Cooperative Spectrum Sharing with Space Time Block Coding and Non-orthogonal Multiple Access Md Fazlul Kader, and Soo Young Shin School of Electronic Engineering, Kumoh National Institute of Technology, Republic of Korea
[email protected],
[email protected]
Abstract—In this paper, we have proposed a novel two-phase cooperative spectrum sharing protocol on the basis of Alamouti space time block coded (STBC) non-orthogonal multiple access. The network scenario comprising of a primary transmitterreceiver pair and a secondary transmitter-receiver pair. During the first two time slots, the primary transmitter transmits two STBC primary symbols to the cooperative secondary transmitter. The secondary transmitter acting as a decode-and-forward relay for the primary system is allowed to transmit its own secondary signal superposed on the STBC coded primary signal in exchange of cooperation during the next two time slots. Simulation and theoretical results demonstrate the efficacy of the proposed protocol compared to the conventional super positing coding based overlay scheme in terms of the outage probability and the ergodic capacity. Index Terms—Cooperative relaying, cognitive radio, space time block coding, non-orthogonal multiple access, spectrum sharing.
I. I NTRODUCTION To figure out the spectrum scarcity problem, cognitive radio (CR) was first investigated by J. Mitola III [1]; it has gained a substantial interest to the wireless research community. Cooperative diversity which has recently been incorporated into cognitive radio networks (CRNs) is another important technology for wireless networks to combat fading and ameliorating performance. Furthermore, multi-antenna deployment at wireless nodes may raise system capacity and significantly enhance the transmission reliability without causing bandwidth expansion [2]. Alamouti space time block coding (A-STBC) proposed in [3] is a method of encoding which can achieve full diversity gain with linear processing at the receiver; it does not need to sacrifice its data rate. Outage performance of the cooperative networks using A-STBC is investigated in [4], [5]. But in these works [4], [5], the authors did not consider the CR spectrum sharing environment. Performance of the non-cooperative CR networks using A-STBC is investigated in [6]. The authors investigated the capacity and the bit error rate for the secondary network under spectrum sharing environment in [6]. Nonorthogonal multiple access (NOMA) using successive interference cancellation (SIC) is an another promising technique [7]– [9] for future wireless networks for enhancing the spectrum efficiency. In NOMA, multiple user’s signals are superimposed in the power domain and the SIC process is implemented at the receiver. A low power is assigned to the users having high channel gains and a high power is assigned to the users
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having low channel gains. Consequently, the users with better channel status can decode their own information by applying SIC. On the contrary, the users having low channel gains do not perform SIC and assume other user’s signal having better channel conditions as a noise. Superposition coding (SC) based collaborative primarysecondary transmission schemes under single relay scenario are proposed in [10]–[13], where a secondary user (SU) gets the opportunity to access the licensed spectrum only in 2nd transmission phase. The outage probability (OP) is investigated in [10], [13] whereas only the data rate is investigated in [11], [12]. In [13], the authors extended the work proposed in [10] by considering two antennas at the secondary transmitter (ST). At phase-1, the ST receives the primary transmitter’s (PT’s) signal by both antennas and are combined using maximal ratio combining (MRC) whereas the ST is transmitting with a randomly selected single antenna at phase-2. The channel gain between the ST and the primary receiver (PR) has no impact on the performance of the primary system (PS) in [10], [13] which may not be a feasible solution in a practical scenario. However, none of these works investigated STBCNOMA in the CR spectrum sharing context. The integration of STBC and NOMA in CRNs will further boost the spectral efficiency and increase reliability by sacrificing complexity. However, it is desirable that the future radio devices will have higher processing capabilities which can be observed from the existing channel coding technologies such as Turbo decoder. In this work, we have proposed a cooperative spectrum sharing protocol in CRNs by applying STBC and NOMA where the ST acting as a decode-and-forward (DF) relay, gets opportunity to access the channel with the primary user (PU) in exchange of cooperation. Our contributions can be summarized as follows:
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•
• •
We propose a novel cooperative spectrum sharing protocol, where a PU can use whole portion of its time slots and spectrum without leasing to the SU. The ST co-exist with the PU in phase-2 by allocating its power to forward the primary symbol and its own transmission based on the NOMA approach. We investigate the OP and the ergodic capacity (EC) for both the PS and secondary system (SS). Closed-form expressions of the primary and secondary outage probabilities over Rayleigh fading channel are derived.
ICUFN 2016
Fig. 1: System model under consideration. TABLE I (a): The transmission and the encoding sequence for the two-branch STBC in Phase-1 t1 t2
Ptx0 x p0 -x∗p1
Ptx1 x p1 x∗p0
TABLE I (b): The transmission and the encoding sequence for the two-branch NOMA-STBC in Phase-2 t3 t4
Stx0 √ z0 = ΦPST X p0 + (1 − Φ)PST Xs0 √ -z∗1 =- ΦPST X∗p1 +(- (1 − Φ)PST X∗s1 )
Proposed protocol shows better performance compared to the conventional SC based overlay model [12]. The remaining part of this paper is organized as follows. In Section II, we introduce the cooperative relay based system and channel models. Outage analysis of the proposed scheme is illustrated in Section III. Theoretical results are validated by the simulation results, and are presented in Section IV, and finally we have drawn conclusion of this paper in Section V. •
II. S YSTEM AND C HANNEL M ODELS We consider a half-duplex two-phase cooperative spectrum sharing protocol comprising of a PS with a PT-PR pair and a SS with a ST-SR pair. The system model of our concern is shown in Fig. 1. For the simplicity of the analysis, we assume that the direct link between the PT and PR is not strong enough to achieve its target rate RP due to poor channel conditions, shadowing or physical obstacles etc. [14] and is thus not considered for data communication. In such situation, the PT seeks cooperation from the neighboring nodes to forward data to its receiver with the predetermined target rate, RP . Therefore, in our proposed system model, the communication between the PT and the PR is only possible with the help of the ST which acts as a relay to cooperate the primary transmission. The ST is considered as a base station and equipped with two transmit antennas and one receive antenna. The PT is equipped with two transmit antennas whereas both the PR and the SR are equipped with single antenna only. The system configuration is considered in such a way that the Alamouti two-branch
Stx1 √ z1 = ΦPST X p1 + (1 − Φ)PST Xs1 √ z∗0 = ΦPST X∗p0 + (1 − Φ)PST X∗s0
transmit diversity with one receiver [3] can be implemented for both phases. It can also be considered that PR ignores the PT’s signal during phase-1, the strength of which is always weaker compared to phase-2 signal; it can be considered as a selection combining [12]. Assume that the channel over all the links are subject to Rayleigh flat fading with additive white Gaussian noise (AWGN) and all the signals follow independent fading path to avoid correlation. In Rayleigh flat fading, αi, j is the link gain between any two nodes i and j. We assume that the channel coefficient hi, j is a independent and identically distributed Gaussian random variables with zero mean and variance λi, j , i.e., hi, j ∼ CN(0, λi, j ). Therefore, the link gain αi, j is denoted by αi, j = |hi, j |2 , where αi, j is an exponentially distributed random variable with mean value or scale parameter λi, j (λi, j >0) [15]. Additionally, assume that the receivers have the full knowledge of the channel state information and the channel coefficients remain static during the both transmission phases. Note that bold face letters denote vectors. The transmit power at PT and ST is denoted as PPT and PST respectively as well as ρ represents the transmit signal to noise ratio (SNR). Subscript P denotes primary and S denotes secondary. During cooperation, primary transmission is carried out over two phases through the help of the ST. During phase-1, at a given symbol period, two primary symbols x p0 and x p1 are transmitted simultaneously from the transmit antenna Ptx0 and Ptx1 respectively. In the next symbol period, the complex conjugates of x p0 and x p1 are transmitted. The transmission
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and the encoding sequence for the two-branch STBC in phase1 is shown in Table I (a). The achievable data rate of the link PT→ST is then given as follows [16] 1 ρ = log2 (1 + ||h||2 ) 2 2 where the channel vector h can be represented as h0 h1 h= −h∗ h∗ CP1
1
CP2 =
(1)
=
0
where h0 and h1 are the channel coefficients from 1st and 2nd transmit antenna of the PT to the receive antenna of the ST. Note that the factor 21 represents that the overall transmission is split into two phases. On the other hand, the factor of ρ2 in (1) accounts for the fact that the total transmit power of the transmitter in A-STBC is equally distributed to the antennas. Let λh0 and λh1 are the channel means from 1st and 2nd transmit antenna of the PT to the receive antenna of the ST respectively. Assume that λh0 = λh1 =λh . Under this assumption the achievable data rate of the link PT→ST is then given as follows CP1 =
of the links ST→PR and ST→ SR are respectively given as
1 ρ 1 log2 (1 + ∑ |hi |2 ) 2 2 i=0
1 log2 (1 + 2
1 log2 (1 + 2
CS =
1 2Φ 1 2β
1
∑ |gi |2
i=0
1
∑ i=0
1 2 ρΦ 1 2 ρβ
)
|gi |2 + ρ1 1
∑ |gi |2
i=0
1
)
(3)
∑ |gi |2 + 1
i=0
1 1 1 log2 (1 + ρβ ∑ |ei |2 ) 2 2 i=0
(4)
Hence, the maximum end-to-end capacity of the primary link is represented as Ce2e = min(CP1 ,CP2 )
(5)
Therefore, the EC of the PS and the SS is given respectively as follows
(2)
CPE = E[Ce2e ]
(6)
CSE = E[CS ]
(7)
where E represents the expectation operator. In the 2nd transmission phase, the composite signal z0 and z1 as shown in Table I (b) are simultaneously transmitted from the transmit antenna Stx0 and Stx1 of the ST respectively during time slot 3. Moreover, during time slot 4, the complex conjugates of z0 and z1 are transmitted. Note that the symbols XP0 and XP1 contain the identical information as x p0 and x p1 from phase 1 whereas XS0 and XS1 are the secondary symbols. Assume that the channel condition between the ST and SR is better than the channel condition between the ST and PR i.e., αST −SR > αST −PR . Let, Φ(0 ≤ Φ ≤ 1) is the power allocation factor of the ST. According to the NOMA protocol [7], more power ΦPST is allocated to relay the primary traffic and less power (1 − Φ)PST or β PST is allocated for the transmission of the own secondary signal where Φ + (1 − Φ)(= β ) = 1 but Φ > β . So, the corresponding SR will recover its signal by using SIC and the PR will recover its signal by considering SU signal as noise. The fractional transmit power allocation (FTPA) method described in [8] is assumed for NOMA. Let g0 and g1 are the channel coefficients from 1st and 2nd transmit antenna of the ST to the receive antenna of the PR as well as e0 and e1 are the channel coefficients from 1st and 2nd transmit antenna of the ST to the receive antenna of the SR. Again, Let λg0 , λg1 and λe0 , λe1 are the channel means from 1st and 2nd transmit antenna of the ST to the receive antenna of the PR and SR respectively. Assume that λg0 = λg1 =λg and λe0 = λe1 =λe . Under this assumption the achievable data rate
III. O UTAGE P ROBABILITY A NALYSIS This section presents the closed-form solution of the OP for the PS and the SS for our proposed spectrum sharing protocol. Here, we consider that SIC is implemented at the SR. The PS is in outage if the cooperative phases are unable to satisfy the predetermined primary target rate RP . So, the OP of the PS can be expressed as PPOUT = Pr {min(CP1 ,CP2 ) < RP }
= [1 − (1 − Pr {CP1 < RP })(1 − Pr {CP2 < RP })]
(8)
In (8), the cumulative distribution functions (CDFs) of the corresponding links can be represented as 1
Pr {CP1 < RP } = Pr { ∑ |hi |2 < Γ1 } i=0
= 1 − exp(−
Γ1 1 Γ1 i 1 ) ∑( ) λh i=0 λh i!
(9)
1
Pr {CP2 < RP } = Pr { ∑ |gi |2 < Γ2 } i=0
= 1 − exp(− 2RP
Γ2 1 Γ2 i 1 ) ∑( ) λg i=0 λg i!
(10)
2Rth , Rth < Φ < 1 and where Γ1 = 2(2 ρ −1) , Γ2 = ρ{Φ−(1−Φ)R th } Rth +1 Rth = 22RP − 1. On the other hand, the SS is in outage if the data rate from the PT to ST or ST to SR or both links are unable to satisfy
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4
3
ρ=10, SC based overlay ρ=10, Proposed STBC− NOMA ρ=15, SC based overlay ρ=15, Proposed STBC− NOMA
1.8 Secondary ergodic capacity (bits/s/Hz)
3.5 Primary ergodic capacity (bits/s/Hz)
2
ρ=15 dB, SC based overlay ρ=15 dB, Proposed STBC−NOMA ρ=25 dB, SC based overlay ρ=25 dB, Proposed STBC−NOMA
2.5 2 1.5 1 0.5
1.6 1.4 1.2 1 0.8 0.6 0.4
0 0.55
0.6
0.65
0.7 0.75 0.8 0.85 Power allocation factor, Φ
0.9
0.95
0.2 0.05
1
Fig. 2: Ergodic capacity comparison of the PU employing SIC at the SR.
0.1
0.15
0.2 0.25 0.3 0.35 Power allocation factor,β=1−Φ
0.4
0.45
Fig. 4: Ergodic capacity comparison of the SU employing SIC at the SR. 0
10 0
ρ=10 dB
10
ρ=15 dB −1
Secondary outage probability
Primary outage probability
10
SC based overlay −2
10
ρ=25 dB
−3
10
Proposed STBC−NOMA
ρ=15 dB Proposed STBC−NOMA
−4
10
Lines: Theoretical results Markers: Simulation results
Lines: Theoretical results Markers: Simulation results
−2
10
−5
10
0.55
0.6
0.65
SC based overlay
−1
10
0.7 0.75 0.8 0.85 Power allocation factor, Φ
0.9
0.95
1
Fig. 3: Outage probability comparison of the PU employing SIC at the SR.
0.05
0.1
0.15
0.2 0.25 0.3 0.35 Power allocation factor, β=1−Φ
0.4
0.45
Fig. 5: Outage probability comparison of the SU employing SIC at the SR.
IV. R ESULTS AND D ISCUSSIONS the RP and RS respectively. Note that RS is the predefined secondary target rate. So, the OP of the SS can be written as PSOUT = [1 − Pr {CP1 > RP }Pr {CS > RS }]
= [1 − (1 − Pr {CP1 < RP })(1 − Pr {CS < RS })]
(11)
In (11), the OP of the corresponding links can be represented as 1
Pr {CS < RS } = Pr { ∑ |ei |2 < Γ3 } i=0
= 1 − exp(− where Γ3 =
2(22RS −1) ρ(1−Φ)
Γ3 1 Γ3 i 1 ) ∑( ) λe i=0 λe i!
and Pr {CP1 < RP } is given in (9).
(12)
In this section, we present the theoretical results which are validated by the Monte Carlo simulation results to study the performance of the proposed STBC-NOMA based cooperative spectrum sharing model. We investigate the OP and the EC of both the PS and the SS. We choose RP = RS = 0.5 bits/s/Hz for all cases of our results. For a fair comparison between [12] and our proposed model, we assume that each phase requires half time slot. We have used (8, [12]) to calculate the EC of the conventional superposition coding based overlay scheme. The authors did not analyse OP in [12] whereas we have used (6, 7, [12]) and (11, [12]) to plot the OP of the PS and the SS of [12] respectively to compare with our proposed model. In Fig. 2 and 3, we depict the EC and OP of the PS as a function of Φ where Φ varies from 0.55 to 1. It is noted that the value of Φ is chosen carefully to satisfy the condition Γ2 .
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Fig. 2 demonstrates the simulation results of the EC whereas Fig. 3 shows the theoretical results validated by the simulation results of the outage performance of the PS. We consider two cases of ρ where ρ=15 dB and ρ=25 dB respectively. We let, λh =1 and λg = 0.75 assuming that channel condition between the PT and SR is better than the channel condition between the PT and PR. It can be observed that both the EC and OP improve with increasing Φ. This is because more power of the ST is allocated to relay the primary traffic and less power is allocated for its own secondary transmission. It is also clear that our proposed protocol shows better performance compared to the conventional SC based overlay protocol in terms of the OP and the EC. Moreover, we investigate the EC and the OP of the SS as a function of β where β = 1 − Φ which are shown in Fig. 4 and 5 respectively. It is pointed out that the value of Φ is chosen carefully to satisfy the condition Γ2 and Γ3 . We consider two cases of ρ where ρ=10 dB and ρ=15 dB respectively. We let, λh =1 and λe = 1. It is clear from Fig. 4 and 5 that performance of the SS improves with increasing ρ. It is also shown that our proposed scheme outperforms conventional SC based overlay scheme [12] in terms of the EC and the OP. Lastly, it is obvious that the EC and the OP improve with increasing β . V. C ONCLUSION In this paper, we have proposed a novel cooperative spectrum sharing protocol considering space time block coding and non-orthogonal multiple access scheme. We have investigated the EC and the OP of both the primary network and the secondary network over independent Rayleigh fading channel. It is found that our proposed scheme demonstrates performance improvement in terms of the EC and the OP over conventional super position coding based overlay protocol. Moreover, spectrum sharing protocols under multiple primary users and secondary users scenario will be investigated in future. ACKNOWLEDGMENT This research was supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2016-H8601-16-1011) supervised by the IITP (Institute for Information and communications Technology Promotion)
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