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Register a new userCompressed Channel Estimation and Joint Beamforming for Intelligent Reflecting Surface-Assisted Millimeter Wave Systems
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Added by
Peilan Wang
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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In this paper, we consider channel estimation for intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) systems, where an IRS is deployed to assist the data transmission from the base station (BS) to a user. It is shown that for the purpose of joint active and passive beamforming, the knowledge of a large-size cascade channel matrix needs to be acquired. To reduce the training overhead, the inherent sparsity in mmWave channels is exploited. By utilizing properties of Katri-Rao and Kronecker products, we find a sparse representation of the cascade channel and convert cascade channel estimation into a sparse signal recovery problem. Simulation results show that our proposed method can provide an accurate channel estimate and achieve a substantial training overhead reduction.
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This paper investigates the uplink cascaded channel estimation for intelligent-reflecting-surface (IRS)-assisted multi-user multiple-input-single-output systems. We focus on a sub-6 GHz scenario where the channel propagation is not sparse and the number of IRS elements can be larger than the number of BS antennas. A novel channel estimation protocol without the need of on-off amplitude control to avoid the reflection power loss is proposed. In addition, the pilot overhead is substantially reduced by exploiting the common-link structure to decompose the cascaded channel coefficients by the multiplication of the common-link variables and the user-specific variables. However, these two types of variables are highly coupled, which makes them difficult to estimate. To address this issue, we formulate an optimization-based joint channel estimation problem, which only utilizes the covariance of the cascaded channel. Then, we design a low-complexity alternating optimization algorithm with efficient initialization for the non-convex optimization problem, which achieves a local optimum solution. To further enhance the estimation accuracy, we propose a new formulation to optimize the training phase shifting configuration for the proposed protocol, and then solve it using the successive convex approximation algorithm. Comprehensive simulations verify that the proposed algorithm has supreme performance compared to various state-of-the-art baseline schemes.
Intelligent reflecting surfaces (IRSs) constitute passive devices, which are capable of adjusting the phase shifts of their reflected signals, and hence they are suitable for passive beamforming. In this paper, we conceive their design with the active beamforming action of multiple-input multipleoutput (MIMO) systems used at the access points (APs) for improving the beamforming gain, where both the APs and users are equipped with multiple antennas. Firstly, we decouple the optimization problem and design the active beamforming for a given IRS configuration. Then we transform the optimization problem of the IRS-based passive beamforming design into a tractable non-convex quadratically constrained quadratic program (QCQP). For solving the transformed problem, we give an approximate solution based on the technique of widely used semidefinite relaxation (SDR). We also propose a low-complexity iterative solution. We further prove that it can converge to a locally optimal value. Finally, considering the practical scenario of discrete phase shifts at the IRS, we give the quantization design for IRS elements on basis of the two solutions. Our simulation results demonstrate the superiority of the proposed solutions over the relevant benchmarks.
Channel estimation is the main hurdle to reaping the benefits promised by the intelligent reflecting surface (IRS), due to its absence of ability to transmit/receive pilot signals as well as the huge number of channel coefficients associated with its reflecting elements. Recently, a breakthrough was made in reducing the channel estimation overhead by revealing that the IRS-BS (base station) channels are common in the cascaded user-IRS-BS channels of all the users, and if the cascaded channel of one typical user is estimated, the other users cascaded channels can be estimated very quickly based on their correlation with the typical users channel cite{b5}. One limitation of this strategy, however, is the waste of user energy, because many users need to keep silent when the typical users channel is estimated. In this paper, we reveal another correlation hidden in the cascaded user-IRS-BS channels by observing that the user-IRS channel is common in all the cascaded channels from users to each BS antenna as well. Building upon this finding, we propose a novel two-phase channel estimation protocol in the uplink communication. Specifically, in Phase I, the correlation coefficients between the channels of a typical BS antenna and those of the other antennas are estimated; while in Phase II, the cascaded channel of the typical antenna is estimated. In particular, all the users can transmit throughput Phase I and Phase II. Under this strategy, it is theoretically shown that the minimum number of time instants required for perfect channel estimation is the same as that of the aforementioned strategy in the ideal case without BS noise. Then, in the case with BS noise, we show by simulation that the channel estimation error of our proposed scheme is significantly reduced thanks to the full exploitation of the user energy.
In the intelligent reflecting surface (IRS) assisted communication systems, the acquisition of channel state information (CSI) is a crucial impediment for achieving the passive beamforming gain of IRS because of the considerable overhead required for channel estimation. Specifically, under the current beamforming design for IRS-assisted communications, $KMN+KM$ channel coefficients should be estimated if the passive IRS cannot estimate its channels with the base station (BS) and users due to its lack of radio frequency (RF) chains, where $K$, $N$ and $M$ denote the number of users, reflecting elements of the IRS, and antennas at the BS, respectively. This number can be extremely large in practice considering the current trend of massive MIMO (multiple-input multiple-output), i.e., a large $M$, and massive connectivity, i.e., a large $K$. To accurately estimate such a large number of channel coefficients within a short time interval, we devote our endeavour in this paper to investigating the efficient pilot-based channel estimation method in IRS-assisted uplink communications. Building upon the observation that the IRS reflects the signals from all the users to the BS via the same channels, we analytically verify that a time duration consisting of $K+N+max(K-1,lceil (K-1)N/M rceil)$ pilot symbols is sufficient for the BS to perfectly recover all the $KMN+KM$ channel coefficients in the case without noise. In contrast to the conventional uplink communications without IRS in which the minimum pilot sequence length for channel estimation is independent with the number of receive antennas, our study reveals the significant role of massive MIMO in reducing the channel training time for IRS-assisted communication systems.
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 central limit theorem, we conduct an asymptotic analysis of the MMSE estimate, and show that the upper bound on the mean square error of the MMSE estimate is equal to the asymptotic mean square error of the MMSE estimation when the number of reflecting elements at the IRS tends to infinity. Numerical simulations show that the gap between the upper and lower bounds are very small, and they almost overlap with each other at medium signal-to-noise ratio (SNR) levels and moderate number of elements at the IRS.
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