# On the Performance of Partial LIS for 6G Systems
## 2 System and Signal Characterization  
Sixth generation communications are expected to reach the requirements of a peak data rate of, at least 1 Tbps in nomadic access (100 times higher than 5G) and 1 Gbps in a mobile environment (10 times higher than 5G), while the energy efficiency is expected to be 10 to 100 times better than 5G, with a spectral efficiency 5 to 10 times better than 5G. These requirements are expected to be achieved with LIS systems associated with terahertz bands and block transmission techniques. Note that the higher the carrier frequency is, the greater the channel coherence bandwidth. The LIS fits well with terahertz bands because the lower wavelength originates from extremely low antenna sizes, which facilitates the implementation of low-cost LIS panels. Nevertheless, the level of processing increases with the number of antennas, which is the case of the LIS (this can be viewed as a beyond-massive MIMO). Because of this, it is extremely important to study receivers that are as simple as possible. This article associates receivers with low complexity (that simplify the decoding process), with the use of a subset of the LIS panels, known as the partial LIS. By using a subset of the LIS panels, the decoding process becomes less complex, while the performance tends to be kept almost unchanged. Block transmission techniques are commonly used to reduce intersymbol interference. The SC-FDE block transmission technique presents the advantage of exhibiting lower PAPR [14; 15], as compared with OFDM, which makes it well suited for scenarios such as those involving an uplink and for facilitating the efficiency of the power amplification process [18]. Unlike traditional communications between a UE and a base station (BS), the communication between a UE and an LIS system is typically established in a line-of-sight scenario. The LIS can be viewed as a short-range beamformer, while the distance between antenna elements is typically half-wavelength, instead of three to four wavelengths, as in traditional MIMO systems. Moreover, while the individual antenna elements of the LIS establish communications in the far field, the whole array of the LIS system establishes communications in the near field, that is, shorter than the Fraunhofer distance, which is only a few wavelengths. This makes the LIS exhibit special properties. While in traditional beamforming, the focus is established along the azimuth and elevation planes, the LIS also allows for focusing along the distance plane. This property allows for a mitigation of the interference coming from users aligned in terms of azimuth and elevation but placed at different distances. 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 \(y_{n}^{(r)}\). The mapping between the time domain signal and the frequency domain signal, for the \(k\)th subcarrier (assumed invariant during the transmission of a given block), of the transmitted block is defined as \(DFT\Big{\{}s_{n}^{(t)};n=0,1,\ldots,N-1\Big{\}}\ =\ \Big{\{}S_{k}^{(t)};k=0,1,\ldots,N-1\Big{\}}\), i.e., by performing the discrete Fourier transform (DFT) of the time-domain block (a similar method applies, mutatis mutandis, to the received signal block, channel and noise). The received frequency domain signal, in matrix-vector representation, becomes [14]  
\[\mathbf{Y_{k}}=[Y_{k}^{(1)},\ldots,Y_{k}^{(R)}]=\mathbf{H_{k}}\mathbf{S_{k}}+ \mathbf{N_{k}} \tag{1}\]  
where \(\mathbf{S_{k}}=\left[S_{k}^{(1)},\ldots,\,S_{k}^{(T)}\right]^{T}\) stands for the frequency-domain-transmitted data symbols, \(\mathbf{H_{k}}\) denotes the \(T\,\times\,R\,\) channel frequency response for the \(k\)th subcarrier (assumed to be invariant during the transmission of a given block), with \((r,t)\)th element \(H_{k}^{(t,r)}\). Moreover, \(\mathbf{N_{k}}\) is the frequency-domain block channel noise for that subcarrier [14].