## 2 Processing Blocks in SDR Transmitter
### Sample-Wise Pulse Shaping
#### 2.3.1 Mixing
Comprehensive functions are available for visualizing digital, analog, and complex signals--**ListStepPlot** for bit and impulse train signals, **ListPlot** for sample-wise signals,  
\[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]1 (a) I and Q streams after mixing (b) Tx output NOMA signal \(s(nT_{S})\). and **ComplexListPlot** for displaying constellation diagrams of complex symbols, all followed by appropriate option settings as it was done for Figure 6a:  
\[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]2 \[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]3 \[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]4  
and Figure 6b:  
\[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]5 \[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]6 \[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]7 \[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]8  
To track system and link behavior, we define two test points at the transmitter, TP1 and TP2, as shown in \[\mathfrak{R}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}=\underbrace{ I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)}_{\cos}- \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f_{C}t)} _{\sin} \tag{6}\]9  
At this point, the digital processing of the NOMA signal is completed. It then passes through a digital-to-analog (D/A) converter for generating an analog signal, which is passed to the processing chain (RF front-end) and eventually emitted over the air. The essential functions at the receiver are retrieving and decoding the transmitted signals, which for the downlink transmissions also requires implementation of successive interference cancellation (SIC), as depicted in \[\mathfrak{I}\Big{(}\widetilde{v}_{QAM}(t)\cdot e^{-2\pi f_{C}t}\Big{)}= \underbrace{Q_{QAM}(t)}_{v_{lo}(nT_{s})}\cdot\underbrace{I_{lo}(2\pi f_{C}t)} _{\cos}-\underbrace{I_{QAM}(t)}_{v_{l}(nT_{s})}\cdot\underbrace{Q_{lo}(2\pi f _{C}t)}_{\sin} \tag{7}\]0  
The processing tasks at the receiver are applied after quadrature separation, filtering, and downsampling. The strongest signal is decoded first, via a classical decision block. This decoded signal is weighted and subtracted from the originally received signal following the SIC methodology to facilitate decoding of the strongest signal among the remaining signals. The remaining superimposed signals are recovered via similar recursive steps.