# 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
Compared to other error-correcting codes, LDPC codes handle errors better and are more efficient to encode and decode. #### 3.3.1 Reducing Sensitivity to Channel Estimation Errors

LDPC codes provide robust error correction capabilities, helping reduce the system's sensitivity to inaccuracies in channel estimation. This ensures that the system maintains performance even when noise or interference leads to erroneous channel estimates [38]. #### 3.3.2 Improving Performance in Sparse Channels

In large-scale LIS systems, where channels are often sparse and nonlinear, LDPC codes can enhance efficiency by managing the complexity of channel estimation while offering superior error correction [39]. #### 3.3.3 Enhancing Spectral Efficiency and Energy Savings

LDPC codes help LIS systems save power while keeping signals strong. They reduce repeated transmissions, improving data efficiency. They also adapt to channel changes, making LIS networks more energy efficient and better for high data loads [40]. ## 4 Simulation Performance Results

This section presents performance evaluations of the proposed LIS scheme optimized for mm-wave frequencies with SC-FDE signals. The BER performance is analyzed as a function of \(E_{b}/N_{0}\), where \(N_{0}\) is the one-sided noise power spectral density, and \(E_{b}\) is the transmitted bit energy. The effects of cyclic prefix power overhead were not considered. Monte Carlo simulations assessed the system performance using QPSK modulation, with a block length of \(N\) = 256 symbols (the results were consistent for other \(N\) values, as long as \(N\gg 1\)). A Rayleigh fading channel with 16 uncorrelated equal-power paths was used. The Rayleigh model is used due to the dense multipath propagation in LIS systems, the absence of a Line-of-Sight (NLoS) path in many scenarios, and its standard adoption in MIMO research for performance evaluation under multipath conditions. Each block spans 1 s, while the cyclic prefix lasts 0.125 s. In the results for this paper, we considered a carrier frequency of 2 GHz. However, we would like to point out that our technique and main conclusions remain valid for other carrier frequencies with similar propagation characteristics, provided that we achieve the proper scaling (say, doubling the carrier frequency and reducing to half the LIS and scenario dimensions). For MIMO spatial multiplexing, multi-layer transmission was applied, achieving a \(T\)-times symbol rate increase with \(T\) transmitting and \(R\) receiving antennas, in the uplink direction. Feasibility requires \(T\times R\) for the proper detection of \(T\) concurrent symbol streams. The MATLAB code simulates a LIS system using a Uniform Rectangular Array (URA) model. Here is a simple breakdown of its details and feasibility:

1. _LIS channel modeling_: * The receiver is assumed to be in the near field of the LIS. * The beam focuses on both angle and distance, unlike traditional far-field beamforming, which only considers direction. * The simulation includes multipath reflections and time delays (\(\tau\)) to make it more realistic. 2. _Radio and environmental parameters_: * Carrier frequency: 2G Hz; * Antenna spacing: \(\lambda/2\); * User locations: randomly placed inside a room; * Number of antennas: 4 \(\times\) 400 LISs (LIS antenna consist of four panels and each panel has 100 antennas; in total 4 \(\times\) 100 = 400). 3. _Practical feasibility of LIS_: * LIS is modeled as an active antenna system, where each element has independent gain and phase control. * Near-field beamforming is used to focus signals on users. * Power adjustments are applied to keep the system practical. * Real-world feasibility depends on hardware challenges, the real-time processing of many antennas, and precise phase/gain calibration. Also, the MATLAB code includes LDPC encoding and decoding to improve communication reliability. Here is a basic overview of its details and practicality:

1. _LDPC encoding and decoding_: * The LDPC encoder converts input bits into a longer coded sequence to improve error correction.