# The Recent Advancement in Unmanned Aerial Vehicle Tracking Antenna: A Review
## 5 Multiple Input Multiple Output Technology
### MIMO Beam Forming  
MIMO beam-forming is an antenna technology in which multiple antenna arrays are deployed at the transmitter side to align the overall antenna radiation to the desired angle. The various antenna arrays produce the different signal beams which are responsible for the overall antenna gain (azimuth-wise) in the direction of the target herein the airborne platform. As could be in Figure 16, a transmit beam forming technique is the reverse of receive diversity. The depicted diagram could be construed as MISO because of the many input and single output. The signal at the receiver which is the airborne platform is stated as  
\[\overrightarrow{y}=\widetilde{h}x+\widetilde{n} \tag{4}\]  
where \(\overrightarrow{y}\) denotes the received signal vector, \(\widetilde{h}\) is the channel coefficient which can be modeled as Rician if there is clear LoS or Rayleigh if there are scatterers which will result  
Figure 15: Schematic presentation of spatial MIMO. in multi-paths, \(x\) is the information symbol that the UAV GCS intends to transmits to the airborne platform, and \(\vec{n}\) is the noise vector normally denoted as additive white Gaussian noise (AWGN). The sum of independent links present at the receiver is stated  
\[\widetilde{y}=y_{1}+y_{2}+y_{3}+\cdots+y_{L} \tag{5}\]  
\(\{y_{1},\ \cdots y_{L}\}\) represent the various received independent complex wireless signals. Instead of making use of selection combining (SC), a maximum ratio-combining (MRC) algorithm will be used as it is more appropriate herein. By using the MRC algorithm, the aggregate sum of the links is stated as:  
\[\text{MRC}=\omega_{1}^{*}y_{1}+\omega_{2}^{*}y_{2}+\omega_{3}^{*}y_{3}+\cdots+ \omega_{L}^{*}y_{L} \tag{6}\]  
\(\omega_{1}^{*}\) connotes the beam weight complex transpose conjugate. The beam weight is synonymous to \(\theta\) which is the desired angle of arrival (AoA) of the incoming signal of Equation (1). The AoA is the mechanical version of the beam weight complex which is the electronic version of AoA. Equation (6) leads to the derivation of the beam-forming stated as \(\overline{\omega}^{H}\overline{y}\). Note that \(\overline{\omega}^{H}\) is the Hermittian weight of the beamforming. \(\overline{\omega}^{H}\) is also known as the beamformer. The beamformer output is mathematically derived as:  
\[ \begin{array}{ll}Beamformer_{output}&=\overline{\omega}^{H}\left(\overline{ h}x+\overline{n}\right)\\ &=\overline{\omega}^{H}\overline{h}x+\overline{\omega}^{H}\overline{n}\end{array}  \tag{7}\]  
From Equation (7), it could be seen that beamformer output consists of signal component \(\overline{\omega}^{H}\overline{h}x\) and the noise component \(\overline{\omega}^{H}\overline{n}\). The second line of from Equation (7) simply expanded the first line of the equation. By applying some advanced signal-processing techniques, in the absence of interference, the noise component reduces to:  
\[\overline{\omega}^{H}\overline{n}=\sigma_{n}^{2}\left\|w\right\|^{2} \tag{8}\]  
\(\parallel\) is the norm of the vector and \(\sigma^{2}\) is the variance. It could be seen that the problem of beam-forming reduces to that of obtaining a close-form expression of the weight vector stated as  
\[\overline{\omega}=\overline{Ch} \tag{9}\]  
where \(\overline{C}\) is a constant. The optimal beamfomer is the antenna coefficient vector scaled by some constant shown in Equation (10)  
\[C^{2}\left\|h\right\|^{2}=1 \tag{10}\]  
\[C=\frac{1}{\left\|h\right\|}\]  
Substituting Equation (9) into Equation (10) leads to the derivation of the optimal beamfoming vector that that maximizes the received the SNR as  
\[\overline{\omega}_{opt}=\frac{\overline{h}}{\left\|h\right\|}\overline{Ch} \tag{11}\]  
The problem of beam-forming simply reduces to computing the channel coefficient. The channel models must address the multipath scattering effects, time dispersion, and Doppler shifts that arise from relative motion between the transmitter and receiver.