# Joint Diagnosis of RIS and BS for RIS-Aided Millimeter-Wave System
## 1 Introduction  
As a new technology for next generation wireless networks, RIS integrates a large number of passive reflection units with low hardware cost and energy consumption for intelligent transmission, which can improve the spectrum efficiency and the coverage capability of the communication system [1]. There are numerous literatures on the beamforming design of the BS and RIS to maximize the system capacity, which needs to know the channel state information perfectly [2]. However, since the passive RIS elements cannot perform signal processing, channel estimation for RIS-aided systems is challenging. The channel estimation of RIS-aided systems has been studied by some literatures, recently [3, 4, 5, 6, 7]. Specifically, a novel message-passing based algorithm has been proposed in [3] to factorize the cascaded channel by utilizing the slow-varying characteristics of channel and the sparsity of the hidden channel. [PERSON] et al. have proposed a two-timescale channel estimation framework to achieve accurate channel estimation with low pilot overhead [4]. A non-iterative two-stage RIS-aided channel estimation algorithm has been introduced in [5] which has low computational complexity. An aggregated channel estimation approach has been proposed in [6, 7] to reduce the required overhead of channel estimation with sufficient information for data processing. Above all, channel estimation methods assume an ideal scenario of non-blockage on the BS and RIS. However, there is always a possibility of failure of one or more elements in the large array, which will affect the quality of service of communication systems significantly [8, 9]. Additionally, the BS and RIS are easily blocked by rain, water, and snow. References [9, 10] pointed out that the blocked probability of RIS and BS is 0.4 and 0.1, where the blockage of RIS and BS affects the quality of service of communication systems significantly. Thus, the array under test (AUT) technique is proposed [9, 11]. This technique compares the received signal affected by faulty antennas with the signal generated by the ideal channel with free-antennas. Specifically, [PERSON] et al. have proposed a compressed sensing based method to diagnose the faulty antennas at BS [9]. [PERSON] et al. have proposed an atomic norm based algorithm for detecting the faulty elements on the RIS [11]. Nevertheless, thediagnosis algorithm proposed in [9] is suitable for the scenario where the BS is blocked but the RIS is free. Furthermore, the diagnosis algorithm proposed in [11] is suitable for the scenario where the RIS is blocked but the BS is free. However, when the blockage occurs on the BS and RIS at the same time, the above algorithms are not valid. Because the blockage of RIS and BS are affecting the received signal together, it is hard to separate and estimate them. To the best of our knowledge, this is the first contribution proposing diagnosis method for an RIS-aided system considering the scenario where blockages occur both at the BS and RIS. The diagnostic techniques are used to locate faulty reflecting elements and retrieve failure parameters for RIS systems. Specifically, we formulate the diagnosis model for RIS and BS. Then, we propose an iterative algorithm, named Algorithm 1, for joint estimation of the RIS blockage and BS blockage. Next, for the complete blockage scenario, we propose a low complexity algorithm compared to Algorithm 1. Our simulation results demonstrate the superior performance of the proposed algorithms compared to existing ones. _Notation_: We use the following notations throughout the paper. We let a, **a**, **A** represent the scalar, vector, and matrix respectively; \((\cdot)^{\text{T}}\), \((\cdot)^{\text{H}}\), and \((\cdot)^{-1}\) denote the transpose, conjugate transpose, and inverse of a matrix, respectively;  
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Input: Received signal \(\mathbf{y}\); The cascaded channel information \(\mathbf{G}^{\text{BR}}\text{diag}(\mathbf{g}^{\text{R}U})\); The phase coefficients of RIS \(\boldsymbol{\theta}(t)\); The number of iterations \(N_{iter}\).