With the rapid growth and development of information and communication technology, applications in various fields such as cellular networks, internet of things (IoT), and wireless sensor networks (W) have been mounting. As a result, the number of users and connected devices is increasing every day. The need to communicate with minimal delay, high reliability, and at any place and time, etc. persuades us to increase resources such as transmission power and bandwidth, which in turn means a significant increase in energy consumption. But energy efficiency has become one of the critical challenges of this era because of the dangers of climate change, the ecological impact of carbon emission, as well as the cost of energy. In this research, a relay network structure with a decode-and-forward (DF) strategy and a simultaneous wireless information and power transmit (SWIPT) is considered, as a promising solution, to improve energy efficiency. Also, each node has equipped by multiple antennas with a separate full-duplex (FD) approach to enhance the spectral efficiency. Moreover, by using a power-splitting (PS) strategy at the harvester circuit, the FD can be realized. Clearly, it is always necessary to include the imperfections in design and analysis. Therefore, as one of these imperfections, we have considered imperfect channel state information (ICSI) to analyze system performance precisely. We have proposed and solved an optimization problem with maximizing the end-to-end achievable rate objective, we have obtained closed form optimal solutions for power allocation at source and relay, as well as energy harvesting (EH) ratio. In order to obtain numerical answers, a primal-dual algorithm is presented based on the ellipsoid method. Numerical results demonstrate the FD achievable rate superiority under proper self-interference cancellation (SIC) over the HD mode. There is also a big gap between the achievable rates in PCSI and ICSI cases. According to the existing results, passive SIC outperforms active SIC over a wide range of transmission powers. Also, the effect of relay distance from the source node is noticeable for active SIC due to its power consumption. Finally, as expected, the use of additional antennas enhances the multiplexing gain and thus increases the achievable rate without increase in transmission power compared to single-antenna systems. Key Words: Achievable Rate, MIMO Relay Networks, SWIPT, Energy Harvesting, Full-Duplex Systems, Imperfect CSI, Power Allocation
