# Design of Multifunctional Mesosphere-Ionosphere Sounding System and Preliminary Results
## 4 Typical Experimental Results
### Mesospheric Sounding
\begin{array}{c}V_{z}=V_{x}/2=(hg-bf)/2(ab-h^{2})\\ V_{m}=V_{y}/2=(hf-ag)/2(ab-h^{2})\end{array} \right. \tag{18}\]  
Based on the signals of the three vertices of the antenna array, Figure 13(a) shows the wind field estimation result during the same time period of Figure 13. The direction of the arrow represents the direction of the wind field. In the range of 75-83 km, MAI system obtained a relatively stable wind field estimation. This is also consistent with the signal energy distribution in Figure 13. The range of velocity distribution is mainly between 20-60 m/s. But beyond this range, where are marked in grey, it becomes less accurate, which may be caused by the low SNR or the effect of the oblique echoes in 00:40-01:00 LT. Figure 13(b),c are the zonal and meridional wind profiles at 00:50 LT. Beyond 75-83 km,the profiles are also shown as dashed lines. It can be seen that the velocities are distributed in tens of meters per second. At the height of 75-83 km, the zonal wind is mainly between-18 m/s and -23 m/s, which is relatively stable. Conversely, the meridional wind varies rapidly with the height, from -5 m/s to -12 m/s in the range of 75-83 km. In addition to the wind field, the sounding data of MAI system can also be used to inverse the electron density of the low ionosphere. For MF/HF radar, DAE algorithm is often applied to calculate the electron density [35]. According to DAE algorithm, when the ionosphere is modeled into a myriad of thin layers, the transmittance of the _lth_ layer and the reflectivity of the current reflecting _Hth_ layer can be defined as \(\exp[-\Delta hK(h)]\) and \(R(H)\). \(\Delta h\) is a small range separation of two adjacent layers. By ignoring the secondary reflection, the amplitude \(A(H)\) of _hth_ layer's echo can be expressed as Equation (19), where \(Y\) is the other loss besides the ionosphere. \[A(H)=Y\exp[-\Delta h\sum_{h=1}^{H}K(h)]R(H)\exp[-\Delta h\sum_{h=1}^{H}K(h)]=Y \cdot R(H)\exp[-2\Delta h\sum_{h=1}^{H}K(h)] \tag{19}\]  
where \(K(h)\) is the absorption coefficient of the _lth_ layer. In the case of the MAI system, the two orthogonally erected antennas at each vertex of the array make it possible to be used for receiving the O and X wave signals alternately. Since there are different  
Figure 14: Wind field inversion results by FCA at the local time of 00:08-01:08, 1 January, 2018: (**a**) the temporal and spatial characteristics of wind field. Beyond 75–83 km, it is marked in gray for the less of accuracy (**b**) the zonal profile at 00:50; (**c**) the meridional profile at 00:50. Beyond 75–83 km, they are also marked as dashed lines. transmittance and reflectivity parameters for the O and X echo signals, Equation (19) can be specifically written as Equation (20):  
\[\left\{ \begin{array}{l}A_{O}(H)=Y_{O}R_{O}(H)\exp\!\left[-2\Delta h\sum\limits_ {h=1}^{H}K_{O}(h)\right]\\ A_{X}(H)=Y_{X}R_{X}(H)\exp\!\left[-2\Delta h\sum\limits_{h=1}^{H}K_{X}(h)\right] \end{array} \right. \tag{20}\]  
When it is assumed that \(Y_{O}=Y_{X}\), then Equation (21) can be obtained:  
\[\frac{A_{x}(H)}{A_{o}(H)}=\frac{R_{x}(H)}{R_{o}(H)}\exp\!\left[-2\Delta h\! \sum\limits_{h=1}^{H}\left(K_{x}(h)-K_{o}(h)\right)\right] \tag{21}\]  
When the logarithms are taken simultaneously on the left and right sides of Equation (21), it can be transformed into Equation (22):  
\[\left\{ \begin{array}{l}\ln\left[\frac{A_{x}(H)}{A_{o}(H)}\right]=\ln\left[ \frac{R_{x}(H)}{R_{o}(H)}\right]-2\Delta h\sum\limits_{h=1}^{H}\left(K_{x}(h)- K_{o}(h)\right)\\ \ln\!\left[\frac{A_{x}(H)}{A_{o}(H)}\right]-\ln\!\left[\frac{A_{x}(H-1)}{A_{o} (H-1)}\right]=\ln\left[\frac{R_{x}(H)}{R_{o}(H)}\right]-\ln\left[\frac{R_{x}( H-1)}{R_{o}(H-1)}\right]-2\Delta h[K_{x}(H)-K_{o}(H)]\end{array} \right. \tag{22}\]  
In practical calculation, the reflection coefficient \(R_{O/X}(H)\) can be obtained from Equation (23):  
\[R_{O/X}(H)=