# Instantaneous Beam Prediction Scheme against Link Blockage in mmWave Communications
## 3 System Model  
### Beamforming Models  
The proposed beamforming architectures in this work adopt UCA geometry at the MS and BS, as per Figures 1 and 2, respectively. Here, the UCA structure provides various benefits for mmWave communications compared to alternative array configurations. Foremost, the geometric radiation pattern, reduced side lobe levels (SLL), along with symmetric half power beamwidths (HPBW) at endfire and broadside scanning directions. This contrasts with ULA that suffers from beam broadening effects, i.e., reduced directivity and gains. Moreover, UCA supports two-dimensional scanning, as opposed to the one-directional in the case of ULA. Hence, the proposed array eliminates the requirement for back-to-back arrays, which, in return, yields in less antennas and power requirements. Figure 1: Analog beamformer at the MS.  
Additionally, UCA provides an enhanced performance when compared with uniform planar arrays (UPA) for the same number of antennas, since the latter features a rectangular perimeter that possesses separable current distributions among the elements. Consequently, this creates non-uniform radiation patterns. Note that UPA represents a two-dimensional extension of ULA; hence, it uses the same design procedures. As such linear analysis is directly applied to find the principal plane patterns, albeit a higher computational complexity due to the increased dimensionality. This multi-dimensionality enables UPA to support 2D scanning with symmetrical patterns at the detriment of increased side lobes and larger dimensions. Along these lines, this paper adopts UCA in the structure of the beamformer, since it outperforms ULA solutions that exhibit deficient directivity in the broadside directions and UPA designs with a rectangular perimeter that feature separable current distributions among the elements and increased complexity. Along these lines, assuming a MS equipped with an analog beamformer realized using UCA, this UCA is composed of equally spaced \(N_{\text{MS}}\) antennas in the \(x\)-\(y\) plane arranged in a circular geometry with a radius of \(a\). Each \(n_{\text{MS}}\in N_{\text{MS}}\) antenna is connected to a power amplifier to enhance the power density. Moreover, each antenna element is supported by one dedicated analog phase shifter in order to provide continuous beam scanning with parallel antenna feeds. Finally, the array connects to a frequency (RF) chain, \(r_{\text{MS}}\in R_{\text{MS}}\), where \(R_{\text{MS}}\) is the total number of RF chains at the MS (set to 1 for analog beamformer). Figure 1 depicts the beamformer structure at the MS. The resultant beam conducts complete spatial transmission and reception in different pointing angles from one RF chain in cascaded codebook stages (i.e., each stage defines a set of directions of specific bandwidth). The directions are determined by \(c_{i}^{t}\) combining vector of \(i=1,2,\dots,I\) indices at (\(t\)) th time step, where \(I\) represents the number of pointing directions at the MS, as per Figure 3.  
Figure 2: Digital beamformer at the BS. The use of analog beamforming at the MS is due to the limited power resources. On the contrary, BS can be supported with a higher input power due to its stationary nature (flexibility in space and size). Hence, digital beamforming solutions are adopted at the BS and are attributed to the abundant input power and the need to support multi-user connectivity support. Hence, consider a BS composed from \(N_{\text{BS}}\) antennas that are equally spaced in circular ring to form a UCA, where each antenna is connected to one power amplifier and phase shifter. Moreover, each \(n_{\text{BS}}\in\ N_{\text{BS}}\) antenna unit connects to one dedicated RF chain, \(r_{\text{BS}}\) (number of antennas \(N_{\text{BS}}\) is equal to the number of RF chains \(R_{\text{BS}}\)), as per Figure 3. The BS also generates beamforming vectors \(p_{j}^{t}\) in various directions, i.e., \(j=1,2,\ldots,J\), where the variable \(J\) represents the number of BS directions.