In this paper, we consider a multi-user multiple-input multiple-output (MIMO) system aided by multiple intelligent reflecting surfaces (IRSs) that are deployed to increase the coverage and, possibly, the rank of the channel. We propose an optimization algorithm to configure the IRSs, which is aimed at maximizing the network sum-rate by exploiting only the statistical characterization of the environment, such as the distribution of the locations of the users and the distribution of the multipath channels. As a consequence, the proposed approach does not require the estimation of the instantaneous channel state information (CSI) for system optimization, thus significantly relaxing (or even avoiding) the need of frequently reconfiguring the IRSs, which constitutes one of the most critical issues in IRS-assisted systems. Numerical results confirm the validity of the proposed approach. It is shown, in particular, that IRS-assisted wireless systems that are optimized based on statistical CSI still provide large performance gains as compared to the baseline scenarios in which no IRSs are deployed.
While intelligent reflecting surface (IRS) assisted wireless communication has emerged as an important research paradigm, channel state information (CSI) acquisition remains a critical challenge to design the IRS phase-shifts and yield the promised coherent beamforming gains. In this paper, we propose an IRS-assisted opportunistic beamforming (OBF) scheme under proportional fair scheduling, which does not require instantaneous CSI to design the IRS parameters. In a slow-fading environment, we show that with only random rotations at the IRS, the proposed scheme can capitalize on the multi-user …
In this letter, improving the security of an intelligent reflecting surface (IRS) assisted multiple-input single-output (MISO) communication system is studied. Different from the ideal assumption in existing literatures that full eavesdropper's (Eve's) channel state information (CSI) is available, we consider a more practical scenario without Eve's CSI. To enhance the security of this system given a total transmit power at transmitter (Alice), we propose a joint beamforming and jamming approach, in which a minimum transmit power is firstly optimized at Alice so as to meet the quality of servic…
Millimeter-wave (mmWave) communication is one of the key enablers of the fifth-generation cellular networks (5G). However, one of the fundamental challenges of mmWave communication is the susceptibility to blockage effects. One way to alleviate this effect is the use of Intelligent Reflecting Surface (IRS). Nevertheless, due to the large number of the reflecting elements on IRS, the channel estimation turns out to be a challenging problem. This paper proposes a low-complexity channel information acquisition method for IRS-assisted mmWave communication system. Our idea consists in exploiting th…
In this paper, an intelligent reflecting surface (IRS) assisted spectrum sharing underlay cognitive radio (CR) wiretap channel (WTC) is studied, and we aim at enhancing the secrecy rate of secondary user in this channel subject to total power constraint at secondary transmitter (ST), interference power constraint (IPC) at primary receiver (PR) as well as unit modulus constraint at IRS. Due to extra IPC and eavesdropper (Eve) are considered, all the existing solutions for enhancing secrecy rate of IRS-assisted non-CR WTC as well as enhancing transmission rate in IRS-assisted CR channel without …
In this paper, we study an intelligent reflecting surface (IRS)-assisted system where a multi-antenna base station (BS) serves a single-antenna user with the help of a multi-element IRS in the presence of interference generated by a multi-antenna BS serving its own single-antenna user. The signal and interference links via the IRS are modeled with Rician fading. To reduce phase adjustment cost, we adopt quasi-static phase shift design where the phase shifts do not change with the instantaneous channel state information (CSI). We investigate two cases of CSI at the BSs, namely, the instantaneou…
This paper considers an intelligent reflecting surface (IRS) aided multiple-input single-output communication system, where statistical channel state information (CSI) is exploited for transmit beamforming and IRS beamforming. A tight upper bound is derived for the ergodic capacity of the system. Based on which, the joint optimization of transmit beam and IRS beam are studied. Depending on whether a line-of-sight path exists between the access point and user, two different cases, namely, Rician fading and Rayleigh fading, are separately treated. Specifically, for the Rician fading case, an ite…
Intelligent reflecting surface (IRS) is a promising new paradigm to achieve high spectral and energy efficiency for future wireless networks by reconfiguring the wireless signal propagation via passive reflection. To reap the potential gains of IRS, channel state information (CSI) is essential, whereas channel estimation errors are inevitable in practice due to limited channel training resources. In this paper, in order to optimize the performance of IRS-aided multiuser systems with imperfect CSI, we propose to jointly design the active transmit precoding at the access point (AP) and passive r…
Intelligent reflecting surface (IRS) has drawn a lot of attention recently as a promising new solution to achieve high spectral and energy efficiency for future wireless networks. By utilizing massive low-cost passive reflecting elements, the wireless propagation environment becomes controllable and thus can be made favorable for improving the communication performance. Prior works on IRS mainly rely on the instantaneous channel state information (I-CSI), which, however, is practically difficult to obtain for IRS-associated links due to its passive operation and large number of elements. To ov…
This paper investigates the performance of reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) systems with direct links, and the phase shifts of the RIS are designed based on the statistical channel state information (CSI). We first derive the closed-form expression of the uplink ergodic data rate. Then, based on the derived expression, we use the genetic algorithm (GA) to solve the sum data rate maximization problem. With low-complexity maximal-ratio combination (MRC) and low-overhead statistical CSI-based scheme, we validate that the RIS can still br…
The application of intelligent reflecting surface (IRS) depends on the knowledge of channel state information (CSI), and has been hindered by the heavy overhead of channel training, estimation, and feedback in fast-changing channels. This paper presents a new two-timescale beamforming approach to maximizing the average achievable rate (AAR) of IRS-assisted MIMO systems, where the IRS is configured relatively infrequently based on statistical CSI (S-CSI) and the base station precoder and power allocation are updated frequently based on quickly outdated instantaneous CSI (I-CSI). The key idea is…
This letter aims to clarify the impact of channel aging and phase noise on the performance of intelligent reflecting surface-aided wireless systems. We first model mathematically the outdated channel state information (CSI) due to Doppler shifts and phase noise stemming from hardware impairment. Then, a closed-form expression of achievable spectral efficiency under noisy and aged CSI is theoretically derived. Some typical simulation results to numerically demonstrate the performance impact are illustrated.
Illegal intelligent reflecting surfaces (I-IRSs), i.e., the illegal deployment and utilization of IRSs, impose serious harmful impacts on wireless networks. The existing I-IRS-based illegal jammer (IJ) requires channel state information (CSI) or extra power or both, and therefore, the I-IRS-based IJ seems to be difficult to implement in practical wireless networks. To raise concerns about significant potential threats posed by I-IRSs, we propose an alternative method to jam legitimate users (LUs) without relying on the CSI. By using an I-IRS to actively change wireless channels, the orthogonal…
In this paper, we investigate the design of robust and secure transmission in intelligent reflecting surface (IRS) aided wireless communication systems. In particular, a multi-antenna access point (AP) communicates with a single-antenna legitimate receiver in the presence of multiple single-antenna eavesdroppers, where the artificial noise (AN) is transmitted to enhance the security performance. Besides, we assume that the cascaded AP-IRS-user channels are imperfect due to the channel estimation error. To minimize the transmit power, the beamforming vector at the transmitter, the AN covariance…
Large intelligent surface (LIS)-assisted wireless communications have drawn attention worldwide. With the use of low-cost LIS on building walls, signals can be reflected by the LIS and sent out along desired directions by controlling its phases, thereby providing supplementary links for wireless communication systems. In this study, we evaluate the performance of an LIS-assisted large-scale antenna system by formulating a tight approximation of the ergodic capacity and investigate the effect of the phase shifts on the ergodic capacity in different propagation scenarios. In particular, we propo…
We introduce the concept of frequency-mixing intelligent reflecting surface (FMx-IRS), where the elements of the surface continuously change the phases of the incident signals. In this way, the FMx-IRS acts as a frequency mixer and makes the propagation environment nonlinear, thereby introducing new frequencies. We study the basic features of the proposed concept and demonstrate its advantages that stem from the novel type of control over the wireless propagation. The channel decoupling feature and the correlation between reflected channels are elaborated for the architecture, and are validate…
This letter presents a detailed performance analysis of the intelligent reflecting surface (IRS) aided single-input single-output communication systems, taking into account of the direct link between the transmitter and receiver. A closed-form upper bound is derived for the ergodic capacity, and an accurate approximation is obtained for the outage probability. In addition, simplified expressions are presented in the asymptotic regime. Numerical results are provided to validate the correctness of the theoretical analysis. It is found that increasing the number of reflecting elements can signifi…
In this paper, we consider an intelligent reflecting surface (IRS) assisted Guassian multiple-input multiple-output (MIMO) wiretap channel (WTC), and focus on enhancing its secrecy rate. Due to MIMO setting, all the existing solutions for enhancing the secrecy rate over multiple-input single-output WTC completely fall to this work. Furthermore, all the existing studies are simply based on an ideal assumption that full channel state information (CSI) of eavesdropper (Ev) is available. Therefore, we propose numerical solutions to enhance the secrecy rate of this channel under both full and no Ev…
This letter investigates physical layer security in intelligent reflecting surface (IRS)-aided visible light communication (VLC). Under the point source assumption, we first elaborate the system model in the scenario with multiple legitimate users and one eavesdropper, where the secrecy rate maximization problem is transformed into an assignment problem by objective function approximation. Then, an iterative Kuhn-Munkres algorithm is proposed to optimize the transformed problem, and its computational complexity is in the second-order form of the numbers of IRS units and transmitters. Moreover,…
This letter investigates secure transmission in an intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) network. Consider a practical eavesdropping scenario with imperfect channel state information of the eavesdropper, we propose a robust beamforming scheme using artificial noise to guarantee secure NOMA transmission with the IRS. A joint transmit beamforming and IRS phase shift optimization problem is formulated to minimize the transmit power. Since the problem is non-convex and challenging to resolve, we develop an effective alternative optimization (AO) algori…
Intelligent reflecting surfaces (IRSs) have emerged as a promising economical solution to implement cell-free networks. However, the performance gains achieved by IRSs critically depend on smartly tuned passive beamforming based on the assumption that the accurate channel state information (CSI) knowledge is available, which is practically impossible. Thus, in this paper, we investigate the impact of the CSI uncertainty on IRS-assisted cell-free networks. We adopt a stochastic programming method to cope with the CSI uncertainty by maximizing the expectation of the sum-rate, which guarantees ro…
The intelligent reflecting surface (IRS) is an emerging technique to extend the wireless coverage. In this letter, the performance of hybrid automatic repeat request (hybrid-ARQ) for an IRS-assisted system is analyzed. More specifically, the outage performance of the IRS-aided system using hybrid-ARQ protocol with chase combining is studied. Asymptotic analysis also shows that the outage performance improves better than linearly by increasing number of reflectors of the IRS-aided system. The results also verify the potential of combining the ARQ scheme in the link layer of the IRS-aided system…
This letter investigates the joint active and passive beamforming optimization for intelligent reflecting surface (IRS) aided multiuser multiple-input multiple-output systems with the objective of maximizing the weighted sum-rate. We show that this problem can be solved via a matrix weighted mean square error minimization equivalence. In particular, for the optimization of the passive IRS beamforming, we first propose an iterative algorithm with excellent performance based on the manifold optimization. By using the matrix fractional programming technique to obtain a more tractable object funct…
In intelligent reflecting surface (IRS) aided wireless communication systems, channel state information (CSI) is crucial to achieve its promising passive beamforming gains. However, CSI errors are inevitable in practice and generally correlated over the IRS reflecting elements due to the limited training with discrete phase shifts, which degrade the data transmission rate and reliability. In this paper, we focus on investigating the effect of CSI errors to the outage performance in an IRS-aided multiuser downlink communication system. Specifically, we aim to jointly optimize the active transmi…
In this letter, we propose to exploit an intelligent reflecting surface (IRS) to secure multiuser two-way communications. Specifically, two end users simultaneously transmit their signals, where the signal of one user is exploited as information jamming to disrupt the reception of the other user's signal at an eavesdropper. A simple user scheduling scheme is developed to improve the secrecy rate. Analytical results in terms of a lower bound on the average secrecy rate and its scaling laws are derived to evaluate the secrecy performance and obtain valuable design insights. Simulation results ar…
We investigate transmission optimization for intelligent reflecting surface (IRS) assisted multi-antenna systems from the physical-layer security perspective. The design goal is to maximize the system secrecy rate subject to the source transmit power constraint and the unit modulus constraints imposed on phase shifts at the IRS. To solve this complicated non-convex problem, we develop an efficient alternating algorithm where the solutions to the transmit covariance of the source and the phase shift matrix of the IRS are achieved in closed form and semi-closed forms, respectively. The convergen…
We consider a reconfigurable intelligent surface (RIS)-aided massive multi-user multiple-input multiple-output (MIMO) communication system with transceiver hardware impairments (HWIs) and RIS phase noise. Different from the existing contributions, the phase shifts of the RIS are designed based on the long-term angle informations. Firstly, an approximate analytical expression of the uplink achievable rate is derived. Then, we use genetic algorithm (GA) to maximize the sum rate and the minimum date rate. Finally, we show that it is crucial to take HWIs into account when designing the phase shift…
In this letter, we study the outage probability of intelligent reflecting surface (IRS) assisted full duplex two-way communication systems, which characterizes the performance of overcoming the transmitted data loss caused by long deep fades. To this end, we first derive the probability distribution of the cascaded end-to-end equivalent channel with an arbitrarily given IRS beamformer. Our analysis shows that deriving such probability distribution in the considered case is more challenging than the case with the phase-matched IRS beamformer. Then, with the derived probability distribution of t…
This article aims to reduce huge pilot overhead when estimating the reconfigurable intelligent surface (RIS) relayed wireless channel. Motivated by the compelling grasp of deep learning in tackling nonlinear mapping problems, the proposed approach only activates a part of RIS elements and utilizes the corresponding cascaded channel estimate to predict another part. Through a synthetic deep neural network (DNN), the direct channel and active cascaded channel are first estimated sequentially, followed by the channel prediction for the inactive RIS elements. A three-stage training strategy is dev…
The incorporation of reconfigurable intelligent surface (RIS) into massive multiple-input-multiple-output (mMIMO) systems can unleash the potential of next-generation networks by improving the performance of user equipments (UEs) in service dead zones. However, their requirement for accurate channel state information (CSI) is critical, and especially, applications with UE mobility that induce channel aging make challenging the achievement of adequate quality of service. Hence, in this work, we investigate the impact of channel aging on the performance of RIS-assisted mMIMO systems under both s…
Reconfigurable intelligent surface (RIS) provides a promising way to build the programmable wireless transmission environments in the future. Owing to the large number of reflecting elements used at the RIS, joint optimization for the active beamforming at the transmitter and the passive reflector at the RIS is usually complicated and time-consuming. To address this problem, this paper proposes a low-complexity joint beamforming and reflecting algorithm based on fractional programing (FP). Specifically, we first consider a RIS-aided multi-user communication system with perfect channel state in…
This paper studies the performance of a single-input single-output (SISO) system enhanced by the assistance of an intelligent reflecting surface (IRS), which is equipped with a finite number of elements under Rayleigh fading channels. From the instantaneous channel capacity, we compute a closed-form expression of the coverage probability as a function of statistical channel information only. A scaling law of the coverage probability and the number of phase shifts is further obtained. The ergodic capacity is derived, then a simple upper bound to simplify matters of utilizing the symbolic functi…
In this paper, we propose intelligent reflecting surfaces (IRS) assisted secure wireless communications with multi-input and multi-output antennas (IRS-MIMOME). The considered scenario is an access point (AP) equipped with multiple antennas communicates with a multi-antenna enabled legitimate user in the downlink at the present of an eavesdropper configured with multiple antennas. Particularly, the joint optimization of the transmit covariance matrix at the AP and the reflecting coefficients at the IRS to maximize the secrecy rate for the IRS-MIMOME system is investigated, with two different a…
In this letter, we consider an intelligent reflecting surface (IRS) assisted Guassian multiple-input multiple-output (MIMO) wiretap channel in which a multi-antenna transmitter communicates with a multi-antenna receiver in the presence of a multi-antenna eavesdropper. To maximize the secrecy rate of this channel, an alternating optimization (AO) algorithm is proposed to jointly optimize the transmit covariance R at transmitter and phase shift coefficient Q at IRS by fixing the other as a constant. When Q is fixed, existing numerical algorithm is used to search for global optimal R. When R is f…
In this work, we investigate the secrecy performance in an intelligent reflecting surface (IRS)-assisted downlink system. In particular, we consider a base station (BS)-side IRS and as such, the BS-IRS channel is assumed to be known perfectly. Of more importance, we consider the case, in which only outdated channel state information (CSI) of the IRS-user channel is available. We study the impact of outdated CSI on the secrecy performance numerically and analytically. Furthermore, we propose an element subset selection (ESS) method in order to improve the secrecy performance. A key observation …
This paper investigates physical layer security (PLS) in the intelligent reflecting surface (IRS)-assisted multiple-user uplink channel. Since the instantaneous eavesdropper's channel state information (CSI) is unavailable, the secrecy rate can not be measured. In this case, existing investigations usually focus on the maximization of the minimum (max-min) of signal to interference plus noise power ratio (SINRs) among multiple users, and do not consider secrecy outage probability caused by eavesdroppers. In this paper, we first formulate the minimization of the maximum (min-max) secrecy outage…
In this paper, the problem of training signal design for intelligent reflecting surface (IRS)-assisted millimeter-wave (mmWave) communication under a sparse channel model is considered. The problem is approached based on the Cram$\acute{\text{e}}$r-Rao lower bound (CRB) on the mean-square error (MSE) of channel estimation. By exploiting the sparse structure of mmWave channels, the CRB for the channel parameter composed of path gains and path angles is derived in closed form under Bayesian and hybrid parameter assumptions. Based on the derivation and analysis, an IRS reflection pattern design m…
In this paper, an intelligent reflecting surface (IRS) is deployed to assist the terahertz (THz) communications. The molecular absorption causes path loss peaks to appear in the THz frequency band, and the fading peak is greatly affected by the transmission distance. In this paper, we aim to maximize the sum rate with individual rate constraints, in which the IRS location, IRS phase shift, the allocation of sub-bands of the THz spectrum, and power control for UEs are jointly optimized. For the special case of a single user equipment (UE) with a single sub-band, the globally optimal solution is…
This work examines the performance gain achieved by deploying an intelligent reflecting surface (IRS) in covert communications. To this end, we formulate the joint design of the transmit power and the IRS reflection coefficients by taking into account the communication covertness for the cases with global channel state information (CSI) and without a warden's instantaneous CSI. For the case of global CSI, we first prove that perfect covertness is achievable with the aid of the IRS even for a single-antenna transmitter, which is impossible without an IRS. Then, we develop a penalty successive c…
Physical-layer key generation (PKG) can generate symmetric keys between two communication ends based on the reciprocal uplink and downlink channels. By smartly reconfiguring the radio signal propagation, intelligent reflecting surface (IRS) is able to improve the secret key rate of PKG. However, existing works involving IRS-assisted PKG are concentrated in single-antenna wireless networks. So this paper investigates the problem of PKG in the IRS-assisted multiple-input single-output (MISO) system, which aims to maximize the secret key rate by optimally designing the IRS passive beamforming. Fi…
An intelligent reflecting surface (IRS) can adaptively adjust the phase shifts of its reflecting units to strengthen the desired signal and/or suppress the undesired signal. In this letter, we investigate an IRS-aided secure wireless communication system where a multi-antenna access point (AP) sends confidential messages to a single-antenna user in the presence of a single-antenna eavesdropper. In particular, we consider the challenging scenario where the eavesdropping channel is stronger than the legitimate communication channel and they are also highly correlated in space. We maximize the se…
Terahertz (THz) communications have emerged as a promising candidate to support the heavy data traffic and exploding network capacity in the future 6G wireless networks. However, THz communications are facing many challenges for practical implementation, such as propagation loss, signal blockage, and hardware cost. In this article, an emerging paradigm of intelligent reflecting surface (IRS) assisted THz communications is analyzed, to address the above issues, by leveraging the joint active and passive beamforming to enhance the communication quality and reduce overheads. Aiming at practical i…
This work considers a point-to-point link where a reconfigurable intelligent surface assists the communication between transmitter and receiver. The system rate, energy efficiency, and their trade-off are optimized with respect to the number of individually tunable elements of the intelligent surface. The resource allocation accounts for the communication phase and for the overhead due to channel estimation and to reporting the optimized resource allocation to the intelligent surface. Numerical results confirm the optimality of the proposed methods and show the potential gains of reconfigurabl…
This paper considers an angle-domain intelligent reflecting surface (IRS) system. We derive maximum likelihood (ML) estimators for the effective angles from the base station (BS) to the user and the effective angles of propagation from the IRS to the user. It is demonstrated that the accuracy of the estimated angles improves with the number of BS antennas. Also, deploying the IRS closer to the BS increases the accuracy of the estimated angle from the IRS to the user. Then, based on the estimated angles, we propose a joint optimization of BS beamforming and IRS beamforming, which achieves simil…
In this paper, we investigate resource allocation algorithm design for intelligent reflecting surface (IRS)-assisted multiuser cognitive radio (CR) systems. In particular, an IRS is deployed to mitigate the interference caused by the secondary network to the primary users. The beamforming vectors at the base station (BS) and the phase shift matrix at the IRS are jointly optimized for maximization of the sum rate of the secondary system. The algorithm design is formulated as a non-convex optimization problem taking into account the maximum interference tolerance of the primary users. To tackle …
Intelligent reflecting surfaces (IRS) can improve the physical layer security (PLS) by providing a controllable wireless environment. In this paper, we propose a novel PLS technique with the help of IRS implemented by an intelligent mirror array for the visible light communication (VLC) system. First, for the IRS aided VLC system containing an access point (AP), a legitimate user and an eavesdropper, the IRS channel gain and a lower bound of the achievable secrecy rate are derived. Further, to enhance the IRS channel gain of the legitimate user while restricting the IRS channel gain of the eav…
In this paper, we propose to utilize intelligent reflecting surfaces (IRSs) for enhancing the physical layer security of wireless communications systems. In particular, an IRS-assisted secure wireless system is considered, where a multi-antenna transmitter communicates with a single-antenna receiver in the presence of an eavesdropper. To maximize the secrecy rate, both the beamformer at the transmitter and the IRS phase shifts are jointly optimized. Based on the block coordinate descent (BCD) and minorization maximization (MM) techniques, two efficient algorithms are developed to solve the res…
This work gives a blind beamforming strategy for intelligent reflecting surface (IRS), aiming to boost the received signal-to-noise ratio (SNR) by coordinating phase shifts across reflective elements in the absence of channel information. While the existing methods of IRS beamforming typically first estimate channels and then optimize phase shifts, we propose a conditional sample mean based statistical approach that explores the wireless environment via random sampling without performing any channel estimation. Remarkably, the new method just requires a polynomial number of random samples to y…
In this paper, the minimum mean square error (MMSE) channel estimation for intelligent reflecting surface (IRS) assisted wireless communication systems is investigated. In the considered setting, each row vector of the equivalent channel matrix from the base station (BS) to the users is shown to be Bessel $K$ distributed, and all these row vectors are independent of each other. By introducing a Gaussian scale mixture model, we obtain a closed-form expression for the MMSE estimate of the equivalent channel, and determine analytical upper and lower bounds on the mean square error. Using the cent…
Intelligent reflecting surface (IRS) is envisioned to be a promising solution for designing spectral and energy efficient wireless systems. In this letter, we study a multi-IRS-assisted system under Rician fading where the phase shifts adapt to only the line of sight (LoS) components. First, we analyze and optimize the outage probability of the multi-IRS-assisted system in the slow fading scenario for the non-LoS (NLoS) components. We also show that the optimal outage probability decreases with the numbers of IRSs and elements of each IRS when the LoS components are stronger than the NLoS ones…
This paper considers the application of reconfigurable intelligent surfaces (RISs) (a.k.a. intelligent reflecting surfaces (IRSs)) to assist multiuser multiple-input multiple-output (MIMO) uplink transmission from several multi-antenna user terminals (UTs) to a multi-antenna base station (BS). For reducing the signaling overhead, only partial channel state information (CSI), including the instantaneous CSI between the RIS and the BS as well as the slowly varying statistical CSI between the UTs and the RIS, is exploited in our investigation. In particular, an optimization framework is proposed …
Intelligent reflecting surface (IRS) has emerged as a cost-effective solution to enhance wireless communication performance via passive signal reflection. Existing works on IRS have mainly focused on investigating IRS's passive beamforming/reflection design to boost the communication rate for users assuming that their channel state information (CSI) is fully or partially known. However, how to exploit IRS to improve the wireless transmission reliability without any CSI, which is typical in high-mobility/delay-sensitive communication scenarios, remains largely open. In this paper, we study a ne…
In this work, we study the statistically robust beamforming design for an intelligent reflecting surfaces (IRS) assisted multiple-input single-output (MISO) wireless system under imperfect channel state information (CSI), where the channel estimation errors are assumed to be additive Gaussian. We aim at jointly optimizing the transmit/receive beamformers and IRS phase shifts to minimize the average mean squared error (MSE) at the user. In particular, to tackle the non-convex optimization problem, an efficient algorithm is developed by capitalizing on alternating optimization and majorization-m…