# 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 LDPC decoder uses a hard-decision method with a maximum of 20 iterations to decode the received data. * The decoder stops early if the parity check is satisfied. 2. _LDPC integration with LIS_: * LDPC is applied to 4 PSK modulation before transmission. * After LIS-based transmission and reception, LDPC decoding is used to recover the original data. The simulation includes different equalization and interference cancellation methods (MRC, EGC, ZF, and MMSE). Table 2 compares various methods for improving channel estimation in LIS systems based on metrics such as complexity, energy efficiency, interference reduction, estimation accuracy, and spectral efficiency. 1. Pilot power optimization increases the strength of the pilot signals, improving the channel estimation accuracy but slightly reducing the spectral efficiency because it takes up more transmission power. 2. Increasing the number of pilots helps achieve better accuracy but comes with a trade-off: higher complexity and reduced spectral efficiency due to the extra pilot overhead. 3. Iterative estimation improves the accuracy over multiple iterations, but it requires more processing power, making it computationally expensive. 4. Channel selection focuses only on the most useful LIS antennas, reducing the complexity while still maintaining good accuracy and efficiency. 5. Hadamard orthogonal pilot sequences minimize interference between pilots, improving both the accuracy and spectral efficiency while keeping the complexity low. Figure 2 investigates the performance results without LDPC codes in LIS systems with 4 transmitting antennas and 400 receiver antennas (4 \(\times\) 400). Hadamard pilots offer better BER performance than random pilots due to their orthogonality, which enhances channel estimation accuracy. The improvement is most significant for MMSE and ZF, especially at a high SNR (\(E_{b}/N_{0}>\) 6 dB). MMSE and MRC with Hadamard pilots provide better channel estimation accuracy, reducing interference and improving spectral efficiency. ZF with Hadamard pilots performs better than with random pilots but still has lower accuracy than MMSE. More complex methods like MMSE require higher computational power and energy but achieve a lower BER and better spectral efficiency. The MFB curve provides a benchmark for evaluating the performance of a channel, which is modeled as the sum of delayed and independent Rayleigh-fading rays. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline
**Improvement Method** & **Complexity** & **Energy Efficiency** & **Interference Reduction** & **Estimation Accuracy** & **Spectral Efficiency** \\ \hline
**Pilot power optimization** & Moderate & Improves with careful scaling & Minimal impact on interference & Improves SNR for pilots & Moderate (trade-off with data throughput) \\
**Increasing number of pilots** & High (due to increased overhead) & Decreases due to higher overhead & No direct impact & Improves with increased reference & Decreases due to increased pilot \\
**Iterative estimation** & High (due to iterations) & Improves with better estimation accuracy & Moderate (depends on feedback accuracy) & Significantly improves after iterations & Improves by refining estimates \\
**Channel selection** & Low (reduces processing load) & Moving resources on high-impact antennas & High (reduces inter-user) interference & Moderate (focuses on relevant antennas) & Improves by reducing unnecessary overhead \\
**Hadamard orthogonal sequences** & Low (efficient generation) & Moderate (no direct impact on energy efficiency) & High (minimizes optimization optimization) & High (reduces pilot interference) & High (reduces pilot interference) \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of channel estimation improvement methods across key performance metrics. Figure 3 highlights the significant impact of pilot power rates on BER performance in LIS systems with 4 transmitting antennas and 400 receiver antennas (4 \(\times\) 400) without LDPC codes under channel estimation scenarios.