# 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
Figure 6 compares the BER performance versus \(E_{b}/N_{0}\) for various receivers (ZF, MRC, EGC, and MMSE) with Full LIS (400 antennas) and Selected LIS configurations (100 and 20 antennas). A Full LIS achieves the best performance due to maximum spatial diversity, particularly with MMSE and ZF receivers at a higher \(E_{b}/N_{0}\) due to their robustness to interference and noise. Reducing antennas to 100 or 20 degrades the BER, especially for ZF and EGC, due to reduced diversity and weaker channel estimation. MMSE and MRC are more robust under these constraints. A Full LIS offers optimal performance and improves the accuracy but increases the complexity and energy consumption: 100 antennas balance performance and complexity, while 20 antennas suit low-cost systems with acceptable performance trade-offs. Figure 5: BER results on the effects of iterative channel estimation on BER performance. Figure 6: BER results on comparison between “Full-LIS” and “Selected LIS” for different receivers. Figure 7 shows the impact of LDPC coding on the BER performance for various channel estimation techniques. Solid lines (with LDPC) exhibit significantly lower BERs than dashed lines (without LDPC), highlighting LDPC's error-correction benefits. LDPC improves the performances of ZF, MRC, EGC, and MMSE, bringing them closer to the ideal MFB benchmark. Among these, MMSE with LDPC achieve the best BERs, followed by MRC and EGC. Overall, LDPC coding greatly enhances the reliability across different \(E_{b}/N_{0}\) values. Table 4 highlights the key design principles and performance characteristics of ZF, MMSE, MRC, and EGC receiver architectures, illustrating their relative strengths and weaknesses across various metrics base on the BER performance, complexity, energy efficiency, interference reduction, spectral efficiency, and accuracy. 1. BER Performance (Figures 2 and 3)

MMSE and MRC have better performances because they optimize the signal strength and reduce noise, and ZF has a moderate BER because it removes interference but amplifies noise. EGC has the worst BER because it does not consider signal strength differences. 2. Computational Complexity (Figure 6)

MMSE and ZF require matrix operations, making them more computationally expensive. MRC and EGC are simpler because they do not perform matrix inversions. 3. Energy Efficiency (Figure 4)

MMSE and ZF use more energy due to complex calculations, while MRC and EGC are more energy efficient, since they use simpler operations. 4. Interference Reduction (Figure 5)

ZF removes interference completely but may increase noise. MMSE balances noise and interference, making it the most effective. MRC reduces interference but is not as effective as MMSE. EGC does not actively reduce interference. 5. Spectral Efficiency (Figure 7)

MMSE and MRC use the available bandwidth more effectively. ZF performs well but can suffer under high noise. EGC is the least efficient. Therefore, MMSE and MRC achieve better spectral efficiency, while EGC is the least efficient. Figure 7: BER results on the effect of LDPC codes on channel estimates on the \(4\times 32\) LIS configuration with 2 users. Accuracy (Figures 2 and 3)

MMSE and MRC estimate the channel more accurately. ZF is accurate but affected by noise. EGC has poor channel estimation. Overall MMSE and MRC give the most accurate results, while EGC is the least accurate. ## 5 Conclusions

This study demonstrated that pilot-based channel estimation, combined with techniques such as optimized pilot design, data-aided refinement, selective LIS antenna configurations, and the utilization of LDPC codes, significantly enhances the performance of LIS systems. These methods achieved notable improvements, including a reduction in the BER. MATLAB-based simulations validated the effectiveness of these techniques, confirming their suitability for next-generation communication systems.