In this paper, we propose a beamforming design for dual-functional
radar-communication (DFRC) systems at the millimeter wave (mmWave) band, where
hybrid beamforming and sub-arrayed MIMO radar techniques are jointly exploited.
We assume that a base station (BS) is serving a user equipment (UE) located in
a Non-Line-of-Sight (NLoS) channel, which in the meantime actively detects
multiple targets located in a Line-of-Sight (LoS) channel. Given the optimal
communication beamformer and the desired radar beampattern, we propose to
design the analog and digital beamformers under non-convex constant-modulus
(CM) and power constraints, such that the weighted summation of the
communication and radar beamforming errors is minimized. The formulated
optimization problem can be decomposed into three subproblems, and is solved by
the alternating minimization approach. Numerical simulations verify the
feasibility of the proposed beamforming design, and show that our approach
offers a favorable performance tradeoff between sensing and communication.Comment: 5 pages, 2 figures, submitted to ICASSP 201

Liu, Fan

Masouros, Christos

English

arXiv

In this paper, we propose a beamforming design for dual-functional radar-communication (DFRC) systems at the mil-limeter wave (mmWave) band, where hybrid beamforming and sub-arrayed MIMO radar techniques are jointly exploited. We assume that a base station (BS) is serving a multi-antenna user equipment (UE), which in the meantime actively detects multiple targets. Given the optimal communication beam-former and the desired radar beampattern, we propose to design the analog and digital beamformers under non-convex constant-modulus (CM) and power constraints, such that the weighted summation of the communication and radar beam-forming errors is minimized. The formulated optimization problem can be decomposed into three subproblems, and is solved by the alternating minimization approach. Numerical simulations verify the feasibility of the proposed beamforming design, and show that our approach offers a favorable performance tradeoff between sensing and communication

Liu, F

Masouros, C

UCL Discovery

arXiv:1810.09812v2  [eess.SP]  24 Oct 2018HYBRID BEAMFORMING WITH SUB-ARRAYED MIMO RADAR: ENABLING JOINTSENSING AND COMMUNICATION AT MMWAVE BANDFan Liu, Christos MasourosDepartment of Electronic and Electrical Engineering, University College LondonABSTRACTIn this paper, we propose a beamforming design for dual-functional radar-communication (DFRC) systems at the mil-limeter wave (mmWave) band, where hybrid beamformingand sub-arrayedMIMO radar techniques are jointly exploited.We assume that a base station (BS) is serving a user equip-ment (UE) located in a Non-Line-of-Sight (NLoS) channel,which in the meantime actively detects multiple targets lo-cated in a Line-of-Sight (LoS) channel. Given the optimalcommunication beamformer and the desired radar beampat-tern, we propose to design the analog and digital beamform-ers under non-convexconstant-modulus (CM) and power con-straints, such that the weighted summation of the communi-cation and radar beamforming errors is minimized. The for-mulated optimization problem can be decomposed into threesubproblems, and is solved by the alternating minimizationapproach. Numerical simulations verify the feasibility of theproposed beamforming design, and show that our approachoffers a favorable performance tradeoff between sensing andcommunication.Index Terms— Hybrid beamforming, mmWave, radar-communication, alternating minimization1. INTRODUCTIONTo address the explosive growth of wireless devices andservices, the coming 5G network aims at a 1000X increasein the capacity by exploiting the large bandwidth availableat mmWave band [1]. In the meantime, it is expected thatthe mmWave BS could be equipped with the sensing abil-ity, which may find its usage in a variety of scenarios suchas vehicle-to-everything (V2X) communications [2, 3]. Inlight of the above, it is favourable to have joint radar andcommunication functionalities deployed on a single hardwareplatform, which can support simultaneous target detectionand downlink communications.Existing contributions for dual-functional radar-communi-cation (DFRC) system mainly focus on the applications inthe lower frequency bands [4, 5, 6], e.g. sub-6GHz, and arethus difficult to be extended to the mmWave scenarios. Re-cent works propose to implement the radar function to supportV2X communications based on the IEEE 802.11ad WLANprotocol, which operates at the 60GHz band [7, 8]. As theWLAN standard is typically indoor based and employs small-scale antenna arrays, it can only support short-range sensingat the order of tens of meters.To overcome the aforementioned drawbacks, we pro-pose to exploit the large-scale antenna array deployed at themmWave BS, which can compensate the high path-loss im-posed on the mmWave signals. Moreover, the high degreesof freedom (DoFs) of massive antennas make it viable tosupport joint sensing and communication tasks. In order toreduce the hardware complexity and the associated costs,the hybrid analog-digital (HAD) beamforming structure istypically used in such systems, which requires much less RFchains compared to fully digital tranceivers [9]. It is inter-esting to note that, the HAD system is similar to an existingkind of radar called sub-arrayed MIMO radar that trades-offbetween phased-array and MIMO radars [10]. Therefore, it isnatural to combine these two techniques in the design of themmWave DFRC systems.In this paper, we consider a mmWave DFRC scenariowhere the BS detects targets while serving a multi-antennaUE in the downlink. We design analog and digital beamform-ers that can approach a given fully digital communicationbeamformer, while formulating a desired radar spatial beam-pattern that points to the target directions. The proposedapproach is modeled as a weighted minimization problem,which can be decomposed into three sub-problems. Wethen solve the problem via a triple alternating minimiza-tion method. Simulation results verify the feasibility of theproposed scheme, which achieves a favourable performancetradeoff for radar and communication.2. SYSTEM MODELWe consider a mmWave downlink where an Nt-antenna BSserves an Nr-antenna UE in the NLoS channel. In the mean-time, the BS senses the nearby environment by steering theprobing beams to the targets in the LoS channel. An HADbeamforming structure is deployed on the BS, where the num-ber of the RF chains is NRF . Without loss of generality, weassume that both the BS and the UE are equipped with uni-form linear array (ULA).2.1. Communication ModelThe received signal model at the UE can be expressed asy =√ρHFRFFBBs+ n, (1)where ρ denotes the average received power, H ∈ C×Nis the downlink channel matrix, FRF ∈ CN×NRF andFBB ∈ CNRF×NS stand for the analog and baseband (digi-tal) beamformers with NS being the number of data streams,s ∈ CNS×1 is the transmitted symbol vector, which satisfiesthat E(ssH)= INS , and finally n ∼ CN (0, N0IN ) denotesthe Gaussian noise.Following the extended Saleh-Valenzuela model [11, 12],the narrowband mmWave channel matrix can be expressed asH =√NtNrLL∑l=1αlar (θr,l) aHt (θt,l), (2)where L represents the number of scattering paths, αl is thecomplex gain of the l-th path, and ar (θr,l) and aHt (θt,l) de-note the receive and transmit array response vectors, respec-tively, where θr,l and θt,l are the azimuth angle of arrival(AoA) and angle of departure (AoD) for the l-th path. Foran N-antenna ULA, the array response vector can be given asa (θ) =1√N[1, ej2piλd sin(θ), ..., ej2piλd(N−1) sin(θ)]T, (3)where d and λ denote the antenna spacing and the signalwavelength, respectively. Without loss of generality, we setd = λ/2, and assume that the channel is perfectly known tothe BS.While there are several connected patterns between RFchains and antennas, here we consider the partially-connectedstructure for simplicity, which is also known as the sub-arrayed structure. Each RF chain is connected to Nt/NRFantennas via Nt/NRF phase shifters, which formulate a sub-array. The associated analog beamformer can be given in theformFRF =t1 0 · · · 00 t2 0.... . ....0 0 · · · tNRF ∈ CN×NRF , (4)where ti ∈ CNtNRF×1, i = 1, ..., NRF denotes the valuesof the phase shifters at the i-th sub-array, which containsconstant-modulus (CM) entries.2.2. Radar ModelThe above partially connected structure corresponds to an ex-isting kind of radar called sub-arrayed MIMO radar. Ac-cording to [10, 13], phased-array and MIMO radars can beviewed as the special cases of the sub-arrayed radar by lettingNRF = 1 and NRF = Nt, respectively. Hence, the sub-arrayed radar trades-off between the high directionality of thephased-array radar and the high degrees of freedom (DoFs) ofthe MIMO radar. The transmit beampattern of the radar canbe given as [10]G (θ) = aHt (θ)Rat (θ) , (5)where R ∈ CN×N is the covariance matrix of the precodedwaveform, and can be expressed asR = E(FRFFBBssHFHBBFHRF)= FRFFBBE(ssH)FHBBFHRF = FRFFBBFHBBFHRF .(6)It can be seen from (5) that to design the radar beampattern isequivalent to designing the covariance matrix above.Suppose that there are Ntar targets located at the angles{φ1, φ2, ..., φNtar}. The typical sub-arrayed MIMO radarbeamformer can be formulated as [13]Frad =v1 0 · · · 00 v2 0.... . ....0 0 · · · vNtar ∈ CN×Ntar , (7)where vi ∈ CNtNtar×1is composed by the entries of at (φi)that are located at the corresponding slots. The associ-ated radar covariance matrix is therefore given by Rd =FradFHrad, which is a rank-Ntar semidefinite matrix.2.3. Problem FormulationOur aim is to design the analog and digital beamformers, suchthat a high-quality communication link can be established be-tween the BS and the UE, while a well-designed radar beam-pattern is formulated at the BS simultaneously. To guaran-tee the communication performance, the hybrid beamformerFRFFBB should approach the fully-digital communicationbeamformerFcom. Noting the fact that multiplyingFrad withan unitary matrixU will not change the resultant radar beam-pattern, FRFFBB needs to approach FradU for ensuring theradar performance, whereU ∈ CNtar×NS is an auxiliary uni-tary matrix variable. We therefore consider the following op-timization problemminFRF ,FBB ,Uη ‖FRFFBB − Fcom‖2F+(1− η) ‖FRFFBB − FradU‖2Fs.t. FRF ∈ Ap, ‖FRFFBB‖2F = PT ,UUH = INtar ,(8)where η ∈ [0, 1] is a weighting factor that determines theweights for radar and communication performance, Ap rep-resents the feasible set of partially-connected analog beam-formers where CM constraints are imposed on the non-zeroelements of FRF , and finally PT denotes the power budget.Without loss of generality, we assume that NS ≥ Ntar. Notethat we enforce an equality constraint for the transmit power,as the radar is often required to transmit at its maximum avail-able power in practice [14].Due to the non-convexities in both the constraints and theobjective function, the problem (8) is rather difficult to tackle.While the global minimizer for (8) is in general unobtainable,we propose in the following a triple alternating minimization(TAltMin) method that can efficiently yield a near-optimal so-lution to the problem.3. PROPOSED APPROACHBy exploiting the special structure of FRF , the power con-straint of (8) can be recast as‖FRFFBB‖2F =NtNRF‖FBB‖2F = PT . (9)This indicates that the three variables are in fact separable,which yield three sub-problems that are much easier to solve.3.1. Sub-problem for UBy fixing FRF and FBB , problem (8) is equivalent tominU‖FradU− FRFFBB‖2F s.t. UUH = INtar . (10)Problem (10) tends to be a least-squares (LS) problem definedon the Stiefel manifold, which is obviously non-convex. Nev-ertheless, it has been proven that (10) can be classified into theso-called Orthogonal Procrustes problem (OPP) [15], whichcan be optimally solved in closed-form via singular value de-composition (SVD). This is given asU = U˜INtar×NSV˜, (11)where U˜ΣV˜ = FHradFRFFBB is the SVD ofFHradFRFFBB ,and INtar×NS is composed by anNtar×Ntar identity matrixand an Ntar × (NS −Ntar) zero matrix.3.2. Sub-problem for FRFWe then fixU andFBB and solve forFRF , in which case theoriginal problem can be reformulated asminFRFη ‖FRFFBB − Fcom‖2F+(1− η) ‖FRFFBB − FradU‖2F s.t. FRF ∈ Ap,(12)Again, due to the structure of FRF , problem (12) can besolved in a row-wise manner by solving for each non-zeroentry of FRF , which is obtained asminϕi,lη∥∥∥ejϕi,l(FBB)l,: − (Fcom)i,:∥∥∥2F+(1− η)∥∥∥ejϕi,l(FBB)l,: − (FradU)i,:∥∥∥2F,(13)where ϕi,l is the phase of the (i, l) non-zero element of FRF ,and (·)i,: denotes the i-th row for the matrix. Problem (13)is nothing but a phase rotation problem, where the optimalsolution is given by(FRF )i,l = exp(j arg{aHb}), (14)wherea =[√η(Fcom)i,:,√1− η(FradU)i,:]T,b =[√η(FBB)l,:,√1− η(FBB)l,:]T.(15)3.3. Sub-problem for FBBFinally, it remains to obtainFBB whileU andFRF are fixed.By recalling (9), the corresponding sub-problem isminFBBη ‖FRFFBB − Fcom‖2F+(1− η) ‖FRFFBB − FradU‖2F s.t. ‖FBB‖2F =NRFPTNt.(16)To simplify the problem, let us denoteA =[√ηFTRF ,√1− ηFTRF]T,B =[√ηFTcom,√1− ηUTFTrad]T.(17)Then problem (16) can be written compactly asminFBB‖AFBB −B‖2F s.t. ‖FBB‖2F =NRFPTNt, (18)which is an LS problem on the complex sphere. By furtherexpanding the objective function, problem (18) can be rewrit-ten asminFBBtr(FHBBQFBB)− 2Re (tr (FHBBG))s.t. ‖FBB‖2F =NRFPTNt,(19)whereQ = AHA,G = AHB. Since Q is a Hermitian ma-trix, problem (19) can be regarded as the matrix version ofthe trust-region sub-problem (TRS), for which strong dualityholds [16]. Hence, it is possible to obtain the global mini-mum of (19) by solving the associated Karush-Kuhn-Tucker(KKT) equations. Here we adopt [Algorithm 1, 5] to solvethe problem, where low-complexity operations such as eigen-value decomposition and golden-section search are involvedin the process. We refer the readers to [5] for more details.3.4. The TAltMin ProcedureNow we are ready to describe the TAltMin technique, whichhas been summarized in Algorithm 1 as follows.Algorithm 1 Triple Alternating Minimization Algorithm forSolving (8)Input: H,Fcom,Frad, 0 ≤ η ≤ 1, PT , tolerable accuracyε > 0 and the maximum iteration number kmaxOutput: FRF , FBB ,U1. Initialize randomlyU(0), F(0)RF and F(0)BB . Compute theobjective function of (8), denoted as f (0). Set k = 1.while k ≤ kmax and∣∣f (k) − f (k−1)∣∣ ≥ ε do2. ComputeU(k) by solving sub-problem (10).3. Compute F(k)RF by solving sub-problem (12).4. Compute F(k)BB by solving sub-problem (16).5. Compute the objective function f (k) based on the ob-tained variables.6. k = k + 1.end whileThe proposed TAltMin algorithm can be viewed as a coor-dinate descent method, where the convergence can be strictlyguaranteed [17]. In our simulations, we see that Algorithm 1always converges within tens of iterations.SNR (dB)-35 -30 -25 -20 -15 -10 -5 0 5Achievable Rate (bps/Hz)051015202530Optimal Fully Digital PrecoderTAltMin, η = 1TAltMin, η = 0.8TAltMin, η = 0.6TAltMin, η = 0.4Fig. 1. Achievable rate of the mmWave downlink,Nt = 120,NS = Nr = 6, NRF = 24.4. NUMERICAL RESULTSIn this section, we validate the effectiveness of the proposedbeamforming approach viaMonte Carlo simulations. Withoutloss of generality, we assume that Nt = 120, NS = Nr = 6,NRF = 24, and set PT = Nr as the normalized power. In oursimulations, we consider a mmWave channel with L = 10scattering paths. The number of targets in the LoS channelis set as 3, which are supposed to be located at the angles[−30◦, 0◦, 30◦]. Following the standard assumptions, we as-sume that each αl of the mmWave channel subjects to thestandard complex Gaussian distribution, and all the AoAs andAoDs follow the uniform distribution on [−pi, pi].We first show the achievable communication rate in Fig.1 by varying the weighting factor from 0.4 to 1, where thefully digital beamformer at the BS and the combiner at theUE are obtained as the firstNr right and left singular vectors,respectively. It can be observed that with the increase of η,moreweight is allocated to minimizing the Euclidean distancebetween the optimal and the designed communication beam-formers, and hence the achievable rate is on the rise. By let-ting η = 1, we obtain the communication-only performancewith partially-connected hybrid beamformer, where the radarperformance is not addressed. Fig. 2 further illustrates theassociated radar beampatterns, where the weighting factor isset as 0.4 and 0.6, respectively. We see that the BS can effec-tively steer its beams towards the directions of targets whilepreserving the communication performance. Moreover, byusing the proposed TAltMin method, a flexible performancetradeoff can be readily achieved.Angle (°)-90 -60 -30 0 30 60 90Beampattern (dBi)-20-15-10-5051015Ideal BeampatternTAltMin, η = 0.4TAltMin, η = 0.6Fig. 2. Radar beampatterns obtained by TAltMin, Nt = 120,NS = Nr = 6, NRF = 24.5. CONCLUSIONIn this paper, we consider the beamforming design for themmWave downlink, where a hybrid analog-digital beam-forming structure is deployed on the BS, which is adopted foraccomplishing the joint sensing and communication tasks.While the formulated beamforming optimization is noncon-vex, we propose a triple alternating minimization (TAltMin)approach to find a near-optimal solution to the problem. Nu-merical results show that by using the proposed method,a favorable performance tradeoff can be realized for targetdetection and downlink communication.6. REFERENCES[1] T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar,K. Wang, G. N. Wong, J. K. Schulz, M. Samimi, andF. Gutierrez, “Millimeter wave mobile communicationsfor 5G cellular: It will work!,” IEEE Access, vol. 1, pp.335–349, May 2013.[2] J. Choi, V. Va, N. Gonzalez-Prelcic, R. Daniels, C. R.Bhat, and R. W. Heath, “Millimeter-wave vehicularcommunication to support massive automotive sensing,”IEEE Commun. Mag., vol. 54, no. 12, pp. 160–167, Dec2016.[3] H. Wymeersch, G. Seco-Granados, G. Destino, D. Dar-dari, and F. Tufvesson, “5G mmWave positioning forvehicular networks,” IEEE Wireless Commun., vol. 24,no. 6, pp. 80–86, Dec 2017.[4] F. Liu, C. Masouros, A. Li, H. Sun, and L. Hanzo, “MU-MIMO communications with MIMO radar: From co-existence to joint transmission,” IEEE Trans. WirelessCommun., vol. 17, no. 4, pp. 2755–2770, Apr 2018.[5] F. Liu, L. Zhou, C. Masouros, A. Li, W. Luo,and A. Petropulu, “Toward dual-functional radar-communication systems: Optimal waveform design,”IEEE Trans. Signal Process., vol. 66, no. 16, pp. 4264–4279, Aug 2018.[6] A. Hassanien, M. G. Amin, Y. D. Zhang, and F. Ah-mad, “Dual-function radar-communications: Informa-tion embedding using sidelobe control and waveformdiversity.,” IEEE Trans. Signal Process., vol. 64, no.8, pp. 2168–2181, Apr 2016.[7] P. Kumari, J. Choi, N. Gonzlez-Prelcic, and R. W.Heath, “IEEE 802.11ad-based radar: An approach tojoint vehicular communication-radar system,” IEEETrans. Veh. Technol., vol. 67, no. 4, pp. 3012–3027, Apr2018.[8] E. Grossi, M. Lops, L. Venturino, and A. Zappone, “Op-portunistic radar in IEEE 802.11ad networks,” IEEETrans. Signal Process., vol. 66, no. 9, pp. 2441–2454,May 2018.[9] A. F. Molisch, V. V. Ratnam, S. Han, Z. Li, S. L. H.Nguyen, L. Li, and K. Haneda, “Hybrid beamformingfor massive MIMO: A survey,” IEEE Commun. Mag.,vol. 55, no. 9, pp. 134–141, Sept 2017.[10] D. Wilcox and M. Sellathurai, “On MIMO radar subar-rayed transmit beamforming,” IEEE Trans. Signal Pro-cess., vol. 60, no. 4, pp. 2076–2081, Apr 2012.[11] D. Zhang, Y. Wang, X. Li, and W. Xiang, “Hybridlyconnected structure for hybrid beamforming in mmwavemassive MIMO systems,” IEEE Trans. Commun., vol.66, no. 2, pp. 662–674, Feb 2018.[12] N. Gonzlez-Prelcic, R. Mndez-Rial, and R. W. Heath,“Radar aided beam alignment in mmWave V2I com-munications supporting antenna diversity,” in Proc. In-formation Theory and Applications Workshop (ITA), Jan2016, pp. 1–7.[13] A. Hassanien and S. A. Vorobyov, “Phased-MIMOradar: A tradeoff between phased-array and MIMOradars,” IEEE Trans. Signal Process., vol. 58, no. 6,pp. 3137–3151, Jun 2010.[14] P. Stoica, J. Li, and Y. Xie, “On probing signal designfor MIMO radar,” IEEE Trans. Signal Process., vol. 55,no. 8, pp. 4151–4161, Aug 2007.[15] T. Viklands, Algorithms for the weighted orthogonalProcrustes problem and other least squares problems,Ph.D. thesis, Comput. Sci. Dept., Umea Univ., Umea,Sweden, 2008.[16] C. Fortin and H. Wolkowicz, “The trust region subprob-lem and semidefinite programming,” Optim. MethodsSoftw., vol. 19, no. 1, pp. 41–67, 2004.[17] A. Beck, “On the convergence of alternating mini-mization for convex programming with applications toiteratively reweighted least squares and decompositionschemes,” SIAM J. Optim., vol. 25, no. 1, pp. 185–209,2015.

Hybrid Beamforming With Sub-arrayed MIMO Radar: Enabling Joint Sensing and Communication at mmWave Band

Abstract

Similar works

Full text

Available Versions

UCL Discovery

Crossref