1. Introduction
Due to the traditional fixed spectrum allocation, the problem of spectrum scarcity is becoming sharply prominent with the increasing demand of wireless users and applications. Spectrum measurements indicate that the licensed spectrum is largely under-utilized ranging from as low as 15% to 85%, which varies significantly over time and geography [1,2]. Cognitive radio (CR) has been proposed as an effective way to enable an efficient utilization of the licensed spectrum by allowing the unlicensed (secondary) systems to operate in licensed spectrum bands of the licensed (primary) systems while the interference caused by the secondary systems below the tolerable levels [3-6].
Most spectrum sharing protocols are under the condition that the primary direct transmission is good enough, such that the primary system can tolerate additional interference caused by the secondary system [7-12]. In this way, the secondary system will be permitted to access the primary spectrum and works simultaneously with the primary system if it does not affect the primary QoS. [7] and [8] studied the optimal power allocation which maximizes the secondary achievable rate subject to the interference power constraint at the primary receiver, in order to protect primary transmission. In [9], a robust power control scheme is proposed to guarantee the interference temperature of the PUs through operating in the network-centric manner, and keeps the fairness between the SUs through link gain pricing. [10] studied optimization algorithms for decision making to optimize radio resource usage in centralized and decentralized cognitive wireless networks. [11] studied the weighted sum rate maximization problem which maximizes the total throughput also known as the sum rates of all the users while avoiding the interference of unlicensed band secondary users from overwhelming the licensed band primary users. However, the above spectrum sharing strategies cannot work when the direct transmission link of primary system is not good enough to guarantee its reliable transmission. In this case, it is effective to apply cooperative diversity in cognitive systems [13].
Cooperative relaying predominates in spectrum sharing field because of its ability to take advantage of user diversity and improve capacity and reliability in wireless network [14-16], especially when the primary system cannot achieve its QoS, i.e., target rate, through the direct transmission link. [17-21] studied different cooperation forms in cognitive radios. The use of cooperative relaying for the secondary transmissions with a primary user’s QoS constraint is discussed in [18], for which a diversity-multiplexing trade-off is developed. [19] proposed a spectrum sharing protocol based on cooperative decode-and-forward relaying where the outage probability of primary system will not be larger. [20] proposed new robust CR cooperative relay beamformers where either the total relay transmit power or the cognitive destination signal-to-interference-and-noise ratio is optimized subject to a constraint on the primary receiver outage probability. [21] proposed jointly optimizing the beamforming vector and power allocation for the secondary transmitter in order to maximize the rate for the secondary system while meeting the rate requirement for the primary system.
Most of existing works concentrate on secondary transmission rate maximization with only considering the primary system achieves its QoS. However, some service of secondary system, e.g., multimedia applications, may also need QoS guarantee. In this paper, we propose a sum transmission rate maximization based cooperative spectrum sharing protocol, in which both the QoS of primary and secondary systems can be guaranteed. Specifically, the primary signal is forwarded by the selected secondary transmitter with a fraction of its power to achieve the target rate. As a reward, it can achieve its own target rate by using the remaining power to transmit its own signal. We study the secondary user selection and optimal power allocation such that the sum transmission rate of primary and secondary systems is maximized, while the QoS of both primary and secondary system can be guaranteed.
The main contributions of this paper are summarized as follows. First, a sum transmission rate maximization based cooperative spectrum sharing protocol is proposed, where both the primary and secondary systems can achieve their target rate. Second, secondary user selection and optimal power allocation is derived in the proposed spectrum sharing protocol, such that the sum transmission rate of primary and secondary systems is maximized, while the QoS of both primary and secondary system can be guaranteed. Finally, Simulation results are shown to demonstrate the efficiency of the proposed spectrum sharing protocol.
The left of this paper is organized as follows. The system model and the proposed spectrum sharing protocol are presented in Section 2. And in Section 3, we analyze the optimal power allocation. Computer simulation results are demonstrated in Section 4 to illustrate the performance of the proposed spectrum sharing strategy. Finally we make a conclusion in Section V.
2. System Model
We consider an underlay cognitive radio wireless network and the system configuration is shown in Fig. 1. The primary system consists of a primary transmitter (PT) and a primary receiver (PR), which supports relaying function [17-19]. The secondary system comprises of L secondary transmitters (STi), i ∈ {1,2,3,...,L} and a common secondary receiver (SR), which is seeking to exploit possible transmission opportunities. We assume that the secondary system can emulate the radio protocols and system parameters of the primary system.
Fig. 1.System model
The channels over links PT → PR, PT → STi, PT → SR, STi → PR, and STi → SR are modeled on Rayleigh flat fading with channel coefficients denoted by h1, h2,i, h3, h4,i and h5,i, respectively. We assume all channels obey complex Gaussian distribution, i.e., j = 1, 3 and n = 2, 4, 5, where v is the path loss exponent and dj, dn,i are the normalized distance between the respective transmitters and receivers. This normalization is done with respect to the distance between PT and PR, i.e., d1 = 1. The instantaneous channel gain is denoted as rj = | hj|2 or rn,i = | hn,i|2. The variances of the additive white Gaussian noise (AWGN) at all receivers are assumed to be identical and denoted as σ2. The primary and secondary signals are denoted as xp and xs with zero mean and unit variance, i.e., The transmit power at PT and ST is denoted as Pp and Ps, respectively.
3. Secondary User Selection and Performance Analysis
3.1 Secondary user selection
When PT → PR link experiences a poor link quality due to path loss, shadowing, or interference (e.g., when the primary user moves to the cell edge in a primary cellular network), causing the achievable primary rate to fall below a target rate. PT will seek cooperation from neighboring secondary transmitter to enhance its transmission performance by sending out a request-to-cooperate (RTC) signal, in which the primary target rate is embedded. This RTC will be responded by PR with an acknowledge-to-cooperation (ATC) signal.
Upon receiving RTC and ATC signals, STi is able to estimate channel gains r2,i and r4,i. Accordingly, STi decides whether the primary and secondary systems can achieve their target rates when STi accesses to the primary spectrum by calculating the maximum instantaneous rate, when STi uses all of its power to relay primary and secondary signals, respectively.
where are the maximum achievable rates of PT → STi and STi → PR links, respectively.
We denote It is clear that when STi, ∀i ∈ D, accesses to the primary spectrum, both primary and secondary system can achieve their target rates.
Each secondary transmitter STi, ∀i ∈ D, now starts a countdown with initial value
where C is a normalization constant. It is obviouse from (1), (2) and (3) that STb, where b = argminTi, will provide the maximum sum transmission rate for the primary and secondary systems.
Therefore the best secondary transmitter STb has its timer reduced to zero first, and it broadcasts a confirm-to-cooperate (CTC) signal to identify its presence. All other STi, i ∈ D\{b} will back off after hearing CTC. Upon receiving CTC, the primary system is aware that its target rate can be achieved through cooperation and it switches into a two-phase DF relaying mode with STb being the relay node. Otherwise, the primary system do not receive CTC, i.e., |D| = 0, the primary system will work with direct transmission and the secondary system will remain silent.
3.2 Performance analysis
In this section, we will derive the achievable rate of primary and secondary systems with STb accessing to the primary spectrum by the following two-slot cooperative transmission.
In the first transmission slot, PT broadcasts its signal. The achievable rates of PT → PR, PT → STb, PT → SR links can be given as
Then STb generates a composite signal zs by linearly combining the regenerated xp with power αPs (0 < α < 1) and the secondary signal xs with power (1 - α) Ps. Thus
In the second transmission slot, STb broadcasts zs. Thus, the achievable rate at PR can be given as
The achievable rate of PT → SR link is obtained depending on whether SR can successfully decode the primary signal in the first transmission slot
where RPT is primary target rate.
Thus, the primary and secondary achievable rate over two transmission slots can be given as
4. Optimal Power Allocation
In this section, we seek optimal power allocation α to maximize the sum transmission rate of primary and secondary systems under the condition that both of the primary and secondary systems achieve their target rates. This optimization problem can be formulated as
subject to
where RST is the target rate of secondary system, which can be chosen depending on the service of the secondary system. The different importance data rate for PR and SR can be reflected by choosing different target rate RPT and RST.
From (9), we can find that Rp may have two different values
where
Thus, to satisfy the first condition of (12), we can obtain
where It is easy to find that αmin is larger than 0. We can also find that the primary achievable rate should be larger than its target rate, i.e., when the secondary system uses all of its power to forward the primary signal. Otherwise, the secondary system cannot help the primary system achieve the target rate and it will not have chance to be allowed to access the primary spectrum. Thus, we can obtain then it is easy to find αmin < 1.
From (8), we can observe that Rs has two different values. Thus, we will obtain the optimal power allocation in the following two cases with different values of Rs.
Case A: when R13 ≥ RPT,
To satisfy the second condition of (12), we can obtain
where R20 = 22RST - 1. It is easy to find that αmin is smaller than 1. We can also find that the secondary achievable rate should be larger than its target rate, i.e., when the secondary system uses all of its power to transmit its own signal. Otherwise, the secondary system will not be willing to help forward the primary signal. Thus, we can obtain then it is easy to find 0 < αmin < 1.
Assume we can find that f(α) monotonically increases with α. From the above analysis, as we know f(α0) = R12, f(αmin) = RPT, R12 should be larger than RPT, then we can obtain α0 ≥ αmin.
Thus, the optimal α can be obtained by analyzing the relative values of α0 and αmax as follows.
a) Under the condition of α0 ≥ αmax
We can obtain α ≤ α0, thus Rp ≤ R21. Assume L(α) = Rp + Rs, then
where
Obviously, L(α) and Y(α) have the same monotonicity. Take the first derivation of Y(α) with α, we can obtain
where
From (18), we can find that the monotonicity of Y(α) depends on A(α) as the denominator of Y'(α) is always positive. We can find that A(α) is a quadratic convex function of α and its symmetry axis equals to which is larger than 1. Thus, we can obtain that A(α) monotonically increase with α when α ∈ [0,1]. Then, the optimal α can be obtained by analyzing the relative value of A(αmax) and 0.
1) when A(αmax) ≤ 0
We can obtain Y'(α) ≤ 0, α ∈ [αmin,αmax], which indicates that L(α) monotonically decreases with α in this region. Thus, the optimal value of α can be obtained as
2) when A(αmax) > 0
We can obtain that there must exist one and only one station point when α ∈ [−∞,αmax], as A(α) is a quadratic convex function. No matter the station point is in [αmin,αmax] or not, the optimal value of α will be obtained at αmin or αmax. Specifically, the optimal value of α can be obtained as
b) Under the condition of α0 < αmax
When α ∈ [αmin,α0], we can obtain α ≤ α0, thus Rp = R21. The optimal value of α can be obtained with the same analysis as in a).
When α ∈ [α0,αmax], we can obtain α > α0, thus Rp = R12, then
It is easy to find that L(α) is a monotonically decreasing function of α. Thus, the optimal value of α equals to α0.
Thus, the optimal α* in Case A is summarized in Table 1.
Table 1.Optimal α* in Case A
Case B: when R13 < RPT
To satisfy the second condition of (12), we can obtain
It is easy to find that αmax is smaller than 1. In the above we have already known that then we can obtain 0 < αmax < 1.
We have already known that α0 ≥ αmin. Thus the optimal α can be obtained by analyzing the relative values of α0 and αmax as follows.
a) Under the condition of α0 ≥ αmax.
We can obtain α ≤ α0, thus Rp ≤ R21. Then
where
Take the first derivation of G(α) with α, we can obtain
where
From (26), we can find that the monotonicity of G(α) depends on B(α) as C(α) is always positive. We can find that B(α) is a quadratic convex function α, and the symmetry axis equals to which is larger than 1. Thus, we can obtain that B(α) monotonically increases with α when α ∈ [0,1]. The optimal value of α can be obtained with the similar method in case A.a.
b) Under the condition of α0 < αmax.
When α ∈ [αmin,α0], we can obtain α ≤ α0, thus Rp = R21. The optimal value of α can be obtained with the same analysis as in a).
When α ∈ [α0,αmax], we can obtain α > α0, thus Rp = R12 then
It is easy to find that L(α) is a monotonically decreasing function of α. Thus, the optimal value of α equals to α0.
Thus, the optimal α* in Case B is summarized in Table 2.
Table 2.Optimal α* in Case B
4. Simulation Results and Discussions
In this section, simulation results are presented to demonstrate the performance of the proposed spectrum sharing protocol. We consider PT, PR, STb and SR are in a two-dimensional X-Y plane, where PT and PR are located at points (0, 0) and (1, 0), respectively, thus d1 = 1. The channel over PT → PR link experiences 20dB fading. STb moves on the positive X axis, its coordinates are (d2, 0). SR is located at (d2,d5), where d5 = 0.5. Thus, d4 = 1-d2 and The path loss exponent remains at v=4, and Pp/σ2 = 20dB, Ps/σ2 = 10dB, RPT = 2bps/Hz, RST = 0.5bps/Hz.
Fig. 2 shows the optimal power allocation with our proposed spectrum sharing protocol, and the spectrum sharing protocol proposed in [19] where the secondary transmission rate is maximized with only primary QoS guaranteed. We can observe from Fig. 2 that the optimal power allocation α of [19] always equals to αmin which is obtained to guarantee the primary system achieves its target rate. The optimal power allocation α of our proposed spectrum sharing protocol has three different kinds of values. When d2 ∈ [0.1, 051], α equals to αmin, which is the same as the power allocation in [19]. When d2 ∈ (0.51,0.89], α equals to αmax, which is obtained to guarantee the secondary system achieve its target rate. When d2 ∈ (0.89, 1], α equals to α0, which is obtained to maximized the sum transmission rate of primary and secondary systems.
Fig. 2.Optimal power allocation
Fig. 3 shows the achievable rate of the primary and secondary systems with our proposed spectrum sharing protocol, and the spectrum sharing protocol proposed in [19]. We can observe from Fig. 3 that although the access region of protocol in [19] is a little larger than our protocol. However, we can find that in this larger region, the secondary system cannot achieve its target transmission rate. From Fig. 3 we can also observe that when d2 ∈ [0.1,1], both the primary and secondary system can achieve their target rates in our proposed spectrum sharing protocol and the spectrum sharing protocol proposed in [19]. However, the sum transmission rate of our proposed spectrum sharing protocol is larger than the spectrum sharing protocol proposed in [19].
Fig. 3.Achievable rate of primary and secondary systems versus d2
Fig. 4 shows the achievable rates of the primary and secondary systems with our proposed spectrum sharing protocol, and the spectrum sharing protocol proposed in [19] with different Ps/σ2 when d2 = 0.8. We can find that the sum transmission rate of primary and secondary systems becomes larger with Ps/σ2 increases. We can also observe from Fig. 4 that the sum transmission rate of our proposed protocol is also larger than the protocol proposed in [19] with Ps/σ2 changes.
Fig. 4.Achievable rate of primary and secondary systems versus Ps/σ2
5. Conclusion
In this paper, we propose a sum transmission rate maximization based cooperative spectrum sharing protocol, in which both the primary and secondary systems can achieve their QoS. In the proposed spectrum sharing protocol, the secondary system gains spectrum access by acting as a DF relay to assist the primary system achieve its target rate. Specifically, the selected secondary transmitter helps forward the primary signal by using a fraction power. As a reward, it can use the remaining power to transmit its own signal to achieve the target rate, and thus gain spectrum access. We study the secondary user selection and optimal power allocation such that the sum transmission rate of primary and secondary systems is maximized, while the QoS of both primary and secondary systems can be guaranteed. Simulation results are presented to show that the proposed secondary spectrum access scheme can benefit both primary and secondary systems.
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