Self-optimization of coverage and capacity based on a fuzzy neural network with cooperative reinforcement learning
- Shaoshuai Fan^{1},
- Hui Tian^{1}Email author and
- Cigdem Sengul^{2}
https://doi.org/10.1186/1687-1499-2014-57
© Fan et al.; licensee Springer. 2014
Received: 5 September 2013
Accepted: 3 April 2014
Published: 12 April 2014
Abstract
Self-organization is a key concept in long-term evolution (LTE) systems to reduce capital and operational expenditures (CAPEX and OPEX). Self-optimization of coverage and capacity, which allows the system to periodically and automatically adjust the key radio frequency (RF) parameters through intelligent algorithms, is one of the most important tasks in the context of self-organizing networks (SON). In this paper, we propose self-optimization of antenna tilt and power using a fuzzy neural network optimization based on reinforcement learning (RL-FNN). In our approach, a central control mechanism enables cooperation-based learning by allowing distributed SON entities to share their optimization experience, represented as the parameters of learning method. Specifically, SON entities use cooperative Q-learning and reinforced back-propagation method to acquire and adjust their optimization experience. To evaluate the coverage and capacity performance of RL-FNN, we analyze cell-edge performance and cell-center performance indicators jointly across neighboring cells and specifically consider the difference in load distribution in a given region. The simulation results show that RL-FNN performs significantly better than the best fixed configuration proposed in the literature. Furthermore, this is achieved with significantly lower energy consumption. Finally, since each self-optimization round completes in less than a minute, RL-FNN can meet the need of practical applications of self-optimization in a dynamic environment.
Keywords
1 Introduction
Today’s cellular radio technologies are developed to operate closer to Shannon capacity bound. Yet, efficient PHY layer solutions may not necessarily translate to efficient resource utilization as the network performance relies on the dynamics of the radio network environment [1]. To this end, one of the key concepts of the prominent 4G technology, long-term evolution (LTE), is self-organizing network (SON), which is expected to help LTE cope with network and traffic dynamics both during deployment and operation [2]. Essentially, SON, which enables self-configuration, self-optimization, and self-healing, is expected to improve network performance and user quality of experience while reducing capital expenditures (CAPEX) and operational expenditures (OPEX) [3–7].
Coverage and capacity optimization (CCO) is one of the typical operational tasks of SON [2, 8]. CCO allows the system to periodically adjust to the changes in traffic (i.e., load and location) and the radio environment by adjusting the key radio frequency (RF) parameters (e.g., antenna configuration and power) through intelligent algorithms. For the online CCO problem, there is no definite mapping function from the inputs and parameters to be adjusted to the coverage and capacity performance. The main reason is the complexity of adjusting all the configuration parameters affecting both coverage and capacity. In addition, the configuration parameter space is too large, which prohibits exhaustive search [9]. Thereby, most algorithms are designed in a heuristic way.
Among the existing approaches, the artificial intelligence-based approaches that accumulate the operational and optimization experience and form optimization policies based on these experiences are the most promising. The optimization experience, which is shared among SON entities, constitutes traffic and radio conditions, and current configuration and performance. Current configuration is typically defined based on a single optimization parameter (e.g., antenna tilt) and does not take into account the impact of other parameters such as power in optimizing capacity and coverage. Also, learning is typically performed in a selfish manner without considering the learning cooperation of all the entities.
To overcome the aforementioned problems, in this paper, we design a distributed fuzzy neural network (FNN) to guide the joint optimization of coverage and capacity. Our solution introduces a central control mechanism to facilitate cooperative learning by sharing the optimization experience of SON entities. As the core part of the fuzzy neural network, both fuzzy inference rule base and parameters of membership functions are acquired and adapted with reinforcement learning method which can achieve a predefined goal by directly interacting with its uncertain environment and by properly utilizing past experience derived from previous actions. To control coverage and capacity, we jointly optimize antenna tilt and power while considering the varied and non-uniform traffic load distribution of the cells within a specific region.
The rest of the paper is organized as follows. In Section 2, we describe related research in the literature. In Section 3, we discuss the factors that affect our approach and describe the architecture for CCO. In Section 4, we present the details of the proposed reinforcement learning-based FNN optimization (RL-FNN) executed in distributed SON entities. In Section 5, we present the simulation results. Finally, we draw the conclusions in Section 6.
2 Related work
Majority of the coverage and capacity optimization algorithms are heuristic due the complexity of the problem. For instance, local search methods, such as gradient ascent [10] and simulated annealing [11, 12], are adopted for radio network planning. In [10], a heuristic variant of the gradient ascent method was adopted to optimize antenna tilt. In [11, 12], simulated annealing algorithm was used to control the downlink transmit power. The proposed approaches rely on the accurate downlink interference information in an eNodeb’s own and neighboring cells under all possible parameter configurations. However, such information can hardly be predicted due to not having a precise mapping from parameter adjustments to the current performance. Taguchi method, which is superior to the local search methods in exploring the search space, was used in [13] to optimize radio network parameters. Yet, a great number of experiments are needed to explore the large parameter space and determine the impact of different parameter values on the network performance during operation. Finally, in all these algorithms, each iteration step caused by the dynamics in traffic and the radio environment is a trial-and-error process. Due to the risk of negative performance impact, trial-and-error is prohibitive in real networks.
To prevent potential drastic changes in the network performance, the artificial intelligence approach, which can accumulate the operational and optimization experience and form optimization policies based on the experience, has significant potential [14–17]. In [1, 18], a case-based reasoning algorithm enables distributed decision-making. The algorithm stores past successful optimization instances that improved the performance in the memory and applies these instances directly to new situations. In [19–21], a fuzzy Q-learning algorithm was used to learn the optimal antenna tilt control policy based on the continuous inputs of current antenna configuration and corresponding performance, and output of the optimized antenna configuration. Yet, the impact on neighboring cells due to such an adjustment was neglected. To overcome the suboptimal performance of selfish learning, the approaches proposed in [6, 22] permit the cells to share their performance statistics with their neighbor cells so that each SON entity tries to learn the optimal action policy based on the overall reward of the neighborhood instead of local selfish rewards. However, the potential from having SON entities learn cooperatively was not taken into consideration. Also, the fuzzy membership functions in the proposed fuzzy Q-learning algorithms were predefined by intuition or partial operation experience, which may affect the optimization performance. Moreover, in contrast to our approach, these approaches only optimize the antenna tilt.
3 Coverage and capacity optimization under hybrid SON architecture
where P_{ i } is the transmit power on each resource block (RB) which is in direct proportion to the total power of eNodeB i if the power is equally allocated, N is the received noise, and G_{ i j } is the link loss from eNodeB i to user j including path loss, antenna gain, shadowing, multipath fading, etc.
In Equations 3 and 4, A_{ m } denotes the maximum antenna front-to-back attenuation and SLA_{ v } denotes the maximum vertical slant angle attenuation.
While the RET optimization can provide larger gains in terms of cell-edge and cell-center performance [1], power optimization can improve coverage and capacity performance and also power efficiency to some extent. Considering these factors, the antenna tilt and total power are chosen as the parameters to adjust in order to improve the coverage and capacity performance.
Many factors should be considered while adjusting the RF parameters, including cell-edge performance, cell-center performance, inter-cell interference, and traffic load distribution. For instance, a higher value of antenna tilt or a lower value of power may result in coverage outage at the cell-edge but will also result in less inter-cell interference. On the contrary, a lower antenna tilt or a higher power may result in expansion of coverage and improvement of cell-edge performance with the risk of more inter-cell interference. Additionally, the expanded coverage of a cell may relieve the traffic load in neighboring cells at the risk of causing congestion in the expanded cell. Consequently, the fact that all the adjustments have both negative and positive consequences makes this optimization problem very complex to solve.
In Equation 5, T_{i 5%} represents cell-edge coverage, which is computed as the throughput cumulative distribution function (CDF) of 5% tile, and T_{i 50%} denotes the cell-center capacity, computed as the throughput CDF of 50% tile. Also, a weight factor ω is used to balance coverage and capacity performance. In this paper, we give more weight to the coverage performance as it affects user experience more.
where N(i) is the set of its neighbor areas, and α is the weight factor used to measure the importance of the sector’s performance and its neighbors’. Note that this optimization problem is constrained by the maximum power and tilt. Additionally, the various settings of the weights (i.e., ω and α) will affect the optimization target instead of the optimization ability. Note that the setting of these weights depends on the network operators’ optimization targets and strategies. Finally, as each SON entity solves the CCO problem locally, we assume that the KPI information, needed from the neighboring cells, can be easily transferred via LTE X2 interfaces between eNodeBs.
4 Fuzzy neural network with cooperative Q-learning
In this paper, our main goal is to enable all SON entities to take simultaneous actions periodically to optimize RF parameters and learn from each other’s optimization experience. In order to achieve this, we propose using a distributed Q-learning based fuzzy neural network algorithm, which we present in detail in this section.
4.1 Architecture of RL-FNN
The proposed RL-FNN has two generic processes: forward operation and learning. It describes the current state based on the current power and tilt configuration, and the corresponding coverage and capacity performance are taken into account in every forward operation process to obtain the best RF parameters. RL-FNN performs the mapping function of current state to the best RF configuration in the forward operation process, while the mapping function is formed by the learning process. However, considering that the perfect input-output training sample pairs can hardly be acquired in a realistic network, reinforcement learning methods [26, 27] are needed for training the fuzzy neural network.
In addition, we have to keep in mind that in certain applications, the performance of fuzzy neural network highly depends on the fuzzy inference rule base and the particular membership functions, which can strongly affect the performance. Therefore, RL-FNN adopts a two-phase learning process: knowledge acquisition and parameter learning. In the knowledge acquisition phase, cooperative Q-learning method is adopted to acquire the fuzzy inference rule base. In the parameter learning phase, we adopt the reinforced back-propagation method to adjust the parameters of fuzzy membership functions. The details of the forward operation process and the two-phase learning process are explained in the rest of this section.
4.2 Forward operation
4.2.1 Layer 1
Similar to the definition of KPI, S=ω S_{5%}+(1−ω)S_{50%}, where S_{5%} denotes the spectrum efficiency CDF of 5% tile and S_{50%} denotes the spectrum efficiency CDF of 50% tile.
4.2.2 Layer 2
Here, ${c}_{\mathit{\text{ij}}}^{\left(2\right)}$ and ${\sigma}_{\mathit{\text{ij}}}^{\left(2\right)}$ are, respectively, the mean and the standard deviation of the Gaussian membership function of layer 2.
4.2.3 Layer 3
Here, ${O}_{i{k}_{i}}^{\left(2\right)}$ is the degree of membership of the i th linguistic input for the IF part of the k th fuzzy inference rule.
4.2.4 Layer 4
Each of the two output variables of RL-FNN is fuzzified into three linguistic levels - high (H), medium (M), and low (L). So, this layer consists of six nodes. The links from layer 3 nodes to layer 4 nodes denote the THEN part of the IF-THEN fuzzy inference rules. The method of establishing the fuzzy inference rule base will be described in Section 4.3.
Here, ${O}_{{n}_{\mathit{\text{lm}}}}^{\left(3\right)}$ is the n th input to node ${N}_{\mathit{\text{lm}}}^{\left(4\right)}$ for the m th Gaussian fuzzy set associated with the l th output variable.
4.2.5 Layer 5
Here, ${c}_{\mathit{\text{lm}}}^{\left(5\right)}$ and ${\sigma}_{\mathit{\text{lm}}}^{\left(5\right)}$ are, respectively, the mean and the standard deviation of the Gaussian membership function of layer 5. The method of acquiring the Gaussian membership function parameters of layer 2 and layer 5 will be described in Section 4.4.
4.3 Q-learning for knowledge acquisition
In order to achieve self-optimization, each entity in each cell must know what parameter tuning action should be done according to the current operation state which is determined by x=(P,θ,Δ L,Δ S) (defined in Section 4.2). However, it is hard to populate the fuzzy inference rule base, as the complete and accurate knowledge of the network operation can hardly be acquired online, and typically, not enough operational experience can be collected beforehand in such a complex optimization scenario. Therefore, in our approach, cooperative Q-learning algorithm is used for knowledge acquisition.
Here q_{ k i } represents the elementary quality of the i th inference result responding to k th rule, and the higher value of q_{ k i }, the higher the trust for the corresponding power and antenna setting.
Here, the greed action factor ε is decreased to zero as the optimization step increases.
In Equation 19, s_{ t } and a_{ t } denote the state and the action of the fuzzy inference rule at step t, and γ is the discount factor.
In Equation 25, ξ is the learning rate for Q-learning.
Here, ${q}_{\mathit{\text{ki}}}^{j}$ denotes the quality value recorded in self-optimization entity j corresponding to the i th action of the k th rule, and M is the number of the SON entities managed by the central network management system (NMS).
4.4 Reinforced parameter learning
where y^{∗} denotes the best overall experienced value of the JKPI, y(t) denotes the measured JKPI at step t, and e(t)=y^{∗}−y(t) denotes the reinforcement signal. Consequently, as a result of the reinforcement learning, the algorithm adapts parameters of RL-FNN to minimize E(t), which is equivalent to maintaining the overall JKPI at the best experienced value.
Here, Z^{ j } denotes the vector of the mean and standard deviation parameters recorded in self-optimization entity j.
5 Simulation and analysis
The proposed approach is evaluated by system level LTE networks simulator developed in c++. The simulation parameters and placement of transceivers (TRs) are set based on the interference-limited scenario with a hexagonal macro-cell deployment described in [23, 28]. We simulate 7 three-sector cells with an inter-site distance of 500 m. Twenty to sixty users are uniformly distributed in each cell, maintaining 35 m minimum distance to the base station. The user mobility is modeled with random walk with a constant speed of 3 km/h (wrapping around is permitted). Users always have a full buffer (i.e., they have always traffic to send), and we use round robin scheduling.
Simulation parameters
Parameter | Value |
---|---|
Carrier frequency | 2.0 GHz |
Channel bandwidth | 10 MHz |
Propagation loss | −128.1−37.6 log10(d), d in km |
Shadowing standard deviation | 8 dB |
Shadowing correlation distance | 50 m |
Shadowing correlation | Intersite, 0.5; intersector, 1.0 |
Penetration loss | 20 dB |
Thermal noise density | −174 dBm/Hz |
BS maximum transmit power | 46 dBm |
Maximum antenna front-to-back attenuation A_{ m } | 25 dB |
Maximum vertical slant angle attenuation SLA_{ v } | 20 dB |
Horizontal half-power beam width φ_{3d B} | 70° |
Vertical half-power beam width θ_{3d B} | 10° |
BS and UE antenna height | 32 m; 1.5 m |
Power allocation on channels | Equal allocation |
Self-optimization time | 100 ms |
interval(learning time interval) | |
KPI weight factor ω | 0.8 |
JKPI weight factor α | 0.5 |
Initial greed action factor ε | 0.1 |
Reducing rate of greed action | 0.001/s |
factor | |
Discount factor γ | 0.7 |
Learning rate for Q-learning ξ | 0.5 |
Parameter learning factor η | 0.2 |
For comparison, we define a reference RF configuration where all cells have the same fixed antenna tilt of 15° and fixed total power of 46 dBm. This configuration was found to be the best configuration using discrete exhaustive search method for our simulated scenario [22, 23].
5.1 Details on operation of RL-FNN
In this section, we present the details of the RL-FNN algorithm and how it computes the degrees of fuzzy membership functions and does the inference for our simulation scenario.
The membership functions determine which fuzzy set the input value belongs to and the degree of the membership. The shapes of the Gaussian membership functions determined by the optimized means and standard deviations will help to determine these factors in a more accurate way to improve the performance of the fuzzy neural network.
Fuzzy inference rule base acquired by Q-learning
If | Then | If | Then | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Number | P | θ | ΔL | ΔS | P ^{ ′ } | θ ^{ ′ } | Number | P | θ | ΔL | ΔS | P ^{ ′ } | θ ^{ ′ } |
1 | L | L | L | L | L | H | 43 | M | M | H | L | L | L |
2 | L | L | L | M | M | H | 44 | M | M | H | M | H | L |
3 | L | L | L | H | L | L | 45 | M | M | H | H | M | L |
4 | L | L | M | L | M | H | 46 | M | H | L | L | H | H |
5,6 | L | L | M | M,H | L | H | 47 | M | H | L | M | M | H |
7 | L | L | H | L | H | H | 48 | M | H | L | H | L | H |
8 | L | L | M | H | M | H | 49,50 | M | H | M | L,M | L | L |
9 | L | L | H | H | M | L | 51 | M | H | M | H | H | L |
10 | L | M | L | L | H | H | 52 | M | H | H | L | L | H |
11 | L | M | L | M | M | H | 53 | M | H | H | M | M | H |
12 | L | M | L | H | M | L | 54 | M | H | H | H | M | M |
13 | L | M | M | L | L | M | 55,56 | H | L | L | L,M | L | M |
14 | L | M | M | M | M | H | 57 | H | L | L | H | L | L |
15 | L | M | M | H | M | M | 58 | H | L | M | L | H | M |
16 | L | M | H | L | L | H | 59 | H | L | M | M | M | M |
17,18 | L | M | H | M,H | L | M | 60 | H | L | M | H | L | M |
19 | L | H | L | L | M | H | 61 | H | L | H | L | L | M |
20 | L | H | L | M | L | H | 62 | H | L | H | M | H | L |
21 | L | H | L | H | L | M | 63 | H | L | H | H | M | M |
22 | L | H | M | L | M | H | 64,65 | H | M | L | L,M | L | M |
23 | L | H | M | M | M | M | 66 | H | M | L | H | H | M |
24 | L | H | M | H | M | H | 67 | H | M | M | L | M | H |
25,26 | L | H | H | L,M | H | M | 68 | H | M | M | M | M | M |
27 | L | H | H | H | L | L | 69 | H | M | M | H | H | H |
28 | M | L | L | L | M | M | 70 | H | M | H | L | L | H |
29 | M | L | L | M | H | L | 71 | H | M | H | M | L | M |
30 | M | L | L | H | L | L | 72 | H | M | H | H | M | M |
31,32 | M | L | M | L,M | M | M | 73 | H | H | L | L | H | M |
33 | M | L | M | H | M | L | 74,75 | H | H | L | M,H | M | M |
34 | M | L | H | L | M | H | 76 | H | H | M | L | L | L |
35 | M | L | H | M | M | M | 77 | H | H | M | M | M | H |
36 | M | L | H | H | H | M | 78 | H | H | M | H | H | L |
37,38 | M | M | L | L,M | L | H | 79 | H | H | H | L | L | H |
39 | M | M | L | H | L | H | 80 | H | H | H | M | L | M |
40 | M | M | M | L | H | M | 81 | H | H | H | H | H | L |
41,42 | M | M | M | M,H | L | M |
5.2 Evaluation of coverage and capacity
In order to test the CCO performance of RL-FNN, we start the simulation with a poor configuration with very low power and very low antenna tilt, which are 8° and 40 dBm, respectively. After the initialization, RL-FNN approach starts to be executed in all entities periodically to optimize the coverage and capacity performance.
5.3 Additional benefits: energy efficiency
Performance comparison
Indicator | RL-FNN | Reference | Improvement |
---|---|---|---|
(%) | |||
JKPI | 219.6 kbps | 209.2 kbps | 5.0 |
Energy consumption | 42.3 dBm (16.8 W) | 46 dBm (39.8 W) | 57.8 |
Energy efficiency | 13.1 kbps/W | 5.26 kbps/W | 147.1 |
The above simulation results demonstrate that the proposed RL-FNN approach is able to achieve high performance in terms of coverage and capacity with significantly lower energy consumption.
5.4 Performance under abrupt changes
In this section, we evaluate the performance of RL-FNN when a cell is shut down due to, for instance, an unexpected failure or for simply energy-saving purposes. In the simulation, a cell is shut down at the following step 1,201 and all entities execute RL-FNN approach periodically to optimize the coverage and capacity performance.
Modified fuzzy inference rules
If | Then | |||||
---|---|---|---|---|---|---|
Number | P | θ | ΔL | ΔS | P ^{ ′ } | θ ^{ ′ } |
14,15 | L | M | M | M,H | H | L |
18 | L | M | H | H | M | M |
20,21 | L | H | L | M,H | H | H |
23,24 | L | H | M | M,H | L | M |
34 | M | L | H | L | H | M |
35 | M | L | H | M | H | M |
39 | M | M | L | H | M | H |
42 | M | M | M | H | H | M |
43 | M | M | H | L | H | M |
45 | M | M | H | H | M | H |
50 | M | H | M | M | H | L |
69 | H | M | M | H | M | H |
70,71,72 | H | M | H | L,M,H | H | L |
78 | H | H | M | H | H | M |
Performance comparison under abrupt changes
Indicator | RL-FNN | Reference | Improvement |
---|---|---|---|
(%) | |||
JKPI | 169.5 kbps | 126.8 kbps | 33.7 |
Energy consumption | 43.7 dBm (23.2 W) | 46 dBm (39.8 W) | 41.7 |
Energy efficiency | 7.3 kbps/W | 3.2 kbps/W | 128.1 |
In summary, the simulation results demonstrate that the proposed RL-FNN approach can efficiently improve the coverage and capacity performance in a dynamic environment. The results show that in approximately 700 to 800 optimization steps, RL-FNN converges to a better setting than the reference from an initially badly chosen configuration. Also, in 500 to 600 steps, RL-FNN recovers from the coverage hole scenario. However, note that the actual time for reaching these states is determined by the time interval for the cell to collect the load and spectrum efficiency indicator of neighbors and to perform the adjustments. Given these considerations, we assume that the optimization step interval is approximately 0.1 s as our approach can operate with low granularity. Hence, we expect that RL-FNN can operate with convergence times in the order of a minute. Compared to [9, 21, 22] which need nearly 1,000 optimization steps for the one-dimensional optimization of antenna tilt, the convergence rate of RL-FNN is a significant improvement as it adjusts both power and antenna tilt. Such fast convergence rate can only be achieved by cooperative learning enabled by RL-FNN.
6 Conclusions
In this paper, an online approach has been presented for self-optimization of coverage and capacity in LTE networks. The proposed RL-FNN approach is based on the fuzzy neural network combined with Q-learning and reinforced parameter learning. All self-optimization entities operate in a distributed manner and try to optimize power and antenna tilt automatically and cooperatively using the shared optimization experience.
From the simulation results, we conclude that our approach is able to acquire robust optimization policies for different complex scenarios and maintains a significantly better performance in terms of coverage and capacity with low energy consumption. This especially results in a dramatic improvement in energy efficiency. Finally, RL-FNN converges with an acceptable rate and is therefore applicable to different dynamic scenarios and applications.
In our future work, variants of the algorithms will be developed to enhance the cooperation between SON entities especially when abrupt changes happen. Moreover, it would be an interesting future research to extend the current work to heterogeneous networks.
Declarations
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 61231009), National Major Science and Technology Special Project of China (No. 2013ZX03003016), National High Technology Research and Development Program of China (863 Program) (No. 2014AA01A705), and Funds for Creative Research Groups of China (No. 61121001).
Authors’ Affiliations
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