## 4 Experimental Verification and Analysis
Since the G/T value in a digital phased array beamforming system is typically not directly measurable, the method of calculating G/T values through equivalent sensitivity is employed here. Given that the typical indicator for G/T values in a digital phased array beamforming system is \(G/T\geq-9\) dB/K, the following deduction of the required sensitivity value is based on the G/T indicator. The relationship between the input signal power Ps of the receiving terminal antenna and the output signal \(E_{b}/N_{0}\) is  
\[\frac{E_{b}\cdot R_{b}}{N_{0}}=\frac{P_{S}\cdot G}{K\cdot T} \tag{47}\]  
In which \(E_{b}\) is the energy per bit, \(R_{b}\) is the information bit rate, \(K\) is the Boltzmann constant, \(G\) is the antenna gain, and \(T\) is the antenna noise temperature. Equation (47) can be expressed in dB form as  
Figure 16:0  
By moving the other terms to the other side of the equation, we get  
Figure 16:1  
From Equation (49), it can be seen that when the sensitivity \(P_{s}(\text{dB})\) is taken, \(E_{b}/N_{0}(\text{dB})\) reaches the theoretical demodulation threshold corresponding to the DBF system, and the theoretical demodulation threshold can be broken down into  
Figure 16:2  
In which, \(G_{b}\) represents the coding gain, and \(L\) represents the demodulation loss. Substituting Equation (50) into Equation (49) yields the sensitivity expression formula with \(G/T\) value as  
Figure 16:3  
By moving \(P_{\text{min}}\) to the left side of the equation and \(G/T\) to the right side in Equation (51), we obtain the conversion formula for \(G/T\) value:  
Figure 16:4  
In the above formula, the selection criteria for each parameter are as follows:  
1. \(E_{b}/N_{0}(\text{theoretical})\): The system information bit SNR at a bit error rate (BER) of \(10^{-6}\). For the differential QPSK system in question, the value is taken as 10.8 dB;
2. \(G_{b}\): Coding gain, theoretically taken as 4.2 dB;
3. \(R_{b}\): Information bit rate, for this system, taken as 80,000 bps;
4. \(L\): Despreading and demodulation decoding loss, for this system, taken as 1 dB;
5. \(K\): Boltzmann constant, for this system, taken as 1.381 \(\times\)\(10^{-23}\) W/Hz/K. In Equation (51), when calculating \(P_{\text{min}}\) in dBm units, the value of \(K\) should be taken as:  
Figure 16:5In summary, based on Equation (52), at a symbol rate of 40 kbps (corresponding to an information rate of 80 kbps), after substituting the required specifications for \(G/T\geq-9\) dB/K, the required sensitivity threshold can be obtained as:  
Figure 16:6  
That is, when the sensitivity is better than \(-132.97\) dBm, its \(G/T\) value meets the specification requirements of \(G/T\geq-9\) dB/K. From the results of the beamforming sensitivity test in part (2), it can be seen that the measured beamforming sensitivity at each irradiation angle is less than \(-133\) dBm, which meets the actual requirement of sensitivity better than \(-132.97\) dBm. The calculated G/T values for each irradiation angle at three frequency points are shown in Figure 16:7  
From the test results in Table 3, it can be seen that the measured G/T values at all irradiation angles for the three frequency points in the test all meet the requirement of being greater than \(-9\) dB/K. (4) Beam Uniformity Test  
The uniformity of beam gain was tested for various beam pointing angles (spatial coverage: elevation angles 10\({}^{\circ}\)\(\sim\)90\({}^{\circ}\), azimuth angles 0\({}^{\circ}\)\(\sim\)360\({}^{\circ}\)). The CNR of the receiver was used as the basis for beam gain. With a step size of 10\({}^{\circ}\), the uniformity (i.e., the difference between the maximum and minimum values) is required to be within \(\pm\)3 dB. After importing the test script, the extraction and recording of the CNR for all angles were automatically completed.