## 1 Introduction  
A single-channel full duplex (SCFD or in short FD) transmission scheme is considered as one of the promising technologies in the next generation networks. It is a recent method that significantly increases the transmission spectral efficiency. In SCFD, any wireless device is permitted to simultaneously transmit and receive data over the same frequency channel. Conventionally, upload and download bit streams are transmitted either at different instants or over different frequencies [1]. Self interference, which is a major obstacle facing FD implementation, may damage the whole system if it is not well suppressed. Self interference is the interference caused by the terminal on itself due to simultaneous in-band transmission and reception. In other words, self interference manifests when a high power transmitted signal interferes a weak received signal on the same terminal. There are different techniques for self interference mitigation such as antenna directionality and polarization [2; 3; 4; 5; 6]. Even more sophisticated adaptive methods in both analog and digital domains [7; 8; 9; 10; 11; 12; 13] are used in case of multipath and scattered self interference channels. It is noteworthy that digital baseband interference cancellation methods [14] mitigate the self interference. However, they are not enough due to the high level of distortion introduced by the analog circuits in the front end of the transceiver and the limited dynamic range of the analogue-to-digital convertors(ADC). Therefore, despite the reported progress in the cancellation techniques [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13], the interference problem is far from being over, and it becomes worse when FD is implemented in multi-cell networks. In multi-cell networks, and in the half duplex downlink case, there is only one type of intercell interference (i.e., downlink-to-downlink interference), and so is the case for the half duplex uplink (i.e., uplink-to-uplink interference). On the other hand, there are two types of intercell interference in the case of a full duplex downlink; they are downlink-to-downlink interference and uplink-to-downlink interference. The uplink stream in full duplex case is likewise affected by two types of intercell interference (i.e., downlink-to-uplink interference and uplink-to-uplink interference). This double amount of interference limits the performance of the full duplex schemes in multi-cell networks to the extent that it may destroy the merit of the full duplex. Although a large amount of research work has been reported in the area of SCFD-based wireless networks, few papers consider large SCFD-based cellular networks with imperfect self interference cancellation. A simple decode-and-forward full duplex relaying aided with multiple-input-multiple-output (MIMO) was considered in [15]. The dynamic range limitations in both transmitter and receiver sides were modelled. More importantly, a tight upper and lower bounds on the end-to-end achievable rate were derived. In addition, a transmission policy that maximizes the lower bound was proposed. The authors also found a theoretical approximation for the achievable rate which helps to gain insights in the trade-offs of the system design. In an FD-MIMO system, a transceiver filter design was considered in [16], which aimed at maximizing the weighted sum rate (WSR) subject to the system or individual power constraints. The design was based on the relationship between the WSR and weighted minimum-mean-squared-error. In [17], the authors addressed two optimization problems in FD-MIMO cognitive radio networks. The first problem is related with minimizing the sum of mean-squared errors (MSE) of all estimated symbols while the second problem deals with minimization of the maximum MSE per-secondary user (SU) of estimated symbols. Both problems are subject to power constraints at SUs and interference constraints projected to each primary user.