I Introduction
Due to the explosive growth of advent high data rate wireless services and number of users, there are various challenges in the design and management of the cellular networks such as demands for higher spectrum efficiency and massive connectivity while keeping the cost in the most acceptable level for both providers and customers. In this regard, both academic and industrial researchers are working to develop the next generation of cellular networks e.g., fifth generation wireless networks (5G).
One of the basic concepts and key enablers to design 5G, in the most efficient and cost effective manner, is to resort to the concept of software defined networking and virtualization where 5G can be sliced between different services with divers quality of service (QoS) requirements [1]. In this so called networking slicing approach, providing isolation between slices in order to hold the QoS of each services under any users’ variations of other users is of essential which calls for highly efficient resource management in this context [2].
On the other side, to meet the spectrum efficiency demands of data hungry services in 5G, new transmission techniques are underinvestigated where nonorthogonal multiple access (NOMA) techniques are one of the promising approaches here [3]. On of the interesting NOMA techniques to address the mentioned challenges is sparse code multiple access (SCMA) which can enhance the system performance compared to the other access techniques [4, 5]. By applying the SCMA, each subcarrier can be reused more than one time in the coverage area of radio remote head (RRH). In the SCMA technique at the transmitter side the signal of various users are sent on a subcarrier with the SCMA encoder, and at the receiver side, the signal of each user is detected by exploiting the message passing algorithm (MPA) [6].
The SCMA technique is an appropriate access technique for downlink that can increase the overall throughput through user multiplexing and is wellmatched to heavily loaded 5G networks [4, 7, 8, 9, 10, 11, 12, 13, 14]. Notably, the main practical challenge with using the SCMA in the downlink transmission is the complexity of the multiuser detection on the receiver side. In other words, the detection complexity is too high for the mobile terminals. To tackle this issue, low complexity methods for detection are needed. Therefore, the trend of researches is to achieve methods that decrease the complexity of the SCMA receiver [15, 16, 17, 18].
Next generation wireless network should be able to manage the high density networks with massive connectivity and various required QoS. In order to deal with these requirements and manage system efficiently, hierarchical software defined cloudradio access network (CRAN) with centralized management can be an appropriate choice. The CRAN architecture contains several radio remote heads (RRHs) that are responsible for the transmission and reception processes, one baseband unit (BBU) center that is responsible for all the processing and management tasks, and frounthaul links which connect the RRHs to the BBU center.
In practice, due to the various practical reasons, such as estimation errors, feedback quantization, and hardware limitations, uncertain CSI is available at transmitter. To deal with the critical applications, where user outage is interpolated as system failure
[19], robust optimization approaches play a pivotal role to provide the necessary reliability for the system, which is the main focus of this paper.Ia Related Works
This work can be positioned in the intersection of three categories of resource allocation problems, namely, 1) Resource allocation in SCMA based system 2) Resource allocation in CRANs 3) Robust resource allocation. While each of these categories has a specific body of works, in the followings, we present the most related works.
IA1 Resource Allocation in SCMA Based System
Notably, very few works have investigated the radio resource allocation in the SCMA based systems. Most of the existing works study the SCMA structure and link level performance [4, 20, 16, 10]. [21] evaluates the energy efficiency of SCMA method via MATLAB software. In [14], a power and codebook assignment method is studied where the joint sum rate and system energy efficiency is maximized. Moreover, the tradeoff between rate and energy in a SCMA based system is addressed. In [22], the authors investigate resource allocation in a device to device communication based cellular network with SCMA access technique. They propose a maximization optimization problem with minimum signal to interference plus noise ratio (SINR) requirement for both deviceto device and cellular users. In addition, to solve the proposed optimization problem they exploit a Hypergraph based method. [5]
proposes a joint power and codebook allocation method to maximize the total sum rate in a SCMA based heterogeneous cellular network (HetNet) where the power domain nonorthogonal multiple access (PDNOMA) is compared with SCMA from the complexity and total sum rate aspects. In addition, to solve the proposed optimization problem, successive convex approximation (SCA) for low complexity (SCALE) and arithmetic geometric mean approximation (AGMA) methods are deployed.
IA2 Resource Allocation in CRAN
In CRAN networks multiple centralized radio resource allocation algorithms are proposed based on the received global information of the networks. In [23], the authors, considering orthogonal frequency division multiple access (OFDMA) based multicell system, propose a centralized radio resource allocation algorithm which maximizes the system sum rate. Moreover, they study the coordinated multi point (CoMP) technique in the considered system model. The authors of [24] investigate an informationcentric network architecture for devicetodevice communications, in which with the software defined radio (SDN) controller, a dynamic centralized radio resource allocation is applied. In [25], the authors develop an algorithm to find both the user association and bandwidth allocation in an SDbased virtualized informationcentric architecture network. In [26], considering the effective capacity, an optimal power allocation method is proposed in which the effect of the delayQoS on power allocation and the gain from content caching is evaluated.
IA3 Robust Resource Allocation
Due to dynamic and highly variable nature of wireless channels and users’ behavior, considering the error in the system information and specially CSI of resource allocation in wireless networks has been drawn a lot of attention e.g., [27] where different approaches are proposed in this context. Since in 5G, the isolation constraints of each slice is of essential, in this paper, we resort to worst case robust optimization theory where based on the error bound of the CSI minimum value of system sum rate is maximized. [28] investigates the worst case robust beamforming in a PDNOMA based system. In [29], considering two types of users as elastic and streaming, sum rate maximization under the worst case uncertainty in a NOMA based system is investigated. In [30], supposing that only average CSI is available at the BS, rate maximization under outage constraints in a NOMA based system is studied. [31] studies sensitivity analysis of a PDNOMA based virtualized wireless network to imperfect successive interference cancellation (SIC). [19] investigates resource allocation problem for uplink PDNOMA based networks where the impact on user and system performance due to errors resulting from imperfect SIC is examined, and the chance constrained robust optimization method to cope with this type of error is deployed.
As can be concluded non of the aforementioned works investigates the robust radio resource allocation in an SCMA assisted CRAN considering the multiple input single output (MISO).
IB Contribution
The main aim of this paper is to propose a robust radio resource allocation method in a MISOSCMA assisted CRAN in the presence of multiple slices. In this regard, using the worst case approach, the minimum value of system sum rate with minimum rate requirement of each slice, capacity limitation of each RRH and maximum transmit power constraints is maximized.
The proposed robust optimization problem is a nonconvex problem with mixed integer and continues variables, and therefore, to solve it, the common methods for solving the convex optimization problems can not be used directly. Hence, to solve the proposed resource allocation problem, we introduce the worst case optimization problem of our setup. Afterwards, to deal with the nonlinearity feature of joint codebook allocation and user association subproblem we exploit some auxiliary variables and reformulate the proposed optimization problem. Finally, we deploy the SCA based alternate search method (ASM) [32, 33]. Based on the proposed solution, at first by adding some auxiliary variables the main problem is transformed into a new form where the joint codebook allocation and user association subproblem is in an integer linear form. Therefore, in each iteration, to solve the joint codebook allocation and user association subproblem, an integer linear optimization problem is solved, and for beamforming subproblem a convex optimization problem is solved.
Our contributions are summarized as follows:

We consider a MISOSCMA assisted CRAN in the presence of multiple slices where the minimum rate requirement of each slice and maximum frounthaul capacity of each RRH should be satisfied. The considered system model is a good match for the next generation wireless networks in which various services with different QoS requirements have to be served.

We propose a novel robust radio resource allocation problem in which by determining the power allocation and joint codebook allocation and user association methods, the system sum rate is maximized. By exploiting this radio resource allocation policy, we maximize the system spectral efficiency while we consider the reliability for the system with respect to the uncertain CSI.

We define one parameter for both codebook assignment and user association, which decreases the dimension of the proposed optimization problem and also decreases the complexity of its solution.

In order to solve the proposed robust optimization problem, at first we utilize the worst case approach, then we develop an ASM base solution with low complexity.
Ii system model and problem formulation
Iia System Model
We consider a scenario with multiple slices in which the users of each slice spreading over the total coverage area of a CRAN. We assume that all the transmitters are equipped with multiple antennas while the receivers are simply single antenna systems. We denote the set of slices by , and the set of RRHs by where shows high power RRH and illustrates the low power RRH. We assume that the set of all users in the network is denoted by which is the union of the set of users of all the slices, i.e., where . A typical illustration of the considered system model is illustrated in Fig. 1. We assume that the total bandwidth of the network is divided into subcarriers whose bandwidth is less than the coherence bandwidth of the wireless channel. We also denote the channel gain from RRH to user over the subcarrier by where
is the complex field, and the beam vector assigned by transmitter
to user over subcarrier by . We define an indicator variable with if user is scheduled to receive information from RRH over codebook , and if it is not scheduled to receive from transmitter over codebook . In addition we define with if subcarrier assigned to codebook and otherwise . Assume that the information symbol is decided to be transmitted to user from RRH over subcarrier . It should be noted that is the symbol after SCMA encoding. Moreover, for the sake of simplicity, we consider .In this setup, for the sake of simplicity, we suppose that the frounthaul links (the Links among RRHs and cloud center) are not wireless based link. Therefore, there are not any limitation for frounthaul links. In the SCMA based systems the Ndimensional codewords of a codebook are sparse vectors with nonzero entries.
Generally, the detection performance of the SCMA based systems with MPA has the following two properties [34]
: I) with increasing the complexity of the factor graph, the detection performance is degraded and the complexity of the detection process increases; II) if the factor graph does not have any loop, the MPA technique provides an exact solution for signal detection. When the number of the multiplexed signals for each subcarrier increases, the factor graph becomes more complex and the probability of existing loops in the factor graph increases. Therefore, the receiver cannot successfully decode the mixed signals. However, under the constraint of the maximum reused degree (i.e.,
) which is presented in (1), and choosing appropriate , different codebooks can be regarded as orthogonal resources approximatively [35, 36, 37, 38, 9, 14, 5, 21](1) 
In other words, (1) determines that at most users could be scheduled on one subcarrier at the same time due to the above mentioned practical issues.
The received signal of user assigned to RRH on codebook is
The SINR of user from transmitter in codebook is
where is the noise power,
and,
(2)  
Consequentially, the rate function is given by
(3) 
It should be noted that the Shannon’s formula gives an upper bound for the rate function in a SCMA based systems [39].
IiB Nominal Resource Allocation Problem
The optimization problem formulation to find the best beamforming, codebook, and user association approach is formulated as follows:
(4a)  
(4b)  
(4c)  
(4d)  
(4e)  
(4f)  
(4g) 
where is the maximum frounthaul capacity of RRH , (4b) indicates the total available power at each RRH, (4c) shows the frounthaul capacity limitation for each RRH, (4d) demonstrates the minimum rate requirement for each slice, (4e) shows the SCMA constraint and (4f) shows that each user can be assigned to at most one RRH, simultaneously.
IiC Worst Case Resource Allocation Problem
In order to model the uncertainty of CSI, the additive error model for channel model is considered which is given by [40]
(5) 
where indicates the estimated imperfect channel coefficients and denotes the error vector.
Here, we assume uncertain CSI case in which is a norm bounded vector for analytical convenience. In this regard, by supposing the Euclidean ballshaped uncertainty the channel uncertainty sets are defined as follows:
(6)  
where is the error bounds on the uncertainty region of the channel coefficient .
In the worstcase approach, the considered value of channel coefficients have to belong to the related uncertainty sets, and also they have to provides the minimum rate on each codebook for the assigned considered user. Here, the worstcase approach is transformed into the protection function which simplifies the robust problem considerably [29, 41].
Therefore, instead of , we can rewrite
(7)  
where
(8) 
is defined as a normbounded matrix, i.e., where is determined by Proposition 1.
Proposition 1.
With considering , bound is equal to .
Proof.
Based on the worst case approach, considering the error bound of the CSI, the rate functions for the objective function and constrain (4d) should give the minimum achievable rate. Consequently, from (7) and (9), the worstcase SINR of user from transmitter in codebook is defined as follows
where is the noise power,
and,
Consequently, the rate function for user from transmitter in codebook in the objective function and constraint (4d) is given by . gives the minimum achievable rate, since based on the error bound of the CSI, the numerator of the SINR has the minimum value and the denominator has the maximum value.
Based on the worst case approach, considering the error bound of the CSI, the rate functions for constraint (4c) should give the maximum achievable rate. Therefore, from (7) and (9), SINR and rate functions in constraint (4c) are given as follows:
where
and,
Consequently, the rate function for user from transmitter in codebook in constraint (4c) is
Finally, the worst case optimization problem can be represented as
(10a)  
(10b)  
(10c) 
Iii Proposed TwoStep Iterative Algorithm
The proposed nominal optimization problem in (4) is a special case of the worst case optimization problem (10) , e.g., For , we have then, (10) is transformed into (4). Consequently, the solution algorithm of the worstcase optimization problem (10) is investigated.
Since (10) is a nonconvex optimization problem containing mixed integer and continues variables, belongs to the NPhard optimization problem category [43, 44, 45]. Therefore, finding its optimal solution is not trivial and conventional methods for solving the convex optimization problems cannot be used. Therefore, proposing an efficient algorithm with affordable computational complexity is of essential for this case. Consequently, we resort to the ASM method which is a wellknown and efficient algorithm to solve this type of problems and converges to a suboptimal solution and is extensively used in the literature, e.g., [46, 47].
Based on the ASM approach, an optimization problem is decomposed into several subproblems. The number of subproblems is determined based on the subset of variables. These subproblems are iteratively solved until the convergence is achieved. Therefore, for our setup, we consider that in each iteration, the optimization problem (10) is decoupled into two subproblems referred to the codebook allocation and beamforming subproblems. To solve the beamforming subproblem, first we approximate it by a convex optimization problem and then, we use the interior point method (IPM) to solve it. The main steps of the proposed method is shown in Algorithm 1.
In the followings, we explain the approximation method and solution algorithms of the beamforming and joint codebook allocation and user association subproblems.
First, to reach more tractable formulation of (4), we deploy the epigraph transformation [42]. Therefore, four auxiliary variables , , , are utilized. By exploiting the auxiliary variables, the main optimization problem is transformed into a new form in which the joint codebook allocation and user association subproblem is a linear programming problem with low complexity and beamforming problem is in a good shape to transform into a convex problem by applying the minorizationmaximization algorithm (MMA) approach [48]. Consequently, the main optimization problem can be rewritten as follows:
(11a)  
(11b)  
(11c)  
(11d)  
(11e)  
(11f)  
(11g)  
Iiia Beamforming Subproblem
The beamforming problem with fixed codebook allocation and user association is
(12)  
From both left side and right side of constraint (11c), right side of constraint (11f), and left side of constraint (11g), optimization problem (12) is a nonconvex problem. To solve the nonconvexity issue of the beamformng problem the MMA approach is applied which is based on SCA. Here, we apply the first order Taylor approximation to transform the nonconvex constraints with a convex one. The right side of (11c) can be written as:
(13)  
By applying the MMA algorithm, the function presented in (13) can be approximated by a convex function as follows:
(14)  
where and are calculated by the MMA method as
(15)  
For the right side of constraint (11f), the same approach deployed for the right side of (11c) is exploited. To approximate the left side of (11c) to a concave function, we rewrite its first term as
where and .
Then, by applying the fist order Taylor approximation around , we can replace as
(16)  
Since , the main idea behind the MMA algorithm is to find for the next iteration which maximize as follows [49]
(17) 
For the left side of (11g), the mentioned steps used for the left side of (11c) can be accordingly applied. Consequently, by applying the MMA method, an optimization problem with standard convex form is achieved. To solve the optimization problem IPM can be applied. In order to use the interior point method we use the CVX software [50].
IiiB Joint Codebook Allocation and User Association Subproblem
Iv Convergence and Computational Complexity
In this section, convergence and computational complexity of the proposed solution are investigated.
Iva Validity of the Approximation Method
The SCA method with the linear approach is a well known method to approximate the nonconvex optimization problem with a convex one [49, 46, 51, 52]. The applied approximation method for the small values of channel gains () has acceptable accuracy [52]. In the considered system model, due to the fact that the entries of the channel gain matrices have small values the MMA approximation has good accuracy [52].
IvB Convergence
The convergence of Algorithm 1 is investigated in the following theorem.
Theorem 1.
With the iterative approach presented in Algorithm 1, after each iteration, the objective function increases compared to the previous iteration, and finally converges.
Proof.
Consider , in order to achieve convergence of the algorithm we need
(19)  
Inequality (a) in (19) comes from the fact that optimization problem with variables and fixed () is a linear program which its solution is equal or better than that of . Consequently, we have . For inequalities (b) because the final beamforming optimization problem is a convex problem the same argument as used for inequality (a) can be exploited [32, 33]. The approximated beamforming problem is a convex optimization problem in which the optimal value of it at each iteration is achieved. Because at each iteration the parameters of approximation is updated based on the results of the previous iteration, the results of the solution and the value of the objective function in each iteration is improved or stay unchanged in respect to the previous iteration. ∎
IvC Computational Complexity
As explained in Section III, to solve (11) the ASM approach is applied. Complexity of the ASM approach is a linear function of the total number of iterations needed to convergence and complexity of each subproblem. In other words, if shows the number of iterations, indicates the complexity of beamforming subproblem and demonstrates the complexity of joint codebook allocation and user association subproblem, complexity of the main problem is given by
In each iteration, in order to solve both beamforming and joint codebook allocation and user association subproblems, CVX toolbox is applied. The CVX toolbox exploits IPM to solve an optimization problem [50]. Therefore, computational complexity of each subproblem is given by [51, 50]
(20) 
where with indicating the beamforming subproblem and indicating the joint codebook allocation and user association subproblem, is the number of subproblem constraints, is the initial point to approximate the accuracy of the IPM, is the stopping criterion of IPM, and is used to update the accuracy of the IPM. for each subproblem is determined as follows:
V numerical results
In this section, numerical results for various system parameters in a downlink SCMA based CRAN system are presented to evaluate the performance of the proposed resource allocation approach. The system parameters are considered as follows. There exist one high power RRH with m radius and low power RRHs with m radius. The total bandwidth is MHz. The power spectral density of the received AWGN noise is also set to dBm/Hz. Moreover, the channel gain between each user and RRH has Rayle fading with pathloss exponent . The other parameters are variable described in the legend or explanation of each figure. All the considered parameters are summarized in Table I.
Va Comparison of SCMA and Traditional Approaches
In order to investigate the performance of a SCMA based CRAN compared to traditional approaches, we consider an OFDMA based CRAN as a benchmark. All parameters of these two setups are similar excepts that the number of multiplexed signals over each subcarrier. Fig. 2 shows system sum rate versus the maximum available power for SCMA and OFDMA based systems with . This figure presents a comparison between SCMA and OFDMA for both perfect and uncertain CSI cases. From Fig. 2, with the SCMA technology, the system sum rate is increased up to approximately compared to that of OFDMA. This is because via SCMA, each subcarrier can be used in the coverage area of one RRH more than one time without imposing any interference. Due to the uncertain CSI, the system performance for both SCMA and OFDMA decreases.
Fig. 3 depicts convergence of the proposed solution for SCMA and OFDMA based systems. As can be seen, the proposed algorithm converges after a few iterations for both SCMA and OFDMA based systems. However, for the SCMA based system due to the more constraints and more complicated formulation it takes more iterations.
VB Study of the System Parameters
Fig. 4 represents sum rate versus the minimum rate requirement of each slice for both perfect and uncertain CSI cases, , and . Fig. 4 highlights that with increasing the minimum rate requirement of slices, the sum rate decreases. This is because, by increasing the minimum rate requirement, more resources are consumed to satisfy the minimum rate requirements for each slice and there remains less resource leading to smaller amount of sum rate.
Fig. 5 demonstrates sum rate versus the different number of slices with a fixed number of users (), and minimum rate requirement (bps/Hz). From this figure, we can see that with increasing the number of slices, the sum rate decreases. This is because, with increasing the number of slices, due to minimum required rate, the feasibility region of optimization problem shrinks. Consequently, the sum rate decreases.
VC Study of the Users’ Density Distribution and Channel Models
In Fig. 7, we study the effects of user distribution on the system performance. Also, we compare the performance of the proposed solution method to the base line method. For the base line approach we suppose that users are associated to BSs based on their distance to BSs. In other words, each user are associated to the nearest BS. As can be seen, for celledge users user association method has critical role to improve the system performance and coverage. This is because inter cell interference which affects the users throughput, specially for the celledge users, can be controlled with the proposed user association algorithm. While for the baseline method, user association is perdetermined. Consequently, by exploits the proposed user association method, coverage of the considered system is improved.
In Fig. 8, we aim to study the effects of different channel models on the performance of a SCMA based system with the MISO technology considering perfect CSI. This figure depicts sum rate of SCMA for different channel models namely, Rician and Rayleigh. In this figure, the maximum available power is Watts and with perfect CSI. As can be seen the Rician channel model gives more sum rate than that of the Rayleigh fading model. This is due to that, with the Rician model a line of sight signal path is always exist during the data transmission. Moreover, exploiting multiple antenna at receiver in Rayleigh model gives more gain than that of the Rician model as expected from [54].
Parameter  Value of each parameter 

, and  
Number of subcarriers  , 
Pathloss exponent  
Power spectral density of the received  
AWGN noise  dBm/Hz 
Maximum transmit power of high power  
RRH  Watts 
Maximum transmit power of each low  
power RRH  Watts 
Number of low power RRH  
High power RRH radius  m 
Low power RRH radius  m 
, ,  
bps/Hz  
bps/Hz 
From the above results, we can conclude that there is a trade off between performance and robustness which depends on the value of . Consequently, this parameter has an essential role in the system performance.
can be determined based on the level of noise in the channel estimation process and probability distribution function of error
[55, 56, 57].Vi conclusion
In this paper, considering uncertain CSI, we proposed a worstcase radio resource allocation in a SCMA based CRAN with MISO transmission. To solve the proposed optimization problem, we exploited the worst case approach and rewrote the problem via the concept of the protection function to reach more tractable formulation. Then, we applied the ASM method that in each iteration beamforming and joint codebook allocation and user association subproblems are solved separately and the algorithm is continued until convergence is achieved. Numerical results reveal that the proposed optimization problem via SCMA and MISO technologies improves performance of the system significantly even for the uncertain CSI. This results confess the potential of SCMA to be a perfect candidate for the access technique in 5G.
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