Example: Beam Allocation in Multiuser Massive MIMO Reading Notes 1

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A Machine Learning Framework

For existing wireless systems assisted by cloud computing, a large amount of historical scene data may have been collected and stored in the cloud. Use the powerful computing power of the cloud to find optimal or near-optimal solutions for these historical scenarios. By classifying these solutions, the similarities hidden in these historical scenes are extracted as a resource allocation scheme based on machine learning. When a BS is deployed to a new area, there is usually no available data about historical scenarios. In this case, initial historical data can be generated from an abstract mathematical model with actual BS locations, accurate building footprints , presumptive user distribution , requirements , and wireless propagation models. When a new BS is put into use, measurement data of real -time scenarios will be collected from the actual system and then used as historical data for learning.

The proposed machine learning framework is shown in Figure 2. In the cloud, a large amount of historical data of scenes is stored using cloud storage. Historical data has many attributes, including user number, user CSI, user's international mobile subscriber comprehensive management index, etc. Some attributes, such as IMSIs of users , may not be related to specific resource allocation; therefore, the parameter vector $\mathbf{a} of the optimization problem in Eq. 1$ These irrelevant attributes are not included in $a .$ Learning from a large amount of raw data with many attributes generally requires a large amount of memory and computing power, which may affect learning accuracy [8]. Therefore, irrelevant attributes can be removed without causing a large loss in data quality. In order to reduce the dimensionality of the data and make the learning process run faster and more efficiently, feature selection is performed to identify and remove as many irrelevant attributes as possible, which will be discussed in the next section.

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Through feature selection, some key attributes are selected from historical data and presented as feature vectors. However, there may be some operational failures during the data measurement , transmission , and storage processes, causing the values in the feature vector to be abnormal, incomplete, or repeated. Therefore, necessary preprocessing is required to remove erroneous or duplicate feature vectors. All remaining feature vectors are then collected to form a very large data set. Further, all feature vectors in a dataset are randomly divided into a training set and a test set. Normally, 70% - 90% of feature vectors are assigned to the training set.

With the training set, supervised learning algorithms in machine learning are used to discover similarities hidden in historical data. By doing so, a predictive model can be built that will be used to make resource allocation decisions for unexpected future scenarios. More specifically, with the help of cloud computing, advanced computing technology can be utilized to use more computing time to search for solutions to the optimization problem of Eq. 1. Compared with traditional Lagrangian relaxation or greedy methods , the performance of the searched solutions can be significantly improved. Therefore, a high-performance resource allocation solution can be searched offline and associated with each training feature vector, as explained in the next section. All training feature vectors with the same solution are classified into a class, with each class associated with its own solution. The resource allocation problem is now transformed into a multi-class classification problem, outlined in the next
section . To solve multi-class classification problems, a predictive model will be built using two functions. The first is a class that predicts future scenarios, which can be described mathematically as a classifier $I=\text { Classifier }\left(F_{T}\right)$ 。 $F_T$ is the input feature vector extracted from the scene, $I$ means that the scene belongs toOutput class indexofclass $I.$ Then select Ith $I_{th}$ The associated solution of the class is $F_{T}$ The described scenario allocates radio resources. Before deploying the model, the recently built predictive model is evaluated on the test set and further optimized until the evaluation results are satisfactory.

Through backhaul links , the established prediction model and various related solutions are transmitted to the BS . In BS , its new feature vector is first formed using the measurement data of the real-time scene. The new feature vectors are then input into the built prediction model to allocate wireless resources. At the same time, new feature vectors will be collected and temporarily stored on the BS, and then forwarded to the cloud to update the data set, which is very important for tracking the evolution of real scenarios, including user behavior and wireless propagation environments.

Although building predictive models consumes a lot of computing resources, during off-peak hours, the computing work can be performed offline. Moreover, dataset updates and model deployment can also be done during off-peak hours. Therefore, the cloud can be shared with multiple BSs and can flexibly schedule computing tasks to make full use of available computing resources.

Application of Supervised Learning to Resource Allocation

In this section, we take the beam allocation problem in a single-cell multi-user massive multiple-input multiple-output (MIMO) system considered in [13] as an example to demonstrate our proposed resource allocation machine. Efficiency of learning frameworks.

In a single-cell system, assuming $BS$ is located in the center of the circular community, $K$ users are evenly distributed in the cell with unit radius, and each user is equipped with a single antenna. by $BS$ deployed byThe Butler $network [14] of a linear array composed of N$ identical isotropic antenna unitscan form a large number of $N >> K$ fixed beam. In such a fixed-system, a user is served by a beam assigned to it, as shown in Figure 5, where each user is served by a beam of the same color, ( ρ k , θ k $\left(\rho_{k}, \theta_{k}\right)$ represents user $The polar coordinates of k$ . To serve multiple users simultaneously, the key issue is how to efficiently allocate beams to users to maximize the sum rate.

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Since Beam The number of $N$ $The number of K$ , and each user is served by one beam, so only a part of the beams will actively serve users. Therefore, we first need to determine which beams are active. This problem can be solved by applying our machine learning framework. Specifically,theserves as the output of the predictive model. Assuming a LOS channel, due to $K$ users fromThe beam gain obtained by $N$ $The positions of K$ users are determined, so the user layout $u=\left[\left(\rho_{ 1}, \theta_{1}\right),\left(\rho_{2}, \theta_{2}\right), \cdots,\left(\rho_{K}, \theta_{K}\right) \right]$ as input data, which contains radial distance and phase information.

Since the beam gain obtained by a user from different beams varies significantly with its phase, as shown in Figure 5, the reachability and rate when using the beam allocation scheme are mainly determined by $Determined by the phase information of K$ users. Therefore, a user layout dataCharacteristic vector $F_u$ $of u$ $F_{u}$ Select as

$F_{T}=\left[\cos \theta^{(1)}, \ cos \theta^{(2)}, \ldots, \cos \theta^{(K)}\right],\tag{2}$

$\theta^{(1)} \leq \theta^{(2)} \leq \cdots \leq \theta^{(K)}$

Before resource allocation, we first need to train the prediction model by learning a large amount of training user layout data, which can be generated by a computer based on its distribution. For each training user layout, its feature vector formed according to Eq. 2 is associated with its active beam solution ( active beam solution ), which can be obtained by using an offline beam allocation algorithm. Due to the powerful cloud computing capabilities, as mentioned above, optimal exhaustive search or near-optimal metaheuristics algorithms can be used
. In this section, exhaustive search is applied for demonstration assuming a small number of users and beams.

After associating each feature vector in the training set with its active beam solution , all training feature vectors are naturally classified into categories based on their active beam solution. Specifically, feature vectors sharing the same active beam solution belong to the same class. Specifically, the feature vectors sharing the same active beam solution are in the same class. Then, a prediction model of the active beam solution can be established by applying a simple k-NN algorithm , and then the model can be evaluated and optimized to guarantee its performance, as shown in picture 2. For example, it can be improved by adding more training data. The impact of training set size is discussed through Figure 6b.

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The established prediction model is then deployed on the BS for beam allocation. For a new user layout $u_i$ , by forming its eigenvector $F_{u_i}$ , and define its feature vector $F_{u_i}$ to the stored training feature vector $F_{T_{J^{\prime}}}$ , the distance is recorded as $d_{u_{i}, T_{j^{\prime}}}$

$d_{u_{i}, T_{j}}=\left\|F_{u_{i}}-F_{T_{j}}\right\|^{2},\tag{3}$

Select $k$ with the smallest distance $k$ nearest neighbor feature vectors. According to the k-NN algorithm, hereSelect the most common category among $k$ $u_i$ The prediction class of the prediction model outputs the associated active beam solution of its prediction class . Based on the active beam information, each active beam is assigned to its best user with the highest received signal-to-interference-to-noise ratio (SINR) by assuming equal power allocation among users. In addition, new feature vectors $F_{u_i} are also collected$ , to further update the dataset and track the evolution of user layouts.

Figure 6 shows the average sum rate compared with the transmission signal-to-noise ratio (SNR) and training set size under our proposed beam allocation machine learning framework. For comparison, we also plot the average sum rates of optimal exhaustive search and low-complexity beam allocation (LBA) proposed in [13]. As can be seen from Figure 6b, as the number of training data increases, the average sum rate achieved by our proposed machine learning framework also increases, and gradually approaches the average sum rate of the optimal exhaustive search. It can also be seen from Figure 6 that with a larger training set, our algorithm is better than the LBA algorithm proposed in [13], indicating that the resource allocation machine learning framework we proposed is better than traditional technology.

Note that for the k-NN algorithm mentioned earlier , the distance between new data and existing training data is calculated in real time. Therefore, with a large amount of training data, the computational complexity can become very high in a real system. Therefore, it is important to design a low-complexity multi-class classifier, discussed below.

Research Challenges and Open Issues

Low-Complexity Classifier

Designing low-complexity multi-class classifiers requires more advanced techniques. One of the promising techniques is to transform multi-class classification problems into a set of binary classification problems, which can be effectively solved using binary classifiers. So far, support vector machine (SVM) is considered to be one of the most robust and successful algorithms for designing low-complexity binary classifiers by utilizing linear boundaries (hyperplanes) in high-dimensional space. Determine the class of the new feature vector. More specifically, these two categories are divided by only a few hyperplanes.

Accordingly, the class is determined based on which side of the hyperplane the new feature vector falls. Compared with the k-NN algorithm, the complexity of the SVM-based binary classifier is very low.

For the beam assignment example mentioned earlier, the total number of active beam solutions is $2^N$ _ In other words, there are at most $2^N$ categories, which means that the complexity of determining the scene category is $O(2^N)$ . At the same time, the complexity of exhaustive search is $O(N^K)$ . Obviously, our proposed machine learning framework for resource allocation can approach the optimal performance of exhaustive search with lower complexity. It is worth mentioning that severaltypical scenariosQoSFor example,the “great service in a crowd”scenario focuses on providing a great experience even in crowded areas, including stadiums, concerts, and shopping malls. For each typical scenario, hidden user behaviors and common characteristics of the wireless propagation environment may reduce the number of classes, which can be exploited to further reduce the complexity of the classifier. Recently, deep learninghas shown significant advantagesthe hidden common

Multi-BS Cooperation

Fast Evolution of Scenarios

In many real-world scenarios, user behavior and wireless environment are time-varying in nature [19]. That is, the characteristics hidden in the historical scene are also dynamic. In most cases, such evolution is too slow and gentle to be noticeable. This slow evolution can be easily tracked by learning by continuously collecting data and regularly updating the dataset. However, under certain special circumstances this evolution can be very sudden and dramatic. For example, emergency repairs on a very busy road greatly change user location distribution and mobility characteristics; blasting and demolition of high-rise buildings significantly changes the propagation environment. Since predictive models are built with outdated historical data, such rapid evolution can lead to significant performance losses in resource allocation. In machine learning, this problem can be solved by updating the predictive model whenever new data becomes available. However, since cloud computing is shared by many applications, new data can only be temporarily stored in the base station and then forwarded later to update the data set. How to cope with the rapid evolution of scenarios in resource allocation is a challenging topic for future research.

Conclusion

In future wireless communications, traditional resource allocation methods will face huge challenges to meet users' growing QoS requirements when wireless resources are scarce . Inspired by AlphaGo's victory, this paper proposes a machine learning framework for resource allocation and discusses how to apply supervised learning to extract similarities hidden in large amounts of scene history data. By exploiting the extracted similarities, the optimal or near-optimal solution of the most similar historical scenario is adopted to allocate radio resources to the current scenario. Taking beam allocation in multi-user massive MIMO systems as an example, it is verified that the resource allocation based on machine learning proposed in this article is superior to traditional methods. In short, machine learning-based resource allocation is an exciting area for future wireless communications assisted by cloud computing.