Design and Analysis of Wideband Full-Duplex FR2-IAB Networks
Junkai Zhang, Haifeng Luo, Navneet Garg, Abhijeet Bishnu, Mark Holm, Tharmalingam Ratnarajah
IIEEE TRANSACTIONS ON COMMUNICATIONS 1
Design and Analysis of Wideband Full-DuplexFR2-IAB Networks
Junkai Zhang,
Student Member, IEEE , Haifeng Luo,Navneet Garg,
Member, IEEE,
Abhijeet Bishnu,
Member, IEEE,
Mark Holm,
Member, IEEE, and Tharmalingam Ratnarajah,
Senior Member, IEEE
Abstract
This paper develops a 3GPP inspired design for the in-band-full-duplex (IBFD) Integrated Accessand Backhaul (IAB) networks in the frequency range 2 (FR2) band, which can enhance the spectralefficiency (SE) and coverage while reducing the latency. However, the self-interference (SI), which isusually more than 100 dB higher than the signal-of-interest, becomes the major bottleneck in developingthese IBFD networks. With the estimated RF effective channel obtained via RF codebooks given by ourmodified Linde-Buzo-Gray (LBG) algorithm, we design and analyze a subarray-based hybrid precodingFD-IAB system. The SI is canceled in three stages, where the antenna isolation forms the first stageand is assumed to be achieved. The second stage consists of the fiber-Bragg-grating (FBG)-based RFcancellation, where the cancelers are connected with the RF chain pairs. The third stage comprises thedigital cancellation via successive interference cancellation followed by minimum mean squared error(MMSE) baseband receiver. Multiuser interference in the access link is canceled by zero-forcing at theIAB-node transmitter. Simulations show that our staged SI cancellation can enhance the SE. Moreover,the residual SI due to the hardware impairments and channel uncertainty can affect the SE of the FDscheme in the backhaul link.
The work was supported in part by the research grant from Huawei Technologies (Sweden) AB.J. Zhang, H. Luo, N. Garg, A. Bishnu and T. Ratnarajah are with Institute for Digital Communications, The University ofEdinburgh, Edinburgh, EH9 3FG, UK (e-mail: { jzhang15, hluo2, ngarg, abishnu, T. Ratnarajah } @ed.ac.uk.M. Holm is with Radio Basestation Systems Department, Huawei Technologies (Sweden) AB, Gothenburg, Sweden. (e-mail:[email protected]). January 26, 2021 DRAFT a r X i v : . [ c s . I T ] J a n IEEE TRANSACTIONS ON COMMUNICATIONS
Index Terms
Wideband full-duplex millimeter wave (FR2 band), subarray hybrid precoding, integrated accessand backhaul, channel estimation, self-interference cancellation.
I. I
NTRODUCTION
Frequency range 2 (FR2) band (i.e., millimeter wave) communications have been identifiedas the key technology for the fifth-generation (5G) and beyond wireless communications toprovide much larger bandwidth, narrower beam, and high data rate services. Different from theFR1 band ( ≤ . GHz) communications, in the FR2 band ( ≥ . GHz), high path lossand blockages become the major obstacle for broader coverage. However, the short wavelengthsat the FR2 frequencies facilitate the deployment of large-scale arrays of antennas that couldcompensate for such high losses using highly directional narrow beamforming, and providingreliable transmission quality [1], [2]. In the recent 3GPP technical report TR 38.874 (Rel. 16)[3], the Integrated Access and Backhaul (IAB) networks have been proposed for the FR2 bandcommunications, where only the IAB donor (i.e., gNB) connects with the core network by fiber.IAB-nodes can wirelessly communicate with both the access and the backhaul links as well ascan perform IAB specific tasks such as resource allocation, route selection, and optimization[4]. This novel architecture enables cheap and dense deployment while extending the coveragein FR2 bands. Despite the visible advantages of this architecture, the study of IAB networks isstill in its infancy.Full-duplex (FD) transmission, which has been treated as another breakthrough for 5G andbeyond, breaks the rule that downlink and uplink communications should occur in differenttime/frequency slot. In the IAB networks, IAB-nodes are preferred to run under the FD mode[5]. Compared with the half-duplex (HD), thanks to simultaneous transmissions, the FD mode canalmost double the spectral efficiency (SE) without the need for large guard time/band arrangedin standard time-division duplex and frequency-division duplex systems [6], [7]. However, the
DRAFT January 26, 2021UBMITTED PAPER 3 major obstacle of FD communications is the existence of the strong self-interference (SI), whichis usually seen as more than 100 dB stronger than the signal of interest [8]. Therefore, findingefficient SI cancellation (SIC) techniques is important for FD operation and has recently been apopular research topic.For the wideband FD-FR2 communications, we propose three-stage cancellation, which con-sists of the antenna isolation stage (i.e., by isolating the transceiver antennas electromagneticallyfor passive cancellation) [9], the analog cancellation (A-SIC) stage (i.e., by establishing a circuitcanceler between each transceiver pair to replicate the SI channel as accurately as possible)[10], and the digital cancellation (D-SIC) stage (i.e., handling of the residual SI (RSI) left byprevious stages by designing efficient beamformers) [8], [11]. In the A-SIC, the conventionalmicro-strip analog canceler requires a huge number of taps for wideband SIC. However, dueto large insertion losses and the realization of many taps, wideband SIC becomes infeasible inpractice. Thus, a hardware efficient fiber-Bragg-grating (FBG)-based analog canceler has beeninvestigated in [12] for the single antenna system. However, FBG-based A-SIC for multi-antennasystems or IAB networks lacks in the literature.Due to the use of large-scale array systems, the traditional full digital precoding schemefor the FR1 band becomes expensive to implement for the FR2 band. Thus, towards the needfor cost-friendly system design, hybrid precoding has become a powerful and economical toolin the large-scale array systems, which reduces the requirement on the number of RF chainsand simplifies the system complexity [13]. Based on the extension of the standard OrthogonalMatching Pursuit (OMP) algorithm, a novel hybrid precoding design was proposed in [14].Compared with the fully connected hybrid precoding structure [2], to improve the deploymentcost and guarantee the similar performance of the system, authors in [1], [15] and [16] developa subarray hybrid precoding structure, where one RF chain only connects with a portion ofantenna arrays. However, the works that consider the wideband FD multi-user IAB networkswith subarray hybrid precoding in the FR2 band still needs more investigation.
January 26, 2021 DRAFT IEEE TRANSACTIONS ON COMMUNICATIONS
The hybrid precoding design algorithms in [1], [2], [13]–[15] need to access the large andsparse channel matrix, which is hard to acquire in reality. Although the compressed sensing-based channel estimation approaches are presented in [17], yet it is difficult to realize in practicalscenarios. Instead, the RF effective channel is estimated using standard estimation methods inpractice, where the RF precoding and combining matrices are selected from the codebooks. In[2], the RF codebook is designed by the Lloyd type algorithm. A K -means-based beam codebookis proposed by Mo et al. , whose codewords are defined by maximizing the beamforming gain[18]. Unfortunately, their vector-wise codebooks may lead to a low-rank beamforming matrix,which directly amounts to a loss in the degrees of freedom, especially when the number of RFchains is more than one.Further, the hardware impairments (HWI), which takes into account the imperfection in thehardware, such as oscillators noise, amplifiers noise, non-linearities in the digital-to-analogconverters (DACs) and the analog-to-digital converters (ADCs), and etc. [19], have not beenconsidered in most of the studies yet.Based on the above motivations, in this paper, we investigate the design and analysis ofmultiuser FR2 band FD-IAB networks with subarray-based hybrid precoding. The contributionsof this work are given as follows: • RF codebook design and RF effective channel estimation:
For the subarray hybrid precodingscheme, the RF precoders and combiners are selected by scanning from the matrix-wisecodebooks, designed with our modified mean squared error (MSE)-based Linde-Buzo-Gray (LBG) algorithm, and the RF effective channel can be then estimated with standardestimation methods. Simulations show that, with the proposed codebooks, we can achievea similar SE as that with infinite resolution PSs without suffering from losing degrees offreedom. • Staged SIC:
We propose a staged SIC scheme in this paper, where the A-SIC is realizedby FBG-based canceler connected with the RF chain pairs on the IAB-node to reduce the
DRAFT January 26, 2021UBMITTED PAPER 5 space and cost. Compared with the conventional micro-strip analog canceler, our canceleris robust to insertion loss. Simulations show that the A-SIC with FBG can almost perfectlyimitate the SI power by around 25 dB with about 100 taps over 400 MHz bandwidth. • System Analysis with RSI:
In order to explore how the RSI caused by the HWI and RFeffective channel uncertainties can affect the performance of the FD system, we analyzethe SE of the backhaul link by varying the HWI factors and SI effective channel estimationerrors. Simulation results show that as SNR increases, the system becomes more vulnerableto the RSI; however, the tolerance is improved when increasing the codebook size. It isalso shown that at lower values of RSI, FD operation doubles the SE as compared to thatof HD.
Notations: B , B , b , b represent a set, a matrix, a vector, and a scalar, respectively. B H , B − ,and B T are the Hermitian, inverse, and transpose of B , respectively. |B| is the cardinality of B . (cid:107) B (cid:107) F , | B | mn , det { B } , and tr[ B ] are the Frobenius norm, absolute value of the ( m, n )th entry,determinant, and trace of B , respectively. (cid:107) b (cid:107) is the norm of b . arg ( B ) takes the angle of eachentry of B . diag[ B ] takes the diagonal elements of the matrix. blkdiag[ B , B ] is the blockdiagonal matrix formed by matrix B and B . [ B ] : , n and [ B ] m,n denote the first n columnsand the ( m, n ) th entry of B , respectively. Cov[ B ] is the covariance matrix, i.e., E { BB H } . (cid:12) indicates the Hadamard product. d ( · , · ) is the distance measurement. CN ( m, n ) denotes a complexGaussian distribution with mean value of m and variance n , and I K is the K × K identity matrix.Some important notations and their key values used in the simulations are summarized in Table I.II. S YSTEM AND C HANNEL M ODELS
A. System Model
In this section, the system model is described for the wideband FR2 FD-IAB multiusernetworks. According to the technical specifications–TR 38.874 (Rel. 16) provided by the 3rd
January 26, 2021 DRAFT IEEE TRANSACTIONS ON COMMUNICATIONS
TABLE IS
UMMARY OF N OTATIONS AND K EY V ALUES
Notation Physical Meaning Values
N, Q
Number of subcarriers and cyclic prefixes, respectively 512, 128 B Bandwidth 400 MHz f c Carrier frequency 28 GHz N s Number of data streams 4 U Number of users (subarrays) 4 N T , n T Number of transmit antennas at the IAB donor and the IAB-node, respectively × , × R , N R Number of receive antennas at the IAB-node and each user, respectively × , × RFT , n RFT
Number of transmit RF chains at the IAB donor and the IAB-node, respectively 4, 4 n RFR , N RFR
Number of receive RF chains at the IAB-node and each user, respectively 4, 1 P t , P r The average total transmit and receive power across all subcarriers, respectively Define as use σ j , σ k Noise power at the IAB-node and each user, respectively −
174 + 10 log B +10 dB ρ, β HWI factor at the transmitter and the receiver, respectively Define as use N C , N L Number of clusters and number of paths in each cluster, respectively Define as use T s Sampling time /Bτ c,l Path delay QT s / [5] θ rc,l /θ r , φ rc,l /φ r Azimuth and elevation AOAs, respectively Define as use θ tc,l /θ t , φ tc,l /φ t Azimuth and elevation AODs, respectively Define as use α c,l Complex gain CN (0 , Average path loss See (9) d , d Reference distance and distance between transceiver, respectively 1 m, 100 m (0.1 m) p Path loss exponent 3.4 [20] λ Wavelength × /f c κ Rician factor 10 dB η Power of the SI signal attenuated by antenna isolation and A-SIC -80 dB H ab [ n ] The n th ideal channel matrix ( a, b ∈ i, j, k ) – ˆ H effab [ n ] The n th estimated RF effective channel matrix ( a, b ∈ i, j, k ) – ∆ ab [ n ] The n th channel estimation error matrix ( a, b ∈ i, j, k ) Cov [ ∆ ab [ n ]] = σ e,ab Ic a [ n ] , e a [n] The transmitter and receiver HWI of node a , respectively ( a ∈ i, j, k ) – F ( a )RF , F ( a )BB [ n ] RF precoder and the n th BB precoder of node a , respectively ( a ∈ ( i, j, k ) ) – W ( a )RF , W ( a )BB [ n ] RF combiner and the n th BB combiner of node a , respectively ( a ∈ ( i, j, k ) ) – d = 100 m for backhaul and access link channels; d = 0 . m ( ≈ λ [21]) for SI channel. Generation Partnership Project (3GPP), standalone (SA) and non-standalone (NSA) are the twotypical deployments considered for IAB systems [3]. In this work, we adopt the SA modedeployment, which consists of three types of nodes (i.e., node i, j, k ), • the IAB donor also called gNB (i.e., node i ) is a single logical node, which acts as the basestation; • the FD-IAB-node (i.e., node j ), which contributes SI from its transmitter to its receiver; DRAFT January 26, 2021UBMITTED PAPER 7
NGC IAB donorgNB ( 𝑖 ) IAB-node ( 𝑗 ) UEs ( 𝑘 )Wireline Wireless Backhaul
Wireless
Access ! ! ! SI Fig. 1. Illustration of FD-IAB multiuser network under the SA deployment. • the User-equipments (UEs) (i.e., node k ), which consisted with multiusers.The IAB donor connects to the 5G next-generation core network by fiber, and the IAB-node aswell as each of the users only have one parent node to communicate. The wireless link betweennode i and node j is called the backhaul link, while the link between node j and node k istermed as the access link. An illustration of the SA mode FD-IAB multiuser network is depictedin Fig. 1, and more information about the 3GPP architecture can be found in our recent work[4].For the FR2 band, OFDM (Orthogonal Frequency Division Multiplexing) is used in con-junction with the subarray-based hybrid precoding structure [15], where each RF chain onlyconnects with a portion of antenna elements as shown in Fig. 2. Compared with the fullyconnected structure, the subarray structure provides a cost-efficient solution for connecting RFchains to the antenna arrays. For hybrid precoding, RF precoders/combiners are frequency-flatand the same for all subcarriers, whereas the baseband (BB) precoders/combiners are differentfor different subcarriers. Let the data block be of the same length N as the number of subcarriers[2].At the gNB (node i ), N s data streams are transmitted through N RFT
RF chains and N T transmitantennas. In this work, we assume the number of subarrays equipped on the node i and j is equal to the number of devices on node k , i.e., U . Therefore, to guarantee multi-streamtransmission, N s U ≤ N RFT U ≤ N T U should be satisfied on each subarray. The signal transmitted from January 26, 2021 DRAFT IEEE TRANSACTIONS ON COMMUNICATIONS H kj,1 H jj IAB Rx ( 𝒋 )H ji gNB ( 𝒊 ) ! ! ! ! ! !! ! RF Precoder 𝑭 𝑹𝑭(𝒊)
RFChainOFDM Block ! ! ! ! ! ! ! ! ! ! ! RFChainOFDM Block ! ! ! ! ! ! ! ! ! ! ! DigitalBasebandPrecoder 𝑭 𝑩𝑩(𝒊) [𝒏] 𝑵 𝑻𝑹𝑭 ! ! ! ! ! ! RFChain OFDMBlock ! ! ! ! ! ! ! ! ! ! ! RFChain OFDMBlock ! ! ! ! ! ! ! ! ! ! ! 𝒏 𝑹𝑹𝑭
DigitalBasebandCombiner 𝑾 𝑩𝑩(𝒋) [𝒏] ! ! ! ! ! !! ! ! ! ! !! ! RF Precoder 𝑾 𝑹𝑭(𝒋)
UEs ( 𝒌 )IAB Tx ( 𝒋 ) ! ! ! ! ! !! ! RF Precoder 𝑭 𝑹𝑭(𝒋)
RFChainOFDM Block ! ! ! ! ! ! ! ! ! ! ! RFChainOFDM Block ! ! ! ! ! ! ! ! ! ! ! DigitalBasebandPrecoder 𝑭 𝑩𝑩(𝒋) [𝒏] 𝒏 𝑻𝑹𝑭 ! ! ! ! ! ! RFChain OFDMBlockRFChain OFDMBlock 𝑵 𝑹𝑹𝑭
DigitalBasebandCombiner 𝑾 𝑩𝑩,𝟏(𝒌) [𝒏] ! ! ! ! ! ! RF Precoder 𝑾 𝑹𝑭(𝒌) ,1 H kj,U DigitalBasebandCombiner 𝑾 𝑩𝑩,𝑼(𝒌) [𝒏] 𝑵 𝑹𝑹𝑭 𝑾 𝑹𝑭,𝑼(𝒌) ! ! ! ! ! ! ! ! ! ! ! User 1User U ! ! ! N s N s N s /UN s /U AnalogSIC ! ! ! ! ! ! 𝒏 𝑹𝑹𝑭 𝒏 𝑻𝑹𝑭
Fig. 2. Illustration of a wideband FR2 FD-IAB multiuser system with subarray hybrid precoding. the n = 1 , , . . . , N th subcarrier at the node i is given by x i [ n ] = F ( i )RF F ( i )BB [ n ] s i [ n ] (cid:124) (cid:123)(cid:122) (cid:125) (cid:101) x i [ n ] + c i [ n ] , (1)where F ( i )RF = blkdiag (cid:104) F ( i )RF , , F ( i )RF , , . . . , F ( i )RF , U (cid:105) ∈ C N T × N RFT is the block diagonal RF precodermatrix with (cid:110) F ( i )RF ,u (cid:111) U u =1 ∈ C NTU × NRFTU representing the RF precoder matrices of each subarray; F ( i )BB [ n ] ∈ C N RFT × N s represents the BB precoder matrix. The transmit data vector s i [ n ] ∈ C N s × at the subcarrier n has the covariance matrix E (cid:8) s i [ n ] s Hi [ n ] (cid:9) = P t N N s I Ns , where P t is the averagetotal transmit power across all subcarriers. By applying the transmit power constraint with equalpower allocation, we get the constraint on the precoder as (cid:107) F i [ n ] (cid:107) F = N s .At the FD-IAB-node (node j ), separate antennas are configured for transmission and reception(i.e., there are n T transmit antenna arrays and n RFT
RF chains for transmitting to the node k ;and n R antenna arrays with n RFR
RF chains for receiving data from the node i ). Similarly, thesubarray structure divides those antenna arrays and RF chains into U equal parts. Without SIC,the decoded signal at the node j for subcarrier n is expressed as y j [ n ] = (cid:16) W ( j )BB [ n ] (cid:17) H (cid:16) W ( j )RF (cid:17) H ( H ji [ n ] x i [ n ] + H jj [ n ] x j [ n ] + z j [ n ]) (cid:124) (cid:123)(cid:122) (cid:125) (cid:101) y j [ n ] + e j [ n ] , (2) DRAFT January 26, 2021UBMITTED PAPER 9 where W ( j )RF = blkdiag (cid:104) W ( j )RF , , W ( j )RF , , . . . , W ( j )RF , U (cid:105) ∈ C n R × n RFR represents the RF combinermatrix with (cid:110) W ( j )RF ,u (cid:111) U u =1 ∈ C nRU × nRFRU denoting the RF combiner matrices of each subarray; W ( j )BB [ n ] ∈ C n RFR × N s is the BB combiner matrix. H ji [ n ] ∈ C n R × N T and H jj [ n ] ∈ C n R × n T are thereal backhaul channel matrix and the real SI channel matrix at the subcarrier n , respectively. z j [ n ] ∈ C n R × ∼ CN ( , σ j I n R ) is the circularly symmetric Gaussian noise. The vector x j [ n ] denotes the signal transmitted from the node j at the n th subcarrier, given as x j [ n ] = F ( j )RF F ( j )BB [ n ] s j [ n ] (cid:124) (cid:123)(cid:122) (cid:125) (cid:101) x j [ n ] + c j [ n ] , (3)where F ( j )RF = blkdiag (cid:104) F ( j )RF , , F ( j )RF , , . . . , F ( j )RF , U (cid:105) ∈ C n T × n RFT is the RF precoder matrix with (cid:110) F ( j )RF ,u (cid:111) U u =1 ∈ C nTU × nRFTU denoting the RF precoder matrices of each subarray; F ( j )BB [ n ] ∈ C n RFT × N s represents the BB precoder matrix. s j [ n ] ∈ C N s × is the transmit data vector with covariancematrix E (cid:8) s j [ n ] s Hj [ n ] (cid:9) = P t N N s I Ns and is uncorrelated with s i [ n ] . Similarly, the precoder has tosatisfy the constraint of (cid:107) F j [ n ] (cid:107) F = N s .At the UEs (node k ), there are U devices, each is equipped with N R receive antennas and N RFR
RF chains. Thus, the signal decoded at all users from the n th subcarrier is written as y k [ n ] = (cid:16) W ( k )BB [ n ] (cid:17) H (cid:16) W ( k )RF (cid:17) H ( H kj [ n ] x j [ n ] + z k [ n ]) (cid:124) (cid:123)(cid:122) (cid:125) (cid:101) y k [ n ] + e k [ n ] , (4)where y k [ n ] = (cid:2) y Tk, [ n ] , y Tk, [ n ] , . . . , y Tk, U [ n ] (cid:3) T ∈ C N s × with { y k,u [ n ] } U u =1 ∈ C NsU × denotes thedecoded signal at the u th devices. W ( k )RF = blkdiag (cid:104) W ( k )RF , , W ( k )RF , , . . . , W ( k )RF , U (cid:105) ∈ C UN R × UN RFR is the RF combiner matrix with (cid:110) W ( k )RF ,u (cid:111) U u =1 ∈ C N R × N RFR denoting the RF combiner matricesof each user. W ( k )BB [ n ] = blkdiag (cid:104) W ( k )BB , [ n ] , W ( k )BB , [ n ] , . . . , W ( k )BB , U [ n ] (cid:105) ∈ C UN RFR × N s is the BBcombiner matrix with (cid:110) W ( k )BB ,u [ n ] (cid:111) U u =1 ∈ C N RFR × NsU being the BB combiner matrices of eachuser. H kj [ n ] = (cid:2) H Tkj, [ n ] , H Tkj, [ n ] , . . . , H Tkj, U [ n ] (cid:3) T ∈ C UN R × n T is the real access link channelmatrix, with { H kj,u [ n ] } ∈ C N R × n T representing the u th real access link channel matrix. z k [ n ] ∈ C N R × ∼ CN ( , σ k I UN R ) is the noise vector. January 26, 2021 DRAFT0 IEEE TRANSACTIONS ON COMMUNICATIONS
In the above equations, we have considered HWI variables to capture the distortion givenby the non-ideal hardware. Since authors in [19] have mentioned that the independent Gaussianmodel can optimally capture those combined non-ideal hardware effects. Therefore, we define thevectors c i [ n ] ∈ C N RFT × ∼ CN ( , ρ diag [Cov [ (cid:101) x i [ n ]]]) and c j [ n ] ∈ C n RFT × ∼ CN ( , ρ diag[Cov[ (cid:101) x j [ n ]]]) as the transmitter HWI at the node i and j , respectively; and e j [ n ] ∈ C n RFR × ∼CN ( , β diag[Cov[ (cid:101) y j [ n ]]]) and e k [ n ] ∈ C UN RFR × ∼ CN ( , β diag [Cov [ (cid:101) y k [ n ]]]) as the receiverHWI at the node j and k , respectively, ρ, β << . The transmitter (receiver) HWI is uncorrelatedwith the transmit (received) signals. B. General Channel
For the wideband FR2 communications with OFDM, a cyclic prefix of length Q is added toeach subcarrier, which is equal to the number of delay taps for the wideband channel. Due tothe scattering effect, the FR2 signals are likely to arrive in N C clusters, with N L paths reflectedby different obstacles in each cluster. A raised-cosine pulse shaping filter p ( qT s − τ c,l ) with T s -spaced signaling is utilized where the delay τ c,l is defined for the l th path in the c th cluster[22], for simplicity, we let each path has the same delay [5]. Assuming uniform planar arrays(UPAs) with half-wavelength spaced elements, the transmit and receive steering vectors can bewritten as a t ( θ tc,l , φ tc,l ) and a r ( θ rc,l , φ rc,l ) , respectively, where the azimuth θ rc,l /θ tc,l and elevation φ rc,l /φ tc,l angles correspond to the angles of arrival/departure (AoAs/AoDs) for each path in theirclusters. Hence, a typical FR2 channel model between two nodes can be expressed as H [ n ] = A r Π [ n ] A Ht , (5)where A r = [ a r ( θ r , , φ r , ) , . . . , a r ( θ r ,l , φ r ,l ) , . . . , a r ( θ rc,l , φ rc,l )] , (6) A t = [ a t ( θ t , , φ t , ) , . . . , a t ( θ t ,l , φ t ,l ) , . . . , a t ( θ tc,l , φ tc,l )] , (7) DRAFT January 26, 2021UBMITTED PAPER 11 Π [ n ] = (cid:113) N r N t N C N L ¯PL α , χ , [ n ] ... ... ... ... ... α ,l χ ,l [ n ] ... ... ... ... ... α c,l χ c,l [ n ] , (8)and χ c,l [ n ] = (cid:80) Q − q =0 p ( qT s − τ c,l ) e ( − j πnqN ) . N t and N r denote the number of transmit and receiveantennas, respectively. α c,l is the complex gain. ¯PL denotes the average path loss, due to thehigh attenuation of mmWave channel. The close-in path loss model is adopted rather than thefree space path loss [20], given as ¯PL = (cid:18) πd λ (cid:19) (cid:18) dd (cid:19) p , (9)where d , d , λ , and p represent the reference distance, distance between transceiver, wavelength,and path loss exponent, respectively. Moreover, since for arbitrary transmission networks, theline-of-sight (LOS) component has a high probability of being blocked by obstacles. Therefore,an non-line-of-sight (NLOS) path loss exponent is preferred. Furthermore, the steering vector isdefined as a ( θ, φ ) = √ M (cid:2) , a ( θ, φ ) , . . . , a M − ( θ, φ )] T , (10)where a m ( θ, φ ) = e j π r Tm u ( θ,φ ) ; M = AB is the number of antenna arrays in the A × B UPA; r m =[ x m , y m , z m ] T is the coordinate of the m th antenna element; u ( θ, φ ) = [cos θ cos φ, sin θ cos φ, sin φ ] T is the unit-norm direction vector. In this work, the arrays are placed in the XY-plane, and theelevation angles are measured from the z-axis. In addition, the antenna height is assumed to benegligible, i.e., z m ≈ . C. Self-Interference Channel
The most important issue in the FD transmission is the introduction of the SI on the IAB-node.Due to the proximity of the transceiver on the IAB-node, the attenuation of the SI channel issignificantly less than that of the typical communication channels, which distorts the achievablerate of the backhaul link. A stage SIC scheme will be introduced in the Section IV.
January 26, 2021 DRAFT2 IEEE TRANSACTIONS ON COMMUNICATIONS
Since the distinct SI channel model for the FR2 band is still unknown, to the best of ourknowledge, most of the works have considered the hypothetical SI channel for narrowbandcommunications [6], [23]. Fortunately, in [24], a hypothetical model is proposed for the widebandSI channel. According to [23], [24], after some minor modifications, we model the hypothesiswideband SI channel as follows. Unlike the general channel in the previous subsection, the SIchannel is likely to be modeled as a Rician-alike channel with Rician factor κ . The LOS part, H jj, L , is adopted to a near-field model with spherical waveform and is assumed to be frequencyflat. The frequency response of the LOS component is given as H jj, L = (cid:2) a r ( θ r , φ r ) a Ht ( θ t , φ t ) (cid:3) (cid:12) D , (11)where only one AoA/AoD is assumed for the LOS link. The entries of D is [ D ] a,b = γr ab (cid:12) e ( − j π rabλ ) with r ab denoting the distance between the a th element of the receive antenna andthe b th element of the transmit antenna at the IAB-node. γ = √ n R n T is the normalization factorensuring that the norm of H jj, L remains the same after multiplying with the steering vectors.The NLOS part, H jj, N , is expressed similar to the general channel model in (5), but with afew clusters and rays. Consequently, the entire SI channel for subcarrier n can be expressed as H jj [ n ] = (cid:114) κκ + 1 H jj, L + (cid:114) κ + 1 H jj, N[ n ] . (12)III. RF C ODEBOOK D ESIGN AND E FFECTIVE C HANNEL E STIMATION
In practice, the RF precoders/combiners are usually implemented using finite resolution PSs.Motivated by this, the RF precoders/combiners are selected from a pre-designed RF codebooksby the proposed LBG algorithm, followed by the estimation of RF effective channel.
A. MSE Based LBG Algorithm for RF Codebook Design
LBG algorithm is a popular vector quantization scheme and is treated as an extension ofthe Lloyd-Max scalar quantization algorithm [25]. Conventionally, for a matrix quantization, the
DRAFT January 26, 2021UBMITTED PAPER 13 existing codebooks work by vector-wise comparison. This inefficient selection process can leadto a low-rank behavior on the quantized matrix . Therefore, to avoid that, we modify the LBGalgorithm to yield the codebook with matrix entries directly [26], whose steps are described asfollows. • Step 1 (Initialization):Given the training set V = (cid:8) V t RF | t = 1 , , . . . , T, | V t RF | mn = 1 if [ V t RF ] m,n (cid:54) = 0 (cid:9) with T entries, whose each entry is a block diagonal matrix with each block matrix denoted by theangle of a random matrix with CN (0 , entries [27], [28, Lemma 1, 2]. The codebook Y is initialized with an entry Y , obtained by the angle of the mean value of the training setas Y = e j arg (cid:18) (cid:80) Tt =1 V t RF T (cid:19) . (13) • Step 2 (Splitting):This step splits each entry of the codebook Y into two new ones. To achieve that, we perturbeach entry Y i as, Y i = e j arg ( √ − (cid:15) Y i + (cid:15) E i ) Y i +1 = e j arg ( √ − (cid:15) Y i − (cid:15) E i ) , (14)where (cid:15) is a small positive value (e.g., − ), E i is a random matrix with the same propertyas the codewords. • Step 3 (Cluster Assignment):In this step, using the nearest neighbor routine based on MSE, the training set is divided into |Y| clusters. E.g., V t RF is in cluster C if d ( V t RF , Y ) ≤ d ( V t RF , Y j ) , ∀ j = 2 , , . . . , |Y| , Suppose the system has multiple RF chains. With a vector-wise codebook, it is likely that the columns for the RF beamformingmatrix may be assigned to the same vector codeword, which can result in a low-rank matrix and the loss of degrees of freedom.
January 26, 2021 DRAFT4 IEEE TRANSACTIONS ON COMMUNICATIONS t = 1 , , . . . , T , where d ( A , B ) = MN (cid:80) Mm =1 (cid:80) Nn =1 ([ A ] m,n − [ B ] m,n ) , and M , N denotesthe number of rows and columns of the matrix, respectively. • Step 4 (Centroid Update):Each entry of the codebook is updated with the centroid of the corresponding cluster. Thecentroid is computed via the solution of the following optimization problem, that is ˆY i = arg min Y i (cid:88) V t RF ∈C i d (cid:0) V t RF , Y i (cid:1) . (15)Thus, the new centroid ˆY i is given by the angle of the mean value of all V t RF ∈ C i . • Step 5 (Inner loop):Go to step 3 until the maximum number of iterations is reached (e.g., 50 iterations). • Step 6 (outer loop):Go to step 2 until the length of the codebook is equal to the desired codebook length.
B. RF Effective Channel Estimation
There are two phases in RF effective channel estimation: i) RF precoder-combiner pairselection; ii) RF effective channel estimation. We treat the whole OFDM symbols as pilots.The RF beamformers are designed to maximize the desired signal in their corresponding links.Moreover, the same RF codebook Y can be used for RF precoder/combiner selection at all nodes.Since the RF effective channel estimation for the backhaul link, the access link, and the SI linkfollows similar procedure, thus, we only present the estimation steps for the access link.
1) Phase 1 (RF precoder-combiner pair selection):
Given the received access link signal ofthe n th pilot subcarrier at the node k across all users , Y k [ n ] = (cid:16) W ( k )RF (cid:17) H (cid:104) H kj [ n ] F ( j )RF ( S j [ n ] + C j [ n ]) + Z k [ n ] (cid:105) + E k [ n ] , (16)where S j [ n ] ∈ C N s × N s is the matrix of orthogonal pilot signals with S j [ n ] S Hj [ n ] = P t N N s I Ns . C j [ n ] ∈ C N s × N s and E k [ n ] ∈ C N s × N s represent the noise matrices caused by transmit and DRAFT January 26, 2021UBMITTED PAPER 15 receive HWI, respectively, with each column following the definition introduced in Section II-A. Z k [ n ] ∈ C N s × N s is the Gaussian noise matrix with the power of σ k . Note that the BB precoderand combiner are omitted in the above equation since they are assumed to be identity matrices.Similar to beam management [29], [30], in this work, the best RF precoder and combiner areselected from the same codebook Y , which can maximize the receive power of Y k [ n ] amongall subcarriers, that is arg max F ( j )RF , W ( k )RF N (cid:88) n =1 tr (cid:2) Y k [ n ] Y Hk [ n ] (cid:3) (17a)subject to F ( j )RF ∈ Y , W ( k )RF ∈ Y . (17b)
2) Phase 2 (RF effective channel estimation):
Given the RF precoder/combiner, one canestimate the RF effective channel with the help of pilot signal by standard estimation methods,for instance, the least squares (LS) or the minimum MSE (MMSE) channel estimation.Consequently, after estimation, we can write the ideal RF effective channel matrix as thesum of the estimated RF effective channel matrix ˆ H effkj [ n ] and the estimation error matrix (cid:16) W ( k )RF (cid:17) H ∆ kj [ n ] (cid:16) F ( j )RF (cid:17) , given as (cid:16) W ( k )RF (cid:17) H H kj [ n ] F ( j )RF = ˆ H effkj [ n ] + (cid:16) W ( k )RF (cid:17) H ∆ kj [ n ] (cid:16) F ( j )RF (cid:17) , (18)where we assume ∆ kj [ n ] has the covariance matrix of Cov [ ∆ kj [ n ]] = σ e,ab I UN R [31], [32].IV. S TAGED S ELF -I NTERFERENCE C ANCELLATION
In this section, a staged active SIC will be introduced for the FR2 wideband. For the firststage, we assume the antenna isolation has been successfully deployed. The A-SIC is performedin the second stage, followed by the third stage of D-SIC.
A. Analog Cancellation
In the following, the conventional A-SIC idea is presented first. Then, FBG-based canceler isdescribed, followed by the details of the proposed FBG-based canceler design.
January 26, 2021 DRAFT6 IEEE TRANSACTIONS ON COMMUNICATIONS
1) Working Principle and Limitations:
Analog cancellation is essential to avoid receiversaturation since the received SI power is strong due to the short propagation distance [10], [33].A-SIC is based on a subtraction idea, where a replica of the received SI signal generated bythe analog canceler is subtracted from the received signal. The canceler is made up of multipletunable delay lines with a limited number of taps to capture the multi-path nature of the SIchannel, where passive components are utilized to construct tunable delay lines to minimize thenonlinearity effects. With multi-tap RF canceler, one can cancel the SI from reflection paths inaddition to the direct path. By considering the hardware insertion losses, the impulse responseof the multi-tap RF canceler for SISO system can be given as h can ( t ) = ˆ α M (cid:88) i =1 α i β i ( w I,i + jw Q,i ) δ ( t − τ i ) , (19)where ˆ α is the attenuation introduced by coupling the RF signal into the canceler; α i is thepropagation loss of each delay line; β i denotes the tap coupling factor [12, (4)]; and w I,i and w Q,i are tunable weights. The corresponding frequency response of the canceler can be expressedas H can [ n ] = ˆ α M (cid:88) i =1 α i β i ( w I,i + jw Q,i ) e − j ∆ ω nτ i . (20)where ∆ ω = πBN denotes the sampling interval with B being the bandwidth [33]. The optimalweights are tuned to minimize the difference between the frequency components of the cancelerand the SI channel within the band of interest (for details, see [10]). The key factor for efficientwideband RF cancellation is the realization of sufficient number of taps (i.e., delay lines), whichis proportional to the bandwidth and the amount of cancellation required [34].
2) FBG-based Analog Cancellation:
With the conventional canceler, more number of tapscause more insertion losses (i.e., α i and β i are small for large i in (19)), which results in alarge difference between the signal power at the first and the later taps. Therefore, the signalscoupled into the later taps cannot replicate the desired signal level, and degrade the cancellationperformance. Conventionally, electrical attenuators and micro-strips or cables can be used to DRAFT January 26, 2021UBMITTED PAPER 17 。 + CouplerCoupler
FBG !,
FBG !,$
FBG %,
FBG %,$ 。 。 MZM
Photodiode
MUX 𝜆 !, 𝑊 𝜆 !,$ 𝑊 $ 𝜆 !,% 𝑊 % …… Optical Carriersweights
Tap Tap Tap N λ &,’ λ &,( λ &,) …… core cladding Tap 𝜏 ’ 𝜏 ) delays Fiber with Bragg gratings gratings
Transmitter PA OutputReceiver LNA Input
RF InputWeighted and multiplied optical carriers RF Output
Fig. 3. Illustration of the FBG based analog canceler. construct the tunable delay lines. However, it is demonstrated that these electrical componentshave large propagation loss and coupling loss that limit the number of effective taps [12], thuslimiting the operational bandwidth and cancellation performance. Therefore, to overcome thesedrawbacks, a FBG-based analog canceler has recently been investigated in [12], whose structureis illustrated in Fig. 3.Regarding the mechanism of this canceler, the RF reference signal is first converted to the op-tical domain by modulating onto optical carriers through the Mach–Zehnder modulator (MZM).According to the weight calculation, tunable lasers generate the optical carriers according to thegrating wavelengths, and the power of these carriers is adjusted by variable optical attenuators(VOAs). Then, M optical carriers are combined by a multiplexer (MUX) for propagating intoa single fiber. The reference signal modulated on the optical carrier at wavelength λ B,i willbe reflected at the i th grating while propagating through the FBG. This reflection happens atdifferent gratings causes different time delays to the coupled reference signal. The reflectedsignals are detected by photo-diodes, which converts the optical signals back to the RF domainand yields an accumulation of multiple weighted and delayed versions of the input referencesignal as the canceler output [12]. Note that the SI channel is complex; however, since the January 26, 2021 DRAFT8 IEEE TRANSACTIONS ON COMMUNICATIONS weights in the optical domain can only be real and nonnegative, 4 FBGs are needed to realizethe complex response of the canceler.The impulse response of the novel FBG-based canceler can similarly be expressed as in (19);however, with much smaller insertion losses, i.e., α i and β i are almost constant for all i . Theoptimization problem for obtaining the I-Q weights of the SISO system to imitate the estimatedSI channel ˆ H jj [ n ] can be cast as arg min { W abi } Mi =1 (cid:13)(cid:13)(cid:13) ˆ H jj [ n ] − H FBG [ n ] (cid:13)(cid:13)(cid:13) s.t. − ≤ w I,i ≤ , − ≤ w Q,i ≤ . (21)where H FBG [ n ] is the frequency response of the canceler, which can be written according to (20).The constraints come from passive VOAs. Theoretically, almost constant insertion losses of thisdesign allow hundreds of effective taps to be implemented to enlarge the operational bandwidthto meet the requirements in the FR2 scenarios.
3) Proposed FBG Based Analog Cancellation:
The above canceler is for A-SIC in SISOsystem. For MIMO system, n R × n T cancelers are traditionally required to match the n R × n T channel pairs of the SI channel matrix. However, such a canceler deployment will be extremelycostly for the FR2 communications, especially for the FBG-based canceler. In order to reducethe cost, we tap off the SI signal from the RF chains before the RF precoder at the transmitter,and couple the outputs of the analog cancelers back to the RF chains at the receiver after the RFcombiner [35] (see Fig 2). With this architecture, the required number of analog cancelers canbe reduced from n T × n R to n RFT × n RFR , which is of great benefit in terms of cost and practicalimplementation.This architecture requires the canceler to imitate the estimated RF effective SI channel ˆ H effjj [ n ] .We assume the amount of cancellation for the RF effective SI channel to be the same as thatfor the SI channel since the performance of the A-SIC mainly depends on the delay spread andthe number of taps in the canceler. The RF beamformers do not affect the frequency selectivity DRAFT January 26, 2021UBMITTED PAPER 19 of the SI channel. Then for this channel, the I-Q weights for constructing the ab th canceler canbe obtained by solving the following optimization problem as arg min { W abi } Mi =1 (cid:13)(cid:13)(cid:13)(cid:13)(cid:104) ˆ H effjj [ n ] (cid:105) a,b − (cid:104) H eff FBG [ n ] (cid:105) a,b (cid:13)(cid:13)(cid:13)(cid:13) s.t. − ≤ w abI,i ≤ , − ≤ w abQ,i ≤ , (22)where H eff FBG [ n ] represents the frequency response matrix of the canceler. From our previouswork [34], it turns out that the canceler accurately replicated the RF effective SI channel. Thus,the resultant signal after A-SIC can be seen as a scaled version of the actual SI signal.Suppose the scalar η denotes the amount of power attenuated after antenna isolation andA-SIC. Therefore, the attenuated SI signal is cast as √ η W Hj H jj [ n ] x j [ n ] , (23)where W j [ n ] = W ( j )RF W ( j )BB [ n ] . B. Digital Cancellation
After A-SIC, the RSI left by previous stages will be processed in the digital domain at theIAB-node receiver. In practice, since the IAB-node knows its transmitted codeword s j [ n ] and theestimated SI RF effective channel ˆ H effjj [ n ] , with the help of successive interference cancellationtechnique, we can cancel out √ η ˆ H effjj [ n ] F ( j )BB [ n ] s j [ n ] . Therefore, the RF decoded received signalat the node j is cast as ˆ y j [ n ] = (cid:16) W ( j )RF (cid:17) H ( H ji [ n ] x i [ n ] + √ η ∆ jj [ n ] x j [ n ] + z j [ n ]) + √ η ˆ H effjj [ n ] c j [ n ] + e j [ n ] . (24)Next, for decoding data symbols, we employ the MMSE BB combiners, which are described inthe Section V-B. January 26, 2021 DRAFT0 IEEE TRANSACTIONS ON COMMUNICATIONS
V. B
ASEBAND B EAMFORMING D ESIGN
A. Problem Formulation
Given the RF precoder/combiner derived from Section III-B, we aim to design the BBprecoders/combiners for both access and backhaul links, which can maximize the sum SE andmitigate the interference.Let ζ = P t N N s , the SE of the backhaul link is given as R b = 1 N N (cid:88) n =1 log det (cid:40) I N s + (cid:16) W ( j )BB [ n ] (cid:17) H Φ b [ n ] W ( j )BB [ n ] (cid:20)(cid:16) W ( j )BB [ n ] (cid:17) H Ω b [ n ] W ( j )BB [ n ] (cid:21) − (cid:41) , (25) Φ b [ n ] = ζ ˆ H effji [ n ] F ( i )BB [ n ] (cid:16) ˆ H effji [ n ] F ( i )BB [ n ] (cid:17) H (cid:124) (cid:123)(cid:122) (cid:125) known part of the desired signal , (26) Ω b [ n ] = Ω (1) b [ n ] + Ω (2) b [ n ] + Ω (3) b [ n ] + σ j (cid:16) W ( j )RF (cid:17) H W ( j )RF . (27a) Ω (1) b [ n ] = Cov (cid:20) ˆ H effji [ n ] c i [ n ] + (cid:16) W ( j )RF (cid:17) H ∆ ji [ n ] F ( i )RF c i [ n ] (cid:124) (cid:123)(cid:122) (cid:125) transmitter HWI3 + (cid:16) W ( j )RF (cid:17) H ∆ ji [ n ] F ( i )RF F ( i )BB [ n ] s i [ n ] (cid:124) (cid:123)(cid:122) (cid:125) channel estimation error4 (cid:21) = ζρ ˆ H effji [ n ]diag (cid:20) F ( i )BB [ n ] (cid:16) F ( i )BB [ n ] (cid:17) H (cid:21) (cid:16) ˆ H effji [ n ] (cid:17) H + σ e ζ ( ρ + 1)N s (cid:16) W ( j )RF (cid:17) H W ( j )RF , (27b) Ω (2) b [ n ] = Cov (cid:20) η ˆ H effjj [ n ] c j [ n ] + η (cid:16) W ( j )RF (cid:17) H ∆ jj [ n ] F ( j )RF c j [ n ] (cid:124) (cid:123)(cid:122) (cid:125) transmitter HWI + η (cid:16) W ( j )RF (cid:17) H ∆ jj [ n ] F ( j )RF F ( j )BB [ n ] s j [ n ] (cid:124) (cid:123)(cid:122) (cid:125) channel estimation error (cid:21) = ηζρ ˆ H effjj [ n ]diag (cid:20) F ( j )BB [ n ] (cid:16) F ( j )BB [ n ] (cid:17) H (cid:21) (cid:16) ˆ H effjj [ n ] (cid:17) H + σ e ηζ ( ρ + 1)N s (cid:16) W ( j )RF (cid:17) H W ( j )RF , (27c) Ω (3) b [ n ] = β diag (cid:20) Φ b [ n ] + Ω (1) b [ n ] + Ω (2) b [ n ] + σ j (cid:16) W ( j )RF (cid:17) H W ( j )RF (cid:21) . (27d) DRAFT January 26, 2021UBMITTED PAPER 21
The SE of the access link for the u th UE is given as R a,u = 1 N N (cid:88) n =1 log det (cid:40) I N s + (cid:16) W ( k )BB ,u [ n ] (cid:17) H Φ a,u [ n ] W ( k )BB ,u [ n ] (cid:20)(cid:16) W ( k )BB ,u [ n ] (cid:17) H Ω a,u [ n ] W ( k )BB ,u [ n ] (cid:21) − (cid:41) , (28) Φ a,u [ n ] = ζ ˆ H effkj,u [ n ] F ( j )BB ,u [ n ] (cid:16) ˆ H effkj,u [ n ] F ( j )BB ,u [ n ] (cid:17) H (cid:124) (cid:123)(cid:122) (cid:125) known part of the desired signal , (29) Ω a,u [ n ] = Ω (1) a,u [ n ] + Ω (2) a,u [ n ] + Ω (3) a,u [ n ] + σ k (cid:16) W ( k )RF ,u (cid:17) H W ( k )RF ,u . (30a) Ω (1) a,u [ n ] = Cov (cid:20) U (cid:88) v =1 ,v (cid:54) = u ˆ H effkj,u [ n ] F ( j )BB ,v [ n ] s j,v [ n ] (cid:124) (cid:123)(cid:122) (cid:125) multiuser interference + U (cid:88) v =1 ˆ H effkj,u [ n ] c j,v [ n ] (cid:124) (cid:123)(cid:122) (cid:125) transmitter HWI (cid:21) = ζ U (cid:88) v =1 ,v (cid:54) = u ˆ H effkj,u [ n ] F ( j )BB ,v [ n ] (cid:16) ˆ H effkj,u [ n ] F ( j )BB ,v [ n ] (cid:17) H + ζρ ˆ H effkj,u [ n ]diag (cid:20) F ( j )BB [ n ] (cid:16) F ( j )BB [ n ] (cid:17) H (cid:21) (cid:16) ˆ H effkj,u [ n ] (cid:17) H , (30b) Ω (2) a,u [ n ] = U (cid:88) v =1 Cov (cid:20) (cid:16) W ( k )RF ,u (cid:17) H ∆ kj,u [ n ] F ( j )RF c j,v [ n ] (cid:124) (cid:123)(cid:122) (cid:125) transmitter HWI + (cid:16) W ( k )RF ,u (cid:17) H ∆ kj,u [ n ] F ( j )RF F ( j )BB ,v [ n ] s j,v [ n ] (cid:124) (cid:123)(cid:122) (cid:125) channel estimation error (cid:21) = σ e ζ ( ρ + 1)N s (cid:16) W ( k )RF ,u (cid:17) H W ( k )RF ,u , (30c) Ω (3) a,u [ n ] = β diag (cid:20) Φ a,u [ n ] + Ω (1) a,u [ n ] + Ω (2) a,u [ n ] + σ k (cid:16) W ( k )RF ,u (cid:17) H W ( k )RF ,u (cid:21) , (30d) (cid:104) Cov (cid:104) ∆ ji [ n ] F ( i )RF c i [ n ] (cid:105)(cid:105) m,n = (cid:80) p,q (cid:34) E (cid:40) [ ∆ ji [ n ]] m,p (cid:20) F ( i )RF c i [ n ] c Hi [ n ] (cid:16) F ( i )RF (cid:17) H (cid:21) p,q (cid:2) ∆ Hji [ n ] (cid:3) q,n (cid:41)(cid:35) m,n = σ e ζρ (cid:80) p,q (cid:20) E (cid:26) F ( i )RF diag (cid:20) F ( i )BB [ n ] (cid:16) F ( i )BB [ n ] (cid:17) H (cid:21) (cid:16) F ( i )RF (cid:17) H (cid:27)(cid:21) p,q δ m,n δ p,q = σ e ζρ tr (cid:20) F ( i )RF F ( i )BB [ n ] (cid:16) F ( i )BB [ n ] (cid:17) H (cid:16) F ( i )RF (cid:17) H (cid:21) δ m,n = σ e ζρ N s δ m,n . Let F i [ n ] = F ( i )RF F ( i )BB [ n ] . [Cov [ ∆ ji F i [ n ] s i [ n ]]] m,n = ζ (cid:2) E (cid:8) ∆ ji [ n ] F i [ n ] F Hi [ n ] ∆ Hji [ n ] (cid:9)(cid:3) m,n = ζ (cid:80) p,q (cid:104) E (cid:110) [ ∆ ji [ n ]] m,p (cid:2) F i [ n ] F Hi [ n ] (cid:3) p,q (cid:2) ∆ Hji [ n ] (cid:3) q,n (cid:111)(cid:105) m,n = σ e ζ (cid:80) p,q (cid:2) F i [ n ] F Hi [ n ] (cid:3) p,q δ m,n δ p,q = σ e ζ tr (cid:2) F i [ n ] F Hi [ n ] (cid:3) δ m,n = σ e ζ N s δ m,n . January 26, 2021 DRAFT2 IEEE TRANSACTIONS ON COMMUNICATIONS where F ( j )BB [ n ] = (cid:104) F ( j )BB , [ n ] , F ( j )BB , [ n ] , . . . , F ( j )BB , U [ n ] (cid:105) with (cid:110) F ( j )BB ,u [ n ] (cid:111) U u =1 ∈ C n RFT × NsU . ˆ H effkj [ n ] = (cid:20)(cid:16) ˆ H effkj, [ n ] (cid:17) T , (cid:16) ˆ H effkj, [ n ] (cid:17) T , . . . , (cid:16) ˆ H effkj, U [ n ] (cid:17) T (cid:21) T with (cid:110) ˆ H effkj,u [ n ] (cid:111) U u =1 ∈ C N RFR × n RFT . ∆ kj,u [ n ] = (cid:104) ( ∆ kj, [ n ]) T , ( ∆ kj, [ n ]) T , . . . , ( ∆ kj, U [ n ]) T (cid:105) T with { ∆ kj,u [ n ] } U u =1 ∈ C N R × n T . s j [ n ] = (cid:2) s Tj, [ n ] , s Tj, [ n ] , . . . , s Tj, U [ n ] (cid:3) T with { s j,u [ n ] } U u =1 ∈ C NsU × . c j,u [ n ] ∼ CN (cid:18) , ζρ diag (cid:20) F ( j )BB ,u [ n ] (cid:16) F ( j )BB ,u [ n ] (cid:17) H (cid:21)(cid:19) .The optimization problem can be cast as arg max F ( i )BB [ n ] , F ( j )BB [ n ] , W ( j )BB [ n ] , (cid:110) W ( k )BB ,u [ n ] (cid:111) U u =1 U (cid:88) u =1 R a,u + R b (31a)subject to (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) F ( i )RF F ( i )BB [ n ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) F = N s , (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) F ( j )RF F ( j )BB [ n ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) F = N s . (31b)It is worth noting that, the maximization above is equivalent to the separate maximization ofthe SE of each link since the design of F ( j )RF and F ( j )BB [ n ] only aims to maximize the SE of theaccess link. B. Baseband Beamforming Design
For the backhaul link, the n th BB precoder which maximizes the SE is obtained using theright singular vectors V ji [ n ] of the n th estimated RF effective backhaul link channel matrix ˆ H effji [ n ] , that is F ( i )BB [ n ] = [ V ji [ n ]] : , s . (32)Due to the transmit power constraint, the BB precoder is updated as F ( i )BB [ n ] ← √ N s F ( i )BB [ n ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) F ( i )RF F ( i )BB [ n ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) F .Next, the design of the BB precoder F ( j )BB [ n ] at the IAB-node transmitter aims to null themultiuser interference by zero forcing, which is F ( j )BB [ n ] = (cid:16) H effkj [ n ] (cid:17) H (cid:20) H effkj [ n ] (cid:16) H effkj [ n ] (cid:17) H (cid:21) − . (33)Similarly, the BB precoder should be normalized as F ( j )BB [ n ] ← √ N s F ( j )BB [ n ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) F ( j )RF F ( j )BB [ n ] (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) F . DRAFT January 26, 2021UBMITTED PAPER 23
Given the RF decoded signal at the node j in (24), the MMSE BB combiner W ( j )BB [ n ] isdesigned as W ( j )BB [ n ] = E (cid:8) ˆ y j [ n ]ˆ y Hj [ n ] (cid:9) − E (cid:8) ˆ y j [ n ] s Hi [ n ] (cid:9) , (34)where E (cid:8) ˆ y j [ n ]ˆ y Hj [ n ] (cid:9) = Φ b [ n ] + Ω b [ n ] , E (cid:8) ˆ y j [ n ] s Hi [ n ] (cid:9) = ζ ˆ H effji [ n ] F ( i )BB [ n ] since the channelestimation error is uncorrelated with the data vector [31].Finally, the BB combiner at the u th UE W ( k )BB ,u [ n ] can be computed using the left singularvectors U kj,u [ n ] of the n th RF effective channel matrix in terms of each user ˆ H effkj,u [ n ] , that is W ( k )BB ,u [ n ] = [ U kj,u [ n ]] : , NsU . (35)VI. S IMULATIONS
In this section, simulation results will be shown to analyze the performance of our designednetworks. Each subarray (users) has 16 × N C = 8 clusters, each with N L = 10 rays,whereas the NLOS component of the SI channel has N C = 2 clusters, each with N L = 8 rays.Both azimuth and elevation AOAs/AODs can be expressed as the sum of the mean angle of eachcluster and the angle shifts in the cluster. The mean azimuth and elevation AOAs/AODs of eachcluster are assumed to be uniformly distributed in [ − π, π ] , and (cid:2) − π , π (cid:3) , respectively. In eachcluster, the AOAs/AODs have Laplacian distribution with an angle spread of ◦ . The transceiverarrays at the node j has a separation angle of π . Assume σ j = σ k = σ n , we define SNR (cid:44) P r σ ,where P r = P t ¯ P L is the ratio between transmit power and average path loss according to the Friis’law. We let ρ = β are the same for all channels. The SE of the HD scheme is given by scalingthe SE of the FD by 0.5 since non-simultaneous transmission and reception, and removing thepart relevant to the SI. Other key values are defined in Table I. January 26, 2021 DRAFT4 IEEE TRANSACTIONS ON COMMUNICATIONS
10 20 30 40 50 60
Number of Taps B a nd w i d t h ( M H z ) C a n ce ll a ti on A b ilit y ( d B ) (a)
20 40 60 80 100 120 140 160
Number of Taps B a nd w i d t h ( M H z ) C a n ce ll a ti on A b ilit y ( d B ) (b)Fig. 4. Comparison between the performance of (a) traditional micro-strip analog canceler; (b) FBG-based analog canceler (SIchannel has a delay spread of 800 ns). A. Performance of FBG-Based Analog Canceler
Assume the propagation loss of the FBG (coiled into 2 cm) is 0.461 dB/m, and that of themicro-strip is 2.967 dB/m. The FBG based design uses a 20 dB hybrid coupler to couple theRF reference signal into the FBG-based canceler, while the conventional electrical canceler usesa 0 dB coupler. Besides, to explore the best performance, the tap delay varies according tothe number of taps to match the delay spread. Fig. 4 shows the A-SIC abilities (in dB) of thetraditional micro-strip canceler in Fig. 4(a) and the FBG-based canceler in Fig. 4(b) for differentbandwidths and numbers of taps. Simulations are run with 200 ns of significant delay spreadof the SI channel according to the measurement in [36]. Fig. 4(a) shows that creating a largenumber of taps with conventional electrical components (e.g., cables or micro-strips) degradesthe performance rather than improving it due to large insertion losses. It can be seen that lessthan 20 dB of cancellation is achieved under 200 MHz bandwidth. Fig. 4(b) shows that under 400MHz bandwidth, FBG-based canceler can achieve around 30 dB of cancellation in FR2 widebandwith 100 taps, which is also proved in [12]. Note that, this result shows the cancellation ability
DRAFT January 26, 2021UBMITTED PAPER 25 -10 -5 0 5 10 15 20
SNR (dB) S p ec t r a l E ff i c i e n c y ( b it s / s / H z ) FD-subarrayHD-subarrayInfinite resolution8 bits4 bits1 bit (a) -10 -5 0 5 10 15 20
SNR (dB) S p ec t r a l E ff i c i e n c y ( b it s / s / H z ) FD-subarrayHD-subarrayInfinite resolution8 bits4 bits1 bit -2 -1.5 -13456 (b)Fig. 5. SE of 4-subarray hybrid precoding structure with different size of codebooks for (a) backhaul link; (b) access link with4 users. Each subarray (user) has 64 antennas ( × UPA), 1 RF chain and 1 data stream (perfect CSI and SIC, without HWI). that can be achieved between a single RF chain pair. In this work, we assume antenna isolationand our A-SIC can attenuate the SI signal power by 55 dB [9] and 25 dB, respectively.
B. Performance of the Proposed Codebook Design
The SE performance of the backhaul and access links with RF precoders/combiners selectedfrom 1, 4, 8 bits codebooks, respectively, for the subarray structure is plotted in Fig. 5. Weassume perfect SIC, CSI, and hardware. The RF precoders/combiners with infinite resolutionPSs are designed according to [15]. It can be seen that, as the number of bits increases, theperformance becomes closer to the ideal one (i.e., infinite resolution). For the access link, with4 bits codebook, one can even provide a similar performance as the ideal one. It shows thesuccessful applicability of the proposed MSE-based LBG codebook design. However, for bothlinks, there is still a small gap between the ideal one and the curves derived with 8 bits codebook.To reduce the gap, large size of codebook can be used. Moreover, it is obvious that HD operatingyields lower sum rates than that of FD.
January 26, 2021 DRAFT6 IEEE TRANSACTIONS ON COMMUNICATIONS -10 -5 0 5 10 15 20
SNR (dB) S p ec t r a l E ff i c i e n c y ( b it s / s / H z ) FDHDIdeal full digitalIdeal fully connectedIdeal subarraySubarray w/ staged SIC (8 bits)Subarray w/o D-SIC (8 bits)
Fig. 6. SE of backhaul link for different precoding schemes. Both fully connected and subarray hybrid precoding have 4 RFchains and 4 data streams. Each subarray (user) has × UPA. The IAB donor and IAB-node have × UPA for fullyconnected structure. ( ρ = β = − dB, σ e,ji = σ e,jj = σ e,kj = − dB) C. Performance of Different Precoding Schemes
Fig. 6 shows the SE of the backhaul link for different precoding schemes. The ideal curves areplotted by assuming perfect CSI and SIC without HWI. The design of the RF precoders/combinersfor the ideal fully connected and subarray structures follow the process in [15], which have infiniteresolution. The non-ideal curves are plotted by our proposed design algorithm with 8 bits RFcodebook and setting ρ = β = − dB, σ e,ji = σ e,jj = σ e,kj = − dB. It can be observedthat for the FD scheme, these three precoding schemes evaluated in the figure are separated bya significant rate loss. Although the rate loss is evident, the subarray structure can significantlyreduce the hardware complexity and provide the low-computationally intensive precoders, whichis beneficial for industrial implementations. Further, with our staged SIC, the SE of the subarraystructure is very close to its ideal one; however, it shows some degrees of freedom loss at highSNR due to RSI caused by HWI and RF effective channel uncertainties. The losses on degreesof freedom and SE will be further reduced if the number of RF chains increases at the IAB-node receiver. Furthermore, without D-SIC, it is obvious that the SE becomes very low, which DRAFT January 26, 2021UBMITTED PAPER 27 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10
Estimation Error e,jj2 (dB) S p ec t r a l E ff i c i e n c y ( b it s / s / H z ) FD-subarrayHD-subarray1 bit4 bits8 bits
SNR = -10 dB, 0 dB, 10 dB (a) -100 -90 -80 -70 -60 -50 -40 -30 -20
Hardware Impairment = (dB) S p ec t r a l E ff i c i e n c y ( b it s / s / H z ) FD-subarrayHD-subarray1 bit4 bits8 bits
SNR = -10 dB, 0 dB, 10 dB (b)Fig. 7. SE of the backhaul link at SNR = − , , dB with 4-subarray hybrid precoding structure, where RF beamformersare selected from different size of codebooks, in the presence of different values of (a) SI RF effective channel estimation error( ρ = β = − dB, σ e,ji = σ e,kj = − dB); (b) HWI ( ρ = β , σ e,ji = σ e,jj = σ e,kj = − dB). indicates the important rule of D-SIC in the SIC process. D. Effect of RSI on the SE of the Backhaul Link
In Fig. 7, with RF precoders/combiners selected from 1, 4, 8 bits codebooks, we would liketo study how the RSI caused by SI RF effective channel estimation error and HWI can affectthe SE performance of the backhaul link at different SNR values. With ρ = β = − dB and σ e,ji = σ e,kj = − dB, we plot the SE performance of the backhaul link by varying thechannel estimation error of the SI RF effective channel in Fig. 7(a). Interestingly, it is worthnoting that as the size of RF codebook increases, the point of intersection (i.e., the point whereboth the FD and HD have the same performance) shifts to the right at a fixed SNR, which meansthe system can tolerate more RSI caused by channel estimation error. On the contrary, when thecodebook size is fixed, as SNR increases, the intersection point shifts to the left. By assumingall effective channels have the same estimation error of -140 dB, Fig. 7(b) shows the backhaullink SE performance with varying HWI factors. Similar to the trend in Fig. 7(a), with the same January 26, 2021 DRAFT8 IEEE TRANSACTIONS ON COMMUNICATIONS codebook size, as the SNR increase, the system can tolerate less RSI caused by HWI; however,when the codebook size increases, the tolerance is improved at a fixed SNR. From both figures,when ρ and β are small enough, one can see that the double rate can be achieved by the FDcompared to that of the HD. VII. C ONCLUSION
In this paper, we have studied the FR2 wideband FD-IAB networks. We have first developeda low complexity subarray hybrid precoding structure, where the RF beamformers are selectedfrom a matrix codebook given by a modified LBG quantization algorithm. We then introducedthe staged SIC scheme. In order to reduce the deployment cost, we have established the canceleron each RF chain pairs and utilized the FBG-based analog canceler to reduce the effect ofinsertion loss. The RSI left by the A-SIC was handled in the digital domain. We have shownthat our novel A-SIC scheme enables the wideband SIC with a constant insertion loss, comparedwith traditional micro-strip canceler. Simulations have shown that with large HWI and SI RFeffective channel uncertainties, the FD transmission experiences performance limitation in thebackhaul link; however, for small HWI and uncertainties, the FD promises almost double SEcompared with that of the HD.Further work will include investigating multicell FD-IAB systems, optimal power allocation,and efficient antenna cancellation. Besides, the SI channel model will also be studied by real-world measurements or other reliable mathematics models.R
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