    2 0  k ∈G2    1 X  log2 (1 + γ1,k 0 pp,k 0 ) − RT , + (33) 2 0  ¯2 k ∈ G    P  1 X   1βP = Ps − pss,k − psp,k 0   2 0  ¯1 k∈ G  k ∈G 2    1 X   0 − p .  ss,k   2 0 ¯2 k ∈G

The subgradient method confirms that our proposed scheme converges to the optimal β [33] and we can optimally allocate resource for both systems. The subcarrier and power allocation algorithm is demonstrated in Algorithm 1. IV. PERFORMANCE ANALYSIS

In this section, we will analysis the performances of both the primary and secondary systems in our developed JSPA scheme. A. THE OUTAGE PROBABILITY OF THE PRIMARY SYSTEM

Our scheme utilities the situation that the direct transmission of PUs experiences outage. With ST’s help, the information rate of the primary system can reach its target rate and the secondary system can acquire a fraction of the licensed spectrum for its own transmission. If the transmission rate of PUs still cannot reach its target rate even with SUs’ assistance, PUs experience outage. The outage probability of PUs is given by out out Pout 1 − 1 − Pout p = Pd 1,max 1 − P2,max = 1 − 1 − Pr Rmax < Rp 1 − Pr Rmax < Rp 1 2 × Pr Rd < Rp , (34) VOLUME 3, 2015


Algorithm 1 The Subcarrier and Power Allocation Algorithm 1: The primary system predicts the outage probability of its direct transmission. 2: if Rd ≥ Rp then 3: The primary system transmits its signals directly and the secondary system ceases its transmission. 4: else 5: if Rmax ≤ Rp then 6: The primary and secondary systems work in the full access mode. The primary system ceases its transmission and the secondary system occupies all subcarriers. 7: else 8: The primary and secondary systems work in the cooperation mode. 9: Initialize at t = 1 and β = βRt 1 , βRt 2 , βpt = 10−6 , 10−6 , 10−6 ; 10: repeat 11: Calculating pss,k , psp,k 0 and pss,k 0 according to (26); 12: Calculating G1 and G2 according to (29) and ( 30) with the optimal P; 13: Updating β t+1 = β t + α t 1β according to (33); 14: until

t+1

β 15: − β t ≤ ε. 16: end if 17: end if out where Pout 1,max and P2,max are the outage probabilities of links PT → ST and ST → PR, respectively. To easily analysis the performance, we assume that all channels in the same transmission link have the same channel quality. Therefore, we only derive the average performance of both PUs and SUs. As all channels experience Rayleigh fading, the variables |h1,k |2 , |h2,k |2 , |h3,k |2 , and |h4,k |2 follow the exponential distribution with parameters 12 , 12 , 12 and 12 , σ1 σ2 σ3 σ4 respectively. Hence, the average outage probability of the direct transmission is ! Rp K Pout 2K −1 . (35) d = 1 − exp Pp σ12

Pout 1,max is Pout 1,max

Pout 2,max

VOLUME 3, 2015

K = 1 − exp Ps σ22

2

Rp K

! −1 ,

(36)

and Pout 2,max is demonstrated as at the bottom of this page. Substituting (35),(36) and (37) into (34), we can acquire the closed-form expression for the average outage probability of the primary system. B. THE PROBABILITY OF WORKING IN FULL ACCESS AND COOPERATION MODES

The probability of working in the cooperation mode is out (38) Pcoop = Pout 1 − Pout d 1,max 1 − P2,max . The probability of working in the full access is Pfull = Pout p .

(39)

Substituting (34), (35), (36) and (37) into (38) and (39), we can acquire the closed-form expressions for the average probabilities of operating in the full access and cooperation modes, respectively. The probabilities of working in the full access and cooperation modes are demonstrated in Fig. 4. In this figure, we can observe that the probability of working in the full access mode increases when σ12 decreases. The reason is that the secondary system has finite power to assist PUs and the primary system still experiences outage even with the

FIGURE 4. The probabilities of operating in the full access and cooperation modes for the SUs.

assistance of SUs under condition of serious direct channel quality. However, when σ12 is large, the direct transmission of PUs experiences few outages which lead to low probability to work in the cooperation mode. Furthermore, when Ps increases, the probability of working in the cooperation

 2Rp  2Rp     K −1 K −1 2 2 K 2 K 2  Pp σ1 Ps σ2        exp  exp  1− − ,  2 2 2 2 2 2   Pp σ1 − Ps σ2 Pp σ1 Ps σ2 − Pp σ1 Ps σ2    2Rp = 2Rp     K −1 K −1 K 2 K 2         1 − 1 +  exp  ,  2 2  Pp σ1 Pp σ1 

Pp σ12 = Ps σ22 (37) Otherwise

1255




 X X 1 1 Rp = pcoop  log2 1 + γ1,k 0 pp,k 0  log2 (1 + γ1,k 0 pp,k 0 + γ3,k 0 psp,k 0 ) + 2 0 2 ¯2 k∈G

k ∈G2

× 1 − pcoop − pfull

K X

log2 (1 + γ1,k pp,k ).

(40)

k=1

Rs = pfull

K X

 X X 1 1 log2 1 + γ4,k 0 pss,k + log2 1 + γ4,k 0 pss,k 0 . + pcoop  2 2 0 

log2 1 + γ4,k ps,k

¯1 k∈G

k=1

mode increases. The reason is that large Ps means SUs have more power to relay PUs’ data. However, due to the constraint of channel quality between PT and ST, the probability of working in the cooperation mode remains invariant with tremendous Ps . The probability of working in the full access mode increases when Ps decreases as lower power budget means less power to support the QoS requirement of PUs. C. THE AVERAGE TRANSMISSION RATE

According to our proposed resource allocation scheme, the average transmission rate of the primary system is shown in (40) which is at the top of this page. The average transmission rate of the secondary system is (41), which is also shown as at the top of this page. D. THE PRIMARY POWER SAVING EFFICIENCY

The power saving efficiency of PUs is defined as K P

ρ = Pcoop

pp,k −

P

pp,k

k∈G1

k=1 K P

pp,k

k=1 K P

= Pcoop

pp,k −

P k∈G1

k=1 K P

K P

pp,k − 0 k=1 + Pfull K P pp,k k=1

pp,k + Pfull .

(42)

pp,k

k=1

In our developed JSPA scheme, the power of PUs is allocated by the optimal water-filling method. If the primary system experiences outages, the power for retransmission of can be saved in our scheme. As we consider subcarrier and power allocation in both stages, we can make full use of the spectrum for the secondary transmission. E. THE DUAL GAP OF OUR DEVELOPED JSPA SCHEME

Denote Up and Ud as the optimal objective values of the original and dual problem, respectively. Denote function fk,k 0 : (Ak,k 0 , Pk,k 0 ) → R as fk,k 0 (a, p) = (1 − ak ) log2 (1 + γ4,k pss,k ) + (1 − ak 0 ) log2 (1 + γ4,k 0 pss,k 0 ), 1256

(43)

(41)

¯2 k ∈G

where (

1, k ∈ G1 ak = 0, else,

( 1, k 0 ∈ G2 ak 0 = 0, else,

Ak,k0 = [ak , ak 0 ] and Pk,k0 = [psp,k , pss,k , pss,k 0 ]. Denote the function hk,k 0 : (Ak,k 0 , Pk,k 0 ) → R as hk,k 0 (a, p) = [ak psp,k , (1 − ak )pss,k , (1 − ak 0 )pss,k 0 , (1 − ak ) log2 (1 + γ4,k pss,k ) + (1 − ak 0 ) log2 (1 + γ4,k 0 pss,k 0 )]. (44) As ak and a0k are integers, we can relax them into continuous values to make the problem easy to solve. The optimal value of the relaxed problem is denoted as Ur . Proposition 1: For given Lagrange multipliers, the elements of the optimal allocation variables ak and a0k can be 0 − 1 integers and only one is non-zero, for all k, k 0 ∈ A. Proof: See Appendix A in [34]. Proposition 1 informs that binary allocation variables are retrievable and optimal ones from the dual method for (21), which implicates that if (21) can be solved by its dual problem (zero-duality-gap), the relaxation is tight i.e., Up = Ur = Ud and the dual method will be globally optimal. As mentioned in Proposition 1, it is necessary to look into the dual gap of our scheme to confirm the optimality of dual approach and the tightness of relaxation. Theorem 1: The subcarrier and power allocation problem (21) can be solved through its dual problem (24), when the number of subcarriers K is sufficiently large, and the dual gap is bounded as follows: E0 , (45) K max E{(1 − ak ) log2 (1 + γ4,k pss,k ) + Ud − Ur 6

where E0

=

k,k 0

(1 − ak 0 ) log2 (1 + γ4,k 0 pss,k 0 )}. Proof: See Appendix C in [34]. Theorem 1 reveals that when K is sufficient large, the dual gap of (21) and (24) is zero and we can acquire the optimal solution for our scheme. V. SIMULATION RESULTS

In this section, we will evaluate the performances of our proposed JSPA with empirical parameters. In our simulation, we consider a pair of SUs and a pair of PUs. There are 32 subcarriers and each of them experiences quasi-static VOLUME 3, 2015


frequency-selective Rayleigh fading. To easily simulate our scheme, we set σ22 = σ32 = σ42 = 0 dB. σ12 is tested with various values. The power budgets of the primary and secondary systems are Pp = 10 dB and Ps = 10 dB, respectively. The target transmission rate of the primary system is 3 bps/Hz unless otherwise specified. With these parameters, we can guarantee that both systems can work in the cooperation mode with certain probability. In addition, we will plot the scheme in [26], denoted as LWLZ, for comparison where SUs also employ the outage region of the primary direct transmission to assist the primary transmission during the second stage and transmit the secondary message only during the second stage. A. THE OUTAGE PROBABILITY OF THE PRIMARY SYSTEM

The outage probability of the primary system is shown in Fig. 5. In this figure, we evaluate the outage performance of PUs with respect to different σ12 . When σ12 is large, the direct transmission link is suitable for PUs’s transmission. The primary system experiences few outages and the secondary system has few opportunities to access the licensed spectrum. Under this condition, the performance gap between our proposed scheme and direct transmission scheme is small. When σ12 decreases, the secondary system has more opportunities to help the primary system and the outage performance of our proposed JSPA scheme has prominent improvement. Large Rp makes it difficult for the primary system to avoid outage even with the assistance of SUs. Small Ps means that the secondary system has finite ability to help the primary system. However, low Rp and large Ps make the primary system benefit much even the direct channel quality is weak. As the LWLZ scheme also employ the outage region of the primary direct transmission, therefore, the outage performance of the primary outage probability is the same.

different target transmission rates versus Ps . When Ps increases, the secondary system has more power to assist the primary system. As we only ensure that the transmission rate of PUs reaches Rp , the remaining subcarriers and power will be used for the secondary transmission. Larger power budget means that there will be more power allocated for each subcarrier to relay PUs’ data and few subcarriers used for the primary transmission. Therefore, there are more idle subcarriers for the secondary transmission. Large Rp means that it needs more power and subcarriers to help the primary system and SUs only employ few subcarriers for their own transmission. As our scheme considers the resource allocation in both stages, there are more subcarriers allocated for the secondary transmission than [26] who only considers the resource allocation in the second stage.

FIGURE 6. The radio of the subcarriers allocated for secondary system in the cooperation mode, σ12 = −16dB.

C. THE AVERAGE TRANSMISSION RATE OF THE SECONDARY SYSTEM

In the end, we show the average achieved transmission rate of the secondary system. The average rate is acquired by Rs = Pr{Rc }E Rc + Pr{Rf }E Rf (46)

FIGURE 5. The outage probability of the primary system.

B. THE RADIO OF SUBCARRIER ALLOCATED FOR THE SECONDARY TRANSMISSION IN THE COOPERATION MODE

Fig. 6 shows the fraction of subcarriers allocated for the secondary transmission in the cooperation mode with VOLUME 3, 2015

where Pr(Rc ) and Pr(Rf ) are probabilities that the secondary system operates in the cooperation and full access modes, respectively. E {Rc } and E Rf represent the average transmission rates of the secondary system in the cooperation and full access modes, respectively, which are shown in Fig. 4. The average transmission rate of the secondary system is demonstrated in Fig. 7 and Fig. 8. In Fig. 7, we demonstrate the average transmission rate of the secondary system versus σ12 . This figure shows that the secondary transmission rate will increase when the direct channel quality of PUs is serious. Low σ12 means that it is difficult for the primary system to reach its target transmission rate even with the assistance of SUs. Under this condition, SUs operate in the full access with high probability and devote more power for the secondary transmission. In this figure, we also 1257


modes remain invariant. It is because that the probabilities of working in different modes are determined by the channel quality between PT and ST. This figure also shows that large Rp always causes the secondary system to assign a small fraction of power and subcarriers for its own transmission and the average transmission rate decreases. VI. CONCLUSION

FIGURE 7. Average secondary system rate versus σ12 , Ps = 10dB.

In this paper, we propose a reciprocally-benefited spectrum sharing strategy which jointly allocates subcarriers and power for both the primary and secondary systems in SDN with cognitive ability. The primary and secondary systems both can benefit from this scheme. The primary system experiences few outages with SUs’ assistance and the energy for retransmission can be saved when outage is inevitable. The secondary system can acquire opportunities to access the licensed spectrum without sensing the channels. We formulate the optimization problem and optimally allocate power and subcarriers for PUs and SUs. Performance analysis and simulation results show that our scheme outperforms the traditional schemes. REFERENCES

FIGURE 8. Average secondary system rate versus Ps , σ12 = −16dB.

observe that low target rate makes it easy to guarantee the QoS requirement of PUs. The secondary system can operate in the cooperation mode with high probability. The probability of working in the full access mode decreases which causes few subcarriers allocated for its own. Therefore, low target rate leads to few outages for PUs and low transmission rate for the secondary system. In this figure, we also show the protocol in [26] for comparison. As our proposed scheme makes full use of the subcarriers in both stages for the secondary transmission, the performance of the secondary system in terms of the average information rate improves compared with the scheme in [26]. In Fig. 8, we demonstrate the average transmission rate of the secondary system versus Ps under the condition that σ12 = −16dB. Large Ps means that there is more power for the secondary system to assist the primary system and the probability of operating in the cooperation mode increases. Under this condition, there will be more subcarriers allocated for the secondary transmission in the cooperation mode which is shown in Fig. 6 and the remained power for the secondary transmission also increases. Therefore, the average transmission rate of SUs increases. When Ps is large enough, the probabilities of operating in the full access and cooperation 1258

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VOLUME 3, 2015

DAWEI WANG received the B.S. degree from the University of Jinan, China, in 2011. He is currently pursuing the Ph.D. degree with the Department of Information and Communications Engineering, Xi’an Jiaotong University, China. His research interests include wireless physical-layer security, cognitive radio networks, and cooperative relaying networks.

PINYI REN received the B.S., M.S., and Ph.D. degrees from Xi’an Jiaotong University, China. He is currently a Professor with the Information and Communications Engineering Department, Xi’an Jiaotong University. His current research interests include cognitive radio networks, multiple-input and multiple-output systems, game theory in wireless communications, wireless relay, routing, and signal detection.

QINGHE DU received the B.S. and M.S. degrees from Xi’an Jiaotong University, China, and the Ph.D. degree from Texas A&M University, USA. He is currently an Assistant Professor with the Information and Communications Engineering Department, Xi’an Jiaotong University. His research interests include mobile wireless communications and networking with an emphasis on mobile multicast, statistical QoS provisioning, and cognitive radio networks.

LI SUN received the B.S. and Ph.D. degrees in information and communications engineering from Xi’an Jiaotong University, China, in 2006 and 2011, respectively. Since 2012, he has been with the Department of Information and Communications Engineering, Xi’an Jiaotong University, as an Assistant Professor. His research interests include cooperative relaying networks, wireless physical-layer security, and device-todevice communications.

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