Hybrid Beamforming for Terahertz Wireless Communications: Challenges, Architectures, and Open Problems
11 Hybrid Beamforming for Terahertz WirelessCommunications: Challenges, Architectures, andOpen Problems
Chong Han,
Member, IEEE , Longfei Yan, and Jinhong Yuan,
Fellow, IEEE
Abstract —Terahertz (THz) communications are regarded as apillar technology for the sixth generation (6G) wireless systems,by offering multi-ten-GHz bandwidth. To overcome the shorttransmission distance and huge propagation loss, ultra-massive(UM) MIMO systems that employ sub-millimeter wavelengthantennas array are proposed to enable an enticingly high arraygain. In the UM-MIMO systems, hybrid beamforming stands outfor its great potential in promisingly high data rate and reducedpower consumption. In this paper, challenges and features ofthe THz hybrid beamforming design are investigated, in lightof the distinctive THz peculiarities. Specifically, we demonstratethat the spatial degree-of-freedom (SDoF) is less than 5, whichis caused by the extreme sparsity of the THz channel. Theblockage problem caused by the huge reflection and scatteringlosses, as high as 15 dB or over, is studied. Moreover, weanalyze the challenges led by the array containing 1024 ormore antennas, including the requirement for intelligent subarrayarchitecture, strict energy efficiency, and propagation characteri-zation based on spherical-wave propagation mechanisms. Owningup to hundreds of GHz bandwidth, beam squint effect couldcause over 5 dB array gain loss, when the fractional bandwidthexceeds 10%. Inspired by these facts, three novel THz-specific hy-brid beamforming architectures are presented, including widely-spaced multi-subarray, dynamic array-of-subarrays, and true-time-delay-based architectures. We also demonstrate the potentialdata rate, power consumption, and array gain capabilities forTHz communications. As a roadmap of THz hybrid beamformingdesign, multiple open problems and potential research directionsare elaborated.
I. I
NTRODUCTION W ITH the commercialization and global deployment ofthe fifth generation (5G) wireless communications,increasing research attention and efforts are migrating todevelopment of sixth generation (6G) wireless communica-tions. As an important key performance indicator for 6G, thepeak data rate is expected to reach 1 Tbps [1]. Althoughthe trend of exploring higher frequency spectrum is clear,it is still difficult for millimeter wave (mmWave) systems tosupport Tbps data rate, due to the limited consecutive availablebandwidth up to several GHz. Lying between the mmWave andinfrared spectrum, the Terahertz (THz) band spans over 0.1-10 THz, which owns several tens of GHz consecutive available
Chong Han and Longfei Yan are with the Terahertz Wireless Commu-nications (TWC) laboratory, University of Michigan-Shanghai Jiao TongUniversity Joint Institute, Shanghai Jiao Tong University, Shanghai 200240,China (e-mail: [email protected]; [email protected]).Jinhong Yuan is with the School of Electrical Engineering and Telecom-munications, University of New South Wales, Sydney, NSW 2052, Australia(e-mail: [email protected]). bandwidth and is envisioned as an enabling technology for 6Gwireless systems [2].However, the THz band suffers from huge propagation lossdue to the small effective area of the THz antenna, whichis proportional to the square of the wavelength [3]. Thehuge propagation loss significantly limits the wireless com-munication distance. Fortunately, due to the sub-millimeterwavelength, ultra-massive antennas can be arranged, e.g., 1024antennas, to realize THz ultra-massive multi-input multi-output(UM-MIMO) systems [1], [4], which can steer a narrowbeamand generate a high array gain to address the distance con-straint.In terms of beamforming architectures, the fully-digitaland analog are two conventional selections. On one hand, inthe fully-digital architecture, each antenna owns a dedicatedRF chain and DAC/ADC, which are power-hungry [5], [6].Since the number of antennas can be prohibitively high inthe THz UM-MIMO systems, hardware complexity and powerconsumption of the fully-digital beamforming architecture areunbearable for practical use [7], [8]. On the other hand, onlyone RF chain and DAC/ADC are used to control all antennasthrough phase shifters in the analog beamforming architecture.While the power consumption and hardware complexity aresubstantially reduced, the analog beamforming architecturecan only support one data stream, which strictly limits thedata rate and the number of users. As a combination of thesetwo architectures, hybrid beamforming is proposed. With alimited number of RF chains and DAC/ADCs, the hybridbeamforming can achieve comparable data rate with fully-digital architecture, while with reduced hardware complexityand power consumption. Consequently, the hybrid beamform-ing has been treated as an appealing technology in THz UM-MIMO systems [5]. Although the hybrid beamforming tech-nologies have been investigated extensively for the microwaveand mmWave frequencies [6], [9]–[11], the peculiarities of theTHz UM-MIMO systems bring many new challenges for thedesign of THz hybrid beamforming [5], [7], [12].In this paper, we first analyze the distinctive features andchallenges of the THz hybrid beamforming. Specifically, weshow that the spatial degree-of-freedom (SDoF) can be lessthan 5, which is caused by the extreme sparsity of the THzchannel as a result of blockage and huge reflection andscattering losses, e.g., larger than 15 dB. Moreover, we analyzethe challenges led by the array containing as many as 1024 ormore antennas, including the demand for intelligent subarrayarchitecture, strict energy efficiency, and propagation charac- a r X i v : . [ c s . I T ] J a n terization based on spherical-wave propagation mechanisms.We illustrate that owning up to hundreds of GHz bandwidth,beam squint effect could cause over 5 dB array gain loss, whenthe fractional bandwidth exceeds 10%. Then, we survey twotraditional hybrid beamforming architectures and reveal theirlimitations. In light of the challenges and being motivated bythe constraints of existing approaches, we investigate threeinteresting THz-specific hybrid beamforming architectures.Furthermore, typical results are presented to illustrate thedata rate, power consumption, and array gain performance ofthese hybrid beamforming designs in the THz band. Last butnot least, multiple open problems and research directions arediscussed for 6G THz hybrid beamforming design.II. C HALLENGES OF TH Z H YBRID B EAMFORMING
In this section, the challenges and unique features of theTHz hybrid beamforming from the channel and UM-MIMOsystems perspectives are elaborated.
A. Challenges from THz Channel Perspectives1)
Channel sparsity and low SDoF : Owing to the sub-millimeter wavelength, the THz band suffers huge scatter-ing and diffraction losses, compared to the microwave andmmWave frequencies. Therefore, the THz channel is usuallycomposed by a line-of-sight (LoS) path and a few reflectionpaths [3]. The number of multipath is very limited, e.g.,typically less than 5, and the THz channel is much sparserthan the microwave and mmWave channels [5]. Since theSDoF is upper-bounded by the number of multipath, the smallSDoF restricts the spatial multiplexing gain of the THz UM-MIMO systems. Even with a high array gain generated byultra-massive antennas, the poor multiplexing gain still signif-icantly limits the potential of the THz UM-MIMO systems,particularly the data rate. Blockage problem : As aforementioned, the THz channelis composed by a LoS path and several reflection paths. Due tothe huge reflection loss, the LoS path is significantly strongerthan the reflection paths, e.g., more than 15 dB [3]. Theresulting LoS dominance makes the THz wireless links veryvulnerable to blockage. Compared to the mmWave frequen-cies, on one hand, the reflection paths of the THz channel aremuch weaker. On the other hand, the data rate requirement ofthe THz systems is usually much higher than the mmWavesystems. In light of these, when the LoS path is blocked, theremaining reflection paths might be too weak to support highdata rates and the THz link faces a more severe blockageproblem than the mmWave link.
B. Challenges from THz UM-MIMO Systems Perspectives1)
Large-scale antenna array : Since the use of hugenumber of antennas in THz UM-MIMO systems, i.e., morethan 1024 antennas, the power consumption becomes a non-negligible problem. On one hand, due to the high frequencyof the THz band, the power consumption of the individualhardware device is ultra-high, e.g., power amplifier and phaseshifter consume 60 mW and 42 mW, respectively [8]. On the other hand, ultra-massive antennas in the THz UM-MIMOsystems result in the use of a large quantity of devices. Asa result of these two reasons, the THz UM-MIMO systemssuffer prohibitively high power consumption, e.g., several tensof watts [8]. Hence, the reduction of power consumptionis critical to the THz hybrid beamforming design, whileachieving high data rates. Beam squint effect : Note that the fractional band-width is defined as the ratio between the bandwidth andthe central frequency. In traditional microwave frequencies,due to the scarcity of the spectrum resource, the fractionalbandwidth is usually very small, e.g., 20 MHz/2.4 GHz=0.83%at 2.4 GHz. While for mmWave and THz bands, especiallythe THz band, the fractional bandwidth is much larger,e.g., 50 GHz/300 GHz=16.7% at 300 GHz, which causesa severe beam squint problem in THz hybrid beamformingarchitectures. During the beamforming process, the signalson antennas need phase shifts to be concentrated, which arerelated to the carrier frequency. However, most of the existinghybrid beamforming architectures are based on the phaseshifter, which is a frequency-independent device and tunesthe same phase shift for signals with different frequencies.The phase shifter can only tune the “correct” phase shift forone frequency point, while for other frequencies, there is aphase error of the signals [12]. As a result, the generatedbeams are squint and the array gains are reduced, which isthe so-called beam squint problem. In traditional narrowbandhybrid beamforming architecture with limited fractional band-width, the performance degradation caused by the beam squintproblem is acceptable. However, for THz hybrid beamformingarchitectures with large fractional bandwidth, the beam squintproblem can reduce the array gain significantly, e.g., by 5 dB,and needs to be treated seriously [12]. Spherical-wave propagation : Most existing studiesabout MIMO systems assume the planar-wave propagation,which is an approximation and simplification of the spherical-wave propagation. The planar-wave assumption is accuratewhen the communication distance is longer than the Rayleighdistance of the antenna array, i.e., the border between the ra-diating near-field and far-field of the array [13]. The Rayleighdistance equals to the square of the array size divided byhalf of wavelength. For microwave and mmWave systems,this assumption is reasonable since the Rayleigh distanceis pretty short. For instance, considering the array size as0.1m, the Rayleigh distance is only 0.4m and 4m when thefrequencies are 6 GHz and 60 GHz. However, when thefrequency comes to the THz band, e.g., 1 THz, the Rayleighdistance grows to 67m. Hence, the communication distancemight be smaller than the Rayleigh distance in the THz bandand the planar-wave assumption is invalid. Instead, in the THzUM-MIMO channels, the spherical-wave propagation needs tobe considered, which brings additional difficulties in channelmodeling and estimation design and further influences thehybrid beamforming.
III. T
RADITIONAL H YBRID B EAMFORMING A RCHITECTURES AND L IMITATIONS
We first introduce the traditional hybrid beamforming archi-tectures and algorithms in the literature [6], [9]–[11]. Then,by considering the THz-specific challenges, we analyze thelimitations of these architectures if being implemented in THzUM-MIMO systems.
A. Existing Hybrid Beamforming Architectures and Algo-rithms
Among hybrid beamforming architectures, the fully-connected (FC) architecture has been investigated exten-sively [6]. In the FC architecture, each RF chain controls allantennas through phase shifters. The number of phase shiftersequals to the product of the number of antennas and thenumber of RF chains. However, owing to the use of extensivephase shifters, hardware complexity as well as the powerconsumption of FC architecture are still unacceptably highfor practical implementation. To tackle this issue, the array-of-subarrays (AoSA) architecture is desirable [10], in whicheach RF chain connects to only a subset of antennas, i.e.,a subarray, through phase shifters. The resulting number ofphase shifters equals to the number of antennas. To this end,hardware complexity and power consumption of the AoSAarchitecture are substantially lower than the FC architecture.
Hybrid beamforming algorithm design : Most of the ex-isting design target of hybrid beamforming architectures isto maximize the data rate, which is realized by solving theanalog and digital beamforming matrices. For FC architecture,a two-step hybrid beamforming algorithm [9] can be exploitedto maximize the data rate, by decoupling the optimization ofthe analog and digital beamforming matrices. For AoSA ar-chitecture, a successive-interference-cancellation (SIC) basedalgorithm [10] is proposed to decompose the non-convex datarate maximization problem into multiple tractable problems.Alternatively, to make the hybrid beamforming problem moretractable, an efficient approach is to transfer the maximizationobjective of the data rate to the minimization of the Euclideandistance between the fully-digital beamforming matrix and thehybrid beamforming matrix [6]. Through this transformation,the hybrid beamforming design problem can be simplifiedsubstantially. An orthogonal matching pursuit (OMP) algo-rithm is attractive to solve the Euclidean distance minimizationproblem. To further reduce the complexity, various alternatingoptimization algorithms are proposed for the FC and AoSAarchitectures [6], [11], which solve the analog and digitalbeamforming matrices alternatively.
B. Limitations and Remaining Problems
As discussed before, the number of phase shifters in FCarchitecture equals to the product of the number of antennasand RF chains. By contrast, the AoSA architecture owns alimited number of phase shifters, i.e., equals to the number ofantennas. Due to the exhaustive connection between the RFchains and antennas, the FC architecture can support a similardata rate to that of the optimal fully-digital beamforming architecture [6]. On the contrary, the data rate of the AoSAarchitecture is substantially compromised compared to the FCarchitecture, due to the partial connection between antennasand RF chains.The FC and AoSA architectures can be considered as twoextreme architectures for hybrid beamforming. The FC archi-tecture owns a high data rate, while the power consumptionand hardware complexity are high [7], [8]. By contrast, theAoSA architecture owns low power consumption and hardwarecomplexity, while sacrificing the data rate performance [10].As studied in Sec. II-B, a balance of power consumption anddata rate is critical for hybrid beamforming architecture in theTHz band, which can not be achieved in the FC and AoSAarchitectures. Additionally, the low SDoF limitation has notbeen addressed in the FC and AoSA architectures. Employingthese two architectures, the spatial multiplexing gain is stillupper-bounded by the low SDoF, which further limits thedata rate. Moreover, these two architectures are based onphase shifter, where the beam squint problem remains as acritical issue to be addressed, as it could reduce received powerand communication distance. These limitations and remainingproblems require careful design of novel THz-specific hybridbeamforming architectures, in order to bridge the gap betweenthe theory and practical systems.IV. TH Z - SPECIFIC H YBRID B EAMFORMING A RCHITECTURES
In this section, we first introduce a novel widely-spacedmulti-subarray (WSMS) hybrid beamforming architecturewhich can overcome the low SDoF limitation in the THzUM-MIMO systems. Second, we analyze a dynamic array-of-subarrays (DAoSA) hybrid beamforming architecture tobalance the power consumption and data rate. Third, westudy a true-time-delay-based (TTD-based) hybrid beamform-ing architecture, which has the potential to overcome thebeam squint effect for THz communications with ultra-broadbandwidth.
A. THz WSMS Hybrid Beamforming Architecture
In THz UM-MIMO systems, multiple antennas can be usedto explore the multiplexing gain that further enhances the datarate, in addition to beamforming. Most of the studies on the FCand AoSA architectures assume that the antennas are separatedby half of the wavelength, i.e., the antennas are critically-spaced [6], [9]–[11]. With this critically-spaced antenna array,the spatial multiplexing gain is obtained from multipath of thechannel, which is referred as inter-path multiplexing [13]. Asanalyzed in Sec. II-A, due to the channel sparsity, the numberof multipath in the THz channel is restricted, which results ina limited inter-path multiplexing gain and suppresses the datarate.To further enhance the multiplexing gain, the WSMS hybridbeamforming architecture is promising by exploiting intra-path multiplexing for THz UM-MIMO systems, as depictedin Fig. 1 [13]. The antennas array are composed of multiplesubarrays. In each subarray, the antenna spacing is half of thewavelength, which is critically-spaced as in the existing FC
Fig. 1: The THz WSMS hybrid beamforming architecture. and AoSA architectures. By contrast, the subarrays are sepa-rated over hundreds of wavelength, i.e., widely-spaced, whichreduces the correlation between the subarrays. Interestingly,it has been analyzed that by setting the subarrays widely-spaced, the spherical-wave propagation needs to be consideredfor UM-MIMO channel modeling [13]. As a result, onepropagation path between the transmitted and received arrayscan be decomposed into multiple sub-paths at the subarraylevel with distinct phases, which enhance the SDoF and leadto the additional intra-path multiplexing gain. Compared tothe FC and AoSA architectures, the total multiplexing gainof the WSMS architecture is improved by a factor of thenumber of subarrays, by jointly utilizing the inter-path andintra-path multiplexing. Consequently, the data rate of theTHz WSMS hybrid beamforming architecture is significantlyimproved compared to the FC and AoSA architectures.
Algorithm design : In the WSMS architecture, since thesubarrays are widely-spaced, the RF chain connected withone subarray can not connect to other subarrays, which resultsin a block-diagonal analog beamforming matrix. This block-diagonal-structured constraint brings difficulties to solve theanalog and digital beamforming matrices. One method isleveraging the matrix decomposition idea to transfer thisblock-diagonal-structured problem into multiple FC hybridbeamforming problems, which can be solved by the existingFC hybrid beamforming algorithms.
Remarks : In the THz WSMS architecture, the widely-spaced subarrays are useful to overcome the low SDoF chal-lenge in the THz sparse channel. The overall multiplexing gainis improved by a factor of the number of subarrays, whichfurther improves the data rate significantly. However, due tothe trade-off between the multiplexing and beamforming, thegrowth of multiplexing gain reduces the array gain, whichinfluences the SNR as well as the data rate. Therefore, thenumber of widely-spaced subarrays needs to be carefullydesigned to strike a balance between the multiplexing andarray gains.
Fig. 2: The analog part of the THz DAoSA hybrid beamforming architecture.
B. THz DAoSA Hybrid Beamforming Architecture
We need to balance the power consumption and data rateof the THz hybrid beamforming architecture, inspired by thechallenge of large-scale antenna array in THz UM-MIMOsystems in Sec. II-B. To this end, novel hybrid beamformingarchitectures with flexible hardware connection are proposed,e.g., the overlapped architecture [7] and the DAoSA archi-tecture [8]. Specifically, the architecture of DAoSA hybridbeamforming is presented in Fig. 2. The antennas are dividedinto multiple subarrays. Switches are inserted between eachRF chain and each subarray. Through controlling the stateof the switch, i.e., open and closed, the connection betweenthe RF chains and the subarrays can be intelligently adjusted.Particularly, the FC architecture is a special case of DAoSAwith all switches closed. Conversely, the AoSA architectureis another special case of DAoSA, when each RF chainconnects to one closed switch. In the DAoSA design, the phaseshifters that are connected with open switch are non-active anddo not consume power. Therefore, by dynamically designingswitch connections, different levels of data rate and powerconsumption can be achieved, i.e., the power consumption anddata rate can be balanced.
Algorithm design : The algorithm design in the DAoSAarchitecture includes two parts, namely, the switch networkand beamforming matrices. The switch network can be in-telligently designed to maximize the energy efficiency or tominimize the consumed power while meeting the requireddata rate. The beamforming matrices are usually designed tomaximize the data rate. An alternating-selection method canalternatively calculate the switch network and beamformingmatrices [8]. For the switch network part, an original in-tractable integer problem is transferred to a tractable sequenceproblem. Considering the beamforming matrices, due to thedynamical connection of the DAoSA architecture, the openswitches force some entries in the analog beamforming matrixas zero. Since the state of the switches are adaptive, the posi-tions of the zero entries in the analog beamforming matrix areusually irregular, which makes solving the analog and digitalbeamforming matrices intractable. For this sake, an element-by-element (EBE) algorithm can be used to design the analogand digital beamforming matrices [8]. Particularly, the EBE
TABLE I: The wireless backhaul scenario is considered, in which a LoSpath and a ground-reflection path compose the multipath channel that can begenerated by the ray-tracing method [3].
Distance between Tx and Rx 100mHeight of Tx and Rx 30mNumber of antennas at TX and Rx 1024Central frequency 0.3 THzNumber of multipath 2algorithm calculates the analog beamforming matrix element-by-element to address the irregular-structure constraint.
Remarks : Through intelligently determining the connectionbetween subarrays and RF chains, the DAoSA architecture canbalance the power consumption and data rate well. However,there are still some open problems in the DAoSA architecture.First, the algorithm design suffers from high complexity, sinceit contains both switch network design and beamforming de-sign. One solution is using random matrix theory to determinethe state of the switch network matrix with low complexity.Another potential direction is developing a unified frame-work to solve these two problems jointly to further reducethe complexity. Second, the hardware complexity of DAoSAarchitecture needs to be reduced. As presented in Fig. 2,compared to the FC architecture, the DAoSA architecturehas many additional switches, which could put a burden onpractical implementation.
C. THz TTD-based Hybrid Beamforming
To solve the severe beam squint problem in the THz band,TTD-based hybrid beamforming is promising, where TTDis employed to substitute the phase shifter. As analyzed inSec. II-B, the beam squint problem arises from the fact thatthe required phase values in hybrid beamforming are relatedto the frequency, which is not achievable by the frequency-independent phase shifter. This problem is particularly severein wideband THz communications. Fortunately, the TTD isfrequency-dependent in its working band, i.e., the phase shiftadjusted by TTD is proportional to the carrier frequency andcan perfectly match the required phase shift of the widebandTHz hybrid beamforming architectures [12]. Since the TTD-based hybrid beamforming is indeed a universal solution, usingTTD to adjust the phase can mitigate the beam squint problemin all FC, AoSA, WSMS, and DAoSA architectures.
Algorithm design : A codebook-based algorithm to designthe TTD-based hybrid beamforming matrix is introducedin [12]. Based on the existing codebook-based algorithmsfor phase shifter, the proposed algorithm in [12] considersthe frequency-dependent property of the TTD and redesignsthe codebook. In general, the performance of the codebook-based algorithm relies on the size of the codebook. To achievesuperior performance, the codebook size is usually large,which results in a high complexity.
Remarks : By using infinite-resolution TTD to substitutethe phase shifter, the beam squint problem can be addressedperfectly without incurring array gain loss. However, theideal infinite-resolution TTD or high-resolution TTD are fairlypower-hungry and suffer a high hardware complexity [12].On the contrary, the energy-efficient low-resolution TTD is
Fig. 3: The data rate of the THz WSMS, FC and AoSA architectures. Thebandwidth is 5 GHz and the number of RF chains equals to 8. Two widely-spaced subarrays are arranged in the WSMS architecture. more suitable for practical systems. Note that the limitationof the resolution could cause a residual beam squint effect.The relationship between the resolution of TTD and the arraygain loss needs to be analyzed. Furthermore, low-complexitynon-codebook-based algorithms are still lacked for THz TTD-based hybrid beamforming.V. P
ERFORMANCE E VALUATION
We analyze the performance of the THz WSMS, DAoSA,TTD-based hybrid beamforming architectures in this section.The simulation parameters are given in TABLE I.As presented in Fig. 3, by equipping 2 widely-spacedsubarrays, the SDoF and multiplexing gain in the WSMSarchitecture are doubled, which results in an enhanced datarate compared to the FC and AoSA architectures. With 20 dBmtransmitted power, the data rate of the THz WSMS hybridbeamforming architecture is 40 Gbps and 60 Gbps higherthan those of the FC and AoSA counterparts, respectively, byaddressing the low SDoF problem.Moreover, we analyze the data rate and power consumptionof the DAoSA architecture in Fig. 4. In the DAoSA archi-tecture, with more closed switches, both the data rate andpower consumption grow. Particularly, when all 16 switchesare closed, the DAoSA becomes FC such that the data rate andpower consumption reach the maximum values. In the otherextreme case by closing 4 switches, the DAoSA is equivalentto AoSA, where the data rate reduces to the minimum value.Through intelligently controlling the switch network, i.e., thenumber of closed switches varies over [4 , , the data rate andpower consumption can be adjusted adaptively. Therefore, theTHz DAoSA architecture can strike a good balance betweenthe data rate and the power consumption.Next, we compare the array gain of the FC architecturebased on TTD and phase shifter, as illustrated in Fig. 5. Fordifferent carrier frequencies, the FC architecture that employsTTD to adjust the phase can attain a constant array gain. Bycontrast, while using phase shifter, the targeted array gainis reached only at the central frequency. As the frequency Fig. 4: The data rate and power consumption of the THz DAoSA architecture.The bandwidth is 5 GHz and the transmit power equals to 20 dBm. Thenumbers of RF chains and switches are 4 and 16.Fig. 5: The array gain of the TTD-based and phase shifter-based FC architec-ture. The bandwidth is 30 GHz. The number of subcarriers is 30. The steeringazimuth and elevation angles are ◦ and ◦ . deviates away from the central frequency, the array gainreduces with the deviation. In particular, the beam squintproblem causes an array gain loss as large as 5.49 dB.Consequently, the use of TTD is beneficial for widebandTHz hybrid beamforming design, to mitigate the beam squintproblem and guarantee a constant high array gain.VI. O PEN P ROBLEMS AND P OTENTIAL R ESEARCH D IRECTIONS
A. Hardware-efficient Design
As the frequency grows to the THz band, the hardware chal-lenges increase drastically. For instance, the high-resolutionphase shifter, TTD, and DAC/ADC are still difficult to pro-duce. Consequently, the THz hybrid beamforming architec-tures and algorithms by accounting for low-resolution phaseshifter, TTD, and DAC/ADC are urgently needed for practicalimplementation. Another potential research direction is tostudy lens array to realize the THz hybrid beamforming, in which an electromagnetic lens is adopted to focus the THzwave, and a matching antenna array is placed on the focalsurface of the lens. By employing the lens array, the phaseshifters or TTDs are not needed, which reduces the hardwarecomplexity substantially. However, extensive switches are re-quired to select beams from ultra-massive antennas, whichincreases the hardware complexity. Therefore, investigation onhardware-efficient lens array architectures and algorithms areneeded.
B. Influence of Imperfect Channel State Information
Since the number of antennas is extremely high, the THzUM-MIMO channel is a high-dimensional matrix, which in-creases difficulties to obtain perfect channel state information(CSI). Additionally, with ultra-sharp beam generated by THzUM-MIMO systems, the performance degradation broughtby imperfect CSI and beam misalignment is significant.Therefore, on one hand, super-resolution channel and angleestimation methods for THz hybrid beamforming architecturesneed to be developed. One potential solution is using subspace-tracking method to enhance the resolution of the off-gridMUSIC algorithm. On the other hand, the investigation of THzhybrid beamforming algorithms that are robust to imperfectCSI is needed. The probabilistic approach is one attractive ideato develop the robust THz hybrid beamforming algorithm [5].
C. Deep Learning Algorithms for Hybrid Beamforming
Although extensive hybrid beamforming algorithms havebeen investigated, their computational complexity is usuallyon the order of the number of antennas or even the squareof the number of antennas [6], [8]–[11]. For THz hybridbeamforming with ultra-massive antennas, e.g., 1024 antennas,the computational complexity is considerably high. Recently,deep learning (DL) methods have drawn much attention forsolving high-complexity physical communication and resourceallocation problems. In light of this, the authors in [14] proposeto use the deep reinforcement learning approach to solve thehybrid beamforming problem at mmWave frequencies. Whenapplying DL algorithms to THz hybrid beamforming, theunique features and challenges elaborated in Sec. II need tobe carefully considered.
D. Joint Active and Passive Beamforming
As analyzed in Sec. II-A, blockage is a severe constraintin THz communications. When the LoS path is blocked, theremaining paths might be too weak to support high data rateand the connection may even fall into outage. To address theblockage concern, joint active and passive beamforming thatemploys both UM-MIMO at the transmitter and receiver aswell as intelligent reflecting surface (IRS) in the propagationenvironment is an interesting direction to explore, particularlyfor THz communications [15]. The hybrid beamforming ar-chitecture performs active beamforming at the transmitter andreceiver to improve the strength of the signal and the datarate. Meanwhile, IRS composed by a large number of recon-figurable passive elements can provide passive beamforming, to adjust the phase of the incident signal and collaborativelychange the direction of the reflected signal. Through thepassive beamforming performed by IRS, the strength of thereflected signal is improved substantially, which enhances therobustness of the THz communications when the LoS pathis blocked. The performance analysis and joint design of theactive and passive beamforming algorithm in the THz bandare still lacked, which need further studies.VII. C
ONCLUSION
In this paper, we analyze the challenges and features ofthe THz hybrid beamforming design, including the low SDoFlimitation, the blockage issue, the large scale antenna arrayconstraint, the beam squint effect, and the spherical-wavepropagation problem. Then, we introduce two traditional FCand AoSA hybrid beamforming architectures and investigatetheir limitations when being applied to THz band. Further-more, we analyze three THz-specific hybrid beamformingarchitectures, i.e., THz WSMS, DAoSA, and TTD-based archi-tectures. Simulation results are provided to validate their datarate, power consumption, and array gain for THz communica-tions. More importantly, multiple open problems and potentialresearch directions are discussed for THz hybrid beamformingdesign. R
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