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Making Intelligent Reflecting Surfaces MoreIntelligent: A Roadmap Through Reservoir

ComputingZhou Zhou, Kangjun Bai, Nima Mohammadi, Yang Yi, and Lingjia Liu

Abstract—This article introduces a neural network-based signal processing framework for intelligent reflectingsurface (IRS) aided wireless communications systems. Bymodeling radio-frequency (RF) impairments inside the“meta-atoms” of IRS (including nonlinearity and memoryeffects), we present an approach that generalizes the entireIRS-aided system as a reservoir computing (RC) system,an efficient recurrent neural network (RNN) operating ina state near the “edge of chaos”. This framework enablesus to take advantage of the nonlinearity of this “fabri-cated” wireless environment to overcome link degradationdue to model mismatch. Accordingly, the randomness ofthe wireless channel and RF imperfections are naturallyembedded into the RC framework, enabling the internalRC dynamics lying on the edge of chaos. Furthermore,several practical issues, such as channel state informationacquisition, passive beamforming design, and physicallayer reference signal design, are discussed.

Index Terms—Machine learning, Intelligent ReflectingSurface, Reservoir Computing, Memory Effects

I. INTRODUCTION

With the unfolding of the 5th generation cel-lular systems (5G), beyond 5G (B5G) and 6Gtechnologies are rapidly becoming new buzzwordsin telecommunication academia and industry. Thewireless market analyses suggest that we are ex-pected to witness the demand for trillions of wire-less connections and equipment energized by thesurge of affordable and low-energy devices [1]. Thisunprecedented number, however, poses complica-tions and challenges to the cellular communicationssystems design. Intelligent reflecting surface (IRS)assisted wireless networks are deemed as promisingsolutions [2]–[5], where IRSs are utilized to config-ure a more “favorable” wireless channel betweenaccess points (APs) and mobile stations (MSs).

The authors are with the Bradley Department of Electrical andComputer Engineering, Virginia Tech, Blacksburg, VA, USA. Thecorresponding author is L. Liu (ljliu@ieee.org).

IRS controls each reflecting unit (“meta-atoms”)towards an ideal direction to form a fine-grainedreflecting beam. Furthermore, IRS is primarily im-plemented by passive RF components, reducing thecost compared to massive MIMO/small-cell/relayaided systems that resort to active antenna units.Thereby, by adding these configurable IRS compo-nents to the wireless environment, an extra degreeof freedom (DoF) in the wireless environment canbe achieved [3]. By properly adjusting the reflectingcomponents on the IRS, the newly formed beam canconstructively enhance the desired signal or destruc-tively anneal interference power amid transmissionstreams. Overall, the introduction of IRS forges anew path for the realization of a programmableand intelligent channel environment, increasing thenetwork spectrum and energy efficiencies [5].

A. Main ChallengesAlthough IRS is deemed as a cost-efficient ap-

proach toward high system efficiency, continuinginnovations on hardware and software of IRS are yetimperative for the realization, where the followingcritical issues are emerged to be addressed:• Hardware Impairments: Current methods and

apparatus devised for IRS-aided cellular systemshave been developed with the premise of idealradio-frequency components as well as a sim-plistic mathematical modeling approach, such asthe element-wise phase-shift model [5]. However,the presence of memory effects and nonlinearityin hardware, particularly when the operation isconfigured on the entire frequency band, maylead to model mismatch which can deteriorate theperformance compared to the theoretical setup.

• Reflection Optimization: An ideal IRS-aided op-eration is achieved through jointly optimizing thereflection phase on IRS, a.k.a. passive beamform-ing, as well as the active beamforming/receiving

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on APs and MSs. However, the inherent practicalconstraints, such as the finite alphabet feature ofthe tunable phase dictionary, the duplex mode,and the asymmetric number of antennas config-ured on MSs and APs, make the problem vastlycomplicated. Furthermore, hardware implementa-tions on the meta-atoms, either electronically ormechanically, have shown potential bottleneckson achieving adequately fast phase shifting, inwhich the passive beamforming may lag behindthe variations on environment and user mobility.Needless to say, the problem space would rendera naıve exhaustive search intractable.

• Channel Acquisition: To accomplish the jointbeamforming/receiving design, we require multi-fold channel state information (CSI) which in-cludes links from AP to IRS, from IRS to MSs,from AP to MSs, and all the reversed links. Forindirect channels (links with IRS at one end), it ischallenging to obtain the CSI because IRS is de-ployed without transceiver chains, which makesthe reference signal on IRS unavailable to access.Meanwhile, IRS is often configured with a largeamount of “meta-surface” [6], which makes thechannel dimension and the overhead on the CSIestimation prohibitively high. More importantly,the online reference signals in wireless commu-nications systems are very limited due to trainingoverhead constraints defined in communicationstandards [1]. Besides, environment scatters arelocated within the Rayleigh distance of the IRS,which can fundamentally change the channelmodel due to spherical wavefront features.

B. State-of-the-Art

There are attempts in the literature to address theissues raised above:

1) Hardware Impairments: Recent work [7] ana-lyzes the channel capacity loss by hardware impair-ments. The analysis characterizes the imperfectnessof the meta-atoms on IRS as additive Gaussiannoise. It shows that both the system capacity and thederivative of the capacity with respect to the area ofmeta-surface decrease when the scale of reflectivecomponents increases. The research in [8] has in-vestigated that when the hardware impairments aremodeled as phase errors, the transmission can beequivalently treated as a point-to-point Nakagamifading channel. While these are seemingly reason-

able analytical results, they do not provide feasiblesolutions to the hardware impairments.

2) Reflection Optimization: Rather than usingactive RF components to harness spatial diversities(such as relay, and backscatter communications,etc.), IRS seeks to optimize spectral efficiency andat the same time to consume less energy. To addressthe aforementioned challenges raised by the discretephase values and large meta-atoms, [9] introduced aheuristic alternating optimization technique that re-laxes the discrete variables as continuous variables.Similarly, energy efficiency in terms of bit-per-Joule can be considered in the same optimizationframework. This method is infeasible in real-timeand does not explore the dynamics of user mobilitiesand channel environments. Another related workalso extended the optimization on the joint designof pilot patterns and network utilities. Nonetheless,they typically rely on unrealistic assumptions onperfect channel knowledge, synchronous controls,and unlimited user feedback.

3) Channel Estimation: Explicit channel stateinformation is considered an essential component ofthe reflection optimization in IRS systems. Due tolimited RF chains on the reflective surface, the up-link and downlink reciprocity has been widely lever-aged in the channel estimation. In [10], it introducedusing compressed sensing and deep learning-basedapproaches to infer the entire channel by using onlya relatively small number of accessible active RFcomponents on the IRS, where the sparsity/low-rankproperties of the channel are leveraged. However,when receiving RF chains are not installed at theIRS, this method becomes infeasible. A viable wayto solve this challenge is to use implicit chan-nel information instead. [11] introduced learning abeamforming vector via adding a feedback channelin the IRS system. However, the feedback overheadbecomes prohibitively high as the number of meta-atoms increases.

C. Our Contributions

The contribution of this paper is the following:• Unlike the existing formulation of IRS, we con-

sider modeling both the nonlinearity and mem-ory effects of each IRS component, mimickingpractical RF circuits behave, where the memoryeffects are generally not identified and widelyoverlooked in the current literature.

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IRS

IRS Controller

AP

MS

MS

Scatters

Meta-Atom

Fig. 1. An illustration of an IRS-aided wireless system: multipleMSs, one IRS, and one AP.

• By leveraging the similarity between hardwareuncertainties of IRS systems and chaotic featuresof reservoir computing (RC) systems, we gener-alize an entire IRS-aided system as an RC. Thisapproach does not rely on explicitly modelingthe hardware impairments, whereas it could cir-cumvent the model mismatch by universal ap-proximation properties of the RC. This designoffers a promising direction on bridging artificialintelligence (AI) and wireless systems.

• We point out some of practical issues in theimplementation of this RC based framework andfurther investigate possible solutions such as ref-erence signal design and training algorithms.

The remainder of this paper is organized as follows.In Sec. II, we review the formulation and hardwareimpairments of IRS systems. In Sec. III, we intro-duce the RC framework and its mapping to IRS.The practical issues of applying this technique arediscussed in Sec. IV. Finally, the paper is concludedin Sec. V.

II. SYSTEM FORMULATION AND HARDWAREMODEL

We first consider an ideal model of IRS-aidedwireless communications systems where multiplemobile stations (MSs) simultaneously communicatewith one access point (AP) associated with a singleIRS as depicted in Fig. 1. The IRS is equippedwith passive reflecting units, namely, ”meta-atoms”.The entire wireless transmission channel can be

conceptually partitioned into three parts (in uplink):a forward channel from MSs to IRS, a reflectingchannel from IRS to AP, and a direct channel fromMSs to AP. A zero gain of the direct channelindicates a transmission blockage. The downlinkchannel also follows in a similar naming approach.

A. Conventional IRS FormulationAccording to the standard definition of IRS, the

incoming electromagnetic waves are reflected in thedesired direction by using predefined phase-shifts.The conventional embodiment of IRS is constructedby massive meta-atoms, each of which is enabledwith software-controllable properties on configuringthe reflecting direction. The entire formed meta-surface passively forwards RF signals with mod-ified amplitude and phase, in which the opera-tion is fundamentally different from the concept ofamplify-and-forward relay which requires active RFchains [3]. The reconfigurability is either achievedelectronically, by means of positive-intrinsic nega-tive (PIN) diodes or field-effect transistors (FETs),or mechanically via microelectromechanical system(MEMS) switches.

Conventionally, each meta-atom is assumed tobe capable of changing the amplitude and phaseof the incident signal and constructing a reflectiontowards a new direction independently. In otherwords, no signal-coupling effects between IRS unitsare assumed. A math formulation of this perfectreflection is via a diagonal matrix. Each diagonalentry represents the imposed amplitude and phasechange to the incident signal contributed by the cor-responding meta-atom. Optimizing these entries canbring an improved ‘augmented’ channel betweenMSs and AP. However, this formulation, governedby the ideal physical characteristics of the meta-surface can lead to model misspecification issues aswe pointed out in the introduction.

B. Hardware Nonlinearity in IRSOverall, an IRS is composed of layered materials,

generally three layers, as demonstrated in Fig. 2.The outer layer is made of an array of reflect-ing elements printed on a dielectric substrate, inwhich the reflecting elements can interact with RFsignals. This would provide desired amplitude andphase shifts to incident signals based on the devicecharacteristics, including the geometrical alignment

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Fig. 2. A realization of an IRS made of a control circuit, a copperplate and an array of reconfigurable reflecting elements.

between reflecting elements. The intermediate layeris built of a copper plate to avoid energy leakagefrom incident signals. Lastly, the inner layer isa control circuit to calibrate reflecting elementsin real-time based on the desired amplitude andphase. An ideal IRS implementation is considered aswith this reconfigurability without nonlinearity andmemory effects. However, in practice, the memoryeffect is inherently subsistent to devices due tothe charge accumulation along with the reactive-ionetching during the fabrication process.

Passive devices could satisfy the necessity of re-configurability as required by the IRS. The second-order resistor and capacitor (Res-Cap) model is asimple implementation approach where a digitally-controlled resistor with two adjacent capacitorsare employed. By controlling the model’s resis-tance state, the resistor can be switched betweenits high-resistance-state (HRS) and Low-resistance-state (LRS). Eventually, energy from RF signals isdissipated according to the resistance state, and thus,controlling the reflection amplitude. Furthermore,various phase shifts of the reflecting elements canbe realized independently as different time constantsare achieved based on the resistance state.

In recent years, the Ferroelectric Field-EffectTransistor (FeFET) [12] and the Resistive Random-Access Memory (ReRAM) [13] have been intro-duced in neuromorphic applications as two emerg-ing building blocks for emulating artificial neuralnetworks. This makes these emerging devices pos-sible candidates for implementation of IRS, dueto their intrinsic reconfigurability. The FeFET, adescendant of the MOSFET, consists of a ferroelec-tric layer in between its electrode and conductionregion. The ferroelectric thin film could remember

Input Nodes

States Nodes

Output Nodes

Output LayerStates Trans.

Input Layer

Inpu

ts

Reservoirs

Out

puts

x(t)

Fig. 3. A realization of reservoir computing - echo state network: theinput is first mapped to a high dimensional space to create reservoirstates, then the output is obtained through a readout mapping.

the electric field to which it had been exposed,switching the capacitance of the device from high tolow, or vice versa. By controlling the biasing signalacross the device, different amplitude and phasechanges can be achieved as the energy dissipatedin the device is controllable. Similar to the classicalRes-Cap model, the ReRAM is a controllable resis-tor through its conductive filaments. By altering thebiasing signal across the device, various resistancestates can be achieved, and thus, realizing differentamplitude and phase changes.

In practice, the ideal linearity assumption of re-flecting units cannot be satisfied due to the inherentproperties thereof. We can extend our previous for-mulation by including a time-dependent state equa-tion, where the current state would be determinedby the previous state as well as the current incidentsignal, and the state transitions are according to anonlinear function. This new formulation leads to amodeling scheme that accounts for both nonlinearityand the memory effects.

III. RESERVOIR COMPUTING-BASEDREFORMULATION

In this section, we begin by briefly introducingthe architecture of RC. Then, we discuss how RCis analogous to IRS systems. Finally, we elaborateon how the main challenges (pointed out in theintroduction) are accordingly addressed.

A. PreliminaryRC is a computational framework motivated by

RNN mechanism which consists of three parts:an input mapping, a fixed dynamic system, and atrained readout network. A realization of RC, echostate network (ESN) [14], is illustrated in Fig. 3.The constitutive modules of an ESN are as follows:

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1) Input Mapping: The ESN input is first pro-jected to a higher dimensional space by multi-plying to a weight matrix that is initialized withrandom values. Mapping the input signal into ahigh-dimensional space is useful for pattern analysiswhich is a shared concept of kernel-based methods.

2) Reservoir Dynamics: The underlying reser-voir dynamics are characterized by a recurrent equa-tion. The equation basically describes a Markovprocess of the internal states stimulated by the input.In addition, an activation function is added betweentwo consecutive internal states to offer nonlinear-ity. Furthermore, the internal state transition matrixstays fixed during the training stage. In practice,improperly initialized internal weights often lead todiminishing generalization performance. To circum-vent this issue, certain algebraic properties of thetransition matrix has to been satisfied, such as echostate property (ESP) which states that given an inputsequence, the output should not differ far from twodifferent initial states, that is, the effect of initialconditions should vanish as time proceeds.

3) Learning Readout: Given the states of reser-voir, the output is obtained via a dimension reduc-tion process on a subset of the reservoir states. Thecoefficients of the readout mapping are determinedvia minimizing a predefined loss function, where theloss measures the dissimilarity between targets andpredicted outputs. The optimization on the loss canbe either solved using gradient descent or throughthe least-squared framework when Frobenius normis selected as the loss function.

B. Reformulation

Now, we consider how the IRS-aided wirelesssystem can be treated as an RC system, specificallyas an end-to-end RC-based auto-encoder. We analo-gize the signals sent out from all active stations (APsor MSs) to the IRS as the input of the RC; thereby,the IRS serves as the reservoir. Accordingly, thereadout layer is considered as a three-layered feed-forward neural network with identity activationfunctions, which is comprised by IRS coefficients,reflection channel, and receiving processing matri-ces for the uplink or precoding matrix for the down-link at AP. The link between active stations and IRSis considered as the input layer of the RC. A similaridea of analogizing wireless communication systemsto neural networks can be found in [15], where IRSs

are modeled as feed-forward neural networks. How-ever, the formulation is not sufficient to capture theinherent dynamics (by hardware memory effects)of IRS. Accordingly, we optimize a loss functionthat measures the link-level transmission reliabilityor efficiency using the passive beamforming matrix,active receiving and precoding matrices as variables.Technically, the loss function is defined as a distancebetween the received signal and the desired signalusing training dataset.

C. Remarks

Regarding the challenges enumerated in the in-troduction, the introduced RC-based approach hasthe potential to address them, as elaborated below:

1) Hardware Impairments: The hardware im-pairments are solved since the nonlinearity andmemory effects are circumvented by altering thedistortion as needed nonlinear internal state tran-sitions of RC, where chaotic internal states cancreate rich representations of the input. On theother hand, deploying more meta-atoms on the IRSis equivalent to using higher-dimensional internalstates which can reduce the learning loss value,however, increases the risks on overfitting.

2) Passive Beamforming: The optimization pro-cedure on the phase-shift and amplitude adjustmentis naturally considered as learning one of the outputlayers of RC. Meanwhile, the receiving processingmatrix is considered as the final output layer of theRC, whereas the active precoding matrix is treatedas the first layer of the RC in downlink transmission.Since the memory ability is enabled by RC, thelearning can essentially capture the underlying longterm features of the channel environment. Thus,the learned beamformer is to act in a proactivemanner to handle the interference by leveraging thehistorical data, which can potentially solve the lageffects brought by the computation.

3) Channel Acquisition: In the joint optimizationon the uplink passive and active beamforming,the CSI from MSs to IRS is no longer needed.This is because it is treated as the input layerof RC, which does not require to be known inthe framework of RC. Conversely, the downlinkactive precoding and passive beamforming canbe obtained by using channel reciprocity. Moreimportantly, the channel environment betweenAP and IRS is relatively static, where this static

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Fig. 4. Energy Efficiency evaluation of (a) a model-based optimiza-tion approach, and (b) RC based learning approach in an IRS systemwhich is properly trained.

property can be further leveraged to reduce thetraining overhead. Therefore, the reference signalresources for CSI acquisition would be significantlyreduced compared to conventional approaches.

A comparison between RC-based IRS and themethod introduced in [3] (referred as a model-basedapproach) is presented in Fig. 4. For simplicity,the evaluation scenario is configured with one MS,one IRS and one AP. In our analysis, the hardwareimpairments are equivalently characterized aschannel estimation errors and power dissipationat IRS, where the CSI is utilized by model-basedapproach for passive beamforming design, andpower dissipation leads to additive interference onthe transmission link. Remark that more meta-atomscan lead to stronger interference though it poten-tially offers higher beamforming gain. The RC-based approach demonstrates advantages over theconventional one in terms of energy efficiency (EE),which can be attributed to its ability to overcomemodel mismatch by leveraging training dataset.

IV. DISCUSSION

The RC framework is envisioned as an efficient(in terms of spectrum and energy) and effective(in terms of handling hardware impairments) sig-nal processing framework for passive and activebeamforming/receiving design of the IRS systemthanks to the chaotic and high dimensional featuresof the reservoir. In this section, we discuss relatedpractical issues of using this framework. There aretwo prerequisites for conducting the learning forthe RC: 1) the reference signals for adjusting link-level demodulation, namely, training dataset; and2) the CSI from IRS to AP and from MSs to APfor formulating the learning loss function. To thisend, we can directly leverage the reference signalstructure defined in 5G New Radio (NR) standards.For instance, the reference signals are comprisedof demodulation reference signals (DMRS) and thechannel state information reference signals (CSRS).Accordingly, DMRS can be utilized as the trainingdataset, whereas CSRS can be applied to track theCSI. Since the channel environment from IRS toAP is relatively static, the CSI of IRS-AP can beinitialized by a channel sounding process at the verybeginning of the IRS deployment.

In an attempt to track environmental changesbetween IRS and AP, we introduce a channel ac-quisition method based on the uplink-downlink reci-procity. Remark that only AP and MS can send thereference signals due to the availability of active RFchains. To facilitate the estimation, we assume thatfull-duplex transmission is enabled at AP. In thismethod, AP sends CSRS to IRS before receivingthe reference signals reflected back by the IRS.Since the received reference signals contain theback and forth channel information between APand IRS, the channel variation can be accordinglytracked by learning common features of the rowspace and column space of the received referencesignals. In addition, we can incorporate a round-robin scheme into this method by estimating thechannel variations of a subset of the IRS units ateach turn. Accordingly, the entire CSI of the AP-IRSis attained after all the meta-atoms are traversed.

Furthermore, the RC-based framework can be ex-tended to other chaotic neural networks based learn-ing paradigms, such as extreme learning machines.However, structurally and operationally, there is aclear agreement between IRS and RC-based net-

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works that is absent for other neural networks suchas LSTM. In addition, LSTM is very challengingto train, whereas RC is known to achieve bettergeneralization performance compared to other NNsusing extremely limited training dataset [14], wherethe limitation on the training data is one of thefundamental challenges raised in the introduction.The RC characterized IRS also can be incorporatedas a policy network in a reinforcement learning(RL) framework. Accordingly, the objective be-comes maximizing the cumulative reward of theunderlying policy with passive and active beam-forming as the actions. In general, this RL enabledapproach is more robust in dynamic settings - whereit operates the passive and active beamforming in aproactive way.

V. CONCLUSION

In this article, we provided a roadmap for theapplication of RC-based processing techniques inthe design of IRS-aided wireless systems. We drewparallels between reservoir computing and the IRStransmission link, and introduced an ideal mappingthereof. We also pointed out an equivalence betweenlearning readout layers of RC and designing passivebeamforming as well as active receiving.

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