In this letter, we study the beamforming design for channel estimation of multi-functional reconfigurable intelligent surface (MF-RIS)-aided multi-user communications that supports simultaneous signal reflection, refraction, and amplification. A least square (LS) based channel estimator is proposed for MF-RIS by considering both the coupled MF-RIS beams and the introduced thermal noise. With the discrete fourier transform (DFT)-matrix, the MF-RIS beamforming design problem is simplified under the proposed LS channel estimator. The optimal MF-RIS beamforming design that achieves the Cramér–Rao lower bound (CRLB) of channel estimator is obtained with the proposed alternating optimization algorithm. Simulation results demonstrate the effectiveness of the proposed beamforming design in reducing the impact of thermal noise.

Distributed over-the-air computation (AirComp) is a promising technology for fast data aggregation in wireless networks by leveraging multiple access channel to achieve communication and computation simultaneously. However, device-to-device (D2D) links applied are vulnerable to obstacles, and the performance of distributed AirComp is restricted by the device with the worst channel condition. To tackle these issues, we introduce a multi-functional reconfigurable intelligent surface (MF-RIS) to reconstruct the wireless propagation environment, where the MF-RIS can achieve signal reflection, refraction, and amplification simultaneously. Specifically, we propose an MF-RIS-aided distributed AirComp framework, where MF-RIS receives the aggregated data from all devices and then transmits it to each device for post-processing. We formulate a mean-squared error (MSE) minimization problem by jointly optimizing transmit scalar, receive scalar, and MF-RIS coefficients. To address this non-convex problem, we employ an alternating optimization (AO) technique to decompose it into three subproblems, where semi-closed form or closed form solutions are obtained. Then, we extend the single-input single-output (SISO) system into multiple-input multiple-output (MIMO) one. Next, we derive the asymptotic MSE performance for SISO and MIMO cases when the number of RIS elements and that of transmit/receive antennas are very large. Numerical results demonstrate the superiority of MF-RIS in improving MSE performance compared to the baseline without RIS. Additionally, the MF-RIS outperforms its passive counterparts, which reveals the advantages of deploying MF-RIS in distributed AirComp systems to reduce data aggregation error.

The robust beamforming design in multi-functional reconfigurable intelligent surface (MF-RIS) assisted wireless networks is investigated in this work, where the MF-RIS supports signal reflection, refraction, and amplification to address the double-fading attenuation and half-space coverage issues faced by traditional RISs. Specifically, we aim to maximize the system energy efficiency by jointly optimizing the transmit beamforming vector and MF-RIS coefficients in the case of imperfect channel state information (CSI). We first leverage the S-procedure and Bernstein-Type Inequality approaches to transform the formulated problem into tractable forms in the bounded and statistical CSI error cases, respectively. Then, we optimize the MF-RIS coefficients and the transmit beamforming vector alternately by adopting an alternating optimization framework, under the quality of service constraint for the bounded CSI error model and the rate outage probability constraint for the statistical CSI error model. Simulation results demonstrate the significant performance improvement of MF-RIS compared to benchmark schemes. In addition, it is revealed that the cumulative CSI error caused by increasing the number of RIS elements is larger than that caused by increasing the number of transmit antennas.

In this paper, we propose a novel multi-functional reconfigurable intelligent surface (MF-RIS) that supports signal reflection, refraction, amplification, and target sensing simultaneously. Our MF-RIS aims to enhance integrated communication and sensing (ISAC) systems, particularly in multi-user and multi-target scenarios. Equipped with reflection and refraction components (i.e., amplifiers and phase shifters), MF-RIS is able to adjust the amplitude and phase shift of both communication and sensing signals on demand. Additionally, with the assistance of sensing elements, MF-RIS is capable of capturing the echo signals from multiple targets, thereby mitigating the signal attenuation typically associated with multi-hop links. We propose a MF-RIS-enabled multi-user and multi-target ISAC system, and formulate an optimization problem to maximize the signal-to-interference-plus-noise ratio (SINR) of sensing targets. This problem involves jointly optimizing the transmit beamforming and MF-RIS configurations, subject to constraints on the communication rate, total power budget, and MF-RIS coefficients. We decompose the formulated non-convex problem into three sub-problems, and then solve them via an efficient iterative algorithm. Simulation results demonstrate that: 1) The performance of MF-RIS varies under different operating protocols, and energy splitting (ES) exhibits the best performance in the considered MF-RIS-enabled multi-user multi-target ISAC system; 2) Under the same total power budget, the proposed MF-RIS with ES protocol attains$\rm {52.2}\%$,$\rm {73.5}\%$, and$\rm {60.86}\%$sensing SINR gains over active RIS, passive RIS, and simultaneously transmitting and reflecting RIS (STAR-RIS), respectively; 3) The number of sensing elements will no longer improve sensing performance after exceeding a certain number.