# Analysis of Grating Lobe Effects on GEO DSC Distributed Antennas
## 2 DSC Distributed Antenna Cooperative Transmission
### Antenna Arraying  
Combining multiple DSC satellite antennas together to achieve a DSC distributed antenna array provides a wider bandwidth and enhanced signal strength and channel capacity, which can improve the antenna performance and reliability of transceiver signals. Changing the geometric layout of the DSC distributed antenna, such as the orbital height of the satellite antenna, the relative position of the satellites, and the carrier phase, will have an impact on the performance of the DSC distributed antenna array. Depending on the application requirements, DSC distributed antenna arrays can also be flexibly configured and adapted to suit different communication scenarios and environments. For example, for communication scenarios requiring wide coverage, multiple DSC satellite antennas can be configured to achieve higher signal coverage and better communication quality. For scenarios requiring high-speed mobile communications, multiple DSC satellite antenna sets can be configured as one large virtual antenna to achieve better signal tracking and transmission speed.  
The most significant advantage of the DSC distributed antenna array is its ability to achieve an \(EIRP\) value \(N^{2}\) times greater than that of a single antenna. For example, in a binary array, two antennas transmit a sinusoidal signal with the same polarization mode and a carrier frequency of \(f\). The far-field synthesized signal strength \(E(t)\) can be calculated as the following [15]:  
\[E(t)=e_{1}\cos(2\pi ft+\varphi_{1})+e_{2}\cos(2\pi ft+\varphi_{2}) \tag{1}\]  
In Equation (1), \(e_{1}\), \(e_{2}\) are the electric field strengths of the respective signals emitted by the two antennas; \(\varphi_{1}\), \(\varphi_{2}\) are the corresponding carrier phases. Assuming \(e_{1}=e_{2}=e\), only the effect of the phase difference is analyzed.  
If \(\varphi_{1}=\varphi_{2}=0\), then  
\[E(t)=2e\cos(2\pi ft+\varphi) \tag{2}\]  
The two signals are coherently superimposed and the amplitude of the received signal from the target spacecraft becomes twice as large and the power becomes four times as large. If the phase \(\varphi_{1}=\varphi_{2}+\pi\), then \(E(t)=0\), at which point the two signals cancel each other out.  
Figure 3: Block diagram of the DSC distributed antenna system transmit signal synthesis scheme.  
For the more general case of having \(N\) antennas, the signal strength achieved in the far field can be expressed as the following:  
\[E(t)=\sum\limits_{i=1}^{N}e_{i}\cos(2\pi ft+\varphi_{i}) \tag{3}\]  
In Equation (3), \(e_{i}\) and \(\varphi_{i}\) represent the signal strength and carrier phase of the transmitted signal from each antenna, respectively.  
From the perspective of the antenna pattern, a single antenna pattern can be obtained through the Fourier transform of the antenna's near-field distribution. Assuming that the normalized distribution function is an ideal circular distribution, the far-field antenna pattern \(E\) can be obtained by the following [16]:  
\[E=\frac{a\cdot\exp(jk\frac{\rho^{2}}{\gamma})}{\mathrm{j}\rho}J_{1}(ka\frac{ \rho}{r}) \tag{4}\]  
In Equation (4), \(a\) denotes the antenna radius; \(r\) represents the target distance; \(k=2\pi/\lambda\) is the wave number; and \(J_{1}(\cdot)\) refers to the first-order Bessel function.