## 6 Conclusions  
MU-MIMO systems are a key component of future wireless communication in terms of high data rate over a limited frequency resource. In MU-MIMO broadcast channel, IUI occurs inevitably at each device. Therefore, base station has to utilize precoding schemes for IUI reduction.  
In this paper, the precoding scheme which is based on RBD and uses partial nulling concept is proposed in Rayleigh fading system. The Rayleigh fading channel which is frequently used in wireless communication system is used. The proposed scheme obtains the diversity gain from applying partial nulling by excluding the row vectors from channel matrix which is nullified. The dimension of the channel matrix which is used for forming the precoder is reduced by excluding row vectors with low power. When the number of data streams is smaller than the number of receive antennas, the proposed scheme achieves performance enhancement due to diversity gain and does not need extra operation at the receiver.  
The simulation results according to the Monte Carlo method indicate that the performance of the proposed scheme is better than RBD by obtaining the diversity gain when RBD and the proposed scheme have the same data rate. When the BER is \(10^{-3}\), the proposed scheme has 10 dB gain. Since the proposed scheme uses the channel matrix with low dimension to form the precoder, the computational complexity of the proposed scheme is lower than the RBD. When the number of reduced data streamsis not enough for most devices to achieve diversity gain, the performance of the proposed scheme is better than GBD and MGBD. Therefore, the GBD with 6 data streams can achieve same performance as the proposed scheme with 7 data streams. GBD and MGBD cannot avoid the inefficient operation at the receiver. In addition, since MGBD needs three SVD operations, the complexity of the MGBD at the base station is higher than the proposed scheme. Since the proposed scheme has advanced performance and low complexity, the proposed scheme has potential of practical applications in MU-MIMO systems.  
By choosing the whole row vectors at the proposed scheme, the SVD of the channel for each device is not needed and the way to remove the remained IUI at the receiver is simple. However, the whole row vectors which are chosen are not used, the loss of the channel gain at the proposed scheme is greater than the loss of the channel gain at the GBD and MGBD. Therefore, when the number of the data streams is less than \(\frac{2}{3}\) of the number of receive antennas, the performances of the GBD and MGBD are better than the proposed scheme since the loss of the channel gain at the proposed scheme is larger than GBD and MGBD. Thus, further study is needed to decrease the loss of the channel gain at the proposed scheme when the number of the data streams is less than \(\frac{2}{3}\) of the number of receive antennas. In other words, the simple way to remain IUI without the huge loss of the channel gain has to be studied for obtaining performance enhancement with low complexity.  
Conceptualization, H.-S.H.; methodology, H.-S.H. and J.-H.R.; software, H.-S.H.; validation, H.-S.H., J.-H.R., Y.-H.Y., D.H. and H.-K.S.; formal analysis, H.-S.H.; investigation, J.-H.R. and Y.-H.Y. ; writing--original draft preparation, H.-S.H.; writing--review and editing, H.-S.H.; supervision, Y.-H.Y., D.H. and H.-K.S.; project administration, D.H. and H.-K.S. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the MSIT(Ministry of Science and ICT), Korea, under the ITRC(Information Technology Research Center) support program(IITP-2019-2018-0-01423) supervised by the IITP(Institute for Information & communications Technology Promotion) and was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2020R1A6A1A03038540).  
The authors declare no conflict of interest.