1 Introduction

The volume of mobile data is expected to grow exponentially over the next few years, and the challenge for the fifth generation (5G) networks will be to overcome the fundamental limits of the existing cellular networks, with the aim of guaranteeing high quality and high data rate services to an increasing number of users with limited resource availability. 5G wireless communication technologies are expected to satisfy stringent requirements in terms of bit rate per square kilometer, energy consumption and latency [10]. To this end several important features must be addressed [8]. Among these access points densification is considered to be the key approach to boost capacity [7]. In particular, the deployment of Heterogeneous Networks (HetNets) is based on a multi-layer architecture consisting of macrocells overlaid with smaller cells to serve users with different Quality of Service (QoS) requirements, in a spectrum- and energy-efficient manner. Moreover, considering massive Multiple Input Multiple Output (MIMO) and millimeter wave communication technologies - emerging into 5G networks - the cell size of next generation networks has to become smaller [3]. HetNets encompass a broad variety of cells, including microcells, picocells, metro cells, and femtocells, as well as advanced wireless relays and distributed antennas that can be deployed anywhere. However, this massive cells diffusion has as a consequence an exponential increase of the backhaul traffic that may congest and collapse the backhaul network. In addition, backhaul network will be characterized by heterogeneous links, indeed small cells will be used in different environments, such as homes, small offices, hotspots and enterprises, where the available backhaul connections will be different (i.e., optical fibre, subscriber broadband communications links, etc.). As a consequence, massive traffic forwarding is a great challenge for future 5G backhaul networks whose architecture and protocols has to be properly designed [15].

To address this challenge a suitable resource management strategy has to be implemented. Network virtualization (software defined networking, SDN) and radio access network moved into the cloud (CloudRAN concept) provide more computational resources for these resource management functions [21]. However the interaction between lower and upper layers during resource decisions is still mostly unexplored and the few proposed solutions show poor performance. This is mainly due to limited amount of information exchanged among the decisional entities and to the lack of details of the network abstraction process.

In this paper we propose an artificial intelligence (AI) based approach that tries to mitigate this effect by creating two interdependent decisional cores exchanging information, one aware of physical layer aspects and the other controlling pure network resources. The former is responsible for resource requests collecting from user equipments (UEs) and for the optimized association between each UE and its serving cell. The latter distributes the aggregated traffic flows in order to meet the requirements and constraints imposed by the available links. Similarly to human processing of information, two decisional tasks respectively aware of their domain, propose and query partial solutions iteratively. The process stops when a consensus on a common objective has been reached.

In particular, we propose a cross-layer approach, that takes into account both the data traffic load of each cell in the HetNet, and the capacity of the backhaul links that connect the cells. Two iterative procedures are considered whose goals are to minimize the unsatisfied users data rate requests (UDRRs) and minimize the energy consumption by reducing the number of activated cells in the area, respectively. In both cases, at each step the UEs’ cell association procedure receives as input the ability of the backhaul network to satisfy the amount of data transfer request by each cell. At the same time the backhaul network receives as input the requests of the cells and tries to adapt itself to those.

The paper is organized as follows. After a review of related works presented in Section 2, Section 3 introduces the considered network model, while the proposed cross-layer solutions are described in Section 4, and their performance is evaluated in Section 5. Finally, conclusions are drawn in Section 6.

2 Related Works

Despite the expected benefits that will be introduced by HetNets, the massive diffusion of small cells in 5G networks will lead several challenges such as high interference management, energy consumption, resource management, load distribution, and limited backhauling capacity. For this reason in recent years research activities focused on solutions to solve these problems. For example cognitive radio has been considered a viable solution to increase the spectrum efficiency [4], and coordinated/cooperative approaches have been introduced to reduce inter-layer interference [22]. Several adaptive resource allocation techniques [27] as well as cell activation policies [9] have been investigated to reduce energy consumption, while load balancing strategies have been defined to efficiently distribute the traffic among several access points [30]. In this paper we are particularly interested in efficient solutions to manage shortage of backhauling capacity, that is a crucial point for HetNets deployment. Indeed, while in traditional cellular networks the macrocells are deployed following suitable plans, and the main bottleneck is the air interface, in HetNets the backhaul network may become the bottleneck, because the dense deployment of small cells without predefined planning, and using heterogeneous backhaul solutions. For this reason some research efforts have been done to optimize the user association policies taking into account the backhaul constraints. For example in [16], the authors studied the traffic offloading in backhaul-constrained HetNet proposing a network latency aware user association scheme, whose goal is to minimize the latency of the network. The algorithm is distributed, the Base Station (BS) measures the traffic load in both the access and the backhaul links, while each UE selects its serving BS based on its data rates, BSs’ backhaul capacity, and the traffic load in both BSs and their backhaul links. The limited capacity of HetNet backhaul links is taken into consideration also in [11], where the weighted sum rate is maximized imposing a constraint in the optimization problem. A completely different solution to face with limited backhaul capacity is local caching of popular contents at small cell level, in order to reduce the overall traffic load from the core network and, thus, to utilize the backhaul bandwidth more efficiently [24]. Here the problem is to properly decide which content to cache by taking into account the content popularity, due to the limited storage capacity at each small cell. Although these solutions are effective and feasible, in general these target a single part of the entire problem. Differently, the SDN concept allows to implement the management function in a central manner, hence is considered a promising approach to efficiently manage the HetNet infrastructure [26]. Application of SDN techniques into wireless networks is currently a hot research topic, with contributions available in different domains. The network intelligence is concentrated in a SDN controller that acquires the physical topology of the network and the status of all the elements, and then is able to manage the entire network in an efficient manner. This is the framework proposed in [26] based on an intelligent system that equips SDN with awareness and adaptiveness for dynamic networking in 5G HetNets. In [23] the focus was on the user association problem in a cognitive HetNet using SDN. The authors formulated the optimization problem to achieve the best user association with the goal of maximizing the sum rate of the network, and then proposed a solution based on matching theory. The SDN paradigm has been proposed also to balance traffic in environments where multiple heterogeneous communication technologies are available, in order to increase the overall throughput by optimizing load balancing [25, 28]. In particular, SDN allows to activate traffic redirection in case of link failure or congestion in order to exploit the full potential of this environment. The SDN paradigm has been investigated to have a flexible and reconfigurable backhaul infrastructure in future 5G networks, especially in presence of wireless links that are subject to changes in the radio propagation conditions as in [18]. Similarly, in [2] a two-tiers SDN controller model is proposed in order to have flexible data-flow processing and dynamic backhaul reconfiguration. While the limited backhaul capacity is investigated in [17], where an intelligent handover framework is designed for ultra-dense cell HetNets based on SDN paradigm. The objective is reduce handover latency, redundant signaling and overhead, thus reducing the backhaul capacity requirements. In all previous papers, SDN is used to manage the access network in presence of heterogeneous wireless access points or to control the backhaul network. However, only few papers in the literature consider both access and backhaul networks together, but if radio access and transport layers have separate controllers, they must be coordinated in order to harmonize the resource allocation across all the network segments in a scalable manner. Hence, an iterative information exchange between the two layers is needed. In [29] a cross-layer framework based on a controller that controls both the radio access and the backhaul networks through a SDN protocol was proposed. The authors described the elements of the architecture and their main functionalities that should allow to manage mobility, energy consumption, and admission control. However, specific procedures are not considered, but only a high level view of the architecture is provided. Differently, in [14] a procedure to jointly optimize the traffic in the backhaul and in the radio access networks is proposed. The radio access layer sends to the upper layer the achievable data rate estimated knowing the channel state, and the backhaul layer sends the maximum data rates of each backhaul link. The optimization goal is to maximize the sum rate. The algorithm is iterative, and each iteration is activated by changes in the data flow status. Similarly, in this paper we propose a cross-layer approach where both radio access and backhaul networks are considered and work in a coordinated way. Each layer has an abstracted view of the resources available in the other layer in order to make suitable decisions on resource allocation. Differently from previous solutions, we propose two iterative procedures whose goals are to minimize the UDRRs and to minimize the energy consumption by reducing the number of activated cells, respectively. In both cases - for a given configuration of the users data rate requests - the procedure is iteratively performed taking into account both the ability of the access points to serve their users and the backhaul links capacity. At each iteration the users are redistributed among the access points in order to achieve the predefined goals, requiring a new distribution of the traffic load in the backhaul network. The first procedure, whose goal is to reduce the UDRRs, has been already presented in [5].

3 Network Model

3.1 Access Network

This paper focuses on a HetNet where a macrocell is overlapped by S small cells (i.e., micro and femto-cells) that are randomly placed in the macrocell area following a uniform distribution. Hence, the set of the cells \(\mathcal {C}\) has dimension C = S+1, and is composed by cells with different transmission power and coverage. In particular, we consider a dense deployment scenario where many small cells are densely deployed to support huge traffic over a relatively wide area [1]. The number of UEs, U, is chosen following a Spatial Poisson Point Process (SPPP) that is extensively used for modelling HetNets [12].

Each UE in the area can be served by a small cell or the macrocell. Using the traditional association policy, each UE would select as serving cell the one with the highest Signal-to-Interference-plus-Noise Ratio (SINR) measured on specific Downlink (DL) reference signals. However, small cells are characterized by a low transmission power, hence by a reduced coverage that is also limited by the interference from the MBS (Macrocell Base Station), that has a significant higher transmission power. This means that - by adopting a traditional approach - only the UEs in close proximity would select the small cell as a serving cell, which makes this approach not suitable for HetNets. Indeed, the UEs may connect to distant high-power MBS rather than nearby small cell, thus causing an inefficient load distribution. In order to reduce the macrocell load and to maximize the cell splitting, we assume here that the coverage area of the small cells is extended by using the Cell Range Extension (CRE) [31]. This method is based on the use of a bias (i.e., Range Extension Bias - REB) that is a positive value added to the measured signal power received by the UEs from the small cell.

The average SINR of the u-th UE served by the \(\bar {c}\)-th cell can be written as

$$ {\Gamma}_{u}=\frac{P_{u,\bar{c}}}{{\sigma_{n}^{2}}+\sum\limits_{c=1, c \neq \bar{c}}^{C} P_{u,c}} $$
(1)

where

  • P u,c represents the power receivedFootnote 1 by the u-th user from the c-th cell

  • \({\sigma _{n}^{2}}\) is the AWGN noise power.

Actually, the interference experienced by the u-th user that communicates on the k-th physical resource (called here resource block, RB) depends on how many and which cells are simultaneously transmitting on the same k-th RB towards different users. However, in order to decouple our problem from the resource assignment problem we focus on the worst interference condition, meaning that all the cells not involved in the joint transmission act as interferers for a given UE.

Moreover, each UE, u-th, is characterized by a data rate request Q u . As a consequence, the amount of RBs requested by the u-th UE, N u , depends on Q u and on the experienced SINR and can be expressed as

$$ N_{u}=\frac{Q_{u}}{{W}\log_{2}(1+{\Gamma}_{u})} $$
(2)

where W represents the bandwidth of a physical RB.

3.2 Backhaul Network

In an actual scenario each small cell BS (SBS) is connected with other SBSs or with the MBS by heterogeneous links with different capacity, while it is reasonable to assume that the aggregated backhaul traffic at the MBS from and towards the core network is transmitted by high capacity fibre links. Hence, we are interested in optimizing the traffic inside the local backhaul network composed by the macrocell and the small cells in its area. This network has hierarchical topology, as the one represented in Fig. 1. In particular, we consider a tree topology where the macrocell represents the root, and the nodes of the higher levels of the tree are connected with a meshed structure. The small cells (i.e., micro and femto cells) represent intermediate nodes and leaves of the tree. The hierarchical structure reflects the capacity of the links. In particular, the links are coloured depending on their capacity, chosen among the values of 100 Mbps, 50 Mbps and 20 Mbps for core optical links, outer xDSL links and femto-links respectively. The capacity of each link is expressed in units, called U B , of 100 kbps.

Figure 1
figure 1

Backhaul network topology.

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Figure 2 shows the geographical map of the considered area. Cell n.1 is the single macro cell, cells from n.2 to n.13 represent micro cellular coverages, scattered around the macro. Cells n.14 through n.23 are femto cells located in private premises.

Figure 2
figure 2

Heterogeneous coverage map.

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3.3 SDN

The Network Virtualization adopted in the backhaul network allows instantaneous routing decisions based on bandwidth requests from the radio access network. Each backhaul link is considered structural, in the sense that arcs and capacity do not vary over time. Each node performs two main tasks:

  1. 1.

    it collects the inbound traffic flow to be delivered through its air interface to the associated UEs;

  2. 2.

    it forwards the received traffic flows to the appropriate adjacent nodes as instructed by SDN controller.

As in the SDN paradigm, the traffic routing decisions are taken centrally by the controller, following the load balancing and optimization objectives imposed by the network intelligence.

4 Iterative Proposed Solution

This section proposes two cross-layer algorithms that aim to jointly optimize the radio access and the backhaul network resource usage. In particular, the objective of the first procedure is to minimize the total amount of UDRRs (minimum unsatisfied requests - MUR), while that of the second is to minimize the number of activated cells, thus reducing the energy consumption (minimum energy consumption - MEC).

The benefits of CRE cell association strategy for HetNets can be improved if it is combined and jointly optimized with resource allocation and backhaul traffic distribution procedures. Indeed, the CRE association simply forces UEs to select low power nodes by adding a fixed bias to the received signal power, but it does not take into account the load of the selected cell and the capability of the relative backhaul link to support all the small cell traffic. In addition in low traffic conditions, it could be convenient to turn-off some cellsFootnote 2 in order to reduce the energy consumption of the system.

We express the total cell load as the aggregated data requests in terms of requested RBs, so the \(\bar {c}\)-th cell is overloaded if the amount of requested RBs, \(R_{\bar {c}}\), exceeds the number of available RBs, K. Hence, the amount of UDRRs at \(\bar {c}\)-th cell is

$$ O_{\bar{c}}=R_{\bar{c}}-K=\sum\limits_{u\,\in\,\mathcal{U}_{\bar{c}}} \left\lceil \frac{Q_{u}}{{W}\log_{2}(1+{\Gamma}_{u})} \right\rceil-K $$
(3)

where ⌈x⌉ indicates the smallest integer value greater than x and \(\mathcal {U}_{\bar {c}}\) is the set of UEs associated with the \(\bar {c}\)-th cell. If \(O_{\bar {c}}> 0\) the cell is not able to satisfy all the UEs data rate requests.

For what concerns the load of the backhaul link of the \(\bar {c}\)-th cell, it is approximated as the total amount of the data rate requests managed by the cell as

$$ B_{\bar{c}}= \sum\limits_{u\,\in\,\mathcal{U}_{\bar{c}}} Q_{u}. $$
(4)

4.1 MUR Procedure

The ability of the backhaul link of the \(\bar {c}\)-th cell to support the required load depends not only on the capacity of the \(\bar {c}\)-th link, but also on the distribution of the traffic in the network tree. The goal of the MUR procedure is to minimize the amount of the total UDRRs taking into account both the ability of the cell to serve the associated UEs and the backhaul network capacity. The algorithm works as depicted in Fig. 3. At the physical (PHY) layer a new cell association procedure that takes into account CRE and the cell load, called Load Balancing Association (LBA) is performed producing as output the ”Max Rate Request”, that is the amount of data traffic that should be supported by the backhaul link of each node of the network. This request is sent to the network (NET) layer, that using a suitable traffic distribution algorithm called CRAI (Cognitive Radio Artificial Intelligence), tries to satisfy the PHY layer requests. The NET layer produces as output the ”Max Rate Response” that is a proposal on how to distribute the traffic in the backhaul network, indicating whenever the link is overloaded or under-loaded. This cyclic continues for several iterations. The procedure starts and ends at the PHY layer.

Figure 3
figure 3

PHY-NET cycle of the proposed procedure.

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4.1.1 Load Balancing Association

The new cell association procedure proposed here is based on CRE but takes into account also the traffic load of each BS. In particular, in the network initialization phase, each UE is associated to the BS (SBS or MBS) that has the highest SINR taking REB into consideration. Then, at each successive iteration the following steps are executed:

  1. 1.

    each BS determines if the amount of requested RBs is lower than the number of the available RBs (as in Eq. 3);

  2. 2.

    each BS determines if its backhaul link is able to support the total traffic amount generated by its potential associated UEs, \(B_{\bar {c}}\);

  3. 3.

    if at least one of the two previous conditionsFootnote 3 is not satisfied, some UEs are moved towards another serving cell following the LBA procedure as explained below;

  4. 4.

    in each cell RBs are allocated to the UEs following a Proportional Fairness (PF) policy [6, 13].

When the access and/or the backhaul links of some cells of the network are overloaded, the cells are not able to serve some UEs in their coverage area. Hence, the new LBA procedure is performed, whose aim is (i) to select which UEs can be served by different cells and (ii) which are the new serving cells. In particular, let us indicate with \(\hat {\mathcal {S}}\) (with \(\hat {\mathcal {S}}\subset \mathcal {C}\)) the set of cells that are not overloaded (it means that they are able to satisfy all the UEs requests in terms of both access capacity and backhaul capacity). Each overloaded BS determines for each of its associated UE the neighbour cell belonging to \(\hat {\mathcal {S}}\) that is received with the highest SINR value. Then the UEs are sorted in ascending order with the number of RBs requested to the new potential serving cell (i.e., the new cell is received with a lower SINR value, and hence the amount of requested RBs increases). Starting from the first UE in the ordered queue, a new association is performed if the new selected cell is able to support this new UE without overloading. The UEs association with the new serving cell continues until the original cell is not more overloaded or when there are not neighbour cells for the new association of the UEs.

At the end of the association procedure the PHY calculates the aggregated data rate of its associated UEs and sends this information to the NET layer.

4.1.2 CRAI (Cognitive Radio Artificial Intelligence)

Taking into account the PHY layer data rate requests per node, the NET layer is responsible for the network optimization. This process is executed by the CRAI and it is aimed at optimizing the distribution of the data flows among arcs and nodes in order to remove possible loops and avoid congestion in the network. Such an optimization can be defined as a minimum-cost network flow problem where the goal is to find a flow that satisfies all arc capacity and node data rate requests, while minimizing total cost. Defining a flow as a function \(x : A \to \mathbb {Z}_{\ge 0}\), the minimum-cost flow problem can be formulated as follows

$$\begin{array}{@{}rcl@{}} &&\arg \min_{x_{ij}} \sum\limits_{(i,j)\in A}^{} c_{ij} x_{ij} \end{array} $$
(5)
$$\begin{array}{@{}rcl@{}} && \quad s.t.: \quad\,\,l_{ij} \leq x_{ij} \leq u_{ij}, \quad\quad\quad\quad\quad\quad\forall (i,j)\in A \end{array} $$
(6)
$$\begin{array}{@{}rcl@{}} &&\qquad\qquad \sum\limits_{j:(i,j) \in A}^{} x_{ij} - \sum\limits_{j:(j,i) \in A}^{} x_{ji} = b_{i},\quad\, \forall i \in M \end{array} $$
(7)

where M is the set of nodes, A is the set of directed arcs, \(l: A \to \mathbb {Z}_{\ge 0}\) is the lower capacity function on the arcs, \(u: A \to \mathbb {Z}_{\ge 0}\) is the upper capacity function on the arcs, \(c: A \to \mathbb {Z}\) is the flow cost-per-unit function on the arcs and \(b: A \to \mathbb {Z}\) is the node mass balance function on the nodes [20].

The minimum-cost flow problem is solved using the NetworkFlow constraint tool of the Java Constraint Programming solver (JaCoP) [20] in an iterative way. Basing on the request vector from the PHY layer as input parameter, the approach is the following:

  • if a solution for the minimum-cost flow problem is found, the algorithm stops;

  • otherwise an iterative approach is used to determinate the additional minimum capacity for the arcs thanks to which input requests can be fully satisfied.

For both the cases, once a solution is found, the NET layer notifies to the PHY layer for each BS the quantity of units U B available for additional traffic or exceeding the maximum imposed limit causing cell outage.

4.2 MEC Procedure

The MUR procedure is useful when the network load is high and it is needed to suitably distribute the users among multiple access points in order to avoid conditions of overloading in both access and backhaul networks. However, when the traffic load is low, the network optimization can follow different criteria. Indeed, in this condition a dense HetNet deployment can lead to waste of resources, in particular of energy. If the traffic load is low having a high number of small cells partially overlapped among them and overlapped with the macrocell means that the available capacity is only partially exploited. As a consequence, it could be useful to turn-off some small cells thus reducing the energy consumption.

Towards this goal we propose here another procedure whose aim is to suitably select the small cells that can be turned off, while the amount of UDRRs is constrained to a maximum value, α. This means that it is acceptable to have a limited (by α) amount of UDRRs for the sake of saving energy.

The procedure is iterative and at each step the MUR procedure defined before is repeated. At the first step the MUR procedure is performed assuming all the small cells active, then, at each successive iteration, the small cell that presents the lowest amount of data rate requests by its associated users is selected. Then the procedure MUR is repeated assuming that the selected cell and all the cells selected at previous iterations are turned off. The amount of UDRRs is calculated at each iteration for the new HetNet configuration. If the amount of unsatisfied requests is lower than the imposed limit, α, the procedure continues, otherwise it stops and the HetNet configuration achieved at previous step is considered as the final one.

5 Numerical Results

This section presents the numerical results - obtained by means of computer simulations - that are provided in order to validate the effectiveness of the proposed cross-layer methods. The performance of the MUR procedure is expressed in terms of throughput and UDRRs as a function of the mean number of UEs in the area, while that of the MEC procedure is expressed in terms of number of turned-off cells and energy efficiency.

5.1 MUR Procedure Results

The advantages of the MUR method are showed in comparison with a benchmark resource allocation method that does not perform any cross-layer optimization: the PHY layer determines the cell association based on the RBs availability and then sends its rate request to the NET layer that produces a consequent allocation of the resources to the backhaul links.

The MUR procedure is iterative, but in order to have a predefined resolution time, the number of iterations has been assumed fixed. In particular we have verified that the gain tends to reduce when the number of iterations increases, and significant gains are obtained up to the 5-th iteration, then the gain is limited and does not justify additional delays.

Figures 4 and 5 show the system throughput and the UDRRs, respectively. The curves refer to the cases of constant (i.e.,@194 kbps) and variable data rate requests (i.e., @18 kbps, @160 kbps and @460 kbps.) of the UEs. The number of UEs has been selected in the range [350 - 650] because a high traffic load condition is needed to verify the benefits of the proposed method. In both cases, numerical results prove that the proposed cross-layer method performs better than the benchmark resource allocation method.

Figure 4
figure 4

Network througput of the proposed MUR procedure.

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Figure 5
figure 5

Total UDRRs of the proposed MUR precedure.

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The gain of the proposed method is achieved thanks to a more fair distribution of the traffic load among nodes, and hence, among backhaul links. This is shown in Fig. 6 where the Jain Index [19] is shown. This index measures the fairness and is defined as the ratio between the square mean and the mean square value of the traffic load distribution in the cells.

Figure 6
figure 6

Fairness of the load distribution among the network nodes using MUR procedure (variable data rate).

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5.2 MEC Procedure

The MEC procedure can be used in case of low load traffic conditions in order to increase the energy efficiency of the network. For this reason to prove the effectiveness of MEC procedure, we consider a number of UEs in the range [25,175]. For what concerns the traffic we consider only the constant data rate requests case. The same benchmark method considered before is also used to validate the MEC procedure performance in the case of all the cells active.

In this scenario we are interested in verifying the capability of the system to save energy while respecting the UDRR constraint, α. Towards this goal Fig. 7a shows the mean number of cells that can be turned off as function of the number of UEs in the area, considering two different values of α (i.e., α=3 % and α=5 % of the total amount of all users data rate requests).

Figure 7
figure 7

Number of small cells in idle mode and related UDRRs, using MEC procedure.

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Figure 7b shows the behavior of the mean UDRRs value, corresponding to HetNet configurations represented in Fig. 7a. In particular, in Fig. 7 we present two different sets of curves, that have been achieved averaging the results on:

  • MEC - all possible simulation outcomes, including the cases of zero cells turned off (i.e., MEC procedure stops at the initial iteration) in which the UDRRs value can overcome α;

  • filtered MEC - cases in which at least one cell is turned off (i.e., the UDDRs value when all the cells are active is lower than α).

In all the curves we can observe that, obviously, when the number of UEs and the traffic load increases, the mean number of cells that can be turned off decreases while the mean amount of UDRRs increases. In particular, we can note that if a higher amount of UDRRs is admitted, a higher number of cells can be turned off. Moreover, if we observe the filtered MEC curves in Fig. 7b, we can note that when the MEC procedure is active, and hence at least one cell is turned-off, the UDDRs value is effectively limited by its upper bound α. Conversely, if we take into account all simulation outcomes - even those in which the load is high and the MEC procedure is not activated - it is possible to have values of UDRRs higher than α, because there are some cases in which the network is not able to satisfy the requirements neither with all active cells. Up to 100 UEs the curves of the two sets (MEC and filtered MEC) have almost the same behavior, it means that up to 100 UEs the network is almost always under-loaded and, hence, at least one cell is turned off. Conversely, if the number of UEs increases, the possibility of reducing the number of active cells depends on the distribution of the UEs in the area, that is randomly changed at each simulation run. In Fig. 7b we can also note that the proposed system using MEC procedure to reduce the number of active cells and MUR procedure to allocate the available resources in a cross-layer manner, achieves always better performance than the benchmark method where cell deactivation is not considered.

Another interesting parameter is represented by the energy efficiency, E, of the system that here we define as the ratio between the total throughput offered by the HetNet, T, and the total transmitting power, P T . In particular, having three types of small cells (macro, micro and femto) whose transmitting power values are different we have that P T = M P M + μ P μ + f P f where:

  • M,μ,f are the numbers of active macro, micro and femto cells, respectively;

  • P M ,P μ ,P f are the transmitting power values of macro, micro and femto cells, respectively.

Figure 8 represents the energy efficiency of the system, showing that this increases significantly with the number of users.

Figure 8
figure 8

System efficiency using MEC procedure.

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6 Conclusions

HetNet deployment represents a novel networking paradigm based on the concept of access points densification and a multi-layer architecture. It is considered one of the main enhancements of 5G networks to boost capacity and coverage. However, the massive diffusion of access points leads to an exponential increase of the backhaul traffic and to the need of a suitable management of the backhaul network. This paper presented a new cross-layer approach that allows to jointly allocate the resources in the access and the backhaul networks. The proposed iterative procedure is based on a new cell association procedure that is performed at the PHY layer and an optimization of the backhaul network. Moreover an energy efficient approach is considered in the case of low load traffic condition. The results show that the joint decision allows to achieve better results in comparison with a non-iterative benchmark method.