# On the Performance of LDPC-Coded Large Intelligent Antenna System
## 2 System and Signal Characterization  
It is known that OFDM presents a high Peak-to-Average Power Ratio (PAPR), which tends to be problematic in the uplink scenario (i.e., transmission from the user terminal to the base station) [9; 16]. In such a scenario, SC-FDE transmission presents a lower significant PAPR than OFDM signals. This is an important advantage because it allows for more efficient power amplification, which is critical in terminals [9]. The LIS system behaves as a near-field beamformer, meaning that communication takes place beyond the Fraunhofer distance. It has the following characteristics [2]:  
* While MIMO systems have an antenna element separation of 3\(\lambda\) to 4\(\lambda\), the LIS has an antenna element spacing typical of \(\lambda/2\). \begin{table}
\begin{tabular}{l l} \hline \hline
**Acronym** & **Description** \\ \hline AWGN & Additive White Gaussian Noise \\ BER & Bit Error Rate \\ BS & Base Station \\ CSI & Channel State Information \\ CP & Cyclic Prefix \\ DFT & Discrete Fourier Transform \\ EGC & Equal Gain Combining \\ IB-DFE & Iterative Block Decision Feedback Equalization \\ ELAA & Extremely Large Antenna Arrays \\ IB-DFE & Iterative Block—Decision Feedback Equalization \\ IDFT & Inverse DFT \\ IoT & Internet of Things \\ IRS & Intelligent Reflecting Surface \\ LDPC & Low-Density Parity-Check \\ LIS & Large Intelligent Surface \\ m-MIMO & Massive Multiple-Input Multiple-Output \\ MFB & Matched Filter Bound \\ MIMO & Multiple-Input Multiple-Output \\ MRC & Maximum Ratio Combining \\ MMSE & Minimum Mean Squared Error \\ OFDM & Orthogonal Frequency Division Multiplexing \\ QC-LDPC & Quasi Cyclic—Low Density Parity Check \\ QoS & Quality of Service \\ SC-FDE & Single Carrier with Frequency Domain Equalization \\ UE & User Equipment \\ UM-MIMO & Ultra Massive Multiple-Input Multiple-Output \\ ZF & Zero Forcing \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A list of acronyms. * Far-field wireless communications are typically established at propagation distances greater than the Fraunhofer distance (the Fraunhofer distance is only a few wavelengths). * Individual elements of the LIS array can be seen in the far field, but the whole array, which acts in the short field, cannot be seen. * Therefore, the focus is set on the distance, the bearing, and the elevation planes. This acts similar to a lens to focus the sun's energy on a piece of paper. Note that traditional beamforming does not focus on distance, but only on bearing and elevation. * LIS is different from traditional beamforming in that it can suppress the interference between users that are aligned, in terms of bearing and elevation, but at different ranges. This makes the process of concentrating energy even better. Various reception topologies are taken into consideration for SC-FDE signals, including the widely used ZF and MMSE receivers and lower-complexity receivers such as the MRC or the EGC. The levels of complexity of MRC and EGC are lower than ZF and MMSE because the latter receivers require the inversion of the channel matrix for each frequency component, while the former does not require this processing [17; 18]. Note that such matrix inversion is highly demanded from the point of view of processing and, consequently, energy consumption. For the MRC and EGC, consisting of non-optimum receivers having some level of interference generated in the decoding processing, they can be combined with iterative interference cancellation schemes to reduce the inherent residual interference levels. Iterative block decision feedback equalization (IB-DFE) is another type of receiver that is often used in SC-FDE systems [5; 19]. As depicted in Figure 1, the \(n\)th transmitted block, of \(N\) data symbols, sent by the \(t\)th UE is denoted as \(s_{n}^{(t)}\), while the received block by the \(r\)th antenna of the LIS system is denoted as \(y_{n}^{(r)}\). Note that the communication between the UE and the LIS system is established in the near-field, instead of far-field.