# 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
Optimal solution [24]:

\[\hat{\mathbf{H}}_{t}=\mathbf{S}^{H}\Big{(}\mathbf{S}\,\mathbf{S}^{H}\Big{)}^{-1}\mathbf{Y}_{t}\]2

The minimum number of iterations is found when the channel estimate change is very small. This helps avoid unnecessary computations. As the number of pilots \(N_{p}\) increases, the initial channel estimate improves, leading to fewer required iterations \(N_{iter}^{*}\), since the algorithm converges faster. ```
Input:
1. Define system parameters: - \(N\) subcarriers and \(P\) initial pilot subcarriers; - \(\mathbf{S}_{p}\) pilots; - \(\mathbf{Y}_{p}\) received signal matrix; - \(I_{m}\)\(\rightarrow\) maximum number of iterations; - \(\varepsilon\)\(\rightarrow\) refinement threshold. Initial LS estimation:
2. Perform LS estimation on initial pilots : \(\hat{\mathbf{H}}_{p}^{(0)}=\frac{\mathbf{Y}_{p}}{\mathbf{S}_{p}}\). Iterative refinement: For \(i=1\) to \(I_{m}\):
3. Step 1: transmit new pilots \(\mathbf{S}_{p}^{(i)}\) and receive \(\mathbf{Y}_{p}^{(i)}\). 4. Step 2: create a new estimate channel on pilots : \(\hat{\mathbf{H}}^{(i)}\). \[\hat{\mathbf{H}}_{t}=\mathbf{S}^{H}\Big{(}\mathbf{S}\,\mathbf{S}^{H}\Big{)}^{-1}\mathbf{Y}_{t}\]3
5. Step 3: Check convergence : if \(\left\|\hat{\mathbf{H}}_{p}^{(i)}-\hat{\mathbf{H}}_{p}^{(i-1)}\right\|\leq\varepsilon\)\(\rightarrow\) stop iteration. Improved interpolation:
6. Interpolate the final pilot-based channel estimate \(H_{p}^{(i)}\) to all subcarriers: \[\hat{\mathbf{H}}_{t}=\mathbf{S}^{H}\Big{(}\mathbf{S}\,\mathbf{S}^{H}\Big{)}^{-1}\mathbf{Y}_{t}\]4 Output:
7. Estimated channel response \(\hat{\mathbf{H}}=\left\{\hat{\mathbf{H}}_{Total}\right\}\). ```

**Algorithm 4**Improved LS Channel Estimation with Increased Pilot Iteration

### Selective LIS Antenna Configurations and Increasing Channel Estimation Accuracy

This section concentrates on improving LS channel estimation through the selection of ideal antenna configurations from a LIS and improving the overall accuracy of the channel estimation procedure. Optimized Antenna Configurations and LIS Technology for Improved Channel Estimation

In LIS systems, not all antennas contribute equally to the received signal quality. Antennas closer to the transmitter or those experiencing stronger signal conditions have a more significant impact on the channel estimation process. By focusing on these relevant antennas, the system can:

* _Reduce computational complexity:_ focusing on fewer, high-impact antennas reduces the size of the matrices involved in channel estimation and subsequent signal processing, leading to faster computations [36]. * _Maintain estimation accuracy:_ selecting the most relevant antennas ensures that the accuracy of channel estimation remains high, as only the antennas that contribute most to the signal quality are used. * _Enhance scalability:_ this approach is particularly beneficial for LIS systems with hundreds or thousands of antennas, where reducing the number of active antennas directly impacts the system's computational efficiency. * _Energy efficiency:_ selective activation conserves power by disabling less effective antennas, improving overall efficiency. * _Interference:_ by focusing transmission and reception on high-quality antennas, the approach reduces multi-user interference. By strategically selecting the most effective antennas, the accuracy of channel estimation in LIS systems is significantly enhanced. This selective approach ensures that the key antennas contributing to the highest SNR are prioritized, leading to more precise channel estimation. As a result, the BER is reduced, the system capacity increases, and the overall performance of the LIS-based wireless communication system improves [37]. ### LDPC Codes in Mitigating the Effects of Channel Estimation Errors

LDPC codes are very effective because they enable reliable data transmission close to Shannon's channel capacity. They are widely used in modern communication systems due to their high error correction ability and low-complexity decoding in noisy channels.