# A Novel Expectation-Maximization-Based Blind Receiver for Low-Complexity Uplink STLC-NOMA Systems
## 5 Simulation Results  
The BER performance of the proposed novel low-complexity two-user uplink STLC-NOMA system and its mathematical expressions in Section 3 were verified through extensive computer simulations, as shown in Figure 2. Here, we assumed that each STA's transmit power and partial CSI, denoted by \(P_{n}\gamma_{n}\) (received energy), are perfectly estimated at the AP, and set the transmit powers and large-scale fading components of the two STAs to \(P_{1}=P_{2}=P\) and \(\beta_{1}=\beta_{2}=1\), respectively. Figure 2 compares the BER performance of the proposed novel uplink STLC-NOMA (Proposed) with the conventional uplink STLC-NOMA (Conv.) [23], considering the same modulation order \(M\). Specifically, for a fair comparison, we compared the proposed STLC-NOMA systems employing 2, 4, 8, and 16-ASK with the conventional STLC-NOMA systems using binary-PSK (BPSK), quadrature-PSK (QPSK), 8-PSK, and 16-QAM, respectively. Because BPSK with an optimal constellation rotation angle of \(90^{\circ}\) in the conventional STLC-NOMA [21] and 2-ASK in the proposed STLC-NOMA have the same constellation diagram, both have the same BER performance. Somewhat interestingly, the proposed two-user uplink STLC-NOMA system has improved BER performance in the low SNR regime, and this trend becomes more remarkable as the modulation order increases. For modulation orders of \(M=4\) and 8, the BER performance intersects at SNRs of approximately 18 and 31.5 dB, respectively, and for \(M=16\), the proposed STLC-NOMA outperforms the conventional STLC-NOMA in the entire SNR regime. For \(M=4\), the conventional STLC-NOMA is about 3 dB better than the proposed STLC-NOMA in terms of the SNR to satisfy the same BER in the high SNR regime. As discussed in Section 2, however, it is also worth noting that the proposed STLC-NOMA has significantly lower computational complexity at the AP than the conventional STLC-NOMA because it does not employ a joint detector. Figure 2 validates the mathematical BER performance analysis results (6)-(8) in Section 3. It can be observed thatthe analytical BER expression is precisely the same as the Monte-Carlo simulation results for arbitrary modulation order. Moreover, the asymptotic BER expression, exploited to reveal that the proposed uplink STLC-NOMA system achieves optimal spatial diversity order for both STAs, is also well-matched with the simulation results. Figure 3 shows the BER performance of the proposed uplink STLC-NOMA system with the BEE scheme designed in Section 4. Here, 2-ASK is omitted because even the channel gain is not required in this case like the PSK constellation diagram. Specifically, as shown in the first column in Figure 1, the AP can detect the signals transmitted from STAs by distinguishing only the quadrant. The transmit powers and large-scale fading components of both STAs are still set to \(P_{1}=P_{2}=P\) and \(\beta_{1}=\beta_{2}=1\), respectively. For the BEE algorithm, the maximum number of iterations of the EM loop was set to 100, and \(\epsilon=10^{-8}\). Moreover, we set the frame length of each STA to \(L=16\cdot M\) in Figure 3 and \(L=32\cdot M\) in Figure 3, according to the modulation order \(M\). We can observe from Figure 3 that since the accuracy of the clustering method depends on the number of available data points (the number of symbols in a frame), as shown in Figure 4, the longer the frame length, the better the BER performance. For example, with an SNR of 30 dB and modulation orders of 8 and 16, the BER performance is improved by almost 50% when \(L=32\cdot M\) compared to when \(L=16\cdot M\). On the other hand, the proposed BEE algorithm has a trade-off between accuracy and frame length. Specifically, the BEE algorithm has \(\mathcal{O}(L\cdot M)\) computational complexity depending on the frame length \(L\) and modulation order \(M\); hence the complexity linearly increases as the frame length increases.