# Machine Learning Enabled Performance Prediction Model for Massive-MIMO HetNet System
## 1 Introduction
The closed form outage probability of a typical user has been derived in terms of BS density and the maximum number of users served by a BS for a multi-cell massive MIMO system, assuming the BSs are distributed randomly following a Poisson point process (PPP) [16]. Similarly, in HetNet, the network performance is limited by inter-tier interference. The interference experienced by a typical user in a k-tier HetNet has been accurately modeled by the authors of [17], where each tier differs by transmitting power and cell density. Closed-form approximation has been made for the coverage probability, traffic off-loading, and sum-rate considering inter-tier interference. The analysis of HetNet with a multiple antenna system is relatively complex because of the random matrix channel. The expressions for success probability and area spectral efficiency have been formulated for MIMO heterogeneous cellular networks using a Toeplitz matrix representation [18]. With proper analysis of the interference and its cancellation, the association of massive MIMO with HetNet is a promising physical layer solution for next generation wireless networks with several-fold increases in area spectral efficiency (ASE) and coverage probability (CP) [19]. The detailed system model and performance analysis of massive MIMO with HetNet is discussed in the literature [20] and the references therein. The impact of different network settings on the virtual coverage areas for massive MIMO-enabled HetNet has been explicitly studied in the literature [20]. With a theoretic framework for massive MIMO HetNets, tractable expressions have been obtained [21] for evaluating the average achievable rate and ASE. The performance of massive MIMO HetNet systems with limited channel information is discussed in the literature [22]. A wireless backhaul-based downlink rate enhancement technique for multi-antenna HetNet is presented in the literature [23]. A tractable approach is developed for evaluation of the spectral and energy efficiency in a massive MIMO-enabled three-tier network considering the presence of eavesdroppers [24]. The performance of massive MIMO-enabled HetNet in a multi-cell scenario is limited because of the presence of both inter-cell and inter-tier interferences. Therefore, the conventional analytic approach to model the statistical behavior of overall interference is not trivial, as it needs to include many stochastic network parameters. To overcome this challenge, this paper has proposed an ML-based approach to model the massive MIMO enabled HetNet system for predicting the network performance. To the best knowledge of the authors, currently, in the literature, such an approach to predict the performance of such networks has not yet been considered. The main focus of the work is to predict the performance of a two-tier network, in which the base stations of each tier are equipped with massive MIMO systems working in a sub 6-GHz band. This paper assumes perfect channel state information (CSI) at the transmitter. The analysis for imperfect/outdated CSI is beyond the scope of the work and may be considered in future. In this work, the coverage probability (CP) and area spectral efficiency (ASE) are considered to be the network performance metrics that quantify the reliability and achievable rate of the network, respectively. Both metrics are stochastically related with the network parameters. Two separate supervised ML models are inferred to predict the numerical values of CP and ASE from a given set of network parameters of an arbitrary network configuration. The rest of the paper is organized as follows: the system model for a multi-cell massive MIMO HetNet system is given in Section 2, the ML enabled performance prediction model in Section 3, and Section 4 concludes the paper.