# Hybrid Beamforming in Massive MIMO for Next-Generation Communication Technology
## 2 Beamforming
On-Off analog beamforming (OABF) is another analog beamforming system with low complexity. Other antenna elements are detached, and only a subset of the antennas that do not utilize analog signal processing is coupled to the RF chain to transmit data. RF switches are employed for turning one antenna element on and others off. This is why it is called On-Off analog beamforming. Figure 2 displays a block representation of OABF, assuming two antenna elements are connected and others open-circuited. The idea behind creating OABF was to choose a subset of antennas with favorable working conditions and matching phases [5]. The second beamforming technology discussed in this article is digital beamforming. It can be described as the technology where each antenna requires a separate RF chain. The advantages of digital beamforming over analog beamforming include its support for spatial multiplexing, which enables different directivity for various frequency subcarriers, and its ability to detect and eliminate interference by adjusting the period and magnitude of the original bit stream. The baseband is where all signal processing is performed. A digital baseband precoder individually controls each antenna element's amplitude and phase of the broadcast signals [6], as in Figure 3, where we assumed \(\psi\) number of DACs and \(\xi\), number of antenna elements. Based on the angle of arrival (AOA) from the transmitters, there are two different methods of digital beamforming. The ideal array weights needed to drive the antenna array elements to achieve the desired beamforming pattern do not need to be changed if the angles of arrival do not change over time. This type of beamforming is called fixed. The ideal array weights must be adjusted if the wireless channel changes over  
Figure 1: Analog beamforming. Figure 2: On–Off analog beamforming. time. Real-time computation of the ideal array weights is required. This type of digital beamforming is called adaptive beamforming [22]. Various linear precoding techniques limit inter-user interference (IUI), such as zero-forcing (ZF), regularized zero-forcing (RZF), maximum ratio transmission (MRT), etc. Maximum Ratio Transmission (MRT) is a precoding method that uses the Hermitian of the channel matrix to optimize the SINR at the prearranged recipient [23]. To accomplish this, the base station uses the MRT precoding matrix, which is given as follows. \[\mathcal{W}=H^{H}, \tag{1}\]  
where \(W\) is the precoding matrix and MRT is preferred because it does not need channel inversion and is the simplest of precoding techniques. Zero-Forcing (ZF) is a spatial data processing technique in wireless communication systems with multiple transmitting antennas. Its primary objective is to eliminate the interference between multiple users by applying a precoding matrix that cancels out the interference signals. The precoding matrix is designed to make the channel matrix invertible, which is achieved by ensuring that the inverse of the channel matrix is equal to the product of the precoding matrix and the original channel matrix [24] and is given as follows. \[\mathcal{W}=H^{H}(HH^{H})^{-1}, \tag{2}\]  
Equation (2) can act as the left inverse of \(H\), therefore, also called the pseudo-inverse of \(H\). Regularized Zero-Forcing (RZF) is a precoding technique employed in communication networks as an alternative to directly inverting the channel matrix in zero-forcing (ZF) precoding. RZF precoding uses regularized channel inversion, which involves adding a regularization term to the channel matrix's inverse to improve the system's performance. The regularization term helps to balance the noise suppression and signal alignment requirements, resulting in better performance than traditional ZF precoding, and is mathematically represented as follows. \[\mathcal{W}=\mathbb{B}(HH^{H}+\alpha I_{k})^{-1}H^{H}, \tag{3}\]  
where \(\alpha\) gives the regularization factor that needs to be optimized and \(\mathbb{B}\) represents the power normalization parameter and \(I_{k}\) stands for identity matrix.