Millimeter-Wave Massive MIMO with Lens Antenna Array for 5G

Transcription

1 Millimeter-Wave Massive MIMO with Lens Antenna Array for 5G Linglong Dai( 戴凌龙 ) Department of Electronic Engineering Tsinghua University May /82

2 Contents G vision and solutions Lens-based mmwave MIMO Our related wors a. Beamspace channel estimation b. Beam selection c. Power leaage problem d. Beamspace channel tracing e. Beamspace MIMO-NOMA Future research direction 2/82

3 5G Vision 5G ey performance indicators (KPIs) defined by ITU Pea data rate (Gbit/s) User experienced data rate (Mbit/s) Area traffic capacity 2 (Mbit/s/m ) IMT Spectrum efficiency 100 Networ energy efficiency 10 1 IMT-advanced Mobility (m/h) Connection density 2 (devices/m ) 1 Latency (ms) M ITU-R M , IMT vision-framewor and overall objectives of the future development of IMT for 2020 and beyond, Sep /82

4 How to realize 5G? Key requirement of 5G: 1000-fold capacity How to realize this goal from Shannon capacity? Three technical directions for 5G No. of APs Bandwidth C D * W * M * log (1+SINR) No. of antennas Interference mitigation 4/82

5 What is massive MIMO? Use hundreds of BS antennas to simultaneously serve multiple users Conventional MIMO M:2~8, K:1~4 (LTE-A) Massive MIMO M: ~100~1000, K: 16~64 T. L. Marzetta, Non-cooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas, IEEE Transactions on Wireless Communications, vol. 9, no. 11, pp , Nov (2013 IEEE Marconi prize) 5/82

6 Advantages of mmwave massive MIMO Three properties High frequency ( GHz): wider bandwidth (20 MHz 2 GHz) Short wavelength: larger antenna array (massive MIMO) (1~8 256~1024) Serious path-loss: more appropriate for small cell mmwave High frequency Short wavelength Serious path-loss Spectrum expansion Large antenna array Small cell 1000x data rates increase! 6/82

7 Challenges of mmwave massive MIMO Challenges Traditional MIMO: one dedicated RF chain for one antenna Enormous number of RF chains due to large antenna array Unaffordable energy consumption (250 mw per RF chain at 60 GHz) MmWave massive MIMO BS with 256 antennas 64 W (only RF) Micro-cell BS in 4G several W (baseband + RF + transmit power) How to reduce the number of required RF chains? 7/82

8 Contents G vision and solutions Lens-based mmwave MIMO Our related wors a. Beamspace channel estimation b. Beam selection c. Power leaage problem d. Beamspace channel tracing e. Beamspace MIMO-NOMA Future research direction 8/82

9 Lens-based mmwave massive MIMO Basic idea [Brady 13] Concentrate the signals from different directions (beams) on different antennas by lens antenna array Transform conventional spatial channel into beamspace (spatial DFT) Limited scattering at mmwave beamspace channel is sparse Select dominant beams to reduce the dimension of MIMO system Negligible performance loss significantly reduced number of RF chains High- Dimension Digital Precoding RF Chains Conventional MIMO J. Brady, N. Behdad, and A. Sayeed, Beamspace MIMO for millimeter-wave communications: System architecture, modeling, analysis, and measurements, IEEE Trans. Ant. and Propag., vol. 61, no. 7, pp , Jul Beamspace MIMO 9/82

10 Beamspace channel Path 1 Spatial channel Path 2 Lens Antenna array Beamspace channel H = UH 10/82

11 Mathematical principle System model K single-antenna users, BS with N antennas, NRF = KRF chains H H N K y = H x+ n= H Ps+ n, H = [ h, h,, h ] Saleh-Valenzuela channel model [Ayach 14] i= L ( 0) ( ( 0) ) () i ( () i ) 1 j2πψ m h = β a ψ + β a ψ, a( ψ ) = e, N m ( N) K ψ d sinθ λ LoS path NLoS paths ULA steering vector where ψ : spatial direction and θ : physical direction Transform the spatial channel into beamspace H H H y = H U Ps+ n= H Ps + n, ( ) ( ) ( ) H = ψ1 ψ2 ψ N U a, a,, a, where Beamspace channel { } ( ) ( ) DFT matrix realized by lens antenna array ( ( ) ) N = l N 1/2, l = 0,1,, N 1, ψ n = n N + 1/2/ N, n= 1,2,, N 11/82

12 Mathematical principle Sparsity [ ] H = h 1, h 2,, h K = UH = Uh 1, Uh 2,, Uh K h with a small number of dominant elements Approximately sparse Beam selection Select a small number of dominant beams H y H r Ps r + n, H r = H ( l,: ) l P r is the dimension-reduced precoder Only a small number of RF chains J. Brady, N. Behdad, and A. Sayeed, Beamspace MIMO for millimeter-wave communications: System architecture, modeling, analysis, and measurements, IEEE Trans. Ant. and Propag., vol. 61, no. 7, pp , Jul /82

13 Prototype Key parameters AP employs a lens antenna array with 16 elements 2 single-antenna users Frame structure User discover Beam selection (4 out of 16) Beam-frequency channel estimation Precoding Data detection More details: 13/82

14 Contents G vision and solutions Lens-based mmwave MIMO Our related wors a. Beamspace channel estimation b. Beam selection c. Power leaage problem d. Beamspace channel tracing e. Beamspace MIMO-NOMA Future research direction 14/82

15 Outline of our research Lens-based mmwave massive MIMO Research objective 1 Beamspace channel estimation Require accurate beamspace channel Research objective 2 Beam selection Beamspace channel varies fast Research objective 3 Beamspace channel tracing Adaptive support detection-based 2D/3D channel estimation Interference-aware beam selection Solve the power leaage problem Priori-aided channel tracing Research objective 4 Brea the fundamental limit Beamspace MIMO- NOMA Xinyu Gao, Linglong Dai, Abar Sayeed, Low RF-complexity technologies for 5G millimeter-wave MIMO systems with large antenna arrays, IEEE Communications Magazine, vol. 56, no. 4, pp , Apr /82

16 Existing problems Beamspace channel estimation Beam selection requires the information of beamspace channel Channel dimension is large while the number of RF chains is limited We cannot sample the signals on all antennas simultaneously Unaffordable pilot overhead Different hardware architecture compared to hybrid precoding Existing channel estimation schemes for hybrid precoding cannot be used How to estimate the beamspace channel with low pilot overhead? 16/82

17 Channel estimation in TDD model Channel measurements All K users transmit orthogonal pilot sequences to BS over Q instants BS employs a combiner W to obtain the measurements of channel z Channel is estimated, and used according to channel reciprocity z = Wh + n Existing challenges If we use traditional selecting networ to design the combiner W Each row of W will have one and only one nonzero element To mae z contain complete information of h Q N For mmwave massive MIMO systems N is quite large, e.g., 1024 Fast-varying channel at mmwave frequencies Unaffordable pilot overhead! 17/82

18 Proposed Adaptive selecting networ Adaptive selecting networ Utilize 1-bit phase shifter (PS) networ to design W Adaptive: selecting networ for data transmission & combiner for channel estimation Q< N, z has full information sparse signal recovery problem 1-bit PS Low energy consumption Xiny Gao, Linglong Dai, Shuangfeng Han, Chih-Lin I, and Xiaoding Wang, Reliable beamspace channel estimation for millimeter-wave massive MIMO systems with lens antenna array, IEEE Transactions on Wireless Communications, vol. 16, no. 9, pp , Sep /82

19 Problem formulation Sparse signal recovery problem Estimate sparse h of size N with smaller number of measurements Q z = Wh + n Classical CS algorithms can be directly used Classical CS algorithms Deteriorated performance in low SNR region Low transmit power at user side Serious path loss of mmwave signals Lac of beamforming gain Low SNR We should utilize the structural properties of beamspace channel 19/82

20 Structural property 1 i i L Lemma 2. Present as, where is the ith channel component of h h h = N /( L+1) i = c c = Uc 0 i in the beamspace. Then, when the number of BS antennas N goes infinity, any two channel components c i and c j are orthogonal, i.e., H = = Insights lim c c 0, i, j 0,1,, L, i j. N i j Total estimation problem can be decomposed into independent sub-problems Each sub-problem only considers one sparse channel component 20/82

21 Structural property 2 Lemma 3. Consider the ith channel component in the beamspace, and assume V is an even integer. Then, the ratio between the power P V of V strongest elements of c i and the total power P T of c i can be lower-bounded by 1 V /2 P 2 2 ( 2i 1) π V 2 sin. PT N i= 1 2N * Moreover, once the position n i of the strongest element of c i is determined, the other V- * 1 strongest elements will uniformly located around c i n i Insights c i can be considered as a sparse vector with sparsity V N = 256, V = 8, PV / PT 95% The support of c i can be uniquely * determined by n i V V supp c i = mod N ni,, ni ( ) * * π N sin 2N 1 3π N sin 2N 1/ N 1/ N ψ 1/2N 21/82

22 Support detection (SD)-based 2D channel estimation 22/82

23 Performance analysis Lemma 4. Consider the LoS scenario, i.e., h = Nc0 and suppose that the strongest element of h satisfies 2 8σUL ( 1+ α) lnn h *, n, ( 1 μ )( 1 κ ) 2μη where α > 0 is a constant, and we define that N 1 1 sin ( π / 2N ) η sin ( π / 2 N ), κ. n= 1 sin( ( 2n 1 ) π / 2N) sin ( π / 2N ) sin ( 3 π / 2N ) Then, the probability that the position of the strongest element is correctly estimated is lowerbounded by N 1 Lemma 4 can be directly extended to Pr 1. α + 1 N π( 1+ α) lnn the scenario with NLoS components Insights For small * n,, α should also be small The probability decreases Higher accuracy than CS h h n, * 23/82

24 Simulation parameters System parameters MIMO configuration: N K = , NRF = K = 16 Total time slots: Q= MK = 96 ( M = 6 ) Beam selection: IA beam selection Dimension-reduced digital precoder: ZF Channel parameters Channel model: Saleh-Valenzuela model Antenna array: ULA at BS, with antenna spacing d = λ /2 Multiple paths: One LoS component and two NLoS components ( L = 2) LoS component Amplitude: 0 ( ) ( 0) 1 1 β ~ ( 0,1) Spatial direction: ψ ~, 2 2 NLoS components () i 2 () i 1 1 Amplitude: β ~ ( 0,10 ) Spatial direction: ψ ~, 1 i L /82

25 Simulation results Observations SD-based channel estimation outperforms conventional schemes NMSE (db) The performance is satisfying even in the low SNR region The pilot overhead is low, i.e., Q= 96 < N= Conventional OMP-based channel estimation Proposed SD-based channel estimation Achievable sum-rate (bits/s/hz) Fully digital system IA beam selction with perfect CSI SD-based channel estimation (uplin SNR = 0 db) OMP-based channel estimation (uplin SNR = 0 db) SD-based channel estimation (uplin SNR = 10 db) OMP-based channel estimation (uplin SNR = 10 db) SD-based channel estimation (uplin SNR = 20 db) OMP-based channel estimation (uplin SNR = 20 db) Uplin SNR (db) Downlin SNR (db) Xiny Gao, Linglong Dai, Shuangfeng Han, Chih-Lin I, and Xiaoding Wang, Reliable beamspace channel estimation for millimeter-wave massive MIMO systems with lens antenna array, IEEE Transactions on Wireless Communications, vol. 16, no. 9, pp , Sep /82

26 Extension to 3D beamspace channel Lemma 5. Define N1 N2 matrix as C. Define as the submatrix of C l l l i, j = cl N2 i 1 + j S extracting V strongest rows and V strongest columns from. Assume 1 2 C l V1 and V 2 are even integers without loss of generality. Then, the ratio between the power of S and the power of C l can be lower-bounded by 2 V1/2 V2/2 S F N i= 1 2( 2i 1) C π j= 1 2( 2j 1) π l F sin sin 2N1 2N2 Insights C ( ) ( ) C l can be considered as a bloc sparse matrix 2 2 N1 = N2 = 32, V1 = V2 = 8, S / C l 91% F F Indices extracted rows and columns are is uniquely determined by C l i, j V1 V1 2 = mod N i,, i V2 V2 2 = mod N j,, j Support of c is supp( c l ) = N2 ( r 1 ) + c, r, c l { } ( ) ( ) 26/82

27 Adaptive SD (ASD)-based 3D channel estimation Key idea l Amplitude distribution of C l with more serious vertical power diffusion 16 ( ) Adaptively adjust supp c based on the power diffusions in both directions Amplitude distribution of C l with more serious horizontal power diffusion Index of vertical beam Index of vertical beam Index of horizontal beam V = V Index of horizontal beam V V V = V /2 1 = 2V = V / V2 = 2V2 Strongest element Marginal element Extracted element 27/82

28 Mathematical description Stage 1 Estimate the strongest element c * * * * * l p i = p / N 2, j = p N2 i 1 Assume V1 = V2 to obtain the initial support Estimate nonzero elements, and define four marginal values M = e i *, j * V /2 M = C e i *, j * + V /2 1 Stage2 Serious vertical power diffusion ( ) C l ( ) 2 l ( 2 ) e * * C l ( ) M e ( * * 4 = C l i + V1 /2 1, j ) 1 2 M /2, 3 = i V1 j ( M M ) < ( M M ) min, min, V1 = 2 V1, V2 = V2 /2 min ( M1, M2) > min ( M3, M4) Serious horizontal power diffusion ( ) V1 = V1/2, V2 = 2V2 Repeat stage 1 until the power diffusions in both directions are the same 28/82

29 Simulation parameters System parameters MIMO configuration: N = N1 N2 = = 1024, NRF = K = 16 Total time slots: Q = 256 Initialization for ASD algorithm: V1 = V2 = 8 Combiner W : Bernoulli random matrix, i.e., W( i, j) { 1, + 1 } / Q Data transmission: IA beam selection & dimension-reduced ZF precoder Channel parameters Channel model: Saleh-Valenzuela (SV) model Antenna array: UPA at BS, with antenna spacing d1 = d2 = λ /2 Multiple paths: One LoS component and two NLoS components ( L = 2) LoS component ( 0) ( 0) ( 0) Amplitude: β ( 0,1) Spatial direction: ϕ, θ ( 0.5,0.5) NLoS components i 2 () l () l Amplitude: ~ 0,10 Spatial direction: ϕ, θ 0.5,0.5 β () ( ) ( ) 29/82

30 Simulation results Observations ASD-based channel estimation outperforms conventional scheme The performance is satisfying even in the low SNR region The pilot overhead is low, i.e., Q= 256 N=1024 Beam selection can achieve near-optimal performance with estimated channel NMSE (db) Conventional OMP-based channel estimation Proposed ASD-based channel estimation Achievable sum-rate (bits/s/hz) Fully digital ZF precoder with perfect CSI IA beam selction with perfect CSI ASD-based channel estimation (uplin SNR = 0 db) OMP-based channel estimation (uplin SNR = 0 db) ASD-based channel estimation (uplin SNR = 10 db) OMP-based channel estimation (uplin SNR = 10 db) ASD-based channel estimation (uplin SNR = 20 db) OMP-based channel estimation (uplin SNR = 20 db) Uplin SNR (db) Downlin SNR (db) Xiny Gao, Linglong Dai, Shuangfeng Han, Chih-Lin I, and Xiaoding Wang, Reliable beamspace channel estimation for millimeter-wave massive MIMO systems with lens antenna array, IEEE Transactions on Wireless Communications, vol. 16, no. 9, pp , Sep /82

31 Contents G vision and solutions Lens-based mmwave MIMO Our related wors a. Beamspace channel estimation b. Beam selection c. Power leaage problem d. Beamspace channel tracing e. Beamspace MIMO-NOMA Future research direction 31/82

32 Outline of our research Lens-based mmwave massive MIMO Research objective 1 Beamspace channel estimation Require accurate beamspace channel Research objective 2 Beam selection Beamspace channel varies fast Research objective 3 Beamspace channel tracing Adaptive support detection-based 2D/3D channel estimation Interference-aware beam selection Solve the power leaage problem Priori-aided channel tracing Research objective 4 Brea the fundamental limit Beamspace MIMO- NOMA Xinyu Gao, Linglong Dai, Zhijie Chen, Zhaocheng Wang, and Zhijun Zhang, Near-optimal beam selection for beamspace mmwave massive MIMO systems, IEEE Communications Letters, vol. 20, no. 5, pp , May /82

33 Existing problem Magnitude maximization (MM) beam selection Directly select beams with large power, which enjoys low complexity Different users may select the same beam Severe interference Number of RF chains is uncertain and unfixed Unfavorable for practical system design A. Sayeed, et al., Beamspace MIMO for high-dimensional multiuser communication at millimeter-wave frequencies, in Proc. IEEE GLOBECOM 13, Dec /82

34 Interference-aware (IA) beam selection Motivation Select the best beam (but not the strongest beam) for each user The required number of RF chains is fixed and certain Stage 1: Identify IUs and NIUs Classify all users into two user groups Interference-users (IUs): users who share the same strongest beam Noninterference-users (NIUs): users who have distinct strongest beams Stage 2: Search the best unshared beam Select the strongest beam for each NIU Select a fixed number of beams for IUs in the remained beam set Beams with the greatest contribution to sum-rate are selected 34/82

35 Illustration Beam index Stage 1 Stage 2 35/82

36 Stage 1: Identify IUs and NIUs Inspiration b { 1 2 } The strongest beam of each user enjoys most of the total power Can we directly choose = b *, b *,, b * K? ( 0) Lemma 1. Assume that spatial directions ψ for = 1, 2,, K follow the i.i.d. uniform distribution within [ 0.5,0.5]. The probability P that there exist users sharing the same strongest beam is N! P = 1. K N N K! ( ) P 87% when N = 256 and K = 32 Serious inter-beam interference! Definitions NIUs: one user is NIU if its strongest beam is different from any other strongest beams, i.e., b * b *,, b *, b *,, b * IUs: any two users 1 and 2 are IUs if b { } K * * b1 = b2 36/82

37 Stage 2: Select the best unshared beam Select the optimal beam set opt * Select the beams for NIUs NIU = b NIU * Choose IU beams from { 1, 2,, N} \ { b NIU} as a candidate opt Combine IU and NIU to form the set Based on, select = K beams of beamspace channel H The dimension-reduced MIMO system ( l ) y H Ps n, H H,:, H r r + r = l IU opt Search the optimal by maximizing the achievable sum-rate R R = ( + γ ) opt IU = arg max R, IU Form the optimal set of selected beams for all K users K = 1 { } log 1, 2 γ = m h h p H r, r, p H r, rm, 2 2 IU 2 + σ = opt opt opt IU NIU 37/82

38 Simulation parameters System parameters MIMO configuration: N K = , NRF = K = 32 Dimension-reduced digital precoder: Zero forcing (ZF) Channel parameters Channel model: Saleh-Valenzuela model Antenna array: ULA at BS, with antenna spacing d = λ /2 Multiple paths: One LoS component and two NLoS components ( L = 2) LoS component Amplitude: 0 ( ) ( 0) 1 1 β ~ ( 0,1), Spatial direction: ψ ~, 2 2 NLoS components () i 1 () i 1 1 Amplitude: β ~ ( 0,10 ), Spatial direction: ψ ~, 1 i L /82

39 Simulation results Observations IA beam selection can achieve the near-optimal sum-rate performance IA beam selection enjoys higher energy efficiency The number of required RF chains is certain and fixed 150 Fully digital system Conventional MM beam selection (2 beams per user) Conventional MM beam selection (1 beam per user) Proposed IA beam selection (1 beam per user) Fully digital system Conventional MM beam selection (2 beams per user) Conventional MM beam selection (1 beam per user) Proposed IA beam selection (1 beam per user) Achievable sum-rate (bits/s/hz) Energy efficient (bps/hz/w) SNR (db) Number of users K Xinyu Gao, Linglong Dai, Zhijie Chen, Zhaocheng Wang, and Zhijun Zhang, Near-optimal beam selection for beamspace mmwave massive MIMO systems, IEEE Communications Letters, vol. 20, no. 5, pp , May /82

40 Contents G vision and solutions Lens-based mmwave MIMO Our related wors a. Beamspace channel estimation b. Beam selection c. Power leaage problem d. Beamspace channel tracing e. Beamspace MIMO-NOMA Future research direction 40/82

41 Outline of our research Lens-based mmwave massive MIMO Research objective 1 Beamspace channel estimation Require accurate beamspace channel Research objective 2 Beam selection Beamspace channel varies fast Research objective 3 Beamspace channel tracing Adaptive support detection-based 2D/3D channel estimation Interference-aware beam selection Solve the power leaage problem Priori-aided channel tracing Research objective 4 Brea the fundamental limit Beamspace MIMO- NOMA Tian Xie, Linglong Dai, Jianju Li, et al., On the power leaage problem in beamspace MIMO systems with lens antenna array, submitted to IEEE Transactions on Communications, /82

42 Existing problem Power leaage in beamspace channel Fixed spatial sample points of the lens antenna array v.s. continuously distributed angle of paths The power of one path will lea onto the adjacent elements Conventional precoding schemes select one beam for one path, where most power of one path is not collected. Amplitude Spatial Lens resolution samples 1/N Amplitude Spatial Lens resolution samples 1/N φ 1 (a) No power leaage Spatial direction (b) φ 2 Worst power leaage Spatial direction For the worst power leaage case, more than 50% power of one path will be leaed! 42/82

43 Conventional precoding structure Single RF per user (srf/user) precoding [Amadori s 15] Ignore the power leaage and select one beam for each path The number of required RF chains is relatively low Significant loss in SNR and achievable rate due to the insufficient collected power [Amadori s 15] P. Amadori and C. Masouros, Low RF-complexity millimeter-wave beamspace-mimo systems by beam selection, IEEE Trans. Commun., vol. 63, no. 6, pp , Jun /82

44 A straightforward solution Full dimension (FD) precoding Use more RF chains (e.g., 3 RF chains for each path) to collect the leaed power of paths FD precoding is able to collect most leaed power The required energy consumption is high due to a large number of RF chains 44/82

45 Proposed PSN-based precoding Proposed phase shifter networ (PSN)-based precoding Use an analog networ to collect the leaed power Signal on each antenna is rotated via a phase shifter and then connect to one RF chain Collect most leaed power to achieve near-optimal sum rate, while the number of required RF chains is low 45/82

46 Signal model System model Single-antenna users, BS with N antennas, NRF = K RF chains H H y = H x+ n= H P P s+ n H = h, h,, h Beamspace Channel matrix P [ ] RF domain precoder RF BB, Constraints on RF precoder Baseband precoder j If the th RF chain is connected to the lth antenna, RF,l ; otherwise it is zero The element in the RF precoder has non-convex constant modulus constraint 1 2 [ P ] Conventional precoding algorithm cannot be generalized to the PSN-based precoding structure! K = e θ N K P (1) (2) ( NRF ) = p, p,, p RF RF RF RF N N RF How to effectively design the precoding algorithm? 46/82

47 Rotation-based precoding algorithm Observation 1 [Zeng 16] In lens-based massive MIMO systems, users are distinguished based on their angles. Since different users are liely to have different angles, the inter-user interference (IUI) in lens-based massive MIMO systems is not severe We can neglect the IUI and maximize the received signal power Observation 2 H H The diagonal elements in the RF domain channel HRF = H PRF represent the received signal power for the th user. Moreover, we have H = h p = h p H H ( ) H ( ) RF, RF i RF i B where B is the set containing the indices of selected beams for the th user H H Once the B is determined, maximizing H RF equals rotating to the, h ( ) i same direction via p RF [Zeng 16] Y. Zeng and R. Zhang, Millimeter wave MIMO with lens antenna array: A new path division multiplexing paradigm, IEEE Trans. Commun., vol. 64, no. 4, pp , Apr i i 47/82

48 Rotation-based precoding algorithm Observation 3 The channel elements corresponding to the leaed power (wea elements) are distributed around the channel element with the strongest power (strong element) We can leverage the strong element to position each path and then pic up the wea elements Amplitude Lens resolution 1/N Strong element Wea element φ 2 Spatial direction 48/82

49 Rotation-based precoding algorithm RF precoder design (user by user) Adjacent channel elements: two channel elements are adjacent if the differences of their indices are at most one in any dimension Greedy beam selection: Search the channel element with the highest power and add this element to B Update a set A that contains all adjacent elements to the elements in Pic up the element with the highest power in A, and add it to B Repeat such procedure until an end criteria Generate the RF precoder Rotate the elements in to the same direction B Baseband precoder design Employ the maximum ratio transmission (MRT) precoding on the RF domain channel B 49/82

50 Rotation-based precoding algorithm Elevation beam index Azimuth beam index Elevation beam index Elevation beam index Azimuth beam index Azimuth beam index Selected elements Elements adjacent to selected elements Elevation beam index Azimuth beam index 50/82

51 Rotation-based precoding algorithm H h H H h + h p p q H h q Combination without rotation H H h + h p q H h p H h q Combination with rotation 51/82

52 Achievable sum rate performance Observation The proposed PSN-based precoding can effectively overcome the power leaage problem The proposed PSN-based precoding can achieve near-optimal sum rate compared with the optimal FD precoding 52/82

53 Energy efficiency performance Observation Although the FD precoding has the optimal sum rate, its energy efficiency is relatively low due to the large number of required RF chains The proposed PSN-based precoding enjoys higher energy efficiency than the conventional precoding Tian Xie, Linglong Dai, Jianju Li, et al., On the power leaage problem in beamspace MIMO systems with lens antenna array, submitted to IEEE Transactions on Communications, /82

54 Contents G vision and solutions Lens-based mmwave MIMO Our related wors a. Beamspace channel estimation b. Beam selection c. Power leaage problem d. Beamspace channel tracing e. Beamspace MIMO-NOMA Future research direction 54/82

55 Outline of our research Lens-based mmwave massive MIMO Research objective 1 Beamspace channel estimation Require accurate beamspace channel Research objective 2 Beam selection Beamspace channel varies fast Research objective 3 Beamspace channel tracing Adaptive support detection-based 2D/3D channel estimation Interference-aware beam selection Solve the power leaage problem Priori-aided channel tracing Research objective 4 Brea the fundamental limit Beamspace MIMO- NOMA Xinyu Gao, Linglong Dai, Yuan Zhang, et al., Fast channel tracing for terahertz beamspace massive MIMO systems, IEEE Transactions Vehicular Technology, vol. 66, no. 7, pp , Jul /82

56 Existing problems Beamspace channel tracing Fast-varying channel for moving users at mmwave frequencies Real time channel estimation leads to quite high overhead Classical Kalman filter for channel tracing Beamspace channel does not follow the one-order Marov process Search several candidate beams for channel tracing Beam training overhead is high 56/82

57 Priori-aid (PA) channel tracing Key idea Temporal variation law of the physical direction Prediction Structural properties of the beamspace channel Priori information Trac the beamspace channel with quite low pilot overhead Xinyu Gao, Linglong Dai, Yuan Zhang, et al., Fast channel tracing for terahertz beamspace massive MIMO systems, IEEE Transactions Vehicular Technology, vol. 66, no. 7, pp , Jul /82

58 Motion of the th user v d () t vt ϕ ( 1) d t+ ( 2) d t+ θ ( t + 2) θ () t θ ( t + 1) y axis vt x axis : speed : sampling period : direction of motion d () t θ () t T ϕ t ( t +1) ( t + 2) : distance at time t : physical direction at time t { d t, t, ϕ, v} The motion of the th user can be described by () θ () 58/82

59 Motion state of the th user Target Predict θ ( t + 1) according to θ () 1, θ ( 2, ), θ () Solution m t () t v / d () t Define an auxiliary parameter angular speed Define the motion state of the th user at time t λ T () t θ () t, λ () t, ϕ m () t m ( t +1) m Proposition 1. The relationship between and is m sin θ () t + Tλ () t cosϕ λ () t + 1 =Θ ( ) = arctan,, ϕ cos θ 2 2 () t + Tλ () t sin ϕ 1+ 2Tλ () t sin θ () t + ϕ + T λ () t ( t ) m ( t) m () ( ) Corollary 1. The relationship between t and m t+ N is sin () () cos N θ t + NTλ t ϕ λ () t ( t N) ( m ( t) ) θ () t + NTλ () t ϕ 1+ 2NTλ () t sinθ () t + ϕ + N T λ () t + =Θ = arctan,, ϕ cos sin m () ( ) After t has been estimated, θ t+ N can be predicted accordingly T T 59/82

60 How to estimate the motion state? Observations λ λ Consider the triangle with orange lines and utilize the law of sine ( t ) ( t ) ( ) ( ) () ( ) ( ) () Consider the triangle with red lines and utilize the law of sine vt y axis vt ( ) ( ) ( ) ( ) ( ) ( ) v sin θ t+ 1 θ t sin θ t+ 1 θ t sin 1 sin 1 +1 v θ t+ θ t θ t+ θ t = = =, λ () t = = = d ( t+ 1) Tsin π /2+ θ t + ϕ Tcosθ t + ϕ d () t Tsin π /2 θ t+ 1 ϕ Tcos θ t+1 + ϕ ( ) ( ) () ( ) ( ) () ( ) ( ) ( ) ( ) ( ) ( ) v sin θ t+ 2 θ t sin θ t+ 2 θ t sin 2 sin 2 +2 = v θ t+ θ t θ t+ θ t = =, λ () t = = = r ( t+ 2) 2Tsin π / 2 + θ t + ϕ 2Tcos θ t + ϕ d () t 2Tsin π / 2 θ t+ 2 ϕ 2Tcos θ t+2 + ϕ d () t ϕ ( 1) d t + ( 2) d t + t ( t +1) ( t + 2) θ ( t + 2) θ () t θ ( t + 1) x axis 60/82

61 How to estimate the motion state? Solutions θ () θ ( ) ( ) Estimate t, t 1, and θ t 2 by regular channel estimation Use the observations () ( ) () ( ) () ( ) ( ) 2a cos θ t b cos θ t 1 sinθ t θ t 2 ϕ =, λ() t = 2asin θ t bsin θ t 1 2Tcos θ t 2 + ϕ ( ) ( ) () ( ) where a sin θ t 1 θ t 2, b sin θ t θ t 2 The motion state at time t can be estimated as m() t θ() t, λ() t, ϕ One step prediction Why one step? θ () θ ( ) ( ) t, t 1, and θ t 2 may be not accurate enough A miss is as good as a mile According to Proposition 1 θ ( t ) () t T () t () t T () t sin θ + λ cosϕ + 1 = arctan cos θ + λ sin ϕ T 61/82

62 Priori-aid (PA) channel tracing Regular 1 t channel 3 estimation for e 1. Estimate h () t by SD-based channel estimation 2. Detect the physical direction θ () t according to the position of the strongest element end Channel Tracing fort > 3 T 3. Estimate the motion state m( t 1) θ( t 1 ), λ( t 1 ), ϕ 4. Predict the physical direction θ () t 5. Detect the support of h () t based on θ () t 6. Estimate the nonzero elements of h () t by LS algorithm e 7. Form the estimated channel h () t 8. Refine θ () t according to the position of the strongest element end 62/82

63 Some explanations Step 2: how to detect θ () t Find the predefined spatial direction ψ 1/2/ n = n N + N based on * λ * ( N + 1) θ () t =arcsin n Nd 2 Step 5: how to detect the support () ( ( ) ) Based on θ, reversely compute the position of the strongest elements t V V 2 Obtain the support supp( h () t ) = mod N n,, n Step 6: how to realize LS & why it can save pilot overhead LS can be simply realized by the selecting networ of beamspace MIMO The size of support is small, pilot overhead can be saved Step 8: why refine () θ () t Due to error, θ may be inaccurate, leading to the following predict imprecise t When users move nonlinearly, θ t can be traced adaptively () n n 63/82

64 Simulation parameters Channel parameters Channel model: Saleh-Valenzuela model MIMO configuration: N K = 256 4, NRF = K = 4 Antenna array: ULA at BS, with antenna spacing d = λ /2 One LoS path with gain β ~ ( 0,1) Length of one period T =1 Motion state () [ ] User 1: m 1 1 = π / 9,0.0154,3 π / 4 T User 2: m () 1 2 = [ π / 9,0.0071, π / 6 ] T User 3: m () 1 3 = [ 2 π / 9,0.0114,0 ] T User 4: m () 1 4 = [ 0,0.074, 3 π / 4 ] T, m4( 16) = θ4( 16 ), λ4( 16 ),0 T (nonlinear) Algorithms Regular channel estimation: SD-based algorithm, Q =128 pilots/period Channel tracing: PA channel tracing, Q= V = 16 pilots/period 64/82

65 Simulation results Observations PA channel tracing can always trac the physical direction accurately PA channel tracing can much higher accuracy The pilot overhead can be significantly reduced (16 instead of 128) Actual physical direction Traced physical direction 10 1 Conventional OMP channel estimation Proposed PA channel tracing Physical direction (radians) User 1 User 2 NMSE (db) User Time slot t User SNR (db) Xinyu Gao, Linglong Dai, Yuan Zhang, et al., Fast channel tracing for terahertz beamspace massive MIMO systems, IEEE Transactions on Vehicular Technology, vol. 66, no. 7, pp , Jul /82

66 Contents G vision and solutions Lens-based mmwave MIMO Our related wors a. Beamspace channel estimation b. Beam selection c. Power leaage problem d. Beamspace channel tracing e. Beamspace MIMO-NOMA Future research direction 66/82

67 Outline of our research Lens-based mmwave massive MIMO Research objective 1 Beamspace channel estimation Require accurate beamspace channel Research objective 2 Beam selection Beamspace channel varies fast Research objective 3 Beamspace channel tracing Adaptive support detection-based 2D/3D channel estimation Interference-aware beam selection Solve the power leaage problem Priori-aided channel tracing Research objective 4 Brea the fundamental limit Beamspace MIMO- NOMA Bichai Wang, Linglong Dai, Zhaocheng Wang, Ning Ge, and Shidong Zhou, Spectrum and energy efficient beamspace MIMO-NOMA for millimeter-wave communications using lens antenna array, IEEE Journal on Selected Areas in Communications, vol. 35, no. 10, pp , Oct /82

68 Existing problems Fundamental limit of beamspace MIMO - A single beam can only support a single user in existing beamspace MIMO systems - The maximum number of users that can be supported cannot exceed the number of RF chains - Massive users cannot be supported with limited number of RF chains 68/82

69 Proposed Beamspace MIMO-NOMA Non-Orthogonal Multiple Access (NOMA) - Superposition coding at the transmitter - Successive interference cancellation (SIC) at the receiver - Multiple users can be supported at the same time-frequency resources Linglong Dai, Bichai Wang, Yifei Yuan, Shuangfeng Han, Chih-lin I, and Zhaocheng, Non-orthogonal multiple access for 5G: solutions, challenges, opportunities, and future research trends, IEEE Communications Magazine, vol. 53, no. 9, pp , Sep /82

70 Proposed Beamspace MIMO-NOMA Basic principle - Selecting one beam for each user using beam selection algorithms, such as the maximum magnitude (MM) selection and SINR maximization based selection - Interfering users can be simultaneously served within the same beam - The number of supported users can be larger than the number of RF chains - Spectrum efficiency and connectivity density can be improved 70/82

71 Proposed Beamspace MIMO-NOMA System model - beams, users - The set of users in the th beam is ( S S =Φ, RF S = K) - Beamspace channel vector between the BS and the th user in the th beam is denoted by, i j N n= 1 n - Uniform precoding vector for users in the th beam is - We assume that h w h w L h w H H H 1, n n 2 2, n n 2 Sn, n n 2 - After intra-beam SIC, the remaining signal received at the th user in the th beam beam can be written as m 1 H H H yˆ mn, = h mn, n pmn, smn, + mn, n pin, sin, + mn, j pi, jsi, j+ vmn, w h w h w { i= 1 j n i= noise desired signal intra-beam interferences inter-beam interferences 71/82 S j

72 Proposed Beamspace MIMO-NOMA System model - The SINR the th user in the th beam can be represented as: γ mn, H 2 mn, n p 2 mn, = h w ξ mn, where ξ m 1 H 2 H 2 mn, hmn, wn 2 pin, hmn, w j 2 pi, j i= 1 j n i= 1 2 = + + σ S j - The achievable rate of the th user in the th beam is R = log 1+ ( γ ) mn, 2 mn, - Achievable sum rate R NRF S n = R sum mn, n= 1 m= 1 72/82

73 Proposed Beamspace MIMO-NOMA Precoding - Challenge: The number of users is higher than the number of beams, which means that this system is underdetermined Conventional linear precoding cannot be directly used - Solution: An equivalent channel can be determined for each beam to generate the precoding vector The beamspace channel vectors of different users in the same beam are highly correlated we use the beamspace channel vector of the first user in each beam as the equivalent channel vector H% h h L h = 1,1, 1,2,, 1, NRF 73/82

74 Proposed Beamspace MIMO-NOMA Precoding - Precoding matrix: W%,,, H = w % w % 1 2 L w % N = = RF H% H% H% H% ( ) ( ) 1 - After normalizing the precoding vectors, the precoding vector for the th beam can be written as w n n = w % w% n 2 74/82

75 Proposed Beamspace MIMO-NOMA Power allocation - Problem formalization: max { pmn, } N RF S n n= 1 m= 1 R mn, s.t. C : p 0, n, m 1 mn, N RF S n C : p P 2 mn, n= 1 m= 1 C : R R, n, m 3 mn, min - The objective function is non-convex 75/82

76 Proposed Beamspace MIMO-NOMA Power allocation - Theorem 1: R a e 1 = max max + log a + mn, mn, ln 2 ln 2 mn, mn, mn, 2 mn, c a > 0 where { ˆ 2 } e = E s c y mn, mn, mn, mn, - The optimization problem can be reformulated as NRF Sn amn, emn, 1 maxmax max log2, {, } + amn+ pmn c,, mn a n m mn> = = ln 2 ln 2 s.t. C1, C2, C3 { c } { a } { p mn } - Iteratively optimize mn,, mn,,, (All of the three optimization problems are convex) 76/82

77 Simulation Results Simulation parameters = 256, =32 Channel: Saleh-Valenzuela multipath channel (1 LoS + 2 NLoS) 77/82

78 Contents G vision and solutions Lens-based mmwave MIMO Our related wors a. Beamspace channel estimation b. Beam selection c. Power leaage problem d. Beamspace channel tracing e. Beamspace MIMO-NOMA Future research direction 78/82

79 Future research direction 79/82

80 Summary Beamspace MIMO Employ lens antenna array Transform spatial channel to sparse beamspace channel Beam selection to reduce the MIMO dimension and number of RF chains Employ NOMA to brea the fundamental limit of beamspace MIMO Research from our group Lens-based mmwave massive MIMO Research objective 1 Beamspace channel estimation Require accurate beamspace channel Research objective 2 Beam selection Beamspace channel varies fast Research objective 3 Beamspace channel tracing Adaptive support detection-based 2D/3D channel estimation Interference-aware beam selection Solve the power leaage problem Priori-aided channel tracing Research objective 4 Brea the fundamental limit Beamspace MIMO- NOMA 80/82

81 Related Publications 1. Xinyu Gao, Linglong Dai, et al., Low RF-complexity technologies for 5G millimeter-wave MIMO systems with large antenna arrays, IEEE Communications Magazine, vol. 56, no. 4, pp , Apr Bichai Wang, Linglong Dai, et al., Spectrum and energy efficient beamspace MIMO-NOMA for millimeter-wave communications using lens antenna array, IEEE Journal on Selected Areas in Communications, vol. 35, no. 10, pp , Oct Xiny Gao, Linglong Dai, et al., Reliable beamspace channel estimation for millimeter-wave massive MIMO systems with lens antenna array, IEEE Transactions on Wireless Communications, vol. 66, no. 9, pp , Sep Tian Xie, Linglong Dai, et al., On the power leaage problem in beamspace MIMO systems with lens antenna array, submitted to IEEE Transactions on Signal Processing, Xinyu Gao, Linglong Dai, et al., Wideband beamspace channel estimation for millimeter-wave MIMO systems relying on lens antenna arrays, submitted to IEEE Transactions on Signal Processing, Xinyu Gao, Linglong Dai, et al., Fast channel tracing for Terahertz beamspace massive MIMO systems, IEEE Transactions on Vehicular Technology, vol. 66, no. 7, pp , Jul Wenqian Shen, Linglong Dai, et al., Codeboo design for channel feedbac in lens-based millimeterwave massive MIMO systems, IEEE Wireless Communications Letters, Xinyu Gao, Linglong Dai, et al., Near-optimal beam selection for beamspace mmwave massive MIMO Systems, IEEE Communications Letters, vol. 20, no. 5, pp , May Reproducible research: 81/82

82 Xiny Gao Bichai Wang Tian Xie Wenqian Shen 82/82