# An Improved Anti-Interference Precoding of Large-Scale Fading System Based on Channel Inversion
## 1 Introduction  
A massive MIMO (multiple-input multiple-output) system entails a large number (tens or hundreds) of base station antennas serving a much smaller number of terminals. These systems demonstrate large gains in spectral and energy efficiency compared with the conventional MIMO technology [1]. Massive MIMO (multiple-input multiple-output) is no longer a \"wild\" or \"promising\" concept for future cellular networks. In 2018, the key ingredients of Massive MIMO have made it into the 5G standard. The development of fully digital Massive MIMO arrays for mmWave frequencies is well underway [2]. However, its research is prohibitively complicated and costly. In a few years, maybe Massive MIMO with fully digital transceivers will be a mainstream feature at both sub-6 GHz and mmWave frequencies. In [3], researchers focused on new communication paradigms arising in massive multiple-input-multiple-output systems where the antenna array at the base station is of extremely large dimension. The main contributions of [3] are the design of low complexity scheme of multi-antenna transceiver and evaluate the bit-error-rate performance of the transceivers in crowded xMaMIMO scenarios. However, the size of the antenna array of the base station in this solution is extremely large, which will cause great equipment costs. A massive MIMO system entails a large number (tens or hundreds) of base station antennas serving a much smaller number of terminals. As the number of antennas grows, the performance of a massive MIMO system gets limited by the interference caused by pilot contamination. [PERSON] and [PERSON] proposed (under the name of Pilot Contamination Precoding) large scale fading precoding (LSFP) and large scale fading decoding (LSFD) based on limited cooperation between base stations [1]. In [1], researchers focused on the performance gain of the uplink large scale fading decoding in the case of a finite number of base station antennas. It shows that the performance can be improved further by optimizing the transmission powers of the users and presents decentralized LSFD that uses limited cooperation between neighboring cells. However, the research is focus on the transmission performance of the uplink, and the performance optimization of the downlink is not fully considered. As the number of antennas grows, however, the performance of a massive MIMO system gets limited by the interference, contamination and noise. The increasing demands for higher data-rate transmission in cellular networks bring the attentions to Large-scale antenna system (LSAS). LSAS demonstrates large gain in spectral-efficiency and energy-efficiency compared with conventional MIMO schemes [4]. In [5], a multi-cell cooperation method, called pilot contamination precoding (PCP), was proposed. It was found that in a single cell LSAS, when the number of antennas tends to infinity, the communication performance can be idealized, and noise and interference can be completely eliminated. However, when turning to multi-cell LSAS, the system performance is limited by directed inter-cell interference, resulted from unavoidable re-use of nonorthogonal pilot sequences in different cells. This effect is called pilot contamination. In [6], it was observed that if a channel has spatial correlation, then one can use this correlation to drastically reduce the pilot contamination interference in the asymptotic regime as \(\mathrm{M}\rightarrow\infty\). Until recently, it was believed that as the number of base station antennas tends to infinity, the performance of such systems is limited by directed inter-cellular interference caused by unavoidable re-use of training sequences (pilot contamination) by users in different cells. Large-scale fading precoding (LSFP) leads to the effective elimination of inter-cell interference. Crucially, the combining coefficients of LSFP depend only on the large-scale fading coefficients between the users and the base stations. These coefficients change slowly and their number does not depend on the number of base station antennas.