# User-Centric Cell-Free Massive MIMO with Low-Resolution ADCs for Massive Access
## 5 Simulation Results
### Performance Analysis  
In this section, we analyze the SE performance of the proposed AP-UE association algorithm using the results derived from Equation (25). To compare the SE performance of the proposed AP-UE association algorithm, we conduct performance comparisons with the \"scalable algorithm\", \"structured algorithm\", and \"grant algorithm\" association schemes proposed in [12], [21], and [22], respectively. Additionally, a comparison with theoretical performance was also conducted assuming perfect CSI. To provide a comprehensive performance evaluation, we compare our proposed AP-UE association algorithm with an adapted version of the baseline solution from [12]. This adapted baseline assumes that UEs sharing the same pilot sequence do not utilize orthogonal time/frequency resources, aligning with our focus on scenarios where UEs share the same time-frequency resources. The algorithms proposed in [12; 22] ensured the connectivity of all UEs. However, as the number of UEs in the system increases, the number of overserving APs also increases, leading to potential severe pilot contamination. For instance, in Figure 2, the scalable algorithm and the grant algorithm show no overserving APs for \(K=100\), but the average number of overserving APs rises to 17.8% and 25.4% for \(K=160\), and further to 41% and 46.2% for \(K=200\), respectively. In contrast, the proposed algorithm and the structured algorithm effectively prevent overserving APs across all tested scenarios. Furthermore, the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline area & 0.5 km \(\times\) 0.5 km \\ Number of APs & 50 \\ Number of Antennas for AP & 4 \\ Number of Antennas for UE & 1 \\ Bandwidth & 20 MHz \\ UE transmit power (\(\rho\)) & 100 mW \\ Coherence block (\(\tau_{c}\)) & 200 sample \\ Pilot length (\(\tau_{p}\)) & 10 sample \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. algorithm proposed in [21] limits the maximum number of UEs that an AP can support to prevent strong pilot contamination, but this can lead to connectivity issues for UEs with small LSFCs. Specifically, the structured algorithm shows an average of 8.3% unconnected UEs at \(K=160\) and 21.4% at \(K=200\). These results indicate that while the algorithms in [12; 22] cannot avoid the effects of strong pilot contamination, the algorithm in [21] reveals some UEs may not be connected. Overall, the proposed algorithm demonstrates superior performance by ensuring no overserving APs and maintaining connectivity for all UEs in massive access scenarios. Figure 3 presents the SE performance comparison based on the number of UEs for \(b=3\). The performance comparison utilizes combining techniques such as LP-MMSE and MR combining. Figure 3: _Cont._  
Figure 2: Average number of overserving APs and unconnected UEs for each algorithm. In Figure 3, all techniques show similar performance for \(K=100\), as there are no overserving APs or unconnected UEs affecting the outcomes. The LP-MMSE combiner performs better than the MR combiner across all scenarios. However, when the number of UEs increases to \(K=160\), the performance of both the grant algorithm and the scalable algorithm degrades significantly due to an increase in the number of overserving APs. Specifically, both the LP-MMSE and MR combiners in the proposed algorithm only experience a performance reduction of approximately 52% and 37%, respectively, compared to their performance at \(K=100\). In contrast, the structured algorithm, which suffers from unconnected UEs, sees a 93% performance decrease. The scalable algorithm, with fewer overserving APs, experiences a 95% decrease, while the grant algorithm, with the highest occurrence of overserving APs, suffers a 97% decline in performance. This stark contrast highlights the impact of pilot contamination on SE performance for the other algorithms, particularly in environments with dense UE deployment.