# Onboard Processing in Satellite Communications Using AI Accelerators
## 3 Onboard AI Applications
### Use Cases
#### 3.1.5 Antenna Beamforming  
Antenna arrays play an increasingly important role as we move into the era of high-capacity wireless access systems that demand high spectral efficiency. Antenna arrays have become part of the standards for cellular and wireless local area networks. These active antenna arrays will play an equally important role in the next generation of satellite communication systems. In addition, the substantial low earth orbit (LEO) and medium  
Figure 6: Convolutional neural network for RF interface flexible payload reconfiguration. earth orbit (MEO) constellations envisioned by companies such as OneWeb, Telesat, SES, and SpaceX will require antennas capable of beamforming according to traffic requirements. This convergence of trends is driving a shift from passive antennas with fixed, static beam patterns to active, fully steerable, intelligent antennas. Active beamforming antennas, commonly referred to as active phased array antennas, have active phase shifters on each antenna element or subarray to generate an incremental phase shift to beam steer the radiation pattern in a certain direction. In addition, the amplitude of the power received by each antenna allows to control of the shape of the beam; for instance, control of the beamwidth \(\theta_{-3 dB}\), side lobe levels (SLLs), and even the nulls in a certain direction. Hence, controlling both the phase and the amplitude gives us plenty of control of the radiation pattern. Next, a short description of the radiation pattern characteristics is provided. Beamwidth \(\theta_{-3 dB}\)  
A direct radiating array (DRA) antenna beamwidth can be increased or decreased by controlling its effective aperture, which also depends on the number of rows and columns of active elements. An estimation of the required number of elements \(R\) in one dimension for a certain beamwidth can be computed using Equation (1)  
\[R=\frac{\arcsin(\frac{1}{\sqrt{2}})}{\eta d\theta_{-3 dB}}2\lambda_{0} \tag{1}\]  
where \(\eta\) is the antenna efficiency, \(d\) is the inter-element spacing, and \(\lambda_{0}\) is the antenna wavelength. For instance, to obtain \(\theta_{-3 dB}=0.9^{\circ}\) using a DRA with subarray elements separated by \(d=2.5\)\(\lambda_{0}\), and assuming an ideal case with \(\eta=1\), a total number of \(R=16\times 16\) elements is needed. The radiation pattern corresponding to this scenario can be estimated using the planar array factor formula presented in (2)  
\[\mathrm{AF}=I_{UC}\sum_{r_{x}=1}^{R_{x}}\mathrm{e}^{\mathrm{i}(r_{x}-1)(kd_{x} \sin(\theta)\cos(\phi)+\beta_{x})}\times\sum_{r_{y}=1}^{R_{y}}\mathrm{e}^{ \mathrm{i}\left(r_{y}-1\right)\left(kd_{y}\sin(\theta)\sin(\phi)+\beta_{y} \right)}\,, \tag{2}\]  
where \(I_{UC}\) is the unit cell element pattern, \(R_{x}\) is the number of elements in the \(x\)-direction, \(R_{y}\) is the number of elements in the \(y\)-direction, \(k\) is the wave number, \(d_{x}\) is the period in the \(x\)-direction, \(d_{y}\) is the period in the \(y\)-direction, \(\beta_{x}\) is the incremental phase shift in the \(x\)-direction, and \(\beta_{y}\) is the incremental phase shift in the \(y\)-direction. The radiation pattern corresponding to the azimuth cut is illustrated in Figure 7.  
Figure 7: Azimuth cut of a \(16\times 16\) DRA, using subarrays as radiating elements separated by \(2.5\)\(\lambda_{0}\). Low side lobe levels (SLLs) can be easily accomplished using a windowing operation by means of a filter design, such as that of Hamming, Chebyshev, [PERSON], [PERSON], or another known approach. Some of these methods allow one to reduce the side lobe levels to the desired value; however, the drawback of this is a beamwidth increase, hence reducing the directivity of the array. For instance, we can consider the previously presented example, which uses 16 \(\times\) 16 subarray elements used to obtain a radiation pattern with a \(\theta_{-3 dB}=0.9^{\circ}\).