# Robust Transceiver Design for IRS-Assisted Cascaded MIMO Communication Systems
### Related works  
IRSs can be utilized in various ways to help the direct links enhance the performance of the system. In [5], authors utilized an IRS to maximize the weighted sum rate MISO system. Authors in [6] proposed a method to minimize the power consumption in a MISO system equipped with an IRS, and authors in [7] investigate the problem of energy efficiency in an IRS-assisted MISO downlink system. The problem of rate maximization in a MIMO system has been presented in [8], where the authors propose an iterative algorithm to find the best IRS pattern assuming the perfect channel state information (CSI) is given. Recently, the authors in [9] utilized IRS in a relay-aided network to minimize the power consumption and successfully showed that the combination of IRS and relay outperforms other scenarios. While the performance of IRS communication systems has been extensively studied, there is not much research that considers robust design when the perfect CSI is not available [10]. Recently, with the emergence of artificial intelligence, IRSs have shown a great potential to improve the existing protocols and technologies [11]. Authors in [12] investigate the benefit of employing an IRS equipped with a multi-task learning system on the transmit power and achievable throughput of aerial-terrestrial communications. In [13], authors use a reinforcement-learning-based approach to optimize the IRS reflection coefficients for buffer-aided relay selection. One of the earliest studies of the robust transmission designs of IRS-assisted systems was undertaken in [14], where a bounded CSI error model is applied to a problem of power minimization in a MISO transmission system. There, by virtue of semidefinite programming (SDP), the authors turn the original problem into a sequence of convex sub-problems. The robust power minimization subject to the outage probability constraints under statistical cascaded channel error model is considered in [15], where the aim is to optimize the system under worst-case rate constraint. Authors in [16] have proposed a robust algorithm for mean squared error (MSE) minimization for a single user MISO system equipped with an IRS. Their method provides a closed form solution for each iteration. However, it can be used only for the case of a single user system and cannot be extended to more general cases where there are multiple users. Recently, a robust algorithm based on a penalty dual decomposition (PDD) technique is proposed in [10] for sum-rate maximization where they assumed that the channel estimation error follows a complex normal distribution. Exploiting a relay to improve the communication throughput rate is a classic alternative for IRS in communication systems. However, utilizing a relay in a network raises some important questions to be answered. For instance, how should the relay process the received signal before dispatching it to the destination? Now, the relay can receive a signal from the source, process it and transmit it towards the destination in a successive manner. This type of relaying technique is known as half-duplex relaying. Alternatively, while receiving a signal at a certain time instant, the relay can simultaneously transmit the previously received signals. This technique is known as full-duplex relaying [17]. As a consequence of transmitting and receiving at a common resource unit, the relay is confronted with SI. Note that full-duplex relaying potentially increases the total throughput rate of the communication compared to the half-duplex counterpart only if the SI is handled properly at the relay input. By physically isolating the transmitter and receiver front ends of the relay, a significant portion of SI can be reduced [18]. Moreover, analog and/or digital signal processing at the relay input can be utilized to cancel a portion of SI [19; 20; 21; 22]. This can be realized if the estimate of the SI can be obtained at the relay. These SI cancellation procedures can effectively mitigate the destructive impact of SI up to a certain level.