In this paper, the performances of well-known adaptive beamforming algorithms, namely, Sample Matrix Inversion (SMI) and Least Mean Square (LMS), are analyzed. From the simulation results, it is observed that for SMI, as the number of user increases the main lobe spreads in all directions. As a result, beamforming in the user direction may not be correct. To overcome this, LMS algorithm can be used. The LMS algorithm is the best choice in most of the commercial wireless applications due to its low complexity. 5G and beyond 5G networks require beamforming algorithms with high directivity and fast convergence rate. Hence, in this paper, LMS algorithm is modified to improve the convergence rate. Furthermore, improved LMS algorithms are applied to horizontal – vertical Uniform Linear Array. This is also called 2D-ULA. These improved LMS algorithms are called 2D-LMS 1 and 2D-LMS 2. The main drawback of LMS algorithm is its low convergence rate; because of this, LMS algorithm may not track the desired signal when the signal conditions are changing rapidly. Simulation results show that the proposed 2D-LMS 1 and 2D-LMS 2 algorithms have improved convergence rate, higher directivity, low complexity and fast execution time as compared to conventional LMS algorithm. Hence, the proposed algorithms are best suited for 5G and beyond wireless communications.

Smart antenna system involves processing of incoming signals induced on various antenna elements. It has a great potential to steer the nulls to reduce the co-channel interferences (Godara, 1997). Smart antenna system enhances the system capability by directing the narrow beams towards the user of interest, while nulling other users not of interest. Smart antenna system is getting huge popularity because of its capacity to suppress the sidelobes, improved system capability, Space Division Multiple Access (SDMA), high bandwidth, multipath suppression, increased frequency reuse, improved array resolution (Gross, 2005). Because of these potential benefits, smart antenna system finds a wide range of applications. Some of these applications, but not limited to, are mobile communication, satellite communication (Jeng and Lin, 1999), Multiple Input Multiple Output (MIMO) systems (Durgin, 2003), Wireless Local Area Networks (WLAN) (Doufexi et al., 2004), radar (Skolnik, 2001), ubiquitous radar (Skolnik, 2003), mobile ad hoc networks (MANET) (Lal et al., 2004), wireless local loops (WLL) (Weisman, 2002), waveform diversity systems (Ertan et al., 2002), etc.

Telecommunications Journal, Adaptive beamforming, Least Mean Square (LMS), Sample Matrix Inversion (SMI), Smart antenna, ULA