# Design of Multifunctional Mesosphere-Ionosphere Sounding System and Preliminary Results
## 4 Typical Experimental Results
### Mesospheric Sounding  
The sounding of the mesosphere was operated first. MAI system worked in a fixed frequency at 1.98 MHz. The number of coherent accumulations is 1024. As a representative example, Figure 13 shows a typical SNR map of the mesospheric sounding obtained by one receiving antenna. It can be seen that MAI system has successfully realized the MF radar's ability to sound the mesosphere at a small transmitting power. The maximum SNR has reached more than 35 dB. The main altitude distribution of the signals' reflection region is 75-100 km. And the electron density changes rapidly in time and space. Figure 12: The finished product of the prototype: (**a**) 2 kW power amplifier units. Three units together provide 6 kW for transmitting. (**b**) The transmitting excitation source and multi-channel receiver. The aluminum alloy frames are shielded between the modules. Figure 13: SNR map for mesospheric sounding at the local time of 00:08–01:08, 1 January 2018. By employing the FCA algorithm [4; 5], the echo signals of the equilateral triangle antenna array can be used to estimate the drift velocity of the wind field. When the coordinates of the antennas of each vertex of the array is set to \((x_{1},y_{1})\),\((x_{2},y_{2})\),\((x_{3},y_{3})\), and the signal time delay is \(\tau\), the correlation functions between the signals can be obtained: \(\rho(\xi_{12},\eta_{12},\tau)\), \(\rho(\xi_{23},\eta_{23},\tau)\) and \(\rho(\xi_{13},\eta_{13},\tau)\), where \(\xi_{ij}=x_{j}-x_{i}\), \(\eta_{ij}=y_{j}-y_{i}\). Under the hypothetical condition that the correlation function \(\rho\) between the antenna signals is only related to the antenna spacing \((\xi,\eta)\) and the signal time delay \(\tau\), its basic form can be expressed as a concentric ellipse cluster as the Equation (11). \[\rho(\xi,\eta,\tau)=\rho(A\xi^{2}+B\eta^{2}+C\tau^{2}+2H\xi\eta) \tag{11}\]  
When the diffraction pattern of the sounding object has a drift velocity \((V_{x},V_{y})\), Equation (11) can be rewritten to the Equation (12)  
\[\rho(\xi^{\prime},\eta^{\prime},\tau)=\rho(A(\xi^{\prime}-V_{x}\tau)^{2}+B( \eta^{\prime}-V_{y}\tau)^{2}+C\tau^{2}+2H(\xi^{\prime}-V_{x}\tau)\eta(\eta^{ \prime}-V_{y}\tau)) \tag{12}\]  
where \((\xi^{\prime},\eta^{\prime})\) is defined as the Equation (13):  
\[\xi^{\prime}=\xi+V_{x}\tau,\eta^{\prime}=\eta+V_{y}\tau \tag{13}\]  
In terms of eliminating the coefficient \(C\), the correlation function can be expressed by the coefficient parameters \(a,b,f,g,h\) as the Equation (14):  
\[\rho(\xi,\eta,\tau)=\rho(a\xi^{2}+b\eta^{2}+\tau^{2}+2f\xi\tau+2g\eta\tau+2h \xi\eta) \tag{14}\]  
Define \(\tau_{ij}\) as the maximum delay time of \(\rho(\xi_{ij},\eta_{ij},\tau)\), and then the Equation (15) should be satisfied:  
\[\frac{\partial\rho(\xi_{ij},\eta_{ij},\tau)}{\partial\tau}=0,\tau_{ij}=-f\xi_ {ij}-g\eta_{ij} \tag{15}\]  
Define \(\tau^{\prime}_{ij}\) to express the delay time which is determined by \(\rho(\xi_{ij},\eta_{ij},0)=\rho(0,0,\tau^{\prime}_{ij})\), the Equation (16) can be obtained:  
\[\left\{ \begin{array}{c}\rho(\xi_{ij},\eta_{ij},0)=\rho(a\xi_{ij}^{2}+b\eta_{ ij}^{2}+0+2f\xi_{ij},0+2g\eta_{ij},0+2h\xi_{ij}\eta_{ij})=\rho(a\xi_{ij}^{2}+b \eta_{ij}^{2}+2h\xi_{ij}\eta_{ij})\\ \rho(0,0,\tau^{\prime}_{ij})=\rho(a0^{2}+b0^{2}+\tau^{\prime 2}_{ij}+2f0\tau^{ \prime}_{ij}+2g0\tau^{\prime}_{ij}+2h00)=\rho(\tau^{2}_{ij})\\ \tau^{\prime 2}_{ij}=a\xi_{ij}^{2}+b\eta_{ij}^{2}+2h\xi_{ij}\eta_{ij}\end{array} \right. \tag{16}\]  
Then, when the equation \(\rho(\xi_{ij},\eta_{ij},\tau_{ij})=\rho(0,0,\tau^{{}^{\prime\prime}}_{ij})\) is established, the delay time \(\tau^{{}^{\prime\prime}}_{ij}\) can be determined by the Equation (17):  
\[\tau^{{}^{\prime\prime}2}_{ij}=\tau^{\prime 2}_{ij}-\tau^{2}_{ij} \tag{17}\]  
Based on Equations (15)-(17), the coefficients parameters \(a,b,f,g,h\) can be solved. Then, we can use these coefficients to calculate the velocity of the wind field \((V_{z},V_{m})\) as Equation (18):  
\[\left\{