Partial Nulling Regularized Block Diagonalization Using Unfair Channel Selection for Post-Coding with Low-Complexity  
[PERSON]  
1 Department of Information and Communication Engineering, Sejong University, Seoul 05006, Korea; [EMAIL_ADDRESS] (H.-S.H. ); [EMAIL_ADDRESS] (J.-H.R. ); [EMAIL_ADDRESS] (D.H.)  
[PERSON]  
1 Department of Information and Communication Engineering, Sejong University, Seoul 05006, Korea; [EMAIL_ADDRESS] (H.-S.H. ); [EMAIL_ADDRESS] (J.-H.R. ); [EMAIL_ADDRESS] (D.H.)  
[PERSON]  
2 Department of Computer Engineering, Sejong University, Seoul 05006, Korea; [EMAIL_ADDRESS]  
[PERSON]  
1 Department of Information and Communication Engineering, Sejong University, Seoul 05006, Korea; [EMAIL_ADDRESS] (H.-S.H. ); [EMAIL_ADDRESS] (J.-H.R. ); [EMAIL_ADDRESS] (D.H.)  
Footnote 1: email: {j  
systems, resources are shared with multiple users. MU-MIMO systems have the advantage to combine the high throughput at MIMO processing with the benefits of space division multiple access [10]. In MU-MIMO broadcast channel, inter-user interference (IUI) occurs inevitably at each device due to the transmission of multiple spatially multiplexed data stream from the base station to all devices [11]. The channel state information (CSI) of all devices are needed to eliminate IUI [12]. The challenge is that the receiving antennas which are associated with different devices are typically unable to coordinate with each other [10]. Therefore, base station exploits the CSI by using precoding schemes for IUI reduction to allow all devices to share the resources [13]. Dirty paper coding (DPC) [14] that achieves optimal performance is one of the precoding schemes. However, DPC requires a complicated nonlinear operation that is hard to use in practice [15]. In respect of the linear precoding that reduces complexity compared to nonlinear precoder, zero forcing (ZF) scheme [16; 17] eliminates IUI and inter antenna interference (IAI) at the same time. Therefore, when the ZF scheme is used, devices with more than one antenna do not need to concern about IAI and have a reduced computational complexity. However, this type of precoding changes signal-to-noise ratio (SNR) for all antennas of all devices into equal level [18]. Therefore, ZF has sub-optimal performance [18] and allocates fixed power to individual devices. In contrast to the ZF precoding, block diagonalization (BD) [16] scheme that uses singular value decomposition (SVD) allocates flexible power and eliminates IUI only. Therefore, BD scheme has enhanced performance compared to the ZF precoding and devices that have more than one antenna need to remove IAI. MU-MIMO channel is decomposed into multiple parallel SU-MIMO channel by using BD precoding. Since BD precoding only takes the IUI into account, a performance degradation is occurred at low SNR [19]. Regularized BD (RBD) [10; 20; 21] scheme considers the noise term and improves the performance when the noise is the dominant factor. BD and RBD suppress IUI perfectly by using null space of the channels of any other devices and the null space is obtained from SVD operation. In other words, BD and RBD consume most of the transmit antenna resources to achieve perfect IUI nulling so that transmit diversity gain cannot be obtained. Generalized BD (GBD) [22] is the scheme that utilizes the partial nulling concept to get the transmit diversity gain by using SVD of the channel for each device and decreasing the number of data streams. GBD precoding remains controllable IUI that has low power in order to increase the degrees of freedom at the transmitter [22]. The remaining IUI has to be removed at the receiver by using post-coding. The post-coder which belongs to null space of remaining IUI is multiplied by the received signal to remove remaining IUI. Therefore, the computational complexity at the receiver is higher than schemes which do not use post-coder. The modified GBD (MGBD) was proposed with enhanced performance compared to GBD in [23]. MGBD uses part of the antenna resources to obtain diversity gain like GBD.