# Support Vector Machine-Based Transmit Antenna Allocation for Multiuser Communication Systems
### Motivations and Contributions  
Inspired by the pioneering work on learning-based antenna allocation for a single-user system [48], we focus on a wireless downlink multiuser communication system with antenna allocation. Extending the single-user system to multiuser networks, it is important to properly determine one or more communication performance metrics, such as sum rate and bit error rate (BER) [49]. For multiuser communication systems, maximizing the system sum rate might be a proper design target rather than minimizing the BER, due to the presence of interference among multiple users. Moreover, it is easy to obtain a rather trivial solution to the BER minimization problem for a multiuser communication system by selecting only one user (but not multiple users). In [41], learning-based link adaptation methods were designed for multiuser communication networks, where a greedy algorithm was employed for user selection. However, rather than improving fairness by user scheduling, our aim is to maximize the sum rate of all the users in the network by allocating the proper antenna to each user. Hence, we first formulate antenna allocation in the multiuser network as a multiuser sum rate maximization problem and solve it by using multiclass classification algorithms. To the best of our knowledge, this study is the first attempt at machine learning-based antenna allocation for multiuser wireless networks.  
The main contributions of this study are summarized as follows:  
* We interpret the antenna allocation system for multiuser communication as a multiclass classification learning system. For the components of the learning system, such as the training data and the corresponding class labels, we first model the counterparts in the conventional communication system, and we then construct them with a proper format for the learning system.
* We establish a communication system with an SVM module that allocates transmit antennas to each user in multiuser communication networks with partial channel state information at the transmitter (CSIT), as shown in Figure 1. The antenna allocation method is designed for a frequency-division duplex (FDD) system, where only quantized channel gain information is available.
* The parameters of the designed SVM are tuned based on extensive numerical experiments in order to improve the sum-rate performance of the communication system. For the designed SVM, we find that a Gaussian function is a good choice for the kernel function, which is one of the most important parameters for tuning SVMs. (Artificial neural networks (ANNs) can also be employed in our learning system, which may result in a slightly better sum-rate performance at the expense of both higher computational complexity and a larger training dataset than for \(k\)-NN and SVM. Thus, ANNs are not considered in this study as our main focus is on the design of learning systems showing a significant reduction in complexity from the optimization-based approach with marginal sum rate reduction.) From our rigorous simulation, the variance (kernel scale) and penalty parameter (box constraint) of an SVM kernel function are determined by 21.56 and 7.67, respectively.
* Numerical experiments are extensively performed for various configurations of communication systems in order to evaluate the proposed SVM-based antenna allocation method. We find that with lower online computational complexity, the designed SVM method achieves near-optimal performance, as is obtained from the conventional optimization approach. Compared to the \(k\)-NN method, the SVM method is superior not only in terms of sum-rate performance but also prediction complexity performance.