Intelligent Reflecting Surface Assisted Multi-User MISO Communication
The recently completed global standard for 5G new radio air interface focuses on fulfilling key performance indicators for the new generation of cellular networks through several cutting-edge technologies, including Massive multiple-input multiple-output (MIMO), millimeter (mm)-Wave communication and network densification. However, these technologies face two main practical limitations 1) the lack of control over the wireless propagation environment, and 2) the high power consumption of the wireless interface. To address the need for green and sustainable future cellular networks with control over the propagation channel, the concept of reconfiguring wireless propagation environments using Intelligent Reflecting Surfaces (IRS)s has emerged for beyond 5G networks. An IRS comprises of a large number of low-cost passive reflecting elements that can smartly reconfigure the signal propagation for performance enhancement. In this paper, we discuss the role of passive IRSs in reconfiguring wireless propagation environments, introduce an IRS-assisted multi-user MIMO communication system, outline the communication-theoretic model and minimum mean squared error (MMSE) based channel estimation protocol for its design and analysis, and present performance evaluation results to illustrate the efficiency of the proposed system.
The emerging concept of Internet of Things (IoT) has extended the scope of mobile communication services from interpersonal communication to smart inter-connection between billions of devices. The massive number of interconnected devices and the diversified nature of IoT services are posing new challenges to the underlying cellular network resources that need to cater to this explosive growth in traffic. To address these challenges, the 3GPP has recently completed the global standard for Fifth Generation (5G) radio interface in its Release 15 , which focuses on fulfilling key performance indicators for the next generation of cellular networks, including Gb/s peak data rates for mobile broadband, M/km connections for IoT devices, and ms latency for ultra-reliable low-latency communications.
The 5G standard has been a result of various technological advances, including Massive multiple-input multiple-output (MIMO), millimeter wave (mmWave) communications, and network densification. However, these technologies face two main practical limitations. First, they consume a lot of power, which is a critical issue for practical implementation and second, they struggle to provide the users with uninterrupted connectivity and a guaranteed quality of service (QoS) in harsh propagation environments, due to the lack of control over the wireless propagation channel. For example: the network’s total energy consumption scales linearly as more base stations (BS)s are added to densify the network, while each active antenna element in a Massive MIMO antenna array is connected to a radio frequency (RF) chain comprising of several active components like digital-to-analog converter and low-noise amplifier, rendering the total cost and energy consumption of the system to be very high. Moreover, Massive MIMO performance is known to suffer when the propagation environment exhibits poor scattering conditions, which results in low-rank channel matrices , whereas, communication at mmWave frequencies suffers from high path and penetration losses. These two limitations have resulted in the need for green and sustainable future cellular networks, where the network operator has some control over the propagation environment.
An emerging concept that addresses this need is that of a smart radio environment, where the wireless propagation environment is turned into an intelligent reconfigurable space that plays an active role in transferring radio signals from the BS to the users. This concept is now realizable through different emerging technologies, which include deploying smart reflect-arrays  in the environment or coating the environmental objects with reconfigurable meta-surfaces , that apply wave transformations on the impinging electromagnetic waves to shape them in a desirable way, without generating new radio signals and thereby without incurring any additional power consumption. Metasurfaces, in particular, are composed of low-cost and passive sub-wavelength dielectric scattering particles that transform the incident electromagnetic waves into arbitrary specified reflected and refracted radio waves, depending on the specific arrangement of the scattering particles. A reconfigurable meta-surface allows this arrangement to be modified depending on the stimulus it receives from the external world (e.g. a network controller) .
Smart radio environments enabled by intelligent reconfigurable surfaces is a recent but feasible technology with current research activities focusing on fabricating new meta-surfaces and reflect arrays, making them re-configurable using software-defined protocols and implementing testbeds [6, 7, 4]. There are a very few works that study the communication-theoretic performance of this technology. In the present paper, we focus our attention on realizing the vision of smart radio environments in wireless communication systems using passive Intelligent Reflecting Surfaces (IRS)s [8, 9], that reconfigure the propagation environment by reflecting the incoming signals in a programmable manner. This paper will focus on the communication-theoretic modeling of IRS-assisted communication systems without delving into the hardware design of the underlying surfaces, as the latter has been the subject of recent magazine papers [10, 4, 5].
More specifically, this overview article will discuss the role of IRSs in reconfiguring wireless propagation environments along with the current research landscape in Section II, introduce the transmission model of an IRS-assisted multi-user multiple-input single-output (MISO) communication system with focus on identifying different channel models to describe it in Section III and developing a minimum mean squared error (MMSE) based channel estimation protocol in Section IV. Section V will discuss the design of the IRS parameters along with the performance evaluation results. The results show that unprecedented Massive MIMO gains can be realized with a significantly smaller number of active antennas at the BS. However, the performance gains are highly sensitive to the quality of the channel estimates available. Some related research directions and open issues are outlined in Section VI, followed by concluding remarks in Section VII.
Ii Re-configuring Radio Environments using IRSs - Concept and Research Landscape
The propagation environment is defined by the set of physical objects that affect the propagation of electromagnetic waves between the communicating devices. As such it is a fixed entity outside the network operator’s control and often has detrimental effects (path loss, poor scattering) on the communication process. IRS is a technology that can tame these effects and yield a wireless environment with controlled electromagnetic behaviour, by using for example software-reconfigurable metasurfaces as IRSs to coat the walls of the buildings between the communicating devices. One of the ways these reconfigurable surfaces interact with the impinging electromagnetic waves is by reflecting them according to the generalized Snell’s law, i.e. the angles of incidence and reflection of the radio waves do not need to be identical as required by the Snell’s law, but will depend on the phases induced by the elements of the IRSs .
We consider the IRS to be a planar array of a large number of reconfigurable passive elements (e.g., dielectric scattering particles in case of a re-configurable metasurface), where each element is able to independently introduce a certain phase shift onto the incident electromagnetic waves. The combined reflected signals, generated through the smart adjustment of the phase shifts applied by all the elements of the IRS, can achieve desired communication goals, e.g., improve the coverage or make the propagation conditions favorable. Since the IRS is not equipped with sensing capabilities (to keep it completely passive), the radio links are estimated at the BS via appropriate control signals. The BS is then responsible for reporting this data to the IRS controller, which, in turn, is responsible for controlling the phase shifts applied by elements of the IRS. Also note that IRS is significantly different from technologies like amplify-and-forward/decode-and-forward relays, that require dedicated energy sources to generate new signals, and large intelligent surface based Massive MIMO , where the surface is used for transmission instead of reflection.
Fig. 1 shows the concept of an IRS-assisted communication system. User A wants to connects to the Internet via a cellular network. However, the received signal at the user is weak due to the blocking building B1, resulting in a poor QoS. Let us now consider that the nearby buildings B2 and B3 have IRSs installed onto their walls that reflect the radio waves towards User A by introducing, in a programmable manner, phase shifts onto the signals impinging upon them. Using the stimulus provided by the IRSs controller, the IRSs can therefore produce a strong received signal at User A.
The idea of reconfiguring the wireless propagation environment using IRSs has emerged only recently and in different forms, with more focus on controlling the indoor environments. In , the authors designed an electronically tunable metasurface based spatial microwave modulator. Deploying it in a typical office room, they showed that it could maximize the wireless transmission between two antennas (possibly a pair of transmit-receive antennas) or on the contrary minimize it. The authors in  relied on the use reconfigurable reflect-arrays in indoor environments to propose a new spectrum sharing solution. In , the authors envisioned the active re-programming of wireless propagation environments using software-controlled meta-materials that could be embedded in any surface in the environment and that would interact with the radio waves in a fully software-defined fashion.
Very recently, the design of IRSs for outdoor communications environments has been considered. Preliminary contributions appeared in [8, 9], where the authors proposed algorithms to minimize the total transmit power by jointly optimizing the transmit beamforming at the BS and reflect beamforming by passive phase shifters at the IRS, subject to usersâ QoS constraints. Another important contribution appeared in , where the authors designed the phases induced by the IRS elements to maximize either the energy or the spectral efficiency of an IRS-assisted multi-user MISO system. These existing works assume the IRS to have global CSI, which is not true in practice, especially given the IRS has no radio resources of its own to estimate the channels. Moreover, these preliminary works consider independent and identically distributed (i.i.d.) Rayleigh or Rician fading channel coefficients to model the communication links, which is an oversimplification of the conditions encountered in realistic propagation environments. In fact, the choice of channel model can significantly impact the resulting performance prediction.
In the present paper, we focus our attention on these multiple gaps of knowledge that exist towards realizing the vision of re-configurable propagation environments using IRSs. In the next section, we outline the transmission model for an IRS-assisted MISO communication system along with the associated channel modeling considerations. Later, we present the MMSE-based channel estimation protocol to estimate the channels at the BS without any active participation from IRS.
Iii Communication Model
The proposed IRS-assisted multi-user MISO system is illustrated in Fig. 2(a), which consists of a BS equipped with antennas serving single-antenna users. This communication is assisted by an IRS, comprising of nearly passive elements which act as low resolution phase shifters, attached to the facade of a building in the line-of-sight (LoS) of the BS. The IRS is equipped with a smart controller that controls its switching between the No-reflection mode for the channel estimation phase and the reflection mode for the downlink transmission phase, wherein the IRS re-scatters the impinging electromagnetic waves.
Denoting the precoded signal vector transmitted by the BS as having power , the received signal at user during the downlink transmission phase is given as,
where is the channel from the BS to the IRS, is the channel from the IRS to user , the direct channel from the BS to user and is the noise at the user. The IRS is represented by the diagonal matrix , where and represent the phase and the amplitude coefficient for element respectively.
The uplink channel through the IRS given by can be equivalently expressed as , where and . This formulation enables the separation of the response of the IRS in v from the cascaded channel outside the IRS control in , and will assist us in the design of the channel estimation protocol in Section IV.
The most basic yet the most important challenge in the design of IRS parameters is the correct modeling of and . The preliminary theoretical works [12, 8] utilize the i.i.d. Rayleigh channel model, which is an over simplification of the conditions encountered in real-world correlated propagation environments. Moreover, under this setting, the statistics of the received signal do not change with the values of the phase shifts as grow large. As a consequence, only a system with small to moderate dimensions will show any significant performance improvement through the use of an IRS. It is, hence, more practical to replace these i.i.d. models with correlated channel models that account for both the fast-fading effects and the correlation between IRS elements.
The IRS is envisioned to be installed on the facade of a high rise building, in the direct LoS of the BS [8, 13]. As a consequence, will be a deterministic matrix computed using the locations of the BS and the IRS. There are two ways to model this LoS channel.
1) Rank-One Channel: Since the BS and the IRS have co-located elements, so the channel matrix will have rank one, i.e. , where and describe the deterministic array responses of the BS antennas and the IRS elements respectively. This means that the degrees of freedom offered by the channel through the IRS will be equal to one. Therefore, the IRS-assisted link will only yield significant performance gains when . In fact, considering the multi-user layout in Fig. 3(a) with modeled as rank-one and s modeled as Rayleigh correlated, we plot the average signal-to-interference-plus-noise ratio (SINR) performance under the regularized zero-forcing (RZF) precoder in Fig. 3(b). We also plot the performance obtained if there was only a direct link between the BS and the user. The result shows that introducing an IRS produces diminishing performance gains for , irrespective of the values of and . For , however, using an IRS yields an 8 dB gain in the performance.
2) Full-rank Channel: To benefit from the IRS in the multi-user setting, we must have . One way to introduce this rank is to have scattering between the BS and the IRS. Also using distributed IRSs the LoS channel matrix between the BS and the IRSs can be made of high rank.
In addition to channel modeling, the design of channel estimation protocols to obtain channel state information (CSI) poses another main challenge to the design of IRS-assisted communication systems, because the IRS has no active resources of its own to sense the channel and relies completely on the IRS-controller for its operation. It is due to this difficulty, existing works on this technology assume perfect CSI to be available at both BS and IRS. In the next section, we propose an MMSE based channel estimation protocol that does not require any active participation from the IRS.
Iv Channel Estimation Protocol
Channel estimation is necessary to compute the precoding vectors at the BS and the reflect beamforming matrix at the IRS. Given the passive nature of the IRS, we adopt the time division duplex (TDD) protocol and exploit channel reciprocity in estimating the downlink channels using the received uplink pilot signals from the users. For this purpose, we divide the channel coherence period of s into an uplink training phase of s and a downlink transmission phase of s. Throughout the uplink training phase, the users transmit mutually orthogonal pilot symbols , where .
The real difficulty is in the estimation of and s, since the IRS has no radio resources of its own to transmit pilot symbols that enable the BS to estimate or to sense s using the pilot signals received from the users. Therefore, the BS has to estimate all the channels and share this information with the IRS controller. To this end, note that and have been cascaded as in (1), where is a matrix of column vectors. Each vector (shown in red curved arrows in Fig. 2(a)) can be interpreted as the channel from the user to the BS through the IRS when only element of the IRS is ON i.e. and , . We will focus on the MMSE estimation of , and for at the BS.
The total channel estimation time is divided into sub-phases, each of duration s. During the first sub-phase, all elements of the IRS are OFF and the BS estimates the direct channel for all users. During the sub-phase, where , only element of the IRS is ON (i.e. , ) to aid the BS in estimating for all users, while all other IRS elements are OFF.
The expressions of the MMSE estimates for these channel vectors can be derived straightforwardly as follows. For the channel estimation phase of s, the received training signal matrix at the BS can be defined as , where represents the received training signal vector when all the elements of the IRS are OFF and is used to estimate , . It is given as,
where is the noise vector at the BS. Similarly, , represents the received training signal vector when element of the IRS is ON and is used to estimate , . It can be expressed as,
Note that each , , contains the received signals from all the users. However since the users transmit mutually orthogonal pilot symbols, so the received training signal vector in the sub-phase is correlated one-by-one with the pilot symbol of each user to obtain the observation vector with respect to each user as , where represents the pseudo-inverse. These independent observation vectors are then used to obtain the estimates of the channel vector being estimated in the sub-phase for all users. The estimates are computed using the MMSE estimation method . This protocol is also summarized in Fig. 2(b). Later in the numerical results, we will show that channel estimation in an IRS-assisted system is more prone to errors than in a conventional MISO communication system without the IRS.
V IRS Design and Evaluation Results
The design of the IRS phase matrix largely depends on the performance criteria being optimized. Since in the downlink transmission phase, each element of the IRS is designed to maximize signal reflection so , for . Each element therefore just introduces a phase shift. As a consequence, the design must satisfy the unit-modulus constraints on the IRS elements, i.e. , for . These non-convex constraints are generally handled using projection methods to obtain the optimal solutions .
Since this paper intends to be non-technical and provides a flavor of the performance gains realizable through the deployment of an IRS, so we utilize a basic design for the IRS phase shift matrix. The design referred to as Center of Means (CoM) in , assigns the phase shifts so as to reflect the incoming signals in the direction of the mean angle of arrival (AoA) of all the users.
|IRS configuration||Uniform linear array (ULA),|
|BS configuration||ULA, spacing|
|Tx power budget ()||W|
|(Fixed loss at m)||dB (), dB ()|
|(Path loss exponent)||(), (), ()|
|in single-user case||Rank-One: |
|in multi-user case||Full Rank |
|Generated using [(38) ]|
|Single-user case||Maximum ratio transmission|
|Multi-user case||Optimal Linear Precoder |
To evaluate the performance of the IRS-assisted system under the proposed channel estimation protocol, we utilize the parameters’ values described in Table I. We first focus on a single-user scenario shown in Fig. 4(a), where it is well-known that MRT precoding is optimal. The IRS is placed adjacent to the BS with . The user lies on a horizontal line that is in parallel to the one that connects the BS and the IRS, with the distance between these two lines being . Denoting the horizontal distance between the BS and user by , we study the received SNR at the user in Fig. 4(b) by varying the value of . First, it can be observed for the direct communication scenario (i.e. No IRS) that the user farther away from the BS suffers more SNR loss due to signal attenuation by path loss. However, in an IRS-assisted system the user farther away from the BS can still be closer to the IRS and receive stronger reflected signals from it resulting in an improvement in the performance as observed for . Although the SNR performance degrades due to increasing signal attenuation when but the performance is still much better than what would have been achieved without the IRS. As a result, when the channels are perfectly known, the IRS-assisted system can provide signal coverage to a much larger region. For example, it will cover the entire m range with an SNR level of at least dB, whereas the system without the IRS can only cover about m to achieve the same SNR level.
Secondly, by doubling the number of elements at the IRS to , the received SNR scales by about dB for . Thus, the SNR scales with the number of reflecting elements in the order of , corresponding to an array gain of and the reflect beamforming gain of . However, the gain is negligible for because the BS-to-user direct channel is much stronger than the channel through the IRS, so the performance is insensitive to .
Finally, the result shows that the IRS-assisted system is much more sensitive to channel estimation errors than the direct communication system. This is because for a constant channel estimation time of s, the IRS-assisted system has to estimate channel vectors of dimension whereas the direct system only needs to estimate one channel vector. Therefore, the performance of the IRS-assisted system deteriorates much more than the direct system as the channel training SNR decreases ( increases). Moreover, the channel estimation errors are more significant as the user moves away from the IRS. This can be explained by noting that when user is close to the IRS, the channel vectors , , are stronger and can be estimated more accurately.
Next we study the multi-user system shown in Fig. 3(a) where we focus on the minimum user rate as the performance metric to ensure a good balance between system throughput and user fairness. We use the optimal linear precoder from  in the digital domain that maximizes the minimum rate for any given IRS phase matrix. The users’ rates need to account for the rate loss due to channel training. Under the block-fading channel model with coherence time period of s, the net achievable rate of user is given as where . The channel estimation time needs to be selected optimally to ensure a reasonable quality of channel estimates while minimizing the rate loss due to channel training. In Fig. 5(a) we plot the net achievable minimum rate against for a conventional MISO system (No IRS) with active antennas at the BS serving users. We also plot the net minimum rates for IRS-assisted systems with a fewer number of active antennas at the BS. The value of for each is chosen to ensure that the IRS-assisted system performs as well as the conventional system that has active antennas. The result shows that the IRS-assisted MISO system with passive reflecting elements at the IRS and only active antennas at the BS can achieve the same performance as a conventional large MISO system with active antennas. The same performance can also be achieved with and antennas using and reflecting elements at the IRS respectively. Therefore, an IRS-assisted MISO system can perform as well as a conventional large MISO system with a reduced number of active antennas at the BS, making it an energy-efficient alternative to technologies like Massive MIMO and network densification.
Moreover, we observe that the net minimum rate is a unimodal function of . Specifically, s is optimal for all the considered IRS-assisted MISO systems, whereas the conventional system could perform as well with a much lower value of s, thereby showing that the performance of IRS-assisted systems is much more sensitive to the quality of channel estimates available. This can also be observed in Fig. 5(b), where we plot the net achievable minimum rate for the same systems against but under both perfect and imperfect CSI. The results for the imperfect CSI plotted for s match with those shown in Fig. 5(a). We also notice that under channel estimation errors, larger array sizes at the IRS are needed to achieve the same performance as the conventional MISO system with antennas. For example, under perfect CSI, an IRS-assisted system with antennas can achieve the same performance using only instead of reflecting elements. Moreover, as the value of increases the performance gap between perfect and imperfect CSI cases for the IRS-assisted system increases significantly since the number of channels to be estimated increases linearly in . Therefore, accurate CSI acquisition is a critical issue in IRS-assisted communication systems.
Vi Future Research Directions
As IRS-assisted wireless communication is a young-born paradigm that has attracted researchers’ attention just since last year, there exist a number of interesting research directions awaiting exploration. We summarize them as follows.
Vi-a Channel Modeling
Currently i.i.d. Rayleigh or Rician fading is considered to model the IRS-to-users channels whereas rank-one LoS channel is often considered between the BS and the IRS [8, 12, 9]. The former is not realistic given MIMO channels are known to be almost always correlated in practice whereas the latter constitutes a pinhole channel and limits the capability of the system to efficiently serve more than one user. It will be worth studying correlated channel models for the IRS-to-users links and high rank LoS channel for the BS-to-IRS link.
Extending the preliminary works by replacing the conventional i.i.d. Rayleigh model with a correlated Rayleigh model, would require a spatial correlation model for the IRS. The conventional statistical models for arrays of discrete antennas are not directly applicable, since IRS is realized using a completely different technology (reconfigurable meta-surfaces or reflect arrays). The correct modeling of the spatial correlation and channels that utilize the inherent correlation structure of the IRS, require significant attention from researchers who are conversant in both communication and electromagnetic theory.
Vi-B CSI Estimation for Large IRSs
In the current works, the channel sensing limitations of the IRS are ignored and perfect CSI is assumed to be available at the IRS to design its parameters. This paper proposed a channel estimation protocol where the channels through the IRS are estimated at the BS by training all the IRS elements, one-by-one. This can yield a very large channel training overhead and require longer channel estimation time periods, when massive arrays are used to realize the IRS.
Alternate channel estimation protocols need to be developed that do not require explicit channel estimation with respect to all the IRS elements. One way to do this is to use beam training to select the IRS phase matrix from quantized codebooks. However the size of these codebooks will again depend on the size of the IRS. Developing low-overhead channel estimation algorithms for large IRSs remains an open problem.
Vi-C Distributed IRSs
Since the IRS is envisioned to be deployed within the LoS of the BS, the BS-to-IRS channel will most likely face the rank deficiency problem. One way to guarantee high rank channels is to utilize distributed IRSs between the BS and the users. Each user will experience a channel that is generated as the sum of as many rank-one channels as the number of IRSs in the system. There is no current work that deals with the use of multiple IRSs, but this would open several research directions, including finding the optimal positions of the IRSs, jointly designing the parameters of all the IRSs and so on.
Vi-D IRS-Assisted Vehicular Communication
With increasing focus on high mobility communication scenarios, it is important to look into the incorporation of IRSs into vehicular communication systems, where the IRSs can not only improve the coverage area of the underlying cellular network but also help in avoiding signal deterioration and outages when the users move into signal blockage areas. However, these systems entail that the BS attains the CSI and the IRS adapts the induced phases at the pace of the highly time-varying channels. The study of IRS-assisted vehicular communication systems would also require the development of relevant vehicular propagation and channel models.
In this paper, IRS-assisted multi-user MISO communication is envisioned to be an important energy-efficient paradigm for beyond 5G networks, achieving Massive MIMO like gains with a much lower number of active antennas at the BS. The passive reflecting elements of the IRS smartly re-configure the signal propagation in the environment by introducing phase shifts onto the impinging electromagnetic waves. This paper introduced the communication-theoretic model for the design and study of an IRS-assisted MISO communication system and outlined an MMSE based channel estimation protocol. The performance evaluation results confirmed the superior performance of the proposed system over conventional MISO systems, in terms of both coverage and user rates. However, the performance gains were shown to be highly sensitive to the quality of the channel estimates available.
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