# Beamforming Based on a SSS Angle Estimation Algorithm for 5G NR Networks
## 1 Introduction
### Previous Works on Beam-Pair Selection Enhancement  
Although a set of 3 GPP specifications have been already defined for the suitable beam pair selection of the highly directional transmissions required to enable the communication in the mmWave frequency bands, there is a lot of flexibility in how the required procedures are implemented. The authors of [20] proposed a directional cell discovery procedure, where BSs periodically transmit synchronization signals (SSs) in both time-varying random and omnidirectional directions to scan the angular space. The results, derived from actual field measurements for both single and multipath channels, showed that omnidirectional transmissions of SSs have much better performances than random angular search, in both digital and analog cases. Additionally, it was suggested that a low-rate-per-antenna digital BF design with an appropriate search algorithm may be a better choice for the initial cell search, and hybrid or analog BF should be used for the remaining communications once the connection has finally been established in both directions. An extension to the previous work was presented in [21], where the authors proposed several different standalone mmWave design options for the directional search in the initial access (IA) procedure, comprising both the synchronization phase, where the UE discovers the BS, and the random access phase, where the BS detects the random access request from the UE. The work in [22] focused on the mitigation of the total duration of IA-directional searching. They revisited various techniques for exhaustive and iterative beam searching to propose a novel hybrid training method, where the BS performs wide beam searching in the first stage, and the UE performs reverse training according to the best wide beam decided in the first stage. This more complex implementation is based on the initial transmission of SSs in a few directions over wide beams, which are subsequently refined until the communication is satisfactorily directional. Further work motivated by the reduction in the unacceptable overhead of traditional exhaustive searching schemes that lead to substantial delays on real-time communications was presented in [23]. The proposed data-driven multi-armed beam tracking scheme speeds up the beam tracking process by selecting the beamforming/combining vectors that achieve the target quality of service (QoS) based on real-time measurements, rather than the prior knowledge, such as channel and user mobility information in beamforming design. To address the trade-off between maximizing the QoS and minimizing the training latency, the authors of [24] designed an adaptive data-driven beam tracking scheme for multi-user mmWave communication systems. They used real-time measurement data based on a dynamic linearization representation of a time-varying pseudo-gradient parameter estimation procedure. To guarantee the reliability of communication, adaptive data-driven beam tracking was proposed to find a suitable beamformer/combiner pair and meet the given SINR constraint. There is also some additional work based on several sources of side information that successfully help the establishment of the mmWave links with substantially reduced training overheads for the beam-selection stage. Such work included the use of spatial information retrieved from sub-6 GHz frequency bands in an analog mmWave system, proposed in [25]; the leveraging of vehicle's position information and past beam measurements to rank desirable pointing directions that can reduce the required beam training to a small set of pointing directions, discussed in [26]; and also a novel framework of 3D-scene-based beam selection information for mmWave communications, proposed by the authors of [27]. This last work relied only on the environmental data and deep learning techniques of neural networks, used alongside image processing techniques, to improve the suitable beam selection.