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In a practical massive MIMO (multiple-input multiple-output) system, the number of antennas at a base station (BS) is constrained by the space and cost factors, which limits the throughput gain promised by theoretical analysis. This paper thus studies the feasibility of adopting the intelligent reflecting surface (IRS) to further improve the beamforming gain of the uplink communications in a massive MIMO system. Under such a novel system, the central question lies in whether the IRS is able to enhance the network throughput as expected, if the channel estimation overhead is taken into account. In this paper, we first show that the favorable propagation property for the conventional massive MIMO system without IRS, i.e., the channels of arbitrary two users are orthogonal, no longer holds for the IRS-assisted massive MIMO system, due to its special channel property that each IRS element reflects the signals from all the users to the BS via the same channel. As a result, the maximal-ratio combining (MRC) receive beamforming strategy leads to strong inter-user interference and thus even lower user rates than those of the massive MIMO system without IRS. To tackle this challenge, we propose a novel strategy for zero-forcing (ZF) beamforming design at the BS and reflection coefficients design at the IRS to efficiently null the inter-user interference. Under our proposed strategy, it is rigorously shown that even if the channel estimation overhead is considered, the IRS-assisted massive MIMO system can always achieve higher throughput compared to its counterpart without IRS, despite the fact that the favorable propagation property no longer holds.
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This paper studies the feasibility of deploying intelligent reflecting surfaces (IRSs) in massive MIMO (multiple-input multiple-output) systems to improve the performance of users in the service dead zone. To reduce the channel training overhead, we advocate a novel protocol for the uplink communication in the IRS-assisted massive MIMO systems. Under this protocol, the IRS reflection coefficients are optimized based on the channel covariance matrices, which are generally fixed for many coherence blocks, to boost the long-term performance. Then, given the IRS reflecting coefficients, the BS beamforming vectors are designed in each coherence block based on the effective channel of each user, which is the superposition of its direct and reflected user-IRS-BS channels, to improve the instantaneous performance. Since merely the user effective channels are estimated in each coherence block, the training overhead of this protocol is the same as that in the legacy wireless systems without IRSs. Moreover, in the asymptotic regime that the numbers of IRS elements and BS antennas both go to infinity with a fixed ratio, we manage to first characterize the minimum mean-squared error (MMSE) estimators of the user effective channels and then quantify the closed-form user achievable rates as functions of channel covariance matrices with channel training overhead and estimation error taken into account. Interestingly, it is shown that the properties of channel hardening and favorable propagation still hold for the user effective channels, and satisfactory user rates are thus achievable even if simple BS beamforming solutions, e.g., maximal-ratio combining, are employed. Finally, thanks to the rate characterization, we design a low-complexity algorithm to optimize the IRS reflection coefficients based on channel covariance matrices.
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.
We introduce a novel system setup where a backscatter device operates in the presence of an intelligent reflecting surface (IRS). In particular, we study the bistatic backscatter communication (BackCom) system assisted by an IRS. The phase shifts at the IRS are optimized jointly with the transmit beamforming vector of the carrier emitter to minimize the transmit power consumption at the carrier emitter whilst guaranteeing a required BackCom performance. The unique channel characteristics arising from multiple reflections at the IRS render the optimization problem highly non-convex. Therefore, we jointly utilize the minorization-maximization algorithm and the semidefinite relaxation technique to present an approximate solution for the optimal IRS phase shift design. We also extend our analytical results to the monostatic BackCom system. Numerical results indicate that the introduction of the IRS brings about considerable reductions in transmit power, even with moderate IRS sizes, which can be translated to range increases over the non-IRS-assisted BackCom system.
In intelligent reflecting surface (IRS) assisted communication systems, the acquisition of channel state information (CSI) is a crucial impediment for achieving the 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, where $K$, $N$ and $M$ denote the numbers of users, IRS reflecting elements, and antennas at the base station (BS), respectively. To accurately estimate such a large number of channel coefficients within a short time interval, we propose a novel three-phase pilot-based channel estimation framework in this paper for IRS-assisted uplink multiuser communications. Under this framework, we analytically prove 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 for the case without receiver noise at the BS. In contrast to the channel estimation for conventional uplink communications without IRS where the minimum channel estimation time is independent of the number of receive antennas at the BS, our result reveals the crucial role of massive MIMO (multiple-input multiple-output) in reducing the channel estimation time for IRS-assisted communications. Further, for the case with receiver noise, the user pilot sequences, IRS reflecting coefficients, and BS linear minimum mean-squared error (LMMSE) channel estimators are characterized in closed-form, and the corresponding estimation mean-squared error (MSE) is quantified.
Intelligent reflecting surface (IRS) is a promising solution to enhance the wireless communication capacity both cost-effectively and energy-efficiently, by properly altering the signal propagation via tuning a large number of passive reflecting units. In this paper, we aim to characterize the fundamental capacity limit of IRS-aided point-to-point multiple-input multiple-output (MIMO) communication systems with multi-antenna transmitter and receiver in general, by jointly optimizing the IRS reflection coefficients and the MIMO transmit covariance matrix. First, we consider narrowband transmission under frequency-flat fading channels, and develop an efficient alternating optimization algorithm to find a locally optimal solution by iteratively optimizing the transmit covariance matrix or one of the reflection coefficients with the others being fixed. Next, we consider capacity maximization for broadband transmission in a general MIMO orthogonal frequency division multiplexing (OFDM) system under frequency-selective fading channels, where transmit covariance matrices can be optimized for different subcarriers while only one common set of IRS reflection coefficients can be designed to cater to all subcarriers. To tackle this more challenging problem, we propose a new alternating optimization algorithm based on convex relaxation to find a high-quality suboptimal solution. Numerical results show that our proposed algorithms achieve substantially increased capacity compared to traditional MIMO channels without the IRS, and also outperform various benchmark schemes. In particular, it is shown that with the proposed algorithms, various key parameters of the IRS-aided MIMO channel such as channel total power, rank, and condition number can be significantly improved for capacity enhancement.
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