# Beamforming Based on a SSS Angle Estimation Algorithm for 5G NR Networks
## 1 Introduction  
Due to the fast growing pace of high-speed mobile broadband demands triggered by the exponential increases in the numbers of users and distinct services [1, 2], the third generation partnership project (3 GPP) initiated the development and maintenance of the new radio (NR) access technology for the fifth generation (5G) mobile communications, according to a published set of recommendations that represent the basis for the implementation of 5G radio access networks all around the world [3, 4]. Therefore, to fulfill the 5G performance requirements for the different use cases [5, 6, 7, 8, 9], the usage of the mmWave spectrum has been considered as a key technology to enable large radio bandwidths, overcoming the currently saturated frequency spectrum below 6 GHz used in LTE mobile systems. However, the use of higher frequencies for wireless communications is restricted by the harsher propagation characteristics of the mmWave systems that become even more hostile as the operation frequency increases [10].  
To efficiently surpass these impairments, more sophisticated processing techniques are employed, such as beamforming (BF), which is capable of providing highly precise directional transmission links over multiple receive and transmit antenna elements [5, 11],each one with detailed control of both phase adjustment and amplitude scaling to provide both high antenna-array and high spatial-multiplexing gains, overcoming the severe path losses of the mmWave systems [12] while being capable of achieving Gbps data rates in urban deployments [13; 14; 15]. Nonetheless, to achieve the most possible connectivity, there is a need to ensure that the established connection with each device occurs in the best possible set of beams.  
This led to the creation of a distinct set of physical layer (PHY) L1/L2-interoperable procedures known as beam management (BM) procedures, consisting in a variety of control tasks, such as the determination of a suitable beamformed beam pair for idle users, establishing a connection between the device and the network, and retaining the best connectivity possible for already connected users through beam tracking processes, or even the beam recovery procedures needed to reestablish the connection with minimal delay after blockage events, gradual changes in the environment radio propagation conditions, or additional user movements and rotations [16; 17].  
The initial beam establishment (IBE) stage is the first of the three defined 3 GPP BM procedures, which aims at establishing the best beam pair in the downlink (DL) and uplink (UL) directions. This is usually performed by measuring the different RSRP values for each of the transmit-receive candidate beam pairs in a dual-end beam-sweeping procedure, defined as procedure P-1 [18]. The corresponding beam pair link with the highest RSRP value is chosen, as it ideally experiences the best channel conditions available [19]. Therefore, relevant metrics to perform beam pair comparisons are fundamental in NR mobile systems for establishing the most suitable available connection.  
The work proposed in this paper falls in this context. The main goal consisted of the design and subsequent performance evaluation of a new 3 GPP-standard-compliant beam pair selection algorithm based on the SSSs angle estimation (BSAE). This BSAE algorithm was implemented in a NR system model that uses BM techniques at both transmitter (gNB) and receiver (UE) ends to establish the beamformed connection in the DL direction by choosing the best beam pair available for further synchronization, demodulation, and decoding a real-time gNB signal.