Adaptive resource allocation for cognitive radio networks with multiple primary networks
© Ye et al.; licensee Springer. 2012
Received: 24 October 2011
Accepted: 11 July 2012
Published: 12 August 2012
In this article, adaptive resource allocation (ARA) is investigated for multiple primary networks based-cognitive radio networks under a more practical system model, where the bandwidth of each secondary user is assumed to be limited and the maximum allowable interference for each primary network is different. We first formulate the ARA as a constrained optimization problem with the objective function of maximizing the proportional fairness-based ergodic sum capacity. The multiple constraints optimization problem is NP-hard and therefore, we propose a scheme to decompose the optimization problem into two unconstrained optimization problems by designing alternative objective functions and penalty functions. Then, a suboptimal heuristic solution framework based on particle swarm optimization is proposed to solve the unconstrained optimization problems. Computation simulations are carried out and the results show that the proposed scheme outperforms traditional ARA schemes.
Recently, cognitive radio networks (CRNs)  get extensive attentions to alleviate the contradiction between the scarcity and low-utilization of the spectrum resources. In CRNs, two approaches are widely studied for dynamic spectrum access (DSA), termed as underlay mode and overlay mode. In underlay mode, secondary users (SU) transmit over all the frequency bands as long as the serviced SUs do not cause excessive interference to primary users (PU). One possible drawback of this mode is that it requires exact information of all primary receivers’ positions, which usually expenses a high complexity of hardware and computation. On the other hand, the basic idea of overlay is to detect the absence/presence of licensed primary radios, and opportunistically use the idle band for transmissions without causing harmful interference to the authorized signals [2, 3]. Compared to the underlay mode, the overlay mode is more practical and easily accepted by primary systems. Also, the overlay spectrum access can further improve spectrum efficiency by exploiting multiuser diversity and adaptive resource allocation (ARA) algorithm. In this article, we consider the problem of ARA for overlay CRNs.
ARA is one of the most effective methods to improve the spectral efficiency and has widely been investigated in the last decade. Unlike existing wireless communication networks, the ARA problem in CRNs is more challenging. First, the detection errors of spectrum sensing greatly deteriorates the performance of ARA algorithm [4, 5]. The authors of  proposed an iterative algorithm to obtain the optimal sensing time and the corresponding power allocation strategy with imperfect sensing information. The authors of  presented a primal-dual decomposition-based cross-layer scheduling for power allocation and subchannel assignment with raw sensing information. Furthermore, cognitive radios are usually required to be self-regulating, to control the interference to primary systems in a tolerable level [5–7]. The authors of  considered the average interference constraint on the nearest PU receiver. In , a total interference constraint to a certain PU who uses the same channel with SU is imposed. In [8, 9], the interference control is considered as a total power constraint of all SUs.
Besides, because of the absence of the license, the available spectrum resources for SUs are usually temporary and unstable, which results in transmission interruption with high probability. One of considerable solutions is to enable SUs to search for spectrum resources from multiple primary networks (PRNs) simultaneously. The authors of  considered the mobile users operating on different radio access technologies (RATs), and the single-user case is analyzed. In the multiple PRNs, however, the available spectrum resources are usually quite wide as well as discontinuous. This leads to that the cognitive radios operating on such spectrum resources are price prohibitive due to the increase of sampling rate. In addition, different PRNs restrict different power values of CRNs in one resource allocation, which greatly increases the computational complexity of ARA.
This article aims to design an effective ARA algorithm in multiple PRNs environment. Specifically, we assume that the spectrum resources available for SUs are distributed in multiple PRNs, and discontinuous in frequency domain. Furthermore, the sampling rates of SUs are limited for practical consideration. Other constraints concerned in traditional multiuser communications networks like proportional fairness and bit error rate (BER) are also involved in this study.
The ARA problem for CRN in multiple PRNs is formulated as a constrained optimization problem.
A hybrid alternative objective function instead of sum capacity is proposed to balance the tradeoff between the complexity of optimization and the speed of convergence.
The optimization problem is transformed into two unconstrained problems through the design of penalty functions. In particular, we propose multiplicative penalty functions that are independent with channel gains and power limits, contributing to the algorithm more robust.
A particle swarm optimization (PSO)-based heuristic intelligence algorithm is proposed to solve the two unconstrained problems. Specifically, we first present an initial topology of PSO according to the fact that an SU suffers channel fading of the same level for all frequencies (because large scale attenuation plays the key role for wireless channel). The proposed topology can greatly decrease the computation complexity from O(K N ) to O(K 3). Based on this, we design different particle structures for subchannels and power allocation, respectively.
In order to verify the proposed ARA algorithm, three computer simulations are carried out. The first one illustrates the efficiency of the proposed hybrid objective function in terms of convergence and quality; for comparison, we put a classical ARA algorithm  into the same scenario. The simulation results reflect that the proposed outperforms the algorithm in  both in capacity and proportional fairness; at last, we discuss the effect of imperfect sensing information, and a possible optimization of sensing strategy is proposed.
The rest of this article is organized as follows. The following Section “Related studies” introduces the state of the art in ARA for CRNs. In Section “System model and problem formulation”, we describe the system model and formulate the ARA as a constrained optimization problem. In Section “Objective function and problem decomposition”, we decompose the optimization into two unconstrained optimization problems. In Section “Particle swarm optimization based framework”, we discuss the solution to the optimization problems by a PSO based algorithm in detail. The computational complexity of proposed is analyzed in Section “Computational complexity analysis”. To verify the proposed scheme, computer simulations are carried out in Section “Results and discussion”, and the brief conclusions are drawn at last.
The main foundation of ARA is based on that different users suffer from different wireless channel fading. ARA algorithms can adaptively allocate a dimension to the users, and achieve higher capacity. Two classes of resource allocation techniques have widely been addressed in traditional OFDM-based wireless communication systems, namely, (1) margin adaptive (MA)  and (2) rate adaptive (RA) . The MA aims to minimize the overall transmit power, given the constraints on the users transmit rates or BER. The RA aims to maximize users’ capacity sum, given a total power constraint. Both optimization problems are MINP problem, and computationally prohibitive. The authors of  presented a suboptimal resource allocation algorithm by transforming the MA problem into a convex optimization problem. The authors of [11, 14] discussed RA problem with the constraint of proportional rate, and proposed an optimal power allocation scheme by the Newton–Raphson method.
Right now, a lot of research works is currently ongoing to deal with the optimization of the spectrum utilization in CRNs. The authors of  presented a primal-dual decomposition approach for the RA problem with raw sensing information. However, they ignored proportional rate and fairness, which ensure that all users suffering different channel fading can experience the similar quality of service [15, 16]. In this article, we assure proportional fairness among SUs by imposing a set of nonlinear constraints into the optimization problem and formulate a new optimization problem. Regarding to interference control, an important concept named “interference temperature”  is widely used to evaluate the interference on the primary system. Wang et al.  considered the average interference constraint on the nearest PU receiver. Nguyen and Lee  imposed a total interference constraint on PU, who uses the same channel with SU. Although “interference temperature” is an exact measurement, it is difficult to implement in realistic systems. To calculate the aggregation interference on each PU, the sensing algorithm based on receivers is needed, which usually requires information of receivers’ positions and channel gains from each SU transmitter to the corresponding PU receiver. In this article, we simplify the constraint with an only total power limit on specific PRN. This simplification is reasonable since the value of power constraint could be negotiated between PRN and CRN through a spectrum broker . Choi et al.  considered the mobile users who can access different RATs, and the single-user case was analyzed. In this article, we equip the SU as the same capability of operating on crossing bandwidth and extend the scenario to multiuser case. Further, we consider that the sampling capability of SU is limited and only part of the spectrum resources can be exploited at any time.
Because of extra constraints in CRNs, it is nontrivial to obtain optimal solution for ARA problem. Bio-inspired swarm intelligence-based optimization algorithms [19, 20], as an effective alternative solution, have widely been adopted in CRNs. A successful example of exploring the swarm intelligence algorithms in CRN is the testbed designed by Virginia Tech group [21, 22], which shown the flexibility and stability of CRN with the genetic algorithm (GA)-embedded cognitive engine. Newman et al.  proposed a GA-based cognitive radio suitable for Emergency (minimize BER) and Low Power (minimize power consumption, like MA in a traditional network scenarios). Since then, lots of alternative schemes such as the quantum genetic algorithm , cross entropy , and PSO  is exploited to address the problems of resource allocation. PSO is proposed as a new swarm intelligence algorithm in recent years due to its capabilities of convergence rapidity, optima finding, and matching problem easily. In this article, we consider PSO as a tool to solve the problem of resource allocation in CRNs.
System model and problem formulation
Hence, the total available subchannels for CRN is . We assume that the resource allocation period is updated as fast as CSI feedback between CBS and SUs, and perfect instantaneous CSI is assumed available for the CBS. It is also assumed that information of both resource allocation results and CSI are transmitted through a cognitive pilot channel .
where N0 is the two-sided noise spectral density. We assume that the noise is additive white gaussian noise, and all spectrum has the same value of N0. is the SINR gap due to modulation, and BER is the BER for SUs. represents the interference on subchannel m of SU k, from the PRN i. is the channel gain for SU k in subchannel m of the PRN i and is the power allocated in subchannel m of the PRN i, can either be 1 or 0, indicating whether subchannel m of PRN i is allocated to SU k or not.
where represents the power allocated to SU k on subchannel m of PRN i and is the total power constraint for CRN in PRN i.
where is the sum capacity of SU k in one allocation period and γ k is the expected transmit rate of SU k. The maximum value of 1 to be achieved when R1/γ1=R k /γ k ,∀k. To ensure each SU is served in one allocation period, we define a noncontinuous point Φ=0, if ∀R k =0.
where and indicate the assignments of subchannel and power, respectively. The constraint C 1 implies all power value allocated to subchannels are positive; C 2 ensures the interference to PRNs at a tolerable level; C 3 indicates that each subchannel can only be used by one SU at any time; C 4 is the bandpass constraint of SU; C 5 is the proportional fairness constraint.
Objective function and problem decomposition
For a CRN system consisting of N available subchannels and K SUs that can crossover at most m subchannels, there are at most possible subchannel allocations. The feasible set is too huge to exhaust. Besides, the nonlinear constraints C 4 and C 5 in (9) increase the complexity to obtain the optimization solution. Therefore, it is prohibitive to find an optimizer in terms of computational complexity. In this article, we attempt to find a suboptimal alternative to decrease the complexity significantly while still delivering performance close to the global optimum.
Before designing of the suboptimal algorithm, we attempt to simplify the problem in (9) first. In Section “Objective function”, we analyze two equivalent objective functions to delete the constraint C 5, and then a hybrid objective functions is proposed. In Section “Problem decomposition”, the problem in (9) is decomposed into subchannels allocation and power allocation, and each of them has only two constraints. Section “Penalty function” discusses the design of penalty functions, by which transforming the two sub-problems into unconstrained optimization problems.
The global objective function is the maximum of ergodic sum capacity of SUs. It is difficult to achieve due to the constraint of proportional fairness. We need an equivalent objective function that is maximized simultaneously with global objective function. The maximum of proportional fairness and maximum of minimal capacity SU are two alternatives. For convenience, we denote the objective function of maximum of proportional fairness as MPF and maximum of minimal capacity SU as Max–Min–SU.
Due to the noncontinuous of feasible set, generally can only find a set , such that Φ∈(ε,1]. It is nontrivial to find out the Pareto-optimal front of set . The question becomes if there exist a equivalent function such that if and only if . Max–Min–User is one of them.
With the constraint of Φ=1, if , then (ρ∗,p∗)=arg maxmin R k .
where the constraints are the same as in (10). □
Hybrid objective function
where the constraints are the same as in (10). And we will discuss the performance for the three fitness functions in Section “Particle swarm optimization based framework”.
Ideally, subchannel and power should be allocated jointly to achieve the optimal solution in (12). However, due to the mixed binary integer programming, it is prohibitive computational burden at CBS, which leads the increase of computation cost and allocation delay. Hence, we separates the problem (10) into subchannel allocation and power allocation to reduce the complexity, because the continuous variable and binary variable can be handled independently.
where is the allocated power on subchannel n of PRN i.
where f(x) is the original objective function of the optimization problem. h(k) is a dynamically modified penalty value, k is the algorithm’s current iteration number; is the feasible set and H(x) is a penalty factor, which is always problem dependent.
The definition of penalty function in (17) is additive. In this article, two penalty functions based on (17) to solve the constraint C2 in problem (15) and (16) can be formulated as follows.
Additive penalty function
where I A (x) is indicative function. I A (x)=0 if x∉A and I A (x)=1 if x∈A. λ1 and λ2are the Lagrangian multipliers. In our problem, they are dependant on channel gains and power allocation results , resulting in changing in every resource allocation. This will introduce great burden in CBS. To simplify this problem, we propose multiplicative penalty functions, which is independent with and . Formally, the expressions of our proposed are written as follows.
Multiplicative penalty function
By analysis above, we transform the problem (9) into an alternative with objective functions (20) (21) and constraint C 1 in (15) (16). In the next section, we will propose a heuristic algorithm to solve the alterative problem.
Particle swarm optimization based framework
The PSO algorithm was introduced by James Kennedy and Eberhart (1995) as an effective batch of heuristic algorithms . Compared with other algorithms, PSO has better global searching ability at the beginning of the run and a local searching ability near the end of the run . It is also effective for integer programming .
Construct the particle to map the solution of interest problem;
Create the initial topology for swarm and parameters to initial the optimization;
Calculate fitness value for each particle;
Renew particle position;
Return to (2) until the solution satisfies the requirement of interest problem.
Following the work, in this section we design a PSO-based framework to solve the subchannel allocation and power allocation for CR system. At the beginning of Section “PSO structure”, we discuss the design of particle structure to establish the mapping between PSO and resource allocation problem. Then, in order to improve the velocity of convergence, we propose an initial topology of swarm exploiting the channel characteristics in Section “Suboptimal power distribution for a fixed sub-channel allocation”; Section “Particle renew” discusses the particle renew and the process of the proposed algorithm.
Suboptimal subchannel allocation
We name this particle as “base particle” because it is the start of particle structure for subchannel allocation and denote it as a 1×Nsensed dimension vector particlebase. Later we will explain the relationship between “base particle” and “particle” who, in fact, executes the solution searching work.
particlebase is not optimal because we just arrange SU order in a sequential way. Intuitively, we can use sorting algorithm to rearrange SU order to achieve higher objective (fitness) value. Bubble Sorting is a classical sorting algorithm with complexity O(n2). In this article, we use a modified bubble sorting algorithm to rearrange SU order. We denote the SU order as a 1×K dimension vector K and the element of K indicates the SU index. fitness K represents the fitness value with the SU order K and can be calculated by (20). The process is depicted in the following:
Algorithm 1 SU sorting algorithm
Generate K in a random permutation; for k=1 to K−1 for l=1 to K−k−1 Calculate fitness K by (20); Ktemp←Ktemp(l)←K(l + 1)Ktemp(l + 1)←K(l) Calculate fitnessK tempby (20); if fitnessK temp>fitness K K←Ktempelse continue; end for end for
Based on particleinit, we can generate a set of 1×Nsensedimension vector particle as follows:
for i=1 to Npso
where Npso is the number of particles, particle i refer to the i th particle. ω follows uniform distribution in [0,Nsense].
(x,y) represents the operation of modulus after division and we define special point mod(x,y)=x if x/y=m, m is an arbitrary integer. particleshadow,i(n) indicates the n th element of the i th particleshadow.
Substituting (32) into (20) and we can get the fitness(i) of the i th particle.
Suboptimal power distribution for a fixed sub-channel allocation
where c=4.1,χ c1=χ c2=1.149445, and so χ≈0.729 are recommended.
Therefore, the PSO-based resource allocation can be described as follows:
Algorithm 2 PSO-based adaptive resource allocation algorithm
Step 1: Initialization for i=1 to S sensingSpectrum(i) end for calculate |Ω k | for all k according to (28); generate base particle according to Algorithm 1 generate particle and shadow particle according to (30) (31) Step 2: Subchannel Allocation for i=1 to Npso calculate the fitness(i) according to (32) end for renew Gbest, Gparticle, and Pparticle i ∀i renew velocity i and particle i ∀i according to (33) (34) if satisfy the stop conditions go to Step 3 else go to the top of Step 2; end if Step 3: Power Allocation Transform particle according to Section “Max–Min–SU”; for i=1 to Npso calculate the fitness(i) according to (32) end for renew Gbest, Gparticle , and Pparticle i ∀i renew velocity i and particle i ∀i according to (33) (34) if satisfy the stop conditions stop algorithm else go to the top of Step 3; end if
Computational complexity analysis
According to the analysis above, the computational complexity of proposed algorithm can be segmented into four parts: initialization, initialization topology of swarm, subchannel allocation, and power allocation, where subchannel allocation and power allocation can be further segmented into adapting and updating parts.
Computational complexity upper bounds of four algorithms
Adapting of subchannel
Gbest and Renew of subchannel
Updating of subchannel
Adapting of power
Gbest and Renew of Power
Updating of power
Simulation results and discussion
In this section, we present the simulation results to show the performances of the proposed resource allocation algorithm.
where hBSand hMSare the height of base station and mobile station, respectively. Without loss of generality, we assume hBS=32 m and hMS=1.5 m; F i is the central transmission frequency. In this article, three PRNs are assumed to be licensed in LTE potential band, with central frequency F1=1805 MHz, F2=1930 MHz and F3=2110 MHz, respectively. The shadowing is implemented by lognormal distribution with standard deviation values of 6 dB. Each PRN share 20 MHz spectrum with CRN in overlay mode. We assume that the subchannel spacing is approximate to 180 kHz, which is equal to one resource block (RB) in LTE network and hence the maximal available subchannels in each PRN is about 110(19.8 MHz). For small-scale fading, we adopt Clarke’s flat fading model with six independent Rayleigh multipaths the same as in . The power delay profile is assumed exponentially decaying with e−2l, where l is the multipath index. Hence, the relative power of the six multipath components are [0,−0.869,−17.37,−26.06,−34.74,−43.43].
Simulation parameter list
Number of PRN: S
Distance between CBS and PBS: 2d
Height of base station hBS:
Height of mobility station: hMS
Number of SU:K
Total power limit of PRN 1:
Total power limit of PRN 2:
Total Power Limit of PRN 3:
Center frequency of PRN 1: F1
Center frequency of PRN 2: F2
Center frequency of PRN 3: F3
Maximal available bandwidth:
Bandwidth of each subchannel: W
Bandpass limit of SU: ∀k
BER limit of SU: BERmin
Proportional fairness: Φ
Number of particle:Npso
Maximal iteration of subchannel
Maximal iteration of power
Results and discussion
Comparisons with different objective functions
As shown in Figure 9, the proposed hybrid scheme outperforms the other two schemes in terms of both minimum user’s capacity and sum capacity. This is because that the hybrid scheme combines the advantages of the MPF and the MAX–MIN–SU schemes. Specifically, the proposed scheme possesses a medium convergence ability with slight fluctuations (as shown in Figure 9a), which enables the search process jumping out the local traps with high probability; furthermore, with the consideration of maxminR k , the hybrid scheme can also keep the quality of solution in a high level. Figure 9c shows the final resource allocation results with three schemes. We can see that the hybrid scheme has a higher capacity than the other two schemes for most SUs. Therefore, the proposed hybrid objective function can provide better system performance and user experience.
In addition to the comparisons of different objective functions, two other results should be noticed as well. First, we can see that the MPF scheme outperforms the hybrid scheme in terms of proportional fairness while the hybrid scheme outperforms the MPF schemes in terms of capacity. This result reflects the tradeoff between the proportional fairness and the sum capacity, which is consistent with the conclusion in . Second, as shown in Figure 9b, we can see that the improvement of system performance is limited by power allocation (less than 10%). Therefore, we can remove the power allocation process with little performance loss, if the system is subject to the computational complexity constraint.
Comparisons with the conventional algorithm
Impact by spectrum sensing errors
where m is the number of sampling points, γ is the detector threshold and Q(·) is the standard Gaussian complementary CDF. P is the received average signal power and σ2 represents the noise variance, and thus the average SNR is P/σ2.
The utility function U consists of two parts, where ωsuNidle(1−Pf) is reward part and ωpu·NbusyPmis penalty part. This means that when CRN senses correctly an idle subchannels, he would be rewarded and when CRN senses wrongly a busy subchannel, he would be penalized. ωsu and ωpu represent the importance of CRN and PRN, respectively.
In this article, we develop an adaptive resources allocation scheme for CRNs in multiple PRNs environment. An MINP formulation is established to describe the scenario where a CRN exists around multiple PRNs. To obtain an adaptive resources allocations algorithm with polynomial time complexity, we design a hybrid objective function and two penalty functions, transforming the MINP into two unconstrained optimizations. Then, a PSO-based heuristic algorithm with low complexity initial topology is presented. Three computer simulations are carried out to verify the performance of our proposal. The results reflects that the proposed algorithm is efficient in terms of convergence and quality. Through comparisons, we show that the proposed algorithm outperforms traditional ARA algorithm both in sum capacity and proportional fairness.
This study was supported by the National Basic Research Program of China (973 Program) (Grant No. 2009CB320402), and the National Natural Science Foundation of China (Grant No. 61032003 and 61001092).
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