 Research
 Open Access
Energyefficient multicell resource allocation in cognitive radioenabled 5G systems
 Hengwei Lv^{1},
 Pandong Li^{1},
 Qinmengying Yan^{1} and
 Haijian Zhang^{1}Email authorView ORCID ID profile
https://doi.org/10.1186/s1363401805998
© The Author(s) 2019
 Received: 31 May 2018
 Accepted: 20 December 2018
 Published: 18 January 2019
Abstract
In this paper, we propose an energyefficient resource allocation (RA) algorithm in cognitive radioenabled 5th generation (5G) systems, where the scenario including one primary system and multiple secondary cells is considered. Because of the high spectrum leakage of traditional orthogonal frequency division multiplexing (OFDM), alternative modulation schemes regarded as the potential air interfaces in 5G are analyzed, e.g., filter bankbased multicarrier (FBMC), generalized frequency division multiplexing (GFDM), and universal filtered multicarrier (UFMC). Our objective is to maximize the whole energy efficiency of secondary system defined by the ratio of the capacity to the total power consumption subject to some practical constraints. The general formulation leads to a nonconvex mixedinteger nonlinear programming problem with fractional structure, which is challenging to solve due to its intractability and significant complexity. Therefore, we resort to an alternate optimization framework to optimize the variables of subcarrier assignment and power allocation, where successive convex approximation (SCA) is employed so that the general formulation is finally transformed into a solvable convex problem. Numerical results validate the effectiveness of the proposed RA algorithm, and the comparison with some existing RA algorithms is conducted. In addition, the performance of using different 5G candidate waveforms in the energyefficient RA algorithm is also presented and discussed.
Keywords
 5G
 Cognitive radio
 Modulation schemes
 Energy efficiency
 Resource allocation
1 Introduction
With the explosive growth of various communication services, more and more mobile terminals or users are seeking for accessing the communication networks. However, the current 4th generation (4G) communication technologies cannot meet the increasing communication demand, which greatly drives the development of the 5th generation (5G) communication technologies [1–3]. It has been expected that 5G not only should satisfy the great communication needs but the efficient utilization of scarce spectral resource should be also ensured. On the one hand, the current policy of the exclusive spectrum allocation cannot maintain the supply of additional spectrum to accommodate more mobile users, support higher capacity and lower latency requirements, and provide ubiquitous connectivity of the Internet of Things. On the other hand, the inadequate spectrum resource is not efficiently utilized, and a large portion of the spectrum is idle without being accessed by licensed systems [4, 5].
As a result, the concept of cognitive radio (CR) is put forward to solve the problem of 5G spectrum scarcity and improve the spectral efficiency by allowing secondary users (SUs) to occupy the idle spectrum [6, 7]. The CRenabled 5G systems provide the possibility that SUs can autonomously access the most meritorious spectrum and gain higher network capacity [8]. Currently, how to efficiently allocate spectrum resource to SUs becomes one of the key research topics in 5G. Existing resource allocation (RA) works aim at either maximizing the system capacity or minimizing the energy consumption. The large number of users and diverse services in 5G signify the huge system consumption; thus, maximizing the energy efficiency plays a critical role of performance assessment in future communications [9–11]. This paper takes the system consumption into account, and focuses on the energyefficient multicell RA algorithm in CRenabled 5G systems.
1.1 Related work
In the literature, plenty of existent works pay attentions to the RA problem by assuming one primary cell and a single secondary cell. The authors in [12] utilized the spectrum holes in primary user (PU) bands as well as active PU bands to propose a low complexity suboptimal solution for orthogonal frequency division multiplexing (OFDM) and filter bankbased multicarrier (FBMC) systems. Spectrum sensing and resource allocation were jointly considered in [13], and the water filling algorithm is modified for the optimization problem. In [14], the authors proposed an algorithm to maximize the system capacity through exploiting the problem structure to speed up the convergence. The authors in [15] investigated the effective capacity maximization problem under statistical delay guarantee by the Lagrangian dual decomposition method. An energy consumption issue with channel uncertainty was studied in [16], and a fast algorithm is derived to settle the quasiconvex problem. In [17], the resource allocation problem was solved by the Hungarian algorithm and the gradient projection method. However, it is noteworthy that the above RA algorithms may be not suitable for handling more complicated situations where multiple secondary cells are involved, which is the practical scenario in future ultradense 5G networks.
It is quite difficult to solve the CR RA problem of multicell due to the complicated system structure and the existence of cochannel interference between different cells. To make this problem tractable, some RA algorithms have been developed. A distributed algorithm containing two loops [18] was designed for the weighted sumrate maximization problem with multicell uplinkdownlink throughput. An interferencelimited method was presented in [19], where the cochannel interference is assumed to be constant and then transformed into a constraint. In [20, 21], the noncooperative game theory was adopted to solve the problem of multicell, and Nash equilibrium is guaranteed. However, less efforts have been devoted to the research of the energyefficient multicell resource allocation. An iterative subchannel allocation and power allocation algorithm was proposed in [22] for joint optimization of energy and spectral efficiency. In [23], a distributed resource allocation schemebased game theory, taking user fairness and priority into consideration, was proposed to solve the energyefficient RA problem. The problem of power control jointly considering energy efficiency and delay was solved in [24] by noncooperative game. The energyefficient downlink resource allocation in heterogeneous networks was investigated in [25], where a nonconcave nonlinear objective function and nonlinear constraints are incorporated. Fractional programming and branchandbound method are utilized to obtain the solution. The authors in [26] considered an equivalent nonfractional form of the formulated problem and proposed an iterative algorithm to optimize the objective. Nevertheless, the aforementioned literatures did not investigate the impact of spectral leakage of different 5G waveforms on energy efficiency.
1.2 Contributions

A practical energyefficient multicell RA problem in CRenabled 5G systems is formulated. In practice, the interference between the primary system and the secondary cells actually exists due to the spectral leakage; thus, the interference vectors in [27–30] are employed in the proposed RA formulation. To the best of our knowledge, there are few works which consider the quantified interference vectors to formulate the objective function and its corresponding constraints in 5G resource allocation problem.

The general formulation is a mixedinteger nonlinear programming problem, and we propose an efficient RA algorithm to transform the intractable nonconvex problem into a convex one. Specifically, the variables of subcarrier assignment and power allocation are alternately optimized. Once given the subcarrier assignment, a novel transformation is utilized to eliminate the fractional structure and successive convex approximation (SCA) is adopted to solve the power allocation. Moreover, the convergent property can be ensured. The proposed RA algorithm is compared with some existing algorithms, and the simulation results show the advantages of the proposed algorithm.

The impacts of spectral leakage by using different multicarrier modulation schemes on energy efficiency are quantitatively analyzed. Although OFDM has been widely used in many applications, e.g., longterm evolution (LTE), it can hardly satisfy the need of supporting asynchronous transmission to avoid the heavy synchronization signaling overhead caused by massive terminals [31]. Moreover, the significant spectral leakage of OFDM will induce severe adjacent channel interference. In 5G networks, more flexible 5G waveforms [32] are required to overcome the upcoming challenges, e.g., FBMC [33–35], generalized frequency division multiplexing (GFDM) [36], and universal filtered multicarrier (UFMC) [37]. Most of the existing RA algorithms only take either OFDM [14–16] or OFDM/FBMC [12, 20, 38] into account, and it still needs to make a thorough inquiry of the specific influence about different waveforms. In our RA algorithm, all of the above 5G waveforms are compared by evaluating the effect of waveforms on energy efficiency, and the results can provide a reference base for designing and selecting the physical waveform in 5G systems.
The remainder of this paper is organized as follows. In Section 2, the system model is illustrated and the optimization problem is formulated. Section 3 describes the optimization frame of the proposed resource allocation algorithm. The complexity of the proposed algorithm is analyzed in Section 4. The simulation results are presented in Section 5. Finally, we conclude the paper in Section 6.
2 System model and problem formulation
2.1 System model

Considering the downlink transmission, each user receives signals from their own base station respectively, and the signals from other base stations are regarded as interference, i.e., each user is only attached to one cell [38].

Assuming that SUs are randomly located around their own SBS, all base stations serve as accessing points to their corresponding users, and single antenna is equipped for the transmitter and receiver [20].

It is practical to assume that the primary system and all the secondary cells are asynchronized; thus, the interference due to spectral leakage exists between primary and secondary systems [27].

All the secondary cells are synchronized, and the spectrum sensing is assumed to be achieved by a public sensing node. The sensing results are transmitted to the SBSs by a common control channel, i.e., all secondary cells share the same sensing results.

Since the secondary cells and primary cell are subordinate to two different systems, generally, their crossgains are unaccessible. But for simplicity and providing an interference protection to primary cell, we only estimate the channel gains from secondary system to primary cell.
where σ^{2} means additive white Gaussian noise power, I_{ps} denotes the interference from primary system which is induced by the asynchronization transmission, and I_{ss} denotes cochannel interference between secondary cells. The power variable p^{nf} is gathered into the matrix P with size N×F.
Interference vector table of different candidate waveforms in 5G
π(f,l)=1  π(f,l)=2  π(f,l)=3  π(f,l)=4  π(f,l)=5  π(f,l)=6  π(f,l)=7  π(f,l)=8  

V _{PS}  0  0  0  0  0  0  0  0 
V _{OFDM}  8.94E−2  2.23E−2  0.995E−2  0.560E−2  0.359E−2  0.250E−2  0.184E−2  0.112E−2 
V _{ FBMC}  8.81E−2  0  0  0  0  0  0  0 
V _{UFMC}  12.27E−2  0  0  0  0  0  0  0 
V _{GFDM}  4.80E−2  4.18E−2  0.140E−2  0  0  0  0  0 
where \(P_{p}^{l}\) denotes the power on the l_{th} subcarrier occupied by PU, \(h_{\text {ps}}^{nmf}\) denotes the channel gain from PBS to the m_{th} SU of the n_{th} cell on the f_{th} available subcarrier, and \(g^{n{\prime }f}_{\text {nm}}\) denotes the channel gain from the \(n^{\prime }_{\text {th}}\) SBS to the m_{th} SU of the n_{th} cell on the f_{th} available subcarrier.
2.2 Problem formulation
where the first term P_{dp} in the denominator denotes the dynamic power consumption, e.g., power radiation of circuit blocks in radio frequency chain, while the second term P_{sp} is the static power employed for cooling system and power supply, and ξ in the last term means the inverse of power amplifier efficiency [39, 40].
The constraint (6a) is the sum power budget of each secondary cell, where the sum power of all available subcarriers in each cell should be no more than P_{th}. The constraint (6b) limits the power level on each subcarrier, which should not exceed P_{sub}. The last two constraints (6c) and (6d) indicate that each subcarrier must be accessed at most one user at a given time.
As a CRenabled 5G system, the constraint keeping the interference from secondary cells to primary system must be considered. Denote \(h^{nf}_{\text {sp}}\) as the real channel gain from the n_{th} SBS to PU on the f_{th} available subcarrier. According to the last item in the assumptions, \(h^{nf}_{\text {sp}}\) is unknown and needs to be estimated.
The works in [41, 42] give a real propagation model of the channel, which decomposes \(h^{nf}_{\text {sp}}\) into \(L^{nf}_{\text {sp}}\) for large scale fading and \(S^{nf}_{\text {sp}}\) for small scale fading respectively, i.e., \(h^{nf}_{\text {sp}}=L^{nf}_{\text {sp}}S^{nf}_{\text {sp}}\). The \(L^{nf}_{\text {sp}}\) is only decided by shadowing and distance between the communicating parties. The \(S^{nf}_{\text {sp}}\) can be described as the product of two conjugate circular symmetric complex Gaussian variables with zero mean and unit variance. Thus \(S^{nf}_{\text {sp}}\) has a Gamma distribution with unit shape parameter and unit scale parameter, i.e., \(S^{nf}_{\text {sp}}\sim \Gamma (1,1)\).
where \(g_{\text {pp}}^{l}\) is the channel gain from PBS to the PU occupying the l_{th} unavailable subcarrier. The larger the value of β is, the lower the interference threshold is.
3 Optimization method via alternate way
It is noted that Q1 in (12) is a mixedinteger nonlinear programming problem, which is quite difficult to solve. Firstly, the integer indicator variable \(\theta ^{nm}_{f}\) equals to 1 or 0, and the real variable p^{nf} is involved. Both discrete and continuous variables will give rise to high complexity. Secondly, the ratio of a nonconvex function to a linear function in (5) is also a nonconvex structure. Finally, the cochannel interference might also induce the nonconvex property. In this section, an efficient optimization scheme based on alternate optimization and SCA is proposed to transform Q1 into a solvable problem, and for a clear illustration, it is summarized in Algorithm 1, which includes the procedures of subcarrier assignment and power allocation. In the following, these two parts will be described in details.
3.1 Heuristic subcarrier assignment
In order to solve the optimization problem Q1, the subcarrier assignment indicator \(\theta _{f}^{nm}\) should be firstly excluded from the objective function and constraints. Because the problem Q1 will generate M^{NF} possible subcarrier allocation schemes, which is prohibitively expensive especially in a highdimensional system. To avoid the unbearable complexity, a heuristic subcarrier assignment is employed by means of an alternate manner.
For a given power allocation, the problem Q1 is equivalent to maximizing the total system capacity subject to the constraints (6c) and (6d). Generally, it is not sufficient to assign subcarriers to one user with the best channel gain. In this context, the cochannel interference and the power on subcarriers are not taken into account. To realize the maximal capacity of communication networks, subcarriers can be allocated by employing the maximal SINR criterion [43]. In our work, we assume an initial feasible power distribution is given^{1}, and then the subcarrier assignment proceeds on the basis of the maximal SINR criterion.
After accomplishing subcarrier allocation (i.e., the integer variable is excluded), and the residual problem in Q1 is reformulated as Q2:
Once the solution of Q2 is obtained, the subcarrier assignment will be executed until convergence. The procedures of this alternate optimization are summarized in line 2 ∼12 of Algorithm 1.
The convergence property can be derived with the following idea. For a given power allocation \(\mathbf {P}_{t_{1}}\), the maximal SINR criteria maximize the objective within the feasible subcarrier assignment \(\pmb {\theta }_{t_{1}+1}\). And for a fixed \(\pmb {\theta }_{t_{1}}, \; \mathbf {P}_{t_{1}}\) is the optimal solution of maximizing the objective within the feasible power distribution. In other words, the arbitrary optimization of θ and P will improve the objective during the alternate process. Therefore, Algorithm 1 is convergent.
3.2 Power optimization
3.2.1 An equivalent transformation
It is observed that the objective function in Q2 has a ratio structure consisting of a nonconvex function and a linear function, which is known as a fractional programming problem. Generally, the routine method [25, 26, 38] of solving such problem is to transform the objective function into a parametric subtracted form. It needs to update the parameter of the ratio iteratively according to the Dinkelbach algorithm reported in [44] or bisection method [45].
While in this paper, we do not invoke the Dinkelbach procedure to make the subtracted transformation and iteratively update the ratio. Inspired by [39], we solve the problem with the ratio structure by means of a novel equivalent transformation which can directly acquire the optimal value of the ratio. Let us introduce some auxiliary variables x, y, and η. Define the following problem Q3:
In Q3, η is applied to approximate the original ratio, and x and y are used to approximate the denominator and numerator of the objective function in Q2 respectively. For Q3, we have the following theorem.
Theorem: Q3is an equivalent substitute ofQ2.
Proof: The equivalency can be proved by contradiction. Assuming that at the optimal point (x^{∗},y^{∗},η^{∗},P^{∗}), the inequality constraints of (), (), and () do not hold; therefore, there must exist a point (x^{∘},y^{∘},η^{∘},P^{∘}) which improves the optimal value, i.e., η^{∘}>η^{∗}. And this contradicts the initial assumption. Thus, we can conclude that the inequality constraints of (), (), and () must be active at the optimality, i.e., all of (), (), and () must be equality constraints, and it indicates that Q2 can be substituted by Q3. In the subsequent subsection, we mainly concentrate on how to solve the power allocation problem Q3. □
3.2.2 Power allocation based on SCA
On the basis of theorem, we can find the solution of Q3 instead of solving Q2 with fractional structure. However, it is clear that solving Q3 directly is still troublesome due to the nonconvexity of constraints () and (). The constraint () has a relatively simpler structure than (), so we firstly show how to deal with ().
and it can be found that the constraint (17) is convex.
where σ^{2}+I_{ps} is simplified as δ^{2}. The left side of (18) can be seen as the sum of three terms. The term −y^{2} approximates the capacity which is a concave function of y, and the other two terms originate from the formula of capacity. The expression (18) leads to a nonconvex feasible area; thus, the critical situation lies in how to construct a convex set from (18) on the given approximated point \(\left \{\widetilde {\mathbf {P}}_{t_{2}},\widetilde {x}_{t_{2}},\widetilde {y}_{t_{2}}\right \}\).
By introducing a logarithmic manipulation P= exp(P^{′}) and bringing it into (21), then the final optimization problem after approximation is formulated as Q4:
where \(\psi \left (\exp \left (\mathbf {P}^{\prime }\right)\right)\triangleq \delta ^{2}+\sum \limits _{n^{\prime }\neq n,n^{\prime }\in \mathcal {N}}^{N} \exp \left ({p^{\prime }}^{n{\prime }f}\right)g^{n{\prime }f}_{nm}\).
For the above problem in Q4, we have the following two propositions.
Proposition 1
Q4 is a convex optimization problem.
Proof
Firstly, the sum of exponential functions is convex, so the constraints () ∼ () and () are all convex sets. The constraint () is a linear constraint which is also convex. Lastly, \(\sum \limits _{n=1}^{N}\sum \limits _{f=1}^{F}\log _{2}\left (\widetilde {\phi }\left (\exp \left (\mathbf {P}^{\prime }\right)\right)\right)\) is a linear function of P^{′}, and it has been proved that the logsumexp function is convex [46], so we can find that the left side of () in Q4 is the sum of linear functions and two concave functions, which implies () is also a convex set. Therefore, the convexity of the constraint sets is verified, i.e., Q4 is a convex problem. □
The problem Q4 can be efficiently solved by the existing convex optimization algorithms [46], or the optimization toolbox CVX [47]. However, the solution of Q4 subject to constraints only corresponds to initial approximate point \(\left \{\widetilde {\mathbf {P}}_{t_{2}},\widetilde {x}_{t_{2}},\widetilde {y}_{t_{2}}\right \}\). In order to produce an improvement point compared to \(\left \{\widetilde {\mathbf {P}}_{t_{2}},\widetilde {x}_{t_{2}},\widetilde {y}_{t_{2}}\right \}\), herein, the SCA in [48, 49] for constraints is employed. Once we obtain the solution of Q4, it will take the place of the previous approximated point according to (16) and (20), and the iteration procedure goes on until convergence. The iterative procedure is summarized in line 4 ∼10 of Algorithm 1.
Proposition 2
Each iteration of SCA makes an improvement compared to the previous iteration and the iteration procedure is convergent.
Proof
It is assumed that the optimal solution obtained at the iteration t_{2} is \(\left \{\mathbf {P}^{*}_{t_{2}}, {y}^{*}_{t_{2}}, {x}^{*}_{t_{2}}\right \}\), which is also feasible and satisfies the constraints of Q3 for the next approximation. This mainly results from the fact that the approximated parts of the constraints () and () are less than the original corresponding parts of constraints () and (). It indicates that the iteration sequences of the objective are nondecreasing. In addition, the constraints are bounded. Therefore, the process of successive convex approximation finally converges, which proves Proposition 2. □
where Π is a function of variable α.
It can be verified that the approximation of (16) and (20) satisfies the above three conditions. In (23), the first condition guarantees the approximation is tightening the constraints of () and (), and the solution of approximated problem is also a feasible point for the next approximation; the second condition ensures the improvement of the objective during each iteration; the last condition ensures the satisfaction of the KKT conditions after a series of iteration approximation.
4 Complexity analysis
In this section, the computational complexity of the proposed algorithm is analyzed. The optimization toolbox CVX is applied to solve Q4 via the interior point method (IPM), which dominates the main complexity of the whole algorithm. In IPM, by contaminating the objective and inequality constraints, a logarithmic barrier function is constructed and optimized along a central path through Newton method. With selfconcordance for this function, the number of Newton steps is proportional to the square root of the number of inequality constraints, and the complexity of each Newton increases cubically with the number of inequality constraints [46, 50].
The analogous means of [50] can be adopted to transform the constraints with logsumexp into a set of equivalent constraints with selfconcordance. The total number of equivalent constraints is 6FN+N+2FLN+L+2FN^{2}. Therefore, the whole complexity is \(\mathcal {O}\left (T_{1}T_{2}\left (FLN+FN^{2}\right)^{3.5}\right)\) after eliminating the multiplicative factors and nondominant terms, where T_{1} and T_{2} are the numbers of alternate optimization and successive convex approximation, respectively.
5 Simulation results and discussions
Simulation parameters
Parameters  Value 

Cell range  0.1 ∼2 km 
Total subcarrier, F_{tot}  12 
Number of cells, N  4 
Number of users, M  3 
Number of available subcarrier, F  8 
Inverse of drain efficiency, ξ  5 
P _{dp}  3.1 W 
P _{sp}  1.9 W 
Pathloss (dB)  128.1+37.6log10(d) 
Bandwidth  15 KHz 
σ ^{2}  −174 dBm/Hz 
In Fig. 5, we also observe that the proposed algorithm achieves higher energy efficiency in both cases of either lowpower budget or highpower budget. With the same power consumption, the proposed algorithm has the largest capacity, i.e., our algorithm needs the least consumption to achieve the same capacity. The reason is that a linear pricing factor is required to impose the penalty for the DPGA in [23], which is avoided in the proposed algorithm. For IILA in [19], the cochannel interference is assumed to be constant, while the proposed algorithm makes an improvement for the cochannel interference by using the successive convex approximation.
In the second parts of the experiments, the impacts of the proposed algorithm with different system parameters on energy efficiency by using various 5G waveforms are presented. The first three figures are obtained under ideal channel gain, and the last one is obtained under estimated channel gain.
In Fig. 11, the number of cells is fixed to 3, and the number of SUs is set to 2, 3, 4, 5, and 6. According to Fig. 11, it can be found that the number of the SUs will bring higher energy efficiency. This results from the fact that the increasing number of the SUs enlarges the system capacity when the system power budget remains constant, i.e., the ratio of capacity to consumption is increased. Therefore, more SUs benefit the energy efficiency performance. However, we also can forecast that under the conditions of given number of subcarriers, more SUs means less accessing opportunity and worse quality of service (QoS). The tradeoff of the system energy efficiency and the QoS of SUs also need to be considered.
6 Conclusions
This paper proposes an energyefficient resource allocation algorithm aiming at solving the awkward nonconvex problem involving multiple cells with multiple SUs per cell. The heuristic subcarrier assignment and convex approximation are adopted to sequentially transform the nonconvex form into a convex one. Numerical results validate the superiority of the proposed algorithm for achieving higher energy efficiency compared with some existing algorithms. Furthermore, the impacts of potential modulation schemes in 5G on energy efficiency are also investigated, and we reach the conclusion that the waveform with less spectral leakage is more suitable for energyefficient 5G systems.
Generally, it makes no difference whether the initial power is feasible or not, which will be demonstrated by the subsequent simulation.
Declarations
Acknowledgements
This work was supported by the National Natural Science Foundation of China with Grant Number 61501335 and Hubei Provincial Natural Science Foundation of China (No. 2018CFB225).
Funding
National Natural Science Foundation of China with Grant Number 61501335 and Hubei Provincial Natural Science Foundation of China (No. 2018CFB225).
Availability of data and materials
Not applicable.
Authors’ contributions
HL and PL conceived and designed the study. HZ performed the experiments. HL wrote the paper. PL, HZ, and QY reviewed and edited the manuscript. All authors read and approved the manuscript.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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