# An Improved Anti-Interference Precoding of Large-Scale Fading System Based on Channel Inversion
## 3 Advanced LSFP
### Lsfp
#### 3.1.1 Downlink LSFP  
In Step 1, base station of a cell performs channel estimation according to the uplink signal and uplink pilot training sequence sent by a user to obtain a large-scale attenuation factor and sends it to the network hub controller of the cellular network. In Step 2, the network hub controller receives the large-scale fading factors sent by all the base stations in the area group and forms a large-scale fading factor precoding matrix. In Step 3, the network hub controller sends the large-scale fading factor precoding matrix to each base station. In Step 4, before the base station sends the information to a user, it performs a precoding operation on the signal according to the large-scale fading factor precoding matrix. In the Downlink PCP (pilot contamination precoding) proposed for the downlink pilot contamination precoding [5], the PCP matrix is expressed as:  
\[W^{k}=\left(B^{k}\right)^{-1} \tag{4}\]  
where \(B^{k}\) denotes a matrix composed of a large-scale fading factor \(\beta_{j}^{kl}\), that is, the zero-forcing pilot contamination precoding (ZF-PCP). In the LSFP proposed in [8], the LSFP matrix is expressed as:  
\[W^{k}=\gamma_{A}\left(B^{k}\right)^{-1} \tag{5}\]  
where \(\gamma_{A}\) denotes a normalization factor that defines the power limit and \(B^{k}\) denotes a matrix composed of the large-scale fading factor. \(\beta_{j}^{kl}\), that is, the zero-forcing large-scale fading precoding (ZF-LSFP). By applying the asymptotic theory, it has been proven that systems using zero-forcing precoding can achieve communication performance. At a limited number of antennas, the ZF-PCP and ZF-LSFP with zero-forcing precoding achieve average performance, and there are also pilot contamination, noise and interference in the LSAS. In [4; 7], an optimized precoding scheme named the Optimized LSFP (O-LSFP) was proposed; this scheme aims to optimize the precoding matrix in the field of limited antennas. **Lemma 1**. : \[W=\left[ \begin{array}{ccc}\left(W^{1}\right)^{T}&\cdots&\left(W^{K}\right)^{T }\end{array} \right]^{T}\] (6)  
\[B=Diag\left[ \begin{array}{ccc}B^{1}&\cdots&B^{K}\end{array} \right] \tag{7}\]  
\[\rho_{j}^{kln}=\left[\frac{\delta_{u}^{2}}{\varphi_{f}L}+\beta_{j}^{kl} \right]\left[\frac{\delta_{d}^{2}}{\varphi_{r}}+T\sum_{s}\beta_{j}^{ns}\right] \tag{8}\]  
\[P^{kln}=Diag\left[ \begin{array}{ccc}\rho_{1}^{kln}&\cdots&\rho_{L}^{kln} \end{array} \right] \tag{9}\]  
\[P^{kl}=Diag\left[ \begin{array}{ccc}p^{kl1}&\cdots&p^{klK}\end{array} \right] \tag{10}\]  
_W denotes an O-LSFP matrix, \(B\) denotes a large-scale fading factor matrix and \(P^{kl}\) denotes a matrix obtained by a large-scale fading factor \(\beta_{j}^{kl}\) operation._  
The SINR expression, after applying the O-LSFP matrix is as follows:  
**Lemma 2**. : \[SINR^{kl}=\frac{T_{3}^{kl}}{T_{1}^{kl}+T_{2}^{kl}}\] (11)\[T_{1}^{kl}=\frac{Tr\left[(W)^{*}P^{kl}W\right]}{MT} \tag{12}\] \[T_{2}^{kl}=\sum_{v\
eq l}\left|BW_{(kl+L-l),v}\right|^{2}\] (13) \[T_{3}^{kl}=\left|BW_{(kl+L-l),l}\right|^{2} \tag{14}\]  
The simulation results presented in [4; 7] show that the number of antennas at a base station must be at the hundred-level to eliminate most of the pilot contamination, noise and interference. However, such a configuration of antennas will inevitably increase the cost of the base station equipment. In [7], the simulation assumed that each base station is equipped with M omnidirectional antennas and each user has a single omnidirectional antenna. In practice, there will be unnecessary power consumption, failing to utilize antenna resources fully and increasing the operating costs. Therefore, in this paper, the LSFP is improved to reduce the pilot contamination, noise and interference performance without reducing the number of antennas at a base station. At the same time, if the number of antennas at a base station antennas stays unchanged, the improved LSFP precoding scheme can improve the performance. Communication transmission rate to improve LSAS communication performance.