Channel estimation for intelligent reflecting surface aided multi-user MISO terahertz system

: Intelligent reflecting surface (IRS) is considered as a promising application in terahertz (THz) communications since it is able to enhance the THz communication with no additional power consumptions. In this letter, we consider the channel estimation problem for an IRS-aided THz multi-user multi-input single-output (MISO) system with lens antenna array. The main challenge of the problem is that we need to estimate multiple channels and some of the channels are cascaded. To deal with the problem, we propose a two-stage channel estimation scheme, where we set different IRS modes to estimate different channels for each stage. In stage 1, we set the IRS to an absorbing mode and estimate the channel without IRS. Removing the influence of the prior estimated channel, in stage 2, we estimate the channel with IRS by setting the IRS to a perfect reflecting mode. And we decompose the total channel estimation problem into a series of independent problems, where we estimate each independent channel component with a least square method.


Introduction
Intelligent reflecting surface (IRS), as a promising technique for future wireless systems, such as terahertz (THz) communications, has attracted growing research interest in both academia and industry over recent years [1,2]. An IRS is a physical meta-surface consisting of a large number of reflecting elements, where each element is equipped with a simple low-cost sensor [3]. And each element is able to reflect incident electromagnetic waves independently by adjusting its phase-shift. Compared to traditional relay schemes that enhance source-destination transmission by generating new signals, IRS does not buffer or process any incoming signals but only reflects the wireless signal as a passive planar array, which incurs no additional power consumptions [4,5].
Previous works about the IRS are mainly focused on optimizing secrecy-rate and data-rate by designing the phase-shifts of the IRS while assuming perfect channel state information (CSI) is obtained by both the base station (BS) and the IRS [6][7][8][9][10]. However, it is difficult to obtain the perfect CSI since the IRS cannot process any induced signals or emit any pilot signals. Therefore, Article available at https://tst.edpsciences.org or https://doi.org/10.1051/tst/2020132051 Terahertz Science and Technology, ISSN 1941-7411 Vol.13, No.2, June 2020 52 the BS needs to estimate all the channels between the BS and the user, which includes the channel between the (BS, IRS), (IRS, user), and (BS, user). To the best of our knowledge, there are limited literatures considering the channel estimation problem for the IRS-aided system. Thus, in this letter, we investigate the channel estimation problem for the IRS-aided THz multi-user multi-input single output (MISO) system with lens antenna array. To solve the problem, we propose a two-stage channel estimation scheme, where we set different IRS modes for the channel estimation in different stages. In stage 1, we estimate the channel between the BS and the user by setting the IRS to an absorbing mode which is able to absorb all induced signals by the IRS. Removing the influence of the prior estimated channel, in stage 2, we set the IRS to a perfect reflecting mode, which can reflect all induced signals by the IRS with few losses. And we find that the channel with the IRS a cascaded channel. To estimate it, we decompose the total channel estimation problem into a series of independent problems, where we estimate each channel component with a least square method.  As shown in Fig. 1, we consider an uplink THz multiuser MISO system, where a BS, which consists of a one dimensional lens antenna array with t N elements, simultaneously receives signals from K single-antenna users. To enhance the THz communication, an IRS equipped with N passive elements is installed on a surrounding wall to overcome unfavorable propagation conditions and enrich the channel with more paths. For each path, due to the severe propagation loss in the THz communication, we only consider a single reflection signal by the IRS and ignore other signals reflected by the IRS more than one time. And we assume only one data stream needs to be transmitted by each user. In t th instant, each user sends a pilot signal,

System model
is the pilot vector for the channel estimation process, where t L (resp. r L and d L ) is the number of paths for channel is the spatial direction, which can be defined as

Channel estimation scheme
In this section, we seek to solve problem (5) To solve problem (13), we first propose a proposition to prove a special property of the IRS beamspace channel, which is the base of our proposed channel estimation scheme.    As shown in Fig. 2, the NMSE performance can be improved with the increasing SNR. Therefore, when the SNR is smaller than 10 dB, the NMSE can be lower when V decreases, but when the SNR is larger than 10 dB, the result will be reversed.

Conclusions
In this letter, we investigate the channel estimation problem for the IRS-aided multi-user MISO system with lens antenna array. Specifically, we propose a two-stage channel estimation scheme, where we first have estimated the channel without IRS by setting the IRS to the absorbing mode, Terahertz Science and Technology, ISSN 1941-7411 Vol.13, No.2, June 2020 60 and then we have estimated the cascaded channel reflected by the IRS with removing the influence of the prior estimated channel. Since we demonstrate that the channel components of the cascaded channel are independent, in stage 2, we decompose the total channel estimation problem into a series of independent problems, where we have estimated each channel component by the least square method. Numerical results show the effectiveness of our proposed channel estimation scheme.