# A Quadrilateral Geometry Classification Method and Device for Femtocell Positioning Networks
## 1 Introduction  
The latest Long Term Evolution-Advanced (LTE-A) standard anticipates the increasing use of small cells (known as femtocells) to provide the geo-location information required to meet the emerging communication and networking needs of future smart city applications [1; 2]. An overview of the LTE positioning methods is provided in [3], which includes the analysis of previous indoor localization methods. The aim of the paper [3] is focused on the investigation of the floor detection techniques in indoor environments. Based on the massive multiple-input multiple-output (MIMO) antennas and the millimeter wave communication technologies, the small cell concept will appear on the fifth generation (5G) cellular networks [4]. To realize the seamless coverage, a larger number of small cells have to be densely deployed in Heterogeneous network (HetNet) scenarios. This trend results in an attractive technological study of LTE outdoor localization. In providing location-specific services, the location of the moving macrocell user equipment (MUE) must be known with a high degree of accuracy. Then, the FeNBs can steer the digital beam-forming (DBF) to suppress the interfering signal generated from the uplink transmission of the outdoor MUE. Additionally, it could allow the call of the MUE to be handed to the indoor FeNBs, thereby improving the system efficiency. MUE localization is conventionally performed using a standalone GNSS/GPS system [5]. However, such systems not only incur a high battery consumption, but may also lack the precision required to provide true location-specific services. In some cases (e.g., indoor environments or built-upurban areas), the GPS signal may be intermittent or too weak to perform localization. Notably, the GPS measurements obtained using the MUE cannot be directly used for localization purposes in femtocell networks, since they cannot be transmitted in real time to the femtocell evolved Node Bs (FeNBs) [6]. Various methods have been suggested for improving the MUE localization performance in wireless networks [7; 8]. Thus, in a more recent 3 GPP specification (Release 11) [9], it is proposed that MUE positioning be performed by the radio access net-work (RAN) itself, rather than the MUE. Existing MUE positioning methods, including those based on time difference of arrival (TDOA), direction of arrival (DOA), or hybrid TDOA / DOA measurements, generally utilize a Gauss-Newton Interpolation (GNI) algorithm to estimate the location of the MUE in two-dimensional (2D) space [8; 10]. Multi-station TDOA positioning systems use optical communications to send the received signal of each FeNB to a reference FeNB, which then uses this information to calculate the TDOA between itself and each transmitting FeNB. Such systems have the advantages of a high accuracy and low system complexity. Furthermore, the common channel error among the different FeNBs is easily eliminated, and thus, the synchronization problem becomes trivial. TDOA positioning systems require at least four FeNBs to locate the moving MUE in three-dimensional (3D) space. However, the accuracy of the localization results depends on the geometry disposition of the selected FeNBs. The geometric dilution of precision (GDOP) contour map of four stations is simulated in [11]. It shows that the square distribution shape provides the best coverage area, the lozenge shape is the second best, the other irregular quadrilateral (IQ) shapes are the third best, and the straight line has the worst coverage area. Still, to the best of the author's knowledge, there is no other optimization approach provided to autonomously determine the optimum geometry disposition of four FeNBs. Accordingly, the present study proposes a normalization multi layer perception (NMLP) geometry classifier to autonomously determine the optimal four FeNBs with a lower GDOP value and an iterative geometry training (IGT) algorithm to obtain the training data for the NMLP geometry classifier.