Resource allocation for spectrumleasing based CRN with delaysensitive traffic
 Yanbo Ma^{1}Email author,
 Xiao Yin^{1},
 Xiao Yang^{1} and
 Qiang Liu^{1}
https://doi.org/10.1186/s1363801708890
© The Author(s) 2017
Received: 27 December 2016
Accepted: 21 May 2017
Published: 15 June 2017
Abstract
In this paper, cooperative resource allocation strategies are characterized for a spectrumleasing based cognitive radio network (CRN), where the primary system leases the licensed band to the secondary system for a fraction of time in exchange for the secondary user (SU) acting as relay. Here, both amplifyandforward (AF) and decodeandforward (DF) relay protocols are considered. Considering the delaysensitive traffic in CRN, the proposed strategies ensure delay provisioning for both primary user (PU) and SU with multiple system design objectives. In particular, we propose a multiobjective optimization framework, which incorporates two important system design objectives: the average sum power minimization and the leased time minimization. By integrating information theory with the concept of effective capacity, the adopted multiobjective optimization problem is recast as a convex optimization one via employing weighting method and sequentially solved by applying the Lagrangian dual method. It is shown that the global optimal solution of the original problem is characterized by a Pareto set which provides a quantitative insight into the tradeoff between the transmit power and leased time. Moreover, to learn the statistics of the wireless channels on the fly, we also put forward a stochastic iterative algorithm to achieve the optimal power and time allocation by employing the stochastic optimization theory. Numerical results not only reveal the nontrivial tradeoff among the considered conflicting system design objectives but also demonstrate that the proposed strategies perform better in saving wireless resources than existing resource allocation policies for different QualityofService (QoS) exponent sets, especially when the delay requirement is strict.
Keywords
1 Introduction
Dynamic spectrum sharing (DSS) in cognitive radio networks has been widely considered as an effective means to allow the secondary users to dynamically access the licensed frequency bands and thereby to overcome the problem of spectrum underutilization caused by the static spectrum allocation. In [1, 2], the dynamic spectrum leasing was proposed as a new paradigm for DSS mechanisms, in which the secondary system is granted to use the licensed frequency bands by the PU in exchange for cooperation. The incentive for PUs to lease their licensed bandwidth is that they will benefit from the enhanced QoS thanks to cooperation with SUs. The spectrumleasing based cooperation can guarantee the benefits of both PUs and SUs simultaneously, achieving a “winwin” situation.
On the observations of the selfish properties of users and the fact that the time for SU to access the licensed band is obtained as a revenue for relaying the primary traffic, there exists competition among PUs and SUs for finite wireless network resources. And with the help of the information theory, there has been extensive research on how to guarantee the benefits of spectrumleasing based CRN via optimally allocate the wireless resources among PUs and SUs [3–18], and a good summary of the state of the art is provided in [3, 4]. Thereinto, the cooperation among PUs and SUs was commonly modeled by the convex optimization problem [5, 6] where the globally optimal resource allocation is analytically derived, or by employing the widely used economical concepts, such as a Stackelberg game [2], a Nash Bargaining game [7–9], contract theory [10, 11], auction theory [12, 13], matching theory [14], etc. For example, aiming to optimally calculate the design parameters of the primary and secondary networks, [5] has considered the problem of maximizing the smaller of secondary transceiver average rates, while preserving a minimum rate for the primary pair. Lu et al. [6] studies the joint optimization of the set of subcarriers used for cooperation, subcarrier pairing, and power allocation such that the transmission rate of the secondary system is maximized, while helping the primary system to achieve its target rate. Toroujeni et al. [12] proposes an auction framework in which the PU tries to find the optimum amount of resources (in both time and frequency) leased to SUs, whereas each SU’s goal is to find the optimum power level to maximize its own profit. Inspired by the matching approach, in [14], the network is modeled as a matching market, where each PU puts forward a proposal representing a combination of relay power and spectrum access time to attract SUs, while each SU maximizes its utility by selecting the most suitable PU.
Nevertheless, all the aforementioned models cannot be directly applied to the spectrumleasing based CRN scenario with the delaysensitive traffic, since Shannon theory places no restriction on the delay of the transmission scheme achieving capacity. Although some works [17, 18] have been done for the delaysensitive traffic, the delay metric is considered in the context of the deterministic delay guarantee, which is practically infeasible for wireless networks due to the timevarying nature of wireless channels. To address this issue, the statistical delay provisioning is adopted to ensure a small steadystate delay violation probability for the delaysensitive traffic. This metric is closely tied back to the welldeveloped theory of effective capacity [19]. It was first introduced by Wu and Negi in [19] to describe the maximum arrival rate a given service process can support in order to guarantee a QoS requirement. From the definition of effective capacity, it is observed that QoS provisioning performance is related with wireless channel service rate via effective capacity. Thus, it can be employed to model crosslayer design between the physical layer system infrastructure and statistical QoS performance at the data link layer. With it, a set of statistical delay QoSdriven resource allocation policies has been addressed [20–22]. In particular, [21] investigates resource allocation including subcarrier and power allocation for LTEA relay networks under statistical QoS constraints. With statistical QoS constraint, maximum acceptable endtoend queuelength bound outage probability has been investigated for a threenode bufferaided relaying network in [22].
Based on the aforementioned motivation, the current work adopts the statistical delay provisioning and effective capacity to allocate the wireless resources in a spectrumleasing based CRN. Specifically, by jointly considering the physical layer and data link layer, we will develop a crosslayer based, QoSoriented power, and time allocation policy. In the considered CRN scenario, the secondary system helps the primary system via threephase cooperative relaying, where both AF and DF relay protocols are discussed. Our work is motivated by the observation that cooperation model brings a waiting delay to the PUs, since SU has to alternately forward the primary traffic and send its secondary traffic on the same channel. Given the competitive and selfish properties of users, two design goals are given. On one hand, the goal of the primary link aims to minimize its expense of radio resources (i.e., the leased time). On the other hand, the object is to minimize the overall power consumption of the network. In practice, these two design objectives are all desirable for the system operators. However, they are conflicting with each other, and each focuses on only one aspect of the system. Via employing the multiobjective optimization theory, these two design objectives are realized simultaneously with statistical delay provisioning.

Firstly, we formulate the resource allocation as a crosslayer optimization problem, where multiple conflicting objectives are interrelated and minimized at the same time. Specifically, by employing multiobjective optimization theory, we model the resource allocation as minimizing both the power consumption of the global network and the leased time to SU simultaneously, while fulfilling the statistical delay QoS constraints of all users. As far as we know, this is the first work that configures cooperative relaying schemes jointly with transmit powers, leased time, and statistical delay QoS requirements.

Secondly, via employing weighting method, the adopted multiobjective optimization problem is recast as a convex optimization one. With it, the closedform expressions of the optimal power and time allocation strategies are derived by using the Lagrangian dual method. We show that the global optimal solution of the original problem leads to a set of Paretooptimal resource allocation policies. That is, we obtain a set of compromises characterized by a Pareto set which provides a quantitative insight into the fundamental tradeoff between the transmit power and the leased time. Furthermore, we also analyze the impact of delay exponents on the overall performance and characterize the properties of the optimal resource allocation strategies.

Thirdly, considering that it is hard or impossible to have a priori knowledge of the cumulative distribution function (CDF) of the timevarying fading channels, we model the channel condition as a stochastic process. Based on the stochastic optimization tools [23–26], a stochastic iterative algorithm is proposed to learn the underlying channel distribution.
The rest of the paper is organized as follows. Section 2 describes the system model of concern and the delay QoS provisioning based on effective capacity. Sections 3 and 4 study the optimal resource allocation strategies such that the minimum power and leased time are consumed while fulfilling the statistical delay provisioning, when employing AF and DF relay protocols, respectively. In Section 5, we propose the stochastic resource allocation algorithms to approach the globally solutions. Numerical results are illustrated in Section 6, followed by the conclusions drawn in Section 7.
2 System overview
In the following, we detail the system model of spectrum leasing, the main system parameters, and the concept of effective capacity.
2.1 System model
We consider two infrastructurebased networks, where the primary network and the secondary network are located in the same area. The primary network is willing to share its licensed spectrum with the secondary network as an exchange for cooperation. Thereinto, a primary transmitter (PT) tends to communicate with primary receiver (PR) with its own spectrum and a secondary transmitter (ST) communicates with secondary receiver (SR) by using the leased spectrum. As introduced, by employing the effective capacity theory a crosslayerbased transmitter structure is formulated, in which an infinite queue (or buffer) operating in a firstinfirstout (FIFO) mode is implemented at the data link layer to store frames to be transmitted. Frames from upper layers are put into the queue. Then at the physical layer, frames from the queue are divided into bitstreams. The reverse operations are executed at the receiver side.
We assume that both the PU and SU experience independent fading, and their fading processes are stationary and ergodic with joint cumulative distribution. The channel coefficients of PT →PR, PT →ST, ST →PR, and ST →SR links are denoted as h _{ pp },h _{ ps },h _{ sp }, and h _{ ss }, respectively. And the corresponding channel variance of each link is denoted by, \(\sigma _{pp}^{2}, \sigma _{ps}^{2}, \sigma _{sp}^{2}, \sigma _{ss}^{2}\). Without loss of generality, we assume that all the noise terms are white Gaussian noise with zero mean and variance \(\sigma _{pp}^{2} = \sigma _{ps}^{2} =\sigma _{sp}^{2} =\sigma _{ss}^{2} = 1\). Additionally, the wireless links are assumed to experience fading from one frame to another but remain invariant within a frame duration. Thus, the channel gains are denoted as γ _{ pp }=h _{ pp }^{2},γ _{ ps }=h _{ ps }^{2},γ _{ sp }=h _{ sp }^{2}, and γ _{ ss }=h _{ ss }^{2}, respectively. γ is defined as γ:={γ _{ pp },γ _{ ps },γ _{ sp },γ _{ ss }}. Let us denote the system’s total spectral bandwidth by B. Suppose that perfect channel state information is always available at transmitter side. We also assume that proper channel code can always be found to commit errorfree transmission.
2.2 Statistical delay QoS guarantees and effective capacity
As mentioned, we will introduce effective capacity to describe the system throughput with statistical delay QoS guarantees. Before going further, we would first spend some words on effective bandwidth [30] which is the dual problem of effective capacity. The stochastic behavior of a source traffic flow can be modeled asymptotically by its effective bandwidth. In particular, it is defined as the minimum service rate required by a given arrival process for which a QoS requirement is guaranteed. As its dual problem, effective capacity defines the maximum rate the channel can support while guaranteeing a given delay QoS requirement in terms of QoS exponent θ>0.
In (7), smaller and larger θ corresponds to slower and faster decaying rate, indicating that the system can guarantee a loose and stringent violation probability requirement, respectively.
where ϱ denotes the nonempty probability of the buffer, and ϱ≈E _{ B }/μ _{ C } and \(\mu _{c} \triangleq {\lim }_{\theta \rightarrow 0} E_{c}(\theta)\) [20], E _{ B } is the effective bandwidth with QoS exponent θ of a source traffic flow. For details, readers are referred to [19, 20, 30].
3 Optimal power and time allocation with AF relay protocol
where p={p _{ p },p _{ sp },p _{ ss }} and t _{ s } are the optimization variables. Notice that, these two objectives conflict with each other. For instance, in order to shorten the leased time from the PU, SU must increase its transmit power to satisfy the delay requirements. In fact, via the concept of Pareto optimality, the tradeoff between these conflicting design objectives can be investigated. In particular, the adopted multiobjective optimization enables the design of a set of Paretooptimal resource allocation strategies [31].
Thereinto, {ω _{ k },k=1,2} are the nonnegative weight factors, and ω _{1}+ω _{2}=1. They denote the importance of each objective function. The optimal solutions to P2 for different values of ω _{ k },∀k, collectively form the Paretooptimal set of P2. That is, by tuning ω _{ k }, we are to investigate the tradeoff between the transmit power and the leased time with statistical delay provisioning.
The underlined optimization problem P2 is a convex optimization problem, and a detailed proof is given in Appendix 1 Proof the convexity of P2. Then we will employ the Lagrangian dual approach [33] to solve this optimization problem with given ω _{ k },∀k.
3.1 Optimizing the dual problem
where n is the iteration index, s>0 is defined as a positive stepsize, and [ ·]^{+} denotes the projection onto the nonnegative orthant. If the step size s follows the diminishing step size policy in [34], the subgradient method above is guaranteed to converge to the optimal dual variables \(\boldsymbol {Z}_{1}^{*}\). The computational complexity of such update method is polynomial in the number of dual variables [33]. Moreover, \(\{\boldsymbol {p}^{*}, t_{s}^{*}\}\) are the optimal solution of maximizing L _{ AF }(p,t _{ s },Z _{1}) for given \(\boldsymbol {Z}_{1}^{*}\).
3.2 Optimal power and time allocation policy with given Lagrangian variables
That is, the problem of minimizing L _{ AF }(p,t _{ s },Z _{1}) in (19) can be solved via decoupling the optimization problem of minimizing \(L^{\prime }_{AF}(\boldsymbol {p},t_{s},\boldsymbol {Z}_{1})\) across fading states. The detailed derivation of this result follows along the lines of ([35], Appendix III), which is omitted here for lack of space.
where \(\Lambda _{0} = \frac {\xi \theta _{s}B}{\omega _{1} \ln 2}\). Notice that, this power policy is the deterministic function of delay QoS exponent θ _{ s } and channel fading states. Apparently, it has a similar expression with the conventional waterfilling policy [36]. We take the first part of formula as the water level just as defined in waterfilling policy. However, it is worth mentioning that our proposed policy (24) is different from the classical waterfilling policy in that the water level in our case is a variable. It depends on delay QoS requirements θ _{ s }. But the water level given in waterfilling policy is a constant and is not related to the system delay requirement. In the proposed policy, if there is no constraint on delay, θ _{ s } will be zero and the water level in (24) will become a constant. At this moment, our policy converges to the conventional waterfilling policy. From this point of view, the proposed policy is a delay QoSbased waterfilling policy.
and \((x)^{+}\triangleq (0,x)\). Refer to Appendix 2 for the details of the proof.
It indicates from (25) and (26) that for some particular channel states, i.e., γ _{ sp }≤γ _{ pp }, no power is assigned over the ST → PR link. In this case, direct transmission (without the help of relay) is preferred so as to save the consumed power. And the power policy of direct transmission follows the expression of delay QoSbased waterfilling approach shown as in (25). Otherwise if γ _{ sp }>γ _{ pp }, both PT and ST should be assigned nonzero powers, which are related through the parameter χ illustrated in (25).
It is observed that (29) is an equation with one unknown variable. Thus, the optimal value of leased time for SU at each fading state can be obtained via solving this equation. More specifically, \(t_{s}^{*}\) is the nonnegative real root of (29), and it is also related with delay QoS exponent θ _{ s }. Till now, we have achieved the optimized jointly power and time assignment, based on the given Z _{1}.
4 Optimal power and time allocation with DF relay protocol
By changing the weight factors, the optimal solutions to P4 can collectively form the Paretooptimal boundary of a powertime region while employing DF relaying protocol.
4.1 Optimizing the dual problem
where \(\{\boldsymbol {p}^{*}, t_{s}^{*}\}\) denote the optimal solution in (35) at dual point \(\boldsymbol {Z}_{2}^{*}\). Using the step size following the diminishing step size policy as in (21), this subgradient method above can be used to calculate the optimal \(\boldsymbol {Z}_{2}^{*}\) with negligible (linear) computational complexity [33].
4.2 Optimal power and time allocation policy with given Lagrangian variables
where \(\Psi _{0} = \left (\frac {1}{\gamma _{pp}}\right)^{\frac {\ln 2 + \theta _{p}B T_{p}}{\ln 2}} \cdot \gamma _{sp}^{\frac {\theta _{p} BT_{p}}{\ln 2}}\), Γ=μ θ _{ s } B/(ω _{1} ln2), Ψ=θ _{ p } B λ/(ω _{1} ln2). The power policies defined in (42), (43), and (44) have been shown to be delay QoSbased waterfilling policies. In particular, the water level of p _{ ss }/t _{ s } depends explicitly on θ _{ s }, while the water levels of the power policy associated with PU, i.e., p _{ sp }/T _{ p },p _{ p }/T _{ p }, are related with θ _{ p }. Moreover, it is interesting to see that the water levels of p _{ p }/T _{ p } and p _{ sp }/T _{ p } are the same and differ from that of p _{ ss }/t _{ s }. From this point of view, the power allocation policies when adopting DF relay protocol is multilevel QoSbased waterfilling policies.
Via solving the Eq. (46), we can get the optimal value of leased time for SU at each fading state.
5 The stochastic resource allocation algorithm
And hats are used to underscore that these iterations are stochastic estimate instead of average values of those in (21). It only requires the fading state of the channels at the current iteration, which can be easily measured. The convergence of the stochastic subgradient iteration can be guaranteed by the following lemma.
Lemma 1
works over time interval T with the constant δ _{ T }(s)→0 as the stepsize s→0.
The proof can be derived along the similar lines to those in ([37], Theorem 9.1), which is omitted here. The Lemma 1 implies the iteration of (47) converges to the optimal {β ^{∗},ξ ^{∗}} with probability 1 as stepsize s→0. Hence, the proposed stochastic policy is capable of iteratively finding the optimal {β ^{∗},ξ ^{∗}}. Thus, the multiobjective resource allocation with guarantees on the effective capacity constraints is obtained, even when the fading channel distribution is unknown a priori. To go further, with (47), a stochastic power and time allocation algorithm with negligible (linear) computational complexity can be brought forward to approach the global solution, shown in Algorithm 1.
To apply our stochastic resource allocation scheme to the spectrumleasing based CRN, we can implement it in a distributed manner. The execution of the distributed iterative algorithm is illustrated as follows. Firstly, system performs some initialization such as setting β[ 0] and ξ[ 0] to some nonnegative values at PT and ST, respectively. In time slot n, ST adjusts the leased time and the transmit power over ST → SR link according to the calculated values \(t_{s}^{*}(\xi [\!n]), p_{ss}^{*}(\xi [\!n])\), and computes its power \(p_{sp}^{*}(\beta [\!n]) \) over ST → PR link which is then fed back to PT. Meanwhile, PT calculates its power value of \(p_{p}^{*}(\beta [\!n])\). With \(p_{p}^{*}(\beta [\!n]), p_{sp}^{*}(\beta [\!n]) \) available, PT updates β[ n+1], which is then delivered to ST. Simultaneously, using values of \(p_{ss}^{*}(\xi [\!n]), t_{s}^{*}(\xi [\!n])\), ST node updates ξ[ n+1]. Similarly, in time slot, n+1 PT and ST work together well to calculate the corresponding power and time values and update the Lagrange multipliers. Eventually, the dual variable β[ n],ξ[ n] will converge to the global solution β ^{∗},ξ ^{∗}. Simultaneously, thanks to zero duality gap, the optimal solutions \(p_{ss}^{*}(\xi [\!n]), p_{p}^{*}(\beta [\!n]), p_{sp}^{*}(\beta [\!n]) \) will also converge to the globally optimal variables \(p_{ss}^{*}, p_{p}^{*}, p_{sp}^{*}\).
Lemma 1 holds true for \(\hat {\lambda }, \hat {\mu }\), which can guarantee the convergence of this iteration. Furthermore, similar stochastic subgradient iteration algorithm as Algorithm 1 can also be proposed.
6 Numerical results
In this section, we evaluate the performance of the proposed algorithms and the tradeoff between the consumed sum power and leased time by simulations. Throughout our simulation, we consider a CRN with one pair of primary transceiver and one pair of secondary transceiver, which operate in timeslotted mode. The channel gains γ _{ pp }, γ _{ ps }, γ _{ sp }, and γ _{ ss } undergo identical Rayleigh fading independently, and the average channel gains of all links are the same, which are set to 3. We assume the system bandwidth is B=1 kHz and the duration of the cooperative communication is 1 ms, i.e., T _{ p }=0.5 ms. Furthermore, we assume that all users hold still, and the arrival rate of the source traffic flow is assumed to be constant. In the simulations, we set E _{ p }=1 and E _{ s }=1. To facilitate discussion of the impact of the weight factor on the overall transmission power and leased time, five sets of weight factor are supposed as following, {ω _{1}=0.1, ω _{2}=0.9} which is labeled as w1, {ω _{1}=0.3, ω _{2}=0.7} labeled as w2, {ω _{1}=0.5, ω _{2}=0.5} labeled as w3, {ω _{1}=0.7, ω _{2}=0.3} labeled as w4, and {ω _{1}=0.9, ω _{2}=0.1} labeled as w5. More detailed parameters will accompany with results in figures to be shown.
7 Conclusions
In this paper, we have studied the resource allocation for spectrumleasing CRN with effective capacitybased delay provisioning for delaysensitive traffic. In such network, the secondary system can have the opportunities to access the licensed spectrum by employing AF/DF relay protocols to assist the primary data transmission. By integrating the multiobjective optimization theory and the concept of the effective capacity, we have formulated two optimization problems aiming to minimizing both the overall power consumption and the average leased time while fulfilling statistical delay provisioning. To solve the established problems, we resort to the weighting method that yields a convex optimization one. Then by the Lagrangian dual method, the closedform expressions of the optimal power and time allocation strategy have been derived given the underlying statistical delay QoS constraint. We also analyze the fundamental tradeoff between the transmit power and the leased time via a Pareto set, the impact of delay exponents on the overall performance, and characterize the properties of the optimal resource allocation strategies. Furthermore, we have presented stochastic resource allocation schemes that can learn the statistics of the fading channels and adaptively approach the optimal strategies on the fly. The numerical results for Rayleigh fading channels demonstrate that our proposed policies exhibit excellent performance compared with minpower policy and equal time policy.
8 Appendix
9 Proof the convexity of P2
Firstly, the objective function in P2 is convex given that ω _{1}(p _{ p }+p _{ sp }+p _{ ss })+ω _{2} t _{ s } is linear with respect to p _{ p },p _{ sp },p _{ ss },t _{ s } and that the integral preserves convexity. Then, we will demonstrate the constraint functions are all convex, guaranteeing that the feasible set of this optimization problem is convex. By evaluating the Hessian matrix of \(f(p_{p}, p_{sp})= 1+ \frac {p_{p}}{T_{p}} \gamma _{pp} +\frac {\frac {p_{p}}{T_{p}} \gamma _{ps} \frac {p_{sp}}{T_{p}}\gamma _{sp} }{ \frac {p_{p}}{T_{p}} \gamma _{ps} + \frac {p_{sp}}{T_{p}}\gamma _{sp}} \) at p _{ p } and p _{ sp }, we can prove that f(p _{ p },p _{ sp }) is concave. Thus, the log2(f(p _{ p },p _{ sp })) is concave as log(·) function can preserve concavity. Considering that exponential function e x p(·) and the integral preserve convexity, the first constraint function in P2 is convex. Given a convex function f(x), its perspective g(x,t)=t f(x/t) is also convex for t>0 [33]. For this reason, \(t_{s}\log _{2}\big (1+ \frac {p_{ss} \gamma _{ss}}{t_{s}}\big)\) is the convex function of (p _{ ss },t _{ s }). Then, the second constraint function is convex given that exponential function e x p(·) and the integral preserves convexity. Therefore, the problem in P2 is a convex optimization problem and there exists a unique optimal solution.
10 Proof of optimal solution in (25) and (26)
Thus, the optimality of solution \(p_{p}^{*}\) and \(p_{sp}^{*}\) in (25) and (26) is proved.
11 Endnote
^{1} The unit for service rate and the effective capacity is bits per frame.
Declarations
Acknowledgements
This work was supported by the National Science Foundation of China with Nos. 61571272, 61201269, and 61403230. The authors would like to thank the anonymous reviewers for their constructive comments, which helped a lot to improve the presentation of this paper.
Authors’ contributions
In this research paper, the authors proposed an resource allocation algorithm. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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