## 3 Wireless Communication Schemes for Aircraft
### Beamforming Scheme  
The multiple antennae enhances performance of SNR by spatial diversity and array gain. The case of spatial diversity has an effect on NLoS that is the Rayleigh fading channel because a scattering environment gives a multiple degree of freedom though the antennae are highly correlated, the other is a valid LoS that is the Rician fading channel [35; 36]. We assume only in the beamforming scheme the destination node has an uniformly linear K-element array which are almost correlated between antennae, but the fading channel is independent due to NLoS. So, the destination node gets diversity gain, not array gain. The diversity gain is achieved by using MRC (maximum ratio combining), SC,and EGC (equal gain combining) techniques. In this paper, analog and digital beamforming schemes with MRC are considered when an incident signal from source node is processed. Thus, beamforming schemes have advantages that are array antenna gain and narrowband beamforming. However, there are disadvantages that the system complexity and energy consumption may increase. For an example, a structure is represented in Figure 2, which should process \(K\) signals that as incident to each antenna of the destination node in which the received signal [37] can be given by:  
\[y_{BF}=\sum_{n=0}^{K-1}{{{h}_{n}}{{x}_{n}}+{{n}_{n}}}. \tag{13}\]  
where \({{{h}_{n}}}=[{{{h}_{0}},...,{{{h}_{K-1}}}}]^{T}\) is a Nakagami fading channel coefficient vector that is from independent fading paths, \({{{n}_{n}}}=[{{{n}_{1}},...,{{{n}_{K-1}}}}]^{T}\) AWGN vector, and \({{{x}_{n}}}=\sqrt{{{{P}_{i}}}}s\). Where \(s\) is the packet from the source node. When the transmitted signal arrives at each antenna of the destination node, the phase is not synchronized due to time delay. Thus, to calibrate the phase shift weight vector is multiplied to each antenna, which is given by:  
\[r={{w}^{H}}{{y}}={{w}^{H}}{{h}}{{x}}+{{w}^{H}}{{n}} \tag{14}\]  
where \({{{w}^{H}}}=[{{{w}_{0}},...,{{{w}_{K-1}}}}]\) is the weight vector. According to this, the instantaneous SNR [37; 38] of each antenna can be expressed by:  
\[{{{\sigma}_{BF}}}=\frac{{{{|{w}^{H}}{{h}}|^{2}}}}{E\left({{{|{w}^{H}}{{n}}|^{ 2}}}\right)}=\frac{{2{{|{w}^{H}}{{h}}|^{2}}}}{{{{N}_{0}}{{w}^{H}}w}}=\frac{{ 2{{|{w}^{H}}{{h}}|^{2}}}}{{{{N}_{0}}{{|{w}}|^{2}}}}=\frac{{2{{|{h}}|^{2}}}}{{{{ N}_{0}}}}. \tag{15}\]  
where we suppose that the received signal is synchronized by the weight vector \(w=h\). Thus the output SNR based on MRC can represented by:  
\[{{{\sigma}_{MRC}}}=\sum_{n=0}^{K-1}{{{\sigma}_{n}}}=K\sigma \tag{16}\]  
where we assume that the SNR at each antenna is given through i.i.d. Rayleigh fading. Thus, the distribution of \({{{\sigma}_{MRC}}}\) is chi-squared with 2K degrees of freedom where K is the number of antenna. The outage probability of beamforming in Rayleigh fading for a given threshold \({{{\mu}_{0}}}\)[39] can be given by:  
\[{{{\rho}_{BF}}} =\Pr\left\{{{{{\sigma}_{MRC}}}<{{{\mu}_{0}}}}\right\}\] \[=1-exp(\frac{{{{-{\mu}_{0}}}}}{{{{\tau}_{SD}}}})\sum_{n=1}^{K}{ \frac{{{{({{\mu}_{0}}}/{{{\sigma}_{SD}}})^{n-1}}}}{{{(n-1)!}}}} \tag{17}\]  
where \({{{\tilde{\sigma}}_{SD}}}\) is the average SNR between the source node and the destination node. In the ABF, the weight vector can be implemented by a low noise amplifier and phase shifter, and then the signals are integrated by combiner. However, in terms of the DBF the roles of the phase shifter and combiner are integrated in the digital signal processing unit. Thus, the energy consumption of the phase shifter is not considered in the DBF. The ABF structure (Figure 3) consists of the LNA, PS, and CB, which are the phase shifter and combiner, and the RF chain (RFC) is comprised of \({{{P}_{BAS}}}\) Baseband power consumption of the sensor board, \({{{P}_{MIX}}}\) Mixer, \({{{P}_{SYN}}}\) Local Oscillator, \({{{P}_{LNA}}}\) Low Noise Amplifier, \({{{P}_{FIL}}}\) Filter, \({{{P}_{IFA}}}\) Intermediate Frequency Amplifier, and \({{{P}_{ADC}}}\) Analog-to-Digital Converter, respectively.