# Study of 5G-NR-MIMO Links in the Presence of an Interferer
## 3 Alamouti MIMO Link in the Presence of Different Interferer Techniques
### General Interferer  
As mentioned above, the rapid rise in the need to connect thousands of wireless mobile components in a specific area is binding to improve the spectral efficiency per unit area, especially in frequency bands below 6 GHz. To achieve those high requirements, the deployment of many small cells per area is necessary [30; 31; 39]. The mobile or modern wireless architecture has a wide range of manufacturers under license and unlicensed standards. Multiple manufacturers that communicate with UE pieces in the same local network area without sharing synchronization in the radio management or without common schedulers create serious and complicated problems. Problems include Inter-Cell Interference (ICI) [40] and Cross-Link Interference (CLI) between neighboring small cells of different directional transmissions [31]. These situations require a state of continuous decoding ability when a strong interference signal power is present, or under minimum SINR conditions [37]. A prevention situation that creates severe chain reactions such as rolling modulation and multiple handovers to far cells is also considered. False decoding of the packet detection in the front receiver process also creates a complicated situation. Even systems with a Frequency-Hopping Spread Spectrum (FHSS) scheme and a Direct Sequence Spread Spectrum (DSSS), which are embedded in protocols and standards such as Wireless Local Area Networks (WLANs), Bluetooth, and Wireless Personal Area Network (WPANs), create a situation of mutual interference and receive strong interference signals one from the other [41]. The most realistic and complicated situations are the HetNet scenario and the multi-Access Point (AP), and the multi-user scenario. These scenarios are common in 5G-NR under the dynamic TDD assumption, which produces dynamic switch point between uplinks/downlinks [42]. These scenarios create three complicated issues. The first is \begin{table}
\begin{tabular}{c c c} \hline \hline  & \(\mathbf{RX_{1}}\) & \(\mathbf{RX_{2}}\) \\ \hline \(JX_{1}\) & \(g_{11}\) & \(g_{12}\) \\ \(JX_{2}\) & \(g_{21}\) & \(g_{22}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Definition of complex channel gain between the interference and receive antennas. that every component, user, small cell, and macrocell base-station, can play the rule of interfering, transmit, and receiving simultaneously. The second involves the complexity of un-decode-ability in the presence of strong interference signals [37], much more so than the SIR threshold to achieve a discovery production threshold. Third, distinguishing between data symbols and interference symbols when combining multi-interference signals with different power levels that are out of synchronization with discovery times [32], or hidden beyond a powerful interference signal, is also very challenging. This subsection describes a general interferer's specific case based on these scenarios, combined with the Alamouti-STC scheme. The mathematics analysis in the frequency domain contributes to a critical study that describes the impact of synchronization errors on Alamouti-STC-based cooperative MIMO schemes [32]. In this analysis, we describe UE transmitting an Alamouti-STC scheme, with the same assumptions made at the beginning of this section, to other UEs that act as a general interferer or a general jammer device. That jammer or interferer also transmits the Alamouti-STC. The interferer symbols \(j_{1}\) and \(j_{2}\) are defined in Table 5.  
We therefore can write Equation (10) as  
\[\bar{R}= \begin{bmatrix}r_{1}(1)\\ r_{1}^{*}(2)\\ r_{2}(1)\\ r_{2}^{*}(2)\end{bmatrix} =\sqrt{P} \begin{bmatrix}h_{11}&h_{12}\\ h_{12}^{*}&-h_{11}^{*}\\ h_{21}^{*}&h_{22}\\ h_{22}^{*}&-h_{21}^{*}\end{bmatrix}\begin{bmatrix}s_{1}\\ s_{2}\end{bmatrix} +\sqrt{\frac{P}{SR}} \begin{bmatrix}g_{11}&g_{12}\\ g_{12}^{*}&-g_{11}^{*}\\ g_{21}&g_{22}\\ g_{22}^{*}&-g_{21}^{*}\end{bmatrix}\begin{bmatrix}j_{1}\\ j_{2}\end{bmatrix} +\sqrt{\frac{P}{SNR}} \begin{bmatrix}n_{1}(1)\\ n_{1}^{*}(2)\\ n_{2}(1)\\ n_{2}^{*}(2)\end{bmatrix}