# On Self-Interference Cancellation and Non-Idealities Suppression in Full-Duplex Radio Transceivers
## 2 Proposed System Model and Techniques
### Linearization  
A performance analysis of the FD transceiver's Tx chain components is carried out separately, and results are shown through constellation diagrams and spectrum analyzers. Figure 11a-c shows the signal trajectory of the ideal, imbalance, and compensated IQ mixer of the Tx chain, respectively. Figure 11c shows that the compensated IQ mixer follows nearly the same signal trajectory as that of an ideal IQ mixer (Figure 11a). Figure 11d-f shows the constellation diagram of the ideal, imbalance, and compensated IQ mixer of the TX chain, respectively. It is clear from the constellation diagram Figure 11f that the compensated results are approximately nearer to those of the ideal IQ mixer (Figure 11d). The IQ mixer in the Tx chain is tested separately with its linearization techniques before putting it into the transceiver design, and then the combined results are evaluated. The signal used to test the IQ mixer model is a simple 16-quadrature amplitude modulation (QAM) signal. PA linearity analysis is carried out by examining PA PSD and its input to output relationship. Figure 12 shows the output vs. input relationship of PA with and without linearization techniques. The non-linear amplifier shows great diversity due to intermodulation products of the third order. However, after applying linearization techniques, the output is the linear product of input. Figure 13a,b shows the results of PA before and after applying linearization techniques. It is clear from the figures that inter-modulation products have approximately equal power spectral density as linear gain and, hence, result in large signal distortion. In contrast, linearization techniques help with insufficient reduction of spectral regrowth and reduce PA intermodulation product. However, the results obtained from PD linearization are better than those received by applying the FF linearization technique. The downside of PD  
Figure 10: SINR using analog and digital cancellation techniques. (**a**) SINR after analog SI cancellation 30 dB and 40 dB antenna isolation with CSI technique, Kautz and GALL filter; (**b**) SINR after both analog and digital SI cancellation. linearization techniques is that they have computational complexities, but they provide better results. Figure 11: The signal trajectory and the constellation diagram of IQ mixer of transmitter chain with 25% gain and 25\({}^{\circ}\) phase imbalance. (**a–c**) show the signal trajectory of the ideal, imbalance, and compensated IQ mixer of the Tx chain, respectively. (**d–f**) show the constellation diagram of the ideal, imbalance, and compensated IQ mixer of the TX chain, respectively. Figure 12: Output vs. input relationship of PA with and without linearization techniques. Unlike the transmitter chain, receiver chain performance analysis is carried out using the metric BER vs. SNR. LNA linearity analysis is performed separately and examined through spectral power density and output to input relationship of LNA with and without linearization techniques. Figure 14 shows the relationship between LNA output and input. Non-linear LNA output shows non-linear behavior as input increases above 0 dBm and offers a sizeable non-linear behavior. However, after applying linearization techniques, the output and input relationship become linear, and output increases linearly with the increase of input. Figure 15 shows the PSD of LNA. Linearization techniques help in a reduced amount of spectral regrowth and decrease the intermodulation product power spectral density. Figure 14: Output vs. input relationship of LNA with and without linearization techniques. Figure 13: Doherty amplifier technique with feedforward linearization technique (**a**); and pre-distortion linearization technique (**b**). After the linearization of LNA and IQ mixer, Rx performance is carried out, and BER is calculated before and after the linearization of Rx front-end components. Figure 16 shows the curve of Rx BER vs. SNR. Due to linearization techniques, improved BER is achieved.