# Study of 5G-NR-MIMO Links in the Presence of an Interferer
## 3 Alamouti MIMO Link in the Presence of Different Interferer Techniques  
This section discusses three types of jammer strategies or interference that could be present in a certain space. Those classifications are a general interferer, a smart jammer, and a contiguous PBN jammer. We assume that the general interferer and the smart jammer have a slow-fading channel, are located in the same environment, are using OSTBC transmissions with \(2\times 2\) MIMO array, and transmits a CE with FD assume and TDD access. In addition, they have a different scheduler, i.e., a HetNet scenario [2; 30]. We will discuss the interference effects on the receive symbols. Each jammer or interference technique has a different impact on the target communication system, so different Anti-Jamming (AJ) methods to cancel the jammer effects are needed. It is essential to examine the specific target's effects, especially in the mathematical design, BER, the constellation diagram, and SIR measurements. This is significant because if the same advanced cancellation technique, such as RF analog cancellation or beamforming with null-space-like spatial multiplexing [27], or interference rejection combining (IRC) algorithm [13; 36] are not effective, jammer or interference symbols are received. The issues of interference management in the Radio Access Network (RAN) and Radio Link Control (RLC), to optimize the power and spectral efficiency, are critical, especially in 5G-NR access. We have a new problem in the demodulation and the decoder process called digital interference cancellation. Comparing the different jammers is necessary because we want to model and distinguish between the different effects in BER and SIR execution. It is essential to emphasize the effects of orthogonality violation in the spectrum, which results from the multiplicity of interferences between the transmitter and the receiver. Space-time coding is used to achieve spatial diversity. It is possible because of the underlying propagation physics in a multi-path communication channel [27]. That is, every pair path transmits between the transmission to the receiver is sufficiently uncorrelated. In Appendix A, we analyze mathematically and illustrate the significant impairment in the orthogonal spectrum assumption. We present a system consisting of a \(2\times 2\) Alamouti STC transmitter, \(TX\), a receiver, \(RX\), as described in the previous section, and an interferer transmitter, \(JX\), as illustrated in Figure 2. We assume a far-field between the receiver and the transmitter and interference [4; 5]. Figure 2: Illustration of \(2\times 2\) Alamouti space time coding (STC) in the presence of interference. In a general case where several neighboring interferences are present in the space, the received signal vector \(\vec{R}\) is  
\[\vec{R}=\sqrt{P}H_{TR}\vec{S}+\sum_{l=1}^{L}\sqrt{\frac{P_{l}}{5 IR_{l}}}H_{JR_{l}} \vec{J}_{l}+\sqrt{\frac{P}{SNR}}\vec{N} \tag{9}\]  
assuming the signal's transmission power is equal to \(P\), where \(L\) is the number of interferences. When considering a single dominant interference, i.e., a very high Dominant Interferer Proportion (DIP) ratio [38] the received signal vector \(\vec{R}\) becomes  
\[\vec{R}=\sqrt{P}H_{TR}\vec{S}+\sqrt{\frac{P}{SR}}H_{JR}\vec{J}+\sqrt{\frac{P}{ SNR}}\vec{N} \tag{10}\]  
We presented expressions \(H_{TR}\vec{S}\) and \(\vec{N}\) in the previous section. SIR and SNR are the signal to interference and the signal to noise power ratios, respectively, at the receiver site. We will now discuss the expression \(H_{JR}\vec{J}\). Like the signal, the jammer consists of two transmission antennas, \(JX_{1}\) and \(JX_{2}\). The jammer transmits through a MIMO channel model with four flat fading paths assumed to be independent and uncorrelated. These four paths are represented by complex channel gains \(g_{11}\), \(g_{12}\), \(g_{21}\), and \(g_{22}\).