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Green fronthaul allocation and power management in CloudRAN
EURASIP Journal on Wireless Communications and Networking volume 2018, Article number: 188 (2018)
Abstract
In cloud radio access network (CloudRAN), most previous research aims to reduce the energy consumption of the total system and ignores specific requirements of energysaving in mobile users. For the meantime, some efforts have been made to devise efficient signal quantization techniques for fronthaul capacity restriction to improve the performance of CloudRAN. To improve the usercentric energy efficiency (EE), we propose two kinds of optimization algorithms in orthogonal frequency division multiple accessbased CloudRAN in this paper, whereby Gaussian quantization and uniform scalar quantization methods are utilized. For singleRRH scenario, alternative iterative optimization algorithms are proposed to maximize users’ EE, by jointly allocating resources. Furthermore, in more general scenario for multiple RRHs, authors investigate a modified particle swarm optimization (MPSO) algorithm to solve more complex problems, which remain nonlinear and nonconvex. Simulation results demonstrate the proposed schemes in this paper outperform conventional solutions and improve EE of users.
Introduction
Motivation
With the rapid increment of mobile network, it is estimated that mobile data traffic will rise approximately 1000 times from 2010 to 2020, and the cost is predicted to decrease 100 times by 2020 [1]. The rapid increase of data traffic has brought about a fastgrowing high burden on the existing communication system, which include more strict requirements on spectrum efficiency (SE), energy efficiency (EE), capital expenditures, and operating expenditures. In order to achieve above targets, China Mobile raised CloudRAN in [2], which is considered as one promising candidate for nextgeneration communication technologies [3].
CloudRAN is a cloudbased, green, clean, and collaborative radio access network [4]. Figure 1 shows a simplified diagram of a CloudRAN structure. In this paper, each single mobile user is corresponding to one or more remote radio heads (RRHs). RRHs, as limited function transceivers, are attached to the central cloud via a limitedcapacity fronthaul link. The baseband unit (BBU) pool, also called as “cloud,” consists of multiple BBUs, for the better adaptation to nonuniform traffic. The BBU pool is attached to the core internet via a backhaul link, through gateway relays. Different from a traditional communication system, CloudRAN requires fewer BBUs and saves network operating costs.
Energysaving problem has attracted lots of attention in CloudRAN research field. But according to the authors knowledge, most of the previous research aim to reduce the energy consumption of the total system and ignore specific requirements of energy saving of mobile users [5–7]. To reduce the interference between different channels [8] and decrease design complexity, we introduce orthogonal frequency division multiple access (OFDMA) to CloudRAN systems in this paper. Nevertheless, the fronthaul link capacity of CloudRAN is limited, which is different from a conventional cellular system [9]. To further improve system performance of CloudRAN, signal quantization techniques have been applied in related research [10].
Overall, our motivation is to design resource allocation scheme to improve the energy efficiency of users, under “signal quantization” mechanism in CloudRAN system in this paper. In singleRRH scenario, authors use fractional programming and Lagrangian dual decomposition to jointly allocate power and fronthaul capacity. But in a more general scenario for multiple RRHs, the above optimization methods could not be directly utilized because of the more complex problems, in which objective functions and constraints also remain nonlinear and nonconvex. Instead, we need to seek a new optimization method to avoid slow convergence and high complexity. Actually, there exists a clear conflict between optimizing EE only and optimizing SE only. We will consider it in another paper, due to space limitation.
This paper focuses on the algorithm for jointly allocating user uplink transmit power and fronthaul capacity. The optimization process mainly occurs in the physical layer and does not know any design details of frames, including the number of signaling and specific bit values. Moreover, this article assumes the BBU pool knows all the information (including CSI); when all users do not move in the entire process, the users’ association with RRHs does not change. In the process of resource allocation, there is little signaling overhead among cloud, RRHs, and users. Hence, we could not directly perform quantitative analysis of signaling overhead for CloudRAN systems. However, by using the related technologies, such as aggregation of BBU pool to increase the fault tolerance, “signal quantization/compression” for fronthaul link, the CloudRAN system could reduce the signaling overhead greatly.
Related work
In CloudRAN, the EE performance metric has attracted considerable attention because of the rapid growth of carbon emission and running cost of wireless communication systems [11, 12]. In [5], crosslayer resource management problem is formulated as a mixedinteger nonlinear programming problem, which could be relaxed into an easytosolve extended sumutility maximization problem. Through jointly ULDL (uplinkdownlink) user association and beamforming design, a NPhard problem of energy minimization is solved by converting to an original DL issue with two separate correlated subproblems for the original and virtual DL transmissions in CloudRAN [6]. Dai and Yu [13] compare the energy efficiencies of the datasharing strategy and compression strategy by utilizing reweighted l_{1} minimization and convex approximation. Wang et al. [14] introduce mobile cloud computing into CloudRAN, while authors establish a joint energysaving issue into a nonconvex optimization with the constraints of task operating time, transmitting power, etc. In general, the above work pays attention to bring down the total energy consumption problems (unit: Joule), ignoring the specific energysaving needs of the users (unit: Bps/W).
OFDMA, as a promising multiaccess technique, has proved its advantages in both frequency and time domains to offer high throughput in the 4G system [15, 16]. As mentioned above, we bring in OFDMA for the CloudRAN in this paper because of its advantages over interference avoidance and encoding design. Thus, complex beamforming design [17, 18] and interference cancellation are not needed in OFDMAbased CloudRAN in this paper. And it also has strong compatibility with the current 4G standards.
But in OFDMAbased CloudRAN system, on account of fronthaul capacity limitation, the conventional energysaving methods cannot be directly used. According to [2], the fronthaul traffic generated by a single user can easily reach multiple Gigabit byte per second (Gbps) because of the dense deployment of RRHs. And in practical CloudRAN system, a fiber link with magnitude of Gbps capacity is often utilized to transmit mobile data. Some signal compression/quantization methods have been studied in various networks [8, 10, 19] to enhance the system performance and save fronthaul capacity resource. Furthermore, how to introduce effective “signal quanzation” techniques to usercentric energysaving problem is still an open issue in OFDMAbased CloudRAN.
Main contributions
The contributions of this paper could be shown below:
∙ Different from the prior work, we aim to resolve the energysaving issue of mobile users in an OFDMAbased CloudRAN. In the UL transmission, under two different quantization methods, a joint resource allocation issue is formulated to maximize the energy efficiency of users, when two corresponding restrictions are user’s UL transmission power and fronthaul capacity of RRHs. By solving the above problems, this paper intends to provide a new research direction for EE improvement in CloudRAN.
∙ In singleRRH scenario, this paper investigates a joint optimized resource allocation scheme to realize usercentric energysaving goal, by utilizing Lagrange dual decomposition and iterative optimization method. Under Gaussian quantization and uniform scalar quantization, some useful insights on the optimal allocation plans can be obtained, respectively.
∙ In a more general scenario for multiRRH, the similar optimization methods could not be directly utilized because of the more complex problems, in which objective functions and constraints also remain nonconvex and nonlinear. Instead, authors design a new ModifiedPSO algorithm to solve this issue. Simulation results confirm the proposed schemes in this paper outperform conventional solutions.
Organization
The rest of this paper is organized as shown below. Section 2 discusses system model of CloudRAN and two quantization ways utilized in fronthaul signal processing. Section 3 solves the joint optimization problem for singleRRH scenario and provide some useful simulation results. Section 4 extends the singleRRH scenario to the general scenario for multiRRH and deals with the joint optimization problem for multiuser. Finally, some concluding remarks are obtained in Section 5.
System model and quantization schemes
As shown in Fig. 1, the UL transmission in a single cluster of CloudRAN is considered. The core network, e.g., Internet, exists in the upper layer of CloudRAN. The central “cloud,” consists of multiple BBUs, is connected to the core network via a backhaul link. The RRH is equipped with single antenna and its number is M, denoted as \(\mathcal {M}=\{1,\ldots,M\}\). The number of singleantenna user is K, \(\mathcal {K}=\{1,\ldots,K\}\). For each RRH m, \(\forall m\in \mathcal {M}\), the capacity of fronthaul constraint is \(T^{\text {total}}_{m}\) bps.
In the uplink transmission process, mobile users send signals to RRHs over wireless channel firstly. Second, each RRH quantizes its received signal and sends the corresponding digital codewords to the BBU pool. Third, the BBU pool joint decodes the users’ messages carried on the signals from all the RRHs in the same cluster and upload the decoded messages through backhaul links.
The detailed models of signals and fronthaul link are showed as follows.
Signal model at RRH in OFDMAbased CloudRAN
In a system model, the total bandwidth B Hz, which is between K users and M RRHs, is divided equally over N subcarriers (SCs), \(\mathcal {N}=\{1,\ldots,N\}\). Single SC n is assigned to a single user simultaneously and Ω_{k} is denoted the SCs assigned to user \(k,\forall k \in \mathcal {K}\).
The signals received by RRH m at SC n is defined as
where
n∈Ω_{k} is the SC assigned to the user k,
h_{m,n,k} means the channel gain from kth user to mth RRH at nth SC,
p_{k,n} is the UL transmit power of kth user,
\(s_{k,n}\sim \mathcal {CN}(0,1)\) is the transmit signal of kth user at nth SC,
\(z_{m,n}\sim \mathcal {CN}\left (0,\sigma ^{2}_{m,n}\right)\) is the aggregation of additive white Gaussian noise (AWGN).
In this paper, we assume the SC allocation scheme Ω_{k} is scheduled for simplicity. In practical use, to improve the system performance, dynamic SC allocation scheme is often considered by allocating appropriate SCs to users of favorable wireless link conditions. We will pay more attention to more specific SC allocation strategies in future work.
Because the received symbol at SCs by each RRH is independent with each other, so we assume independent signal quantization at different RRHs. By utilizing a scalar quantization method [20], the quantized signal of y_{m,n} could be rewritten as
e_{m,n} denotes the quantization error for the received symbol y_{m,n} with zero mean and variance q_{m,n}.
After being quantified, \({\tilde {y}}_{ {m,n}}\) is transformed into serial bits and sent to the BBU Pool via fronthaul link.
Utilizing maximal ratio combining (MRC) technique [21, 22], the SNR of s_{k,n} is written as
where n∈Ω_{k}, \(k\in \mathcal {K}\).
Two quantization schemes
The first signal quantization method is Gaussian quantization (GQ). In Gaussian test channel (GTC) [23], e_{m,n} given in (2) is Gaussian distributed, \({e_{m,n}} \sim \mathcal {CN}\left ({0,{q_{m,n}}} \right)\). According to [23], the transmission rate of mth RRH’s fronthaul link via nth SC to forward uplink transmission data is denoted as
(G) superscript means variables in Gaussian test channel. Noise variance is included in the numerator of the second item in the bracket in the above formula (10). That is because the Gaussian white noise generated in the previous stage is used as part of the new signal during the generation of quantization errors at the RRH. Correspondingly, quantization noise becomes a noise component of the new signal to noise ratio.
The variance of e_{m,n} of GQ could be rewritten as:
The corresponding SNR obtained in (3) can be expressed as
Based on ratedistortion theory, the above Gaussian quantization method has the best theoretical performance while it is hard to implement practically. In [8], a more practical uniform scalar quantization (USQ) scheme has been proposed. Due to space limitations, we just list the following conclusion referring the above GQ part. The transmission rate in RRH m’s fronthaul link to forward the received data at SC n must satisfy the following constraint
(U) superscript means variables in USQ scheme. The variance of the quantization error e_{m,n} with USQ scheme can be expressed as
The corresponding signal to noise ratio (SNR) with USQ scheme can be expressed as
From the above expression, it can be seen the SNR of decoding s_{k,n} in CloudRAN is also related to both users’ allocation schemes {p_{k,n}} and RRHs’ fronthaul rate allocations \(T_{k,n}^{(G)}\), \(T_{k,n}^{(U)}\).
Joint optimization of the singleRRH scenario
In this subsection, K is defined as 1 and M is fixed to 1, which cause the omission of k and m. Authors define system bandwidth as B, user’s UL power maximum value as P^{total}, RRH’s fronthaul capacity restriction as T^{total}, and power loss of user except UL transmission power p_{n} as P_{c}. The optimization models based on two quantization schemes are as follows
s.t.
s.t.
Because (P1) and (P2) are both nonlinear nonconvex fractional programming problems, it’s hard to obtain the global optimal solution directly. The following parts aim to solve two optimization problems separately and obtain some meaningful conclusions.
Gaussian quantization
Taking into account nonconvex and nonlinear characteristics, an alternating optimization method is adopted to convert original fractional programming issue to two relatively simple ones.
In (P1), the fronthaul capacity is assumed to have been allocated optimally and denoted \(T^{(G)}_{n}=T^{(G)}_{n,opt}\). Then origin (P1) is rewritten as
Define \(\left \{p_{n}^{opt}\right \}\) as the optimal solution of new problem (15).
Correspondingly, UL transmit power is assumed to have been optimally allocated and denoted \(p_{n}=p_{n}^{opt}\). Then origin (P1) is rewritten as
Define \(\left \{T_{n,opt}^{(G)}\right \}\) as the optimal solution of new problem (17).
Next, before proposing iterative algorithms, authors will give the optimal solution of (15) and (17), respectively. Denote \(\zeta = {{R\left ({{p_{n}},T_{n}^{\left (G \right)}} \right)} \left /\right. {P\left ({{p_{n}}} \right)}}\) as the EE performance of mobile users, \(R(p_{n},T^{(G)}_{n})\) as the total throughput of users, P(p_{n}) as the total power loss. Then, problem (P1) can be converted to \(\mathop {\max }\limits _{\{ {p_{n}},T_{n}^{\left (G \right)}\}} \zeta = {{R\left ({{p_{n}},T_{n}^{\left (G \right)}} \right)} \left /\right. {P\left ({{p_{n}}} \right)}}\).
In problem (17), the object function can be expressed as \(\mathop {\max }\limits _{\{ {p_{n}}\}} \zeta = {{R\left ({{p_{n}}} \right)} \left /\right. {P\left ({{p_{n}}} \right)}}\), which is a typical fractional programming problem. Using Lagrangian duality method in [24], we could offer the propositions as follows.
Proposition 3.1
The optimal conclusion of UL transmit power control in (15) could be written as:
where
In (23), λ^{(i)} is the duality factor for power constraint. \({\chi _{\lambda }^{\left ({i + 1} \right)}}\) means the size of nonnegative step. ∇λ^{(i+1)} represents the size of subgradient for (i+1)th iteration.
Proof
Please refer to Appendix A. □
Different from problem (15), problem (17) is convex when \(T_{n,opt}^{\left (G \right)}\) could be obtained as follows
Proposition 3.2
The optimal conclusion of fronthaul capacity in (17) could be written as:
where
In the above expressions, βis a constant which satisfies \(\sum \limits _{n = 1}^{N} {T_{n,opt}^{\left (G \right)}} = {T^{\text {total}}}\).
Proof
Consult Appendix B for details. □
In Proposition 3.2, if the received SNR ν_{n} is below the threshold \(\frac {{\beta p_{n}^{opt} + \beta {P_{c}}}}{{1  \beta p_{n}^{opt}  \beta {P_{c}}}}\), \(T_{n,opt}^{\left (G \right)}\) is zero. That means the RRH need not transmit quantized signal to the BBU pool. Otherwise, if the received SNR ν_{n} is over the threshold, more quantized data need to be transmitted. The demand for fronthaul capacity is growing with higher values of ν_{n}.
To solve problem (P1), we design the following algorithm based on Propositions 3.1 and 3.2:
It must be particularly pointed out that the algorithm used in this paper is a centralized processing method, which is determined by the characteristics of CloudRAN itself. Compared with traditional communication systems, CloudRANs attenuate the performance of RRHs to reduce network deployment costs, with a formed BBU pool for more efficient centralized processing. Due to the following two reasons: (1) RRHs in CloudRAN only have limited functions, which could not meet the requirements of distributed processing; (2) Distributed processing requires a large amount of information to be exchanged among RRHs during the iterations of the algorithm. This will cause a lot of signaling overhead. We do not consider the usage of “distributed algorithms” in this paper.
Uniform scalar quantization
In the following sections, we aim to settle the problem (P2). Since the objective function of (P2) is similar to that in problem (P1), new integer constraint can be ignored firstly, then the propositions for problem (P1) could be redesigned for (P2). Therefore, an alternating optimization method is adopted to convert original fractional programming issue to two relatively simple ones. After solving two simple problems, the corresponding propositions are as follows.
Proposition 3.3
The optimal conclusion of UL transmit power control for problem (P2) which only contains power constraint could be written as:
where
In (32), λ^{(i)} is the duality factor for power constraint. \({\chi _{\lambda }^{\left ({i + 1} \right)}}\) means the size of positive step. ∇λ^{(i+1)} represents the subgradient in the (i+1)th iteration.
Proof
Similar to Appendix A. Proof of proposition 3.1. □
In Proposition 3.3, characteristic of optimal power allocation scheme \(p_{n}^{opt}\) with the given \(T_{n,opt}^{\left (U \right)}\) is similar to that in Proposition 3.1.
Proposition 3.4
The optimal conclusion of fronthaul rate allocation for problem (P2) which only contains fronthaul capacity constraint could be written as:
where
and β is a constant which satisfies \({\sum \nolimits }_{n = 1}^{N} {T_{n,opt}^{\left (U \right)}} = {T^{{\text {total}}}}\).
Proof
Similar to Appendix 6.2. □
After obtaining Propositions 3.3 and 3.4, the new integer constraint \(T_{m,n}^{\left (U \right)} = 2BD_{m,n}^{\left (U \right)}/N,{D_{m,n}} \in \{ 1,2,\ldots \}\) is considered in problem (P2). Based on Proposition 3.4, we input \({p_{n}} = p_{n}^{opt}\) and output a feasible solution of \(T_{n,opt}^{\left (U \right)}\). Hence, we introduce a new variable (0≤τ≤1) to transform integer constraint as followed
ℜ_{n} is the number which rounds down to \(NT_{ {n,opt}}^{\left (U \right)}/2B\), \(\left \lceil {NT_{ {n,opt}}^{\left (U \right)}/2B} \right \rceil \) denotes the number which rounds up to \(NT_{ {n,opt}}^{\left (U \right)}/2B\). For a given τ, the original \({T_{ {n,opt}}^{\left (U \right)}}\) changes into \({\frac {{2B}}{N}{\Re _{n}}}\) or \({\frac {{2B}}{N}{\Im _{n}}}\). It could be observed the objective function in (P2) is monotonically increasing over \({T_{ {n,opt}}^{\left (U \right)}}\). Hence, we should find the optimal τ_{n,opt} for each \({T_{ {n,opt}}^{\left (U \right)}}\) to ensure \({\sum \nolimits }_{n = 1}^{N} {T_{ {n,opt}}^{\left (U \right)}}\) as large as possible within fronthaul constraint. For a group of input \(\left \{{T_{ {n,opt}}^{\left (U \right)}}\right \}\), we need to design a corresponding group of output {τ_{n,opt}}, which contains N different element. For simplicity, we set the same τ_{n,opt} for all SCs and the subscript n can be ignored. Bisection method could be used to find the optimal τ_{opt}. Due to space limitations, we do not list specific algorithms for finding the optimal τ here. When τ=0, there are still significant differences between the two quantization schemes, mainly because of different target formulas.
Based on Proposition 3.3, Proposition 3.4, a complete algorithm is redesigned to resolve (P2):
SingleRRH scenario: numerical experiment
To evaluate our proposed algorithms for singleRRH scenario K=M=1 and compare with other resource allocation methods, we present related simulation conclusions in this subpart. The rest of this subsection is organized as follows. Different schemes of resource allocation over SCs for two quantization schemes are analyzed in subsection C1. In subsection C2, we analyze the energy efficiency gain causing by different optimization methods for Gaussian test channel. Then, the effect of different parameter τ on energy efficiency gain under USQ method is listed in subsection C3.
Power management and fronthaul capacity allocation over four SCs
In this simulation part, bandwidth B is set to 100 Mhz and N=4. The channel gains are fixed as h_{1}^{2}=1.28×10^{−9}, h_{2}^{2}=6.12×10^{−10}, h_{3}^{2}=2.9×10^{−11}, and h_{4}^{2}=1.5×10^{−11}. The power spectral density of noise is −169 dBm/Hz. User UL maximum power limitation P^{total} and maximum fronthaul limitation T^{total} are set to 0.2W, 0.4 Gbps. In singleuser subsection, power consumption of one user expect UL power is P_{c}/N=0.5 W/8 = 0.0625 W. In Figs. 2 and 3, six resource allocation methods are compared as follows:
Method 1: GQ Max EE: Joint Optimization in this paper. In this scheme, we joint optimize its uplink transmit power and fronthaul rate to maximize usercentric energy efficiency with Gaussian quantization, as mentioned in Algorithm 1.
Method 2: GQ Max EE: Power Optimization only. In this scheme, the RRH allocate its fronthaul link capacity over all SCs equally. Then, under \(T_{n}^{\left (G \right)} = {T^{\text {total}}}/N\), the user only optimize its uplink transmit power over SCs to maximize its energy efficiency.
Method 3: GQ Max EE: Fronthaul Optimization only. In this scheme, the user allocate its uplink transmit power over all SCs equally. Then, with p_{n}=P^{total}/N, the RRH only optimize its fronthaul link capacity over SCs to maximize user’s energy efficiency.
Method 4: GQ Max Throughput: Joint Optimization. In this scheme, we reappear the optimization method in [8] and joint optimize its uplink transmit power and fronthaul capacity to maximize user’s throughput instead of user’s energy efficiency.
Method 5: Equal Fronthaul and Power Allocation. During this scheme, user allocates its uplink transmission power over all SCs equally when RRH allocates its fronthaul link capacity over all SCs equally.
Method 6: USQ Max EE: Joint Optimization in this paper. In this scheme, we joint optimize its uplink transmit power and fronthaul rate to maximize usercentric energy efficiency with uniform scalar quantization, as mentioned in Algorithm 2.
In Figs. 2 and 3, some useful conclusions could be obtained as follows.
Conclusion 1: In Fig. 2, method 1 and method 6 did not tend to allocate all power to SCs compared with methods 3–5. The power resource is almost allocated to two best channel quality subcarriers SC1 and SC2 in method 4. But for method 1 and method 6, the total sum of the allocated power over four SCs is less than P^{total}=0.2W. This states our designed Algorithm 1 and Algorithm 2 works well and saves the uplink transmit power effectively.
Conclusion 2: From Fig. 2, Fig. 3, we can observe that the joint optimization in method 1 and method 6 tend to allocate more power resource and fronthaul capacity to the better channel condition SC, which strategy is consistent with method 4. For instance, the poorest channel condition SC 4 is almost shut down while the best channel SC 1 receive the most resources.
Conclusion 3: All methods, including Algorithm 1 in method 1 and Algorithm 2 in method 6, tend to allocate all fronthaul link capacity over all SCs. For example, the sum of the fronthaul rate of each subcarrier is almost 400 Mhz in all methods. That means the fronthaul capacity boundary T^{total} can be reached.
Energy efficiency gain causing by different methods under Gaussian quantization
Different from the settings above, bandwidth B is set to 100 Mhz and N=32 in this subsection. In an I.I.D Rayleigh fading channel model of six paths, the pass loss model is set as L=30.6+36.7log10(d). The distance between user and RRH is 50 m. Other parameters are consistent with the settings in Subsection 3.3.1. In Fig. 4, parameter P^{total} remains invariant when T^{total} keeps unchanged in Fig. 5.
In Figs. 4 and 5, some useful conclusions could be obtained as follows:
Conclusion 1: Fig. 4 shows Algorithm 1 proposed in this paper always achieves better EE performance compared with other methods. When T^{total} < 1 Gbps, the performance gain of Algorithm 1 is more obvious. However, when T^{total} is continuously growing, the performance gain from power optimization only approximates Algorithm 1. The reason is that each symbol can be quantized by enough bits when T^{total} is sufficiently large. Therefore, the effect of specific fronthaul allocation method is smaller. It shows Algorithm 1 works better for limited fronthaul capacity CloudRAN scenes. Because the channel conditions of RRHs and users are different, the performance of the scheme for average allocating resources is almost the worst.
Conclusion 2: Fig. 4 also indicates method 2 always produces more gain than method 3. That is because optimizing users’ power has more impacts on objective function than optimizing fronthaul capacity. Figure 5 shows that the proposed Algorithm 1 could realize better EE performance, allocate power on each SC effectively, and optimize two variables p_{n} and \(T^{(G)}_{n}\) jointly, when P^{total} is growing. In Fig. 5, the maximum EE gradually grows to a maximum value and stops growth with P^{total} increases when T^{total} keeps unchanged.
The effect of different parameter τ on EE gain for USQ method
In this part, the simulation parameters are the same as the settings in part 3.3.2. Compared with problem (P1), problem (P2) for USQ method has an integer restriction, which is \(T_{n}^{\left (U \right)} = {{2BD_{n}^{\left (U \right)}} \left /\right. N},{D_{n}} \in \{ 1,2,\ldots \},\forall n \in \cal {N}\). Figure 6 assumes stationary P^{total} when T^{total} is fixed in Fig. 7. In this subsection, the effect of different parameter τ is analyzed.
From Figs. 6 and 7, the following conclusions can be obtained:
Conclusion 1: When τ=0, that means the restriction \(T_{n}^{\left (U \right)} = {{2BD_{n}^{\left (U \right)}} \left /\right. N},{D_{n}} \in \{ 1,2,...\}\) does not work and the EE obtained could reach the upper bound. Meanwhile, τ=1 indicates all \({{NT_{n}^{\left (U \right)}} \left /\right. {2B}}\) is set to a large integer as possible. Because objective function of (P2) is monotonically increasing over \({T_{n}^{\left (U \right)}}\), τ=1 causes the lower bound of EE.
Conclusion 2: The performance of the EE obtained by the USQ method is lower than that obtained by GQ method, under the same simulation parameters. This gap is understandable because the GQ method is theoretically optimal and often treated as a performance upper bound. However, in the actual scenario, the GQ method is difficult to achieve. When T^{total} is large enough, the EEUSQ approaches the theoretical EEGQ bound.
New algorithms for multiRRH scenario
During this subsection, authors extend the special singleRRH scenario to general multiRRH scenario, when K>1 and M>1. We assume Ω_{k} as the allocated SCs to single user k. Two corresponding restrictions are kth user’s maximum UL transmit power \(P^{\text {total}}_{k}\) and mth RRH’s maximum fronthaul capacity \(T^{\text {total}}_{m}\). Based on two different quantization schemes, the optimization models in multiRRH scenario are as follows.
s.t.
where
s.t.
where
The similar optimization problems in general scenario for multiuser are more complex. And it is difficult to utilize fractional programming and Lagrangian dual decomposition directly. To address the nonconvex and nonlinear optimization problems, authors come up with a modified particle swarm optimization (MPSO) algorithm. Actually, the MPSO method also could be used for a singleuser scenario, but its effect is not good, because MPSO is a heuristic algorithm, which is suitable for dealing with complex problems. For the singleuser scenario which has been simplified, its performance is not significantly better than Algorithm 1. And MPSO algorithm can only give the optimal strategy scheme within the allowable error range through simulation. However, the analytical expression of the optimal scheme cannot be given theoretically. Instead, we could give the analytical expression in Algorithm 1.
The proposed MPSO algorithm for P3
Particle swarm optimization (PSO), originally got the inspiration from the movement feature of fish and bird, is a populationbased approach to solve optimization problems by changing the candidate solution [25, 26]. In PSO system, particles are moving around in the multidimensional searchspace for particle’s moving, according to the mathematical rule. Every particle adjusts its position based on its local best known position in the search history, but is also directed to the most known optimal positions of other particles. In the standard PSO algorithm, the velocity and position of single particle change are as follows:
where
Q_{max},1≤q≤Q_{max}: The particle number;
D,1≤d≤D: The space dimension;
I_{max},1≤i≤I_{max}: Maximum iterations;
x_{q}=(x_{q1},x_{q2},...,x_{qD}): Position information of particle q in the D dimension;
v_{q}=(v_{q1},v_{q2},...,v_{qD}): Velocity information of particle q in the D dimension;
z_{q}=(z_{q1},z_{q2},...,z_{qD}): Best historic position information of particle q in the D dimension;
s_{g}=(s_{g1},s_{g2},...,s_{gD}): Best historic position information of all particles in the D dimension;
c_{1},c_{2}: The learning factors that determine the size of step;
w: The inertial weight which determine the influences of particle’s previous velocity on next velocity;
ξ,ρ: Randomly distributed numbers between [0,1];
As stated in the formula above, standard PSO is more suitable for solving the nonconstrained problems. Therefore, it is necessary to design an improved MPSO for (P3P4). Based on [27], this subsection considers the application of asynchronous timevarying learning factors c_{1},c_{2} and linear timevarying weights w. To guarantee the particles have the best performance in searching for the global optimal value in the initial stage and good convergence in the final stage, the dynamic range of weight [w_{min},w_{max}] is further considered. The corresponding expression between the dynamic weight w and iteration number i is as follows.
For the same reason, learning factors c1 and c2 are also redesigned. The learning factors of the ith iteration could be represented:
where \({c_{1}^{\text {initial}}},{c_{1}^{\text {final}}},{c_{2}^{\text {initial}}},{c_{2}^{\text {final}}}\) are the initial and final values of C1 and C2, respectively. In this paper, we select the following variable assignments w_{max}=1, w_{min}=0.1, \(c_{1}^{\text {initial}}=c_{2}^{\text {final}}=4\), \(c_{1}^{\text {final}}=c_{2}^{\text {initial}}=0.1\), for better convergence.
In Fig. 8, a numerical example is provided to prove the modified PSO algorithm has obvious advantages over standard PSO in seeking global optimal solution. The fronthaul capacity T^{total} is fixed as 2 Gbps and UL transmission power P^{total} is assumed as 0.2 W. We set M=8, K=8, P_{c}=0.5 W, B = 150 Mhz, N=32. For convenience, each user is preassigned N/K=4 SCs. In an I.I.D Rayleigh fading channel model of six paths, we distribute RRHs and use randomly in a circle with a radius of 100 m, when the pass loss model is set as L=30.6+36.7log10(d). Two different PSO algorithms have the same particle number Q_{max}=250 and maximum iterations number I_{max}=1000. Figure 8 reveals the proposed modified PSO algorithm can achieve better EE performance compared with standard PSO when Q_{max},I_{max} keep the same.
According to experimental tests in Appendix C, proper parameters Q_{max}=2000,I_{max}=2000 are chosen to offer good tradeoff between sufficiently good EE performance and sufficiently short searching time.
Therefore, a new algorithm of MPSO is designed for (P3).
In step 2, \( {x}_{q}^{1}=\left (\{p_{k,n}\}_{q},\left \{T^{(G)}_{m,n}\right \}_{q}\right), \mathbf {v}_{q}^{1}=\left ({\vphantom {\left \{vT^{(G)}_{m,n}\right \}}}\{vp_{k,n}\}_{q},\right.\left.\left \{vT^{(G)}_{m,n}\right \}_{q}\right)\) are the initial position and velocity of qth particle. The utility function of F is designed according to the objective function in (39) in step 3.
The proposed MPSO algorithm for P4
To solve problem (P4), the utility function of F in Algorithm 3 should be set as the objective function in (43). In addition, particle position \( {x}_{q}^{i+1}\) should not only satisfy the constraint in (44, 45), but also ensure integer constraint in (46). Details of the specific adjustment of \( {x}_{q}^{i+1}\) in step 9 for USQ is similar to that in Algorithm 3.
MultiRRH scenario: numerical experiment
Under two different quantization schemes, i.e., GQ and USQ, numerical examples are provided to evaluate the energy efficiency of different optimization methods. In Fig. 9, P^{total} is fixed to 0.2 W when T^{total}= 0.8 Gbps remains unchanged in Fig. 10. The rest of the relevant simulation parameters are set according to Fig. 8. We also compare energy efficiency under different resource allocation schemes in Figs. 9 and 10.

Scheme 1 (Max EE Under GQ: Joint Opt By MPSO): The proposed Algorithm 3 for joint optimization of usercentric energy efficiency under Gaussian quantization.

Scheme 2 (Max EE Under GQ: Joint Opt By SPSO in [25]): The usercentric EE optimized by standard PSO algorithm.

Scheme 3 (Max EE Under GQ: Power Opt Only By MPSO): Optimize power only in problem (P3) when fronthaul resources allocated equally.

Scheme 4 (Max EE Under GQ: Fronthaul Opt Only By MPSO): Optimize fronthaul capacity only in problem (P3), contrary to scheme 3.

Scheme 5 (Max Throughput Under GQ: Interiorpoint Method in [8]): The algorithm presented in [8] for throughput maximization utilizing interiorpoint method.

Scheme 6 (Max EE Under GQ: Equal Fronthaul Allocation and Power): Users allocate uplink transmit power over all SCs equally when RRHs allocate fronthaul link capacity over all SCs equally.

Scheme 7 (Max EE Under USQ: Joint Opt MPSO): In contrast to scheme 1, the quantization method changed into uniform scalar quantization (USQ). During the period of signal processing, the received signal could be firstly converted to inphase/quadrature (I/Q) parts. Secondly, every RRH uses positive integer bits to normalize I/Q parts. From an optimization point of view, the USQ method puts an integer limit condition on fronthaul rate T_{m,n}.
In Figs. 9 and 10, simulation results reveal the following conclusions:
Conclusion 1: All figures show the proposed MPSO in Algorithm 3 7y7 realize better EE all the time, compared with SPSO. Based on simulations of MPSO algorithm in Appendix C, parameter Q_{max}=2000,I_{max}=2000 could offer good tradeoff between sufficiently good EE performance and sufficiently short searching time. In contrast, SPSO could not implement a stable EE value, under the same parameters.
Conclusion 2: Fig. 9 indicates that the theoretical upper information EE obtained by GQ is superior to which obtained by USQ, when T^{total}<2 Gbps. Further, the EEUSQ nearly coincides with EEGQ, when T^{total}>2 Gbps. This trend is consistent with the singleuser scenario in Fig. 6. Besides, when T^{total} is fixed in Fig. 10, there is a significant gap between the EEGQ curve and the EEUSQ curve, which is similar to the conclusion of Fig. 7. At the same time, power optimization generate more gain than fronthaul optimization in Fig. 9. However, Fig. 10 gives the opposite case that fronthaul optimization is better than power optimization, meanwhile T^{total} is fixed and P^{total}<0.1 W.
Conclusion 3: Both two figures shows that the improved MPSO could realize better EE than which obtained by all other schemes. The similar conclusion is that performance gain achieved by Algorithm 3 is not as as significant as the power optimization only, when T^{total} increases. Obviously, the corresponding T^{total} of intersection between scheme 1 and scheme 3 is bigger than that obtained in a single scenario. That illustrates MPSO algorithm is more suitable for a multiuser case, because fronthaul capacity constraints is more serious.
Conclusion
In this article, authors study the joint optimization problem to improve energy efficiency of users in CloudRAN system, under two quantization methods. The main corresponding restrictions are user’s UL transmission power and RRH’s fronthaul capacity. Compared with existing work, this paper firstly take into account “signal quantization” and “fronthaul capacity constraint” in usercentric EE maximization of OFDMAbased CloudRAN. For singleuser scenario, the related algorithms are formulated to maximize the EE of users by optimizing power control and fronthaul capacity allocation. Then we extend singleRRH scenario to the more general scenario of multiple RRHs and resolve the more complex nonconvex and nonlinear problems by devising MPSO algorithms. Simulation results demonstrate that the proposed schemes in this paper outperform conventional solutions and improve EE of users obviously.
Appendix
A. Proof of proposition 3.1
Proof
We denote subscript optimal as opt. In problem (15), the EE performance of mobile users ζ is nonnegative with the optimal value \({\zeta _{opt}} = {{C\left ({p_{n}^{opt}} \right)} \left /\right. {P\left ({p_{n}^{opt}} \right)}}\). An equivalent function is defined \(F(\zeta)=\mathop {\max }\limits _{\left \{ {{p_{n}}} \right \}} C\left ({p_{n}^{opt}} \right)\zeta P\left ({p_{n}^{opt}} \right)\). According to [24], the problem (17) is equivalent to new transformed EE optimization
F(ζ) is strictly monotonic decreasing when ζ increases with F(ζ)≥0. □
Based on the decreasing characteristic of F(ζ), Algorithm 4 is raised to settle the transformed issue by updating ζ in the following algorithm.
When the nonzero duality between the optimal value of \(\mathop {\max }\limits _{\left \{ {{p_{n}}} \right \}} C\left ({{p_{n}}} \right)  {\zeta ^{\left (i \right)}}P\left ({{p_{n}}} \right)\) and its dual problem is nearly zero, the problem of the ith inner loop could be solved by Lagrange dual decomposition method.
The Lagrange function of the problem in the ith inner loop is as follows
where λ is the dual vector associated with the total transmission power limitation in (18). For single SC, the subproblem can be expressed as
where
Since L_{n}(p_{n}) is concave over p_{n}, its corresponding derivative over p_{n} is shown below
By setting \(\frac {{\partial {L_{n}}\left ({{p_{n}}} \right)}}{{\partial {p_{n}}}}=0\), then we have the following expression
where
By denoting α_{n} as (28), η_{n} as (30), the above expression can be expressed as
According to the relevant characteristics of a quadratic equation, to obtain the meaningful solution, we denote
and then we have the following expression
So \(\alpha _{n}^{2}  4{\eta _{n}}\) always set up and the above quadratic equation always have the meaningful solution. At the same time, because p_{n}≥0, we set the constraint
By substituting η_{n} in (30), we can further draw the following conclusion
Because the objective function in (17) is not increasing monotonically over p_{n}, the subgradientbased method is utilized to obtain in λ [28]. The subgradient of the dual function is shown below
where \({p_{n}^{\left (i \right)}}\) means the allocated power at SC n of ith iteration, ∇λ^{(i+1)} is the subgradient applied in (i+1)th iteration. Therefore, the iterative formulas of dual variables in (i+1)th iteration are shown below
where \({\chi _{\lambda }^{\left ({i + 1} \right)}}\) is the positive step size.
Proposition 3.1
is thus proved.
B. Proof of Proposition 3.2
Proof
The Lagrangian of problem (27) can be expressed as
where β is the dual vector corresponding to fronthaul capacity constraint in problem (27). Similar to proof of proposition 3.1, for single SC, the associated subproblem is shown below
where
Since \({L_{n}}\left ({T_{n}^{\left (G \right)}} \right)\) is concave over \(T^{(G)}_{n}\), its corresponding derivative over \(T^{(G)}_{n}\) can be expressed as
By setting \({{\partial {L_{n}}\left ({T_{n}^{\left (G \right)}} \right)} \left /\right. {\partial T_{n}^{\left (G \right)}}} = 0\), then we have the following expression
Since \(T_{n}^{(G)}\geq 0\) always exists, to obtain the meaningful solution, we have
From the above expression of \(T_{n}^{\left (G \right)}\), we can further derive
Assume \({\nu _{n}} = {{{{\left  {{h_{n}}} \right }^{2}}p_{n}^{opt}} \left /\right. {\sigma _{n}^{2}}}\), we can obtain the conclusion in expression (25). □
Under the constraint \(\beta < \frac {1}{{p_{n}^{opt} + {P_{c}}}}\) given above, optimal β can be obtained when the fronthaul link capacity is tight in problem (27). The optimal β_{opt} could be obtained by a bisection algorithm, as a solution to problem (27).
Proposition 3.2
is thus proved.
C. Comparison between different Q _{max} and I _{max} in modified PSO algorithm
In Table 1, the simulation parameters is the same as which in Fig. 8. From this table, we can learn when we set Q_{max}=2000,I_{max}=2000 is suitable. Because when the number of particles Q_{max} and maximum number of iterations I_{max} continue to increase, the final EE stable value keeps the same while the total time calculating by MATLAB grows rapidly.
Abbreviations
 CloudRAN:

Cloud radio access network
 BBU:

Baseband unit
 DL:

Downlink
 EE:

Energy efficiency
 Gbps:

Gigabit byte per second
 GQ:

Gaussian quantization
 MPSO:

Modified particle swarm optimization
 OFDMA:

Orthogonal frequency division multiple access
 PSO:

Particle swarm optimization
 RRH:

Remote radio head
 SC:

Subcarrier
 SNR:

Signal to noise ratio
 UE:

User
 UL:

Uplink
 USQ:

Uniform scalar quantization
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Funding
This work was supported by the 863 Program of China under Grant 2015AA01A703, the National Natural Science Foundation of China under Grants 61422105, 61531011, and 61671144, the Research Project of Jiangsu Province under Grant BE2015156 and the Natural Science Foundation of Jiangsu Province for Colleges and Universities under Grants 17KJB510016.
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Sun, Y., Li, S. & Yang, L. Green fronthaul allocation and power management in CloudRAN. J Wireless Com Network 2018, 188 (2018). https://doi.org/10.1186/s1363801812053
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Keywords
 CloudRAN
 Fronthaul capacity restriction
 Signal quantization
 Usercentric EE
 Joint optimization
 Modified PSO