# Improved Low-Complexity, Pilot-Based Channel Estimation for Large Intelligent Surface Systems
## 3 Receiver Design Considerations for LIS: Proposed Improvements in Channel Estimation
### Optimized Pilot Design and Enhancing the Quality of Pilot Data
#### 3.1.2 Hadamard as Orthogonal Pilot Sequences
The simulation results demonstrate that BER performance improves with increasing power rates (Rate = 1 (0 dB), 2 (\(-\)3 dB), and 4 (\(-\)6 dB)), underscoring the role of accurate channel estimation. Higher pilot power (e.g., power rate = 4) achieves near-optimal performance, particularly in low \(E_{b}/N_{0}\) conditions, while MMSE performs best overall. ZF's sensitivity to noise leads to degraded performance at a lower \(E_{b}/N_{0}\), whereas MRC and EGC show consistent reliability. These findings emphasize the importance of pilot power optimization in mitigating channel estimation errors, balancing improved BER performance with the trade-off in spectral efficiency. Moreover, this chart shows that higher power rates (\(-\)6 dB) improve energy efficiency by reducing the BER at a lower \(E_{b}/N_{0}\). ZF/MMSE has higher complexity but better interference handling, while MRC and EGC are simpler but more sensitive to interference. Figure 3: BER results for power rate [1, 2, and 4] effect on channel estimation. Figure 2: BER results for comparing Hadamard pilot vs. random pilot 4 \(\times\) 400 LIS system. Figure 4 compares the performance results of the BER as a function of \(E_{b}/N_{0}\) for various channel estimation techniques under different pilot configurations. The simulation results demonstrate that increasing the number of pilot symbols from 64 to 128 significantly improves the BER performance across all channel estimation techniques. In this simulation, 64 pilots were used for 128 antennas by employing antenna clustering, compressed sensing, and adaptive pilot allocation (Table 3). Instead of assigning one pilot per antenna, 128 antennas were grouped into 64 clusters, with each cluster sharing a pilot, reducing overhead while maintaining estimation accuracy. The results show at a high \(E_{b}/N_{0}\), methods like MMSE and MRC approach the MFB, achieving a lower BER. In low-\(E_{b}/N_{0}\) conditions, the use of 64 pilots provides a notable advantage, particularly for MMSE, due to enhanced channel estimation accuracy. These findings highlight the trade-off between pilot overhead and improved performance. Overall, increasing the number of pilots reduces the BER but increases the energy consumption and complexity. MMSE and ZF handle interference better, while MRC and EGC are simpler but more sensitive to noise. Figure 5 demonstrates the impact of iterative channel estimation on BER performance across different receiver configurations (ZF, MRC, EGC, and MMSE). As the number of iterations increases from iteration 1 to iteration 3, the BER improves significantly for all methods. Among the configurations, MMSE and ZF show the most substantial improvements, approaching the theoretical MFB performance with additional iterations. MRC and EGC also benefit from iterations but exhibit comparatively moderate gains. These results highlight that iterative techniques effectively enhance channel estimation accuracy, albeit at the cost of increased computational complexity. Conducting three iterations typically achieves a balance between accuracy and computational complexity, providing substan

Figure 4: BER results on the impact of changing the number of pilots on the 4 \(\times\) 400 LIS system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number of Pilots**} & \multicolumn{2}{c}{**Channel Estimation Accuracy**} & \multirow{2}{*}{**Spectral Efficiency**} & \multirow{2}{*}{**Pilot Overhead**} & \multirow{2}{*}{**Recommendation**} \\ \hline
64 & Moderate & Medium & Medium & Best trade-off between accuracy and overhead \\
128 & High & Low & High & Suitable for systems with limited antennas \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the number of 64 and 128 pilots. tial improvements without overburdening the system. This graph shows how different detection and combining methods affect the BER. More iteration improves the accuracy but increases the complexity and energy consumption.