# Topological Interference Management for K-User Downlink Massive MIMO Relay Network Channel
## 1 Introduction  
As the size of a wireless network increases, interference alignment becomes more complex and challenging. Hence, extensive research is being done for enlarging multiple-input-multiple-output (MIMO) communication strategies to achieve an optimal solution and to reduce the complexity of the interference channels. In particular, \(K\)-user MIMO broadcast channels (BC) with a shared relay and channel state information (CSI) are essential for enhancing the performance of a wireless broadcast channel network. It has been demonstrated in [1] that the channel state information at the transmitter (CSIT) is essential for optimizing the wireless-broadcast-channel performance. Considerable study on the design of the beamforming matrix and multiuser interference signals using the space-time interference alignment (STIA) technique is available. In [2], the authors discuss about the fully-associated interference networks, where a relay equipped with several antennas forwards the received signals instantly to the desired receivers. Precisely, the outdated CSI from all the transmitters sends the estimated CSI back to the relay with a handling delay. Recently, the authors in [3, 4] have provided a more distinguished analysis on topology interference management performance with a message passing (TIM-MP) technique for partially connected BC, where the transmitter has access only to the topological information and each receiver can pass itsdecoded message to another receiver. Linear minimum mean square error (MMSE) pre-equalization has been employed in [5] to precode the transmitted signal information using the Alamouti code with a precoded spatial-multiplexing technique that assists in retrieving or decoding the interference signals on the destination-side. The MMSE linear precoder achieves better error performance than the zero forcing-linear precoding method (ZL-LP) due to the presence of a large number of users and antennas at the base stations (BS) [6; 7]. In order to construct a more structured and effective solution for reconstructing the interference signals, the authors in [8; 9; 10] introduces the retrospective interference alignment, linear precoder design and spatial multiplexing techniques, which have the ability to recover using outdated CSIT knowledge. A comparison between the downlink performance of the cell edge users and the quasi-orthogonal space-time code for MIMO systems is beneficial [11; 12]. However, the authors have evaluated the performance without an inter-cell interference coordination scheme, using cooperative base stations. Moreover, the authors in [13; 14] have deliberated on the topological interference alignment for MIMO relay broadcast channels under a span interference alignment method, where the desired signal information is reconstructed without appropriate CSIT knowledge. The common assumption based on the aforementioned works is that they depend on a feedback protocol (or) delayed CSIT knowledge. The author in [15] have extended the analysis with multiuser MIMO user selection and reconfigurable antennas, for switching at the receiver-side. In [16], the author presents multiple relays or a multi-way relaying system with global CSI knowledge. In the above-mentioned schemes, the complexity of the recovered signal or the decomposed signal strength is considerably higher on the receiver-side. It is observed that increasing the number of users and relays increases the interference. In this paper, we propose a new scheme to ratify the difficulties in reconstructing a linear combination of the desired and undesired symbols, using the distributed nature of information and the delayed channel state information at the relay (CSIR) knowledge. The significant feature of this study is to reconstruct the interference signals in the MIMO interference channel from an unknown receiver with imperfect CSIR knowledge.