millimeter-wave massive mimo with lens antenna array for

1/82Millimeter-Wave Massive MIMO with Lens Antenna Array for 5G

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

Linglong Dai（戴凌龙）

Department of Electronic EngineeringTsinghua University

May 2018

http://oa.ee.tsinghua.edu.cn/dailinglong/


Contents

5G vision and solutions1

Our related works3

Future research direction4

a. Beamspace channel estimationb. Beam selectionc. Power leakage problemd. Beamspace channel trackinge. Beamspace MIMO-NOMA

Lens-based mmWave MIMO 2


5G Vision

M.2083-03

User experienceddata rate(Mbit/s)

100

Spectrumefficiency

IMT-2020

3×

500

1106

10

20

100×Mobility(km/h)

Latency(ms)

Connection density(devices/km )2

Networkenergy efficiency

Area trafficcapacity

(Mbit/s/m )2

Peak data rate(Gbit/s)

10

1×

400350

10105

10×1×

10.1

1

IMT-advanced

ITU-R M.2083-0, “IMT vision-framework and overall objectives of the future development of IMT for 2020 and beyond,” Sep. 2015.

5G key performance indicators (KPIs) defined by ITU


How to realize 5G?

Key requirement of 5G: 1000-fold capacity How to realize this goal from Shannon capacity? Three technical directions for 5G

C ≈ D * W * M * log (1+SINR)

No. of APs Bandwidth

No. of antennas Interference mitigation


Use hundreds of BS antennas to simultaneously serve multiple users

Conventional MIMOM:2~8, K:1~4 (LTE-A)

Massive MIMOM: ~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. 3590-3599, Nov. 2010. (2013 IEEE Marconi prize)

What is massive MIMO?


Advantages of mmWave massive MIMO

Three properties– High frequency (30-300 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!


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?

Challenges of mmWave massive MIMO


Contents


Our related works3





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

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. 3814-3827, Jul. 2013.

Conventional MIMO Beamspace MIMO

High-Dimension

DigitalPrecoding

RF Chains


Beamspace channel

=H UH

Spatial channel Beamspace channelLens

Path 2Antenna array

Path 1


System model– single-antenna users, BS with antennas, RF chains

– Saleh-Valenzuela channel model [Ayach’14]

where : spatial direction and : physical direction

– Transform the spatial channel into beamspace

where

,H H= + = +y H x n H Ps n [ ]1 2, , , N KK

×= ∈H h h h NK

( ) ( )( ) ( ) ( )( )0 0

1,

Li i

k k k k ki

β ψ β ψ=

= +h a a ( ) ( )21 ,j m

m Ne

Nπψψ −

∈ = a

LoS path NLoS paths ULA steering vector

sindψ θλ

,H H H= + = +y H U Ps n H Ps n

DFT matrix realized by lens antenna array

( ) ( ){ }1 / 2, 0,1, , 1 ,N l N l N= − − = −Beamspace channel

RFN K=

θψ

( ) ( ) ( )1 2, , , ,H

Nψ ψ ψ = U a a a

( )( )1 / 2 / , 1,2, ,n n N N n Nψ = − + =

Mathematical principle


Sparsity

– with a small number of dominant elements – Approximately sparse

[ ]1 2 1 2, , , , , ,K K = = = H h h h UH Uh Uh Uh

Beam selection– Select a small number of dominant beams

– is the dimension-reduced precoder

– Only a small number of RF chains

kh

r r ,H≈ +y H P s n ( )r ,:l

l∈

=H H

rP

Mathematical principle

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. 3814-3827, Jul. 2013.


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: http://dune.ece.wisc.edu/?page_id=385


Contents


Our related works3





Outline of our research

Xinyu Gao, Linglong Dai, Akbar Sayeed, “Low RF-complexity technologies for 5G millimeter-wave MIMO systems with largeantenna arrays,” IEEE Communications Magazine, vol. 56, no. 4, pp. 211-217, Apr. 2018.


Research objective 2Beam selection

Research objective 3Beamspace channel tracking

Adaptive support detection-based 2D/3D

channel estimationResearch objective 1

Beamspace channel estimation

Interference-aware beam selection

Priori-aided channel tracking

Solve the power leakage problem

Require accurate beamspace

channel

Beamspace channel varies

fast

Research objective 4Break the fundamental limit

Beamspace MIMO-NOMA


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 ?


Existing challenges– If we use traditional selecting network to design the combiner Each row of will have one and only one nonzero element

– To make contain complete information of →– For mmWave massive MIMO systems N is quite large, e.g., 1024 Fast-varying channel at mmWave frequencies

Channel measurements– All K users transmit orthogonal pilot sequences to BS over Q instants– BS employs a combiner to obtain the measurements of channel – Channel is estimated, and used according to channel reciprocity

k k k+=z Wh n

W

Q N≥W

kz kh

Channel estimation in TDD model

W kz

Unaffordable pilot overhead!


Adaptive selecting network– Utilize 1-bit phase shifter (PS) network to design– Adaptive: selecting network for data transmission & combiner for channel estimation– , has full information → sparse signal recovery problem– 1-bit PS → Low energy consumption

Q N< kz

W

Proposed Adaptive selecting network

Xiny Gao, Linglong Dai, Shuangfeng Han, Chih-Lin I, and Xiaoding Wang, “Reliable beamspace channel estimation for millimeter-wavemassive MIMO systems with lens antenna array,” IEEE Transactions on Wireless Communications, vol. 16, no. 9, pp. 6010-6021, Sep. 2017.


Problem formulation

Classical CS algorithms– Deteriorated performance in low SNR region Low transmit power at user side Serious path loss of mmWave signals Lack of beamforming gain

We should utilize the structural properties of beamspace channel

Low SNR

Sparse signal recovery problem– Estimate sparse of size N with smaller number of measurements Q

– Classical CS algorithms can be directly usedk k k+=z Wh n

kh


Structural property 1

Lemma 2. Present as , where is the ith channelcomponent of in the beamspace. Then, when the number of BS antennas N goes infinity,any two channel components and are orthogonal, i.e.,

kh( ) 0

/ +1 Lk ii

N L=

= h c i i=c Uc

ic jclim 0, , 0,1, , , .H

i jNi j L i j

→∞= ∀ = ≠c c

Insights – Total estimation problem can be decomposed into independent sub-problems– Each sub-problem only considers one sparse channel component

kh


Lemma 3. Consider the ith channel component in the beamspace, and assume V is aneven integer. Then, the ratio between the power of V strongest elements of and thetotal power of can be lower-bounded by

Moreover, once the position of the strongest element of is determined, the other V-1 strongest elements will uniformly located around

ic

Insights– can be considered as a sparse

vector with sparsity V

– The support of can be uniquelydetermined by

( ) 1/2

22

1

2 12 sin .2

VV

iT

iPP N N

π−

=

−≥

icic

VPTP

ic*in

*in

1 / N 1 / N

kψ1

1

sin2

NN

π

13sin2

NNπ

1 / 2N

ic

256, 8, / 95%V TN V P P= = ≥

ic*in

( ) * * 2supp mod , ,2 2i N i iV Vn n − = − +

c

Structural property 2


Support detection (SD)-based 2D channel estimation


Lemma 4. Consider the LoS scenario, i.e., and suppose that the strongest element of satisfies

where is a constant, and we define that

Then, the probability that the position of the strongest element is correctly estimated is lower-bounded by

0k N=h c kh

*,k nh

( )( )( )*

2UL

,

8 1 ln,

1 1 2k n

Nh

σ αμ κ μη

+≥

− − −

0α >

( )( ) ( ) ( )1

1 1 sin / 2 ,sin / 2sin 2 1 / 2

N

nN

Nn Nη π

ππ=

−

−

( )( )

sin / 2.

sin 3 / 2NN

πκ

π

( )1

1Pr 1 .1 ln

N

N Nα π α+

≥ − +

Lemma 4 can be directly extended tothe scenario with NLoS components

Performance analysis

Insights – For small , should also be small– The probability decreases– Higher accuracy than CS

*,k nh α


System parameters– MIMO configuration:– Total time slots: ( )– 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– Multiple paths: One LoS component and two NLoS components– LoS component Amplitude: Spatial direction:

– NLoS components Amplitude: Spatial direction:

( )2L =

256 16,N K× = × RF 16N K= =

/ 2d λ=

( ) ( )0 ~ 0,1kβ ( )0 1 1,2 2

~kψ −

( ) ( )2~ 0,10ikβ − ( ) 1 1,

2 2~i

kψ −

1 i L≤ ≤

96Q MK= = 6M =

Simulation parameters


Simulation results

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100

Downlink SNR (dB)

Ach

ieva

ble

sum

-rate

(bits

/s/H

z)

Fully digital systemIA beam selction with perfect CSISD-based channel estimation (uplink SNR = 0 dB)OMP-based channel estimation (uplink SNR = 0 dB)SD-based channel estimation (uplink SNR = 10 dB)OMP-based channel estimation (uplink SNR = 10 dB)SD-based channel estimation (uplink SNR = 20 dB)OMP-based channel estimation (uplink SNR = 20 dB)

0 5 10 15 20 25 3010-2

10-1

100

101

Uplink SNR (dB)

NM

SE

(dB

)

Conventional OMP-based channel estimationProposed SD-based channel estimation

Observations– SD-based channel estimation outperforms conventional schemes– The performance is satisfying even in the low SNR region– The pilot overhead is low, i.e., 96 =256Q N= <



Lemma 5. Define matrix as . Define as the sub-matrix of extracting strongest rows and strongest columns from . Assumeand are even integers without loss of generality. Then, the ratio between the power of

and the power of can be lower-bounded by

Insights– can be considered as a block sparse matrix

– Indices extracted rows and columns are is uniquely determined by

– Support of is

( ) ( )1 2

2 /2 /2

2 21 12 2

1 2

4 1 1 .2 1 2 1

sin sin2 2

V VF

i jl FN i j

N Nπ π= =

≥ − −

S

C

1 2

221 232, 8 /, 91%lF F

N N V V= = = = ≥S C

1

1 1 2mod , ,2 2NV Vi i∗ ∗ − = − +

1 2N N× lC ( ) ( )( )2, 1l li j N i j= − +C c SlC 1V 2V lC 1V

2VS lC

lC

( ),l i j∗ ∗C

2

2 2 2mod , ,2 2N

V Vj j∗ ∗ − = − +

lc ( ) ( ){ }2supp 1 , ,l N r c r c= − + ∈ ∈c

Extension to 3D beamspace channel


Adaptive SD (ASD)-based 3D channel estimation

Amplitude distribution of with more serious vertical power diffusion

lC Amplitude distribution of with more serious horizontal power diffusion

lC

1 2V V=

1 1 / 2V V=1 12V V=2 2 / 2V V= 2 22V V=

Strongest element Marginal element Extracted element

Index of horizontal beam

Inde

x of

ver

tical

bea

m

1 2 4 6 8 10 12 14 161

2

4

6

8

10

12

14

16

Index of horizontal beam

Inde

x of

ver

tical

bea

m

1 2 4 6 8 10 12 14 161

2

4

6

8

10

12

14

16

Key idea– Adaptively adjust based on the power diffusions in both directions( )supp lc


Stage2– Serious vertical power diffusion

– Serious horizontal power diffusion

– Repeat stage 1 until the power diffusions in both directions are the same

Mathematical description Stage 1

– Estimate the strongest element →– Assume to obtain the initial support – Estimate nonzero elements, and define four marginal values

( )* * * * *2 2/ , 1i p N j p N i = = − − ( )l p∗c

1 2V V=

( )e * *1 2, / 2lM i j V= −C ( )e * *

2 2, / 2 1lM i j V= + −C

( )e * *3 1 / 2,lM i V j= −C ( )e * *

4 1 / 2 1,lM i V j= + −C

( ) ( )1 2 3 4min , min ,M M M M<

( ) ( )1 2 3 4min , min ,M M M M>1 1 2 22 , / 2V V V V= =

1 1 2 2/ 2, 2V V V V= =


System parameters– MIMO configuration:– Total time slots:– Initialization for ASD algorithm: – Combiner : Bernoulli random matrix, i.e., – 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– Multiple paths: One LoS component and two NLoS components– LoS component Amplitude: Spatial direction:

– NLoS components Amplitude: Spatial direction:

( )2L =

1 2 32 32 1024,N N N= × = × = RF 16N K= =

1 2 / 2d d λ= =

( ) ( )0 0,1kβ ( ) ( ) ( )0 0, 0.5,0.5k kϕ θ −

( ) ( )2~ 0,10ikβ −

256Q =


( ) ( ) ( ), 0.5,0.5lk

lkϕ θ −

W ( ) { }, 1, 1 /i j Q∈ − +W1 2 8V V= =


-10 -5 0 5 10 15 20 25 3010-2

10-1

100

101

Uplink SNR (dB)

NM

SE

(dB

)

Conventional OMP-based channel estimationProposed ASD-based channel estimation

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., – Beam selection can achieve near-optimal performance with estimated channel

256 =1024Q N=

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100

Downlink SNR (dB)

Ach

ieva

ble

sum

-rate

(bits

/s/H

z)

Fully digital ZF precoder with perfect CSIIA beam selction with perfect CSIASD-based channel estimation (uplink SNR = 0 dB)OMP-based channel estimation (uplink SNR = 0 dB)ASD-based channel estimation (uplink SNR = 10 dB)OMP-based channel estimation (uplink SNR = 10 dB)ASD-based channel estimation (uplink SNR = 20 dB)OMP-based channel estimation (uplink SNR = 20 dB)



Contents


Our related works3






Xinyu Gao, Linglong Dai, Zhijie Chen, Zhaocheng Wang, and Zhijun Zhang, “Near-optimal beam selection for beamspace mmWave massive MIMOsystems,” IEEE Communications Letters, vol. 20, no. 5, pp. 1054-1057, May 2016.











channel


fast


Beamspace MIMO-NOMA


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

Existing problem

A. Sayeed, et al., “Beamspace MIMO for high-dimensional multiuser communication at millimeter-wave frequencies,”in Proc. IEEE GLOBECOM’13, Dec. 2013.


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

Motivation– Select the best beam (but not the strongest beam) for each user – The required number of RF chains is fixed and certain

Interference-aware (IA) beam selection


Beam

inde

x

∗∗ ∗

∗

∗

Illustration

Stage 1 Stage 2


Inspiration– The strongest beam of each user enjoys most of the total power– Can we directly choose ?

kb∗

{ }* * *1 2, , , Kb b b=

Lemma 1. Assume that spatial directions for follow the i.i.d. uniformdistribution within . The probability P that there exist users sharing the samestrongest beam is

( )!1 .

!KNP

N N K= −

−

( )0kψ 1,2, ,k K=

[ ]0.5,0.5−

Definitions– NIUs: one user k is NIU if its strongest beam is different from any other

strongest beams, i.e., – IUs: any two users k1 and k2 are IUs if

kb∗

{ }* * * * *1 1 1, , , , ,k k k Kb b b b b− +∉

* *1 2k kb b=

Stage 1: Identify IUs and NIUs

Serious inter-beam interference !P ≈ 87% when N = 256 and K = 32


Select the optimal beam set – Select the beams for NIUs– Choose beams from as a candidate– Combine and to form the set – Based on , select beams of beamspace channel– The dimension-reduced MIMO system

– Search the optimal by maximizing the achievable sum-rate R

– Form the optimal set of selected beams for all K users

IU IU

K=

( )r r r, ,: ,H

ll

∈ ≈ + = y H P s n H H

H

optIU

IU

optIU arg max ,R=

( )2

1log 1 ,

K

kk

R γ=

= +2

, ,2 2

, ,

Hr k r k

k Hr k r mm k

γσ

≠

=+

h p

h p

opt opt optIU NIU=

{ }opt *NIU NIU= |kb k ∈

{ } { }*NIU1,2, , \ |kN b k ∈

IUoptNIU

Stage 2: Select the best unshared beam


System parameters– MIMO configuration:– Dimension-reduced digital precoder: Zero forcing (ZF)

Channel parameters– Channel model: Saleh-Valenzuela model– Antenna array: ULA at BS, with antenna spacing– Multiple paths: One LoS component and two NLoS components– LoS component Amplitude: , Spatial direction:

– NLoS components Amplitude: , Spatial direction:

( )2L =

256 32,N K× = × RF 32N K= =

/ 2d λ=

( ) ( )0 ~ 0,1kβ ( )0 1 1,2 2

~kψ −

( ) ( )1~ 0,10ikβ − ( ) 1 1,

2 2~i

kψ −

1 i L≤ ≤



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

0 5 10 15 20 25 300

50

100

150

SNR (dB)

Ach

ieva

ble

sum

-rate

(bits

/s/H

z)

Fully digital systemConventional MM beam selection (2 beams per user)Conventional MM beam selection (1 beam per user)Proposed IA beam selection (1 beam per user)

8 10 20 30 40 50 60 640

2

4

6

8

10

12

14

16

18

Number of users K

Ener

gy e

ffici

ent (

bps/

Hz/

W)

Fully digital systemConventional MM beam selection (2 beams per user)Conventional MM beam selection (1 beam per user)Proposed IA beam selection (1 beam per user)

Xinyu Gao, Linglong Dai, Zhijie Chen, Zhaocheng Wang, and Zhijun Zhang, “Near-optimal beam selection for beamspace mmWave massive MIMOsystems,” IEEE Communications Letters, vol. 20, no. 5, pp. 1054-1057, May 2016.


Contents


Our related works3






Tian Xie, Linglong Dai, Jianju Li, et al., “On the power leakage problem in beamspace MIMO systems with lensantenna array,” submitted to IEEE Transactions on Communications, 2017.











channel


fast


Beamspace MIMO-NOMA


Power leakage 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 leak onto the adjacent elements– Conventional precoding schemes select one beam for one path, where most

power of one path is not collected.

Existing problem

For the worst power leakage case, more than 50% powerof one path will be leaked!

Spatial direction

Lens resolutionAmplitude

1φ

1/N


1/N

Spatial direction(a) (b)

Spatial samples

Spatial samples

2φ

No power leakage Worst power leakage


Single RF per user (sRF/user) precoding [Amadori’s 15] – Ignore the power leakage 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

Conventional precoding structure

[Amadori’s 15] P. Amadori and C. Masouros, “Low RF-complexity millimeter-wave beamspace-MIMO systems by beam selection,” IEEETrans. Commun., vol. 63, no. 6, pp. 2212–2222, Jun. 2015.


Full dimension (FD) precoding – Use more RF chains (e.g., 3 RF chains for each path) to collect the leaked

power of paths– FD precoding is able to collect most leaked power– The required energy consumption is high due to a large number of RF chains

A straightforward solution


Proposed phase shifter network (PSN)-based precoding– Use an analog network to collect the leaked power– Signal on each antenna is rotated via a phase shifter and then connect to one

RF chain – Collect most leaked power to achieve near-optimal sum rate, while the

number of required RF chains is low

Proposed PSN-based precoding


System model– Single-antenna users, BS with antennas, RF chains

Signal model

N RFN K=

RF BB ,H H= + = +y H x n H P P s nP [ ]1 2, , , N KK

×= ∈H h h h Beamspace

Channel matrixRF domainprecoder

Baseband precoder

Constraints on RF precoder– If the kth RF chain is connected to the lth antenna, ; otherwise it is

zero – The element in the RF precoder has non-convex constant modulus constraint

Conventional precoding algorithm cannot be generalized to the PSN-based precoding structure!

How to effectively design the precoding algorithm?

[ ]RF ,lj

ke θ=P

RF RF( )(1) (2)RF RF RF RF, , , N N N× = ∈ P p p p


Observation 1 [Zeng’16]– In lens-based massive MIMO systems, users are distinguished based on their

angles. – Since different users are likely 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 – The diagonal elements in the RF domain channel represent the

received signal power for the kth user. Moreover, we have

where is the set containing the indices of selected beams for the kth user – Once the is determined, maximizing equals rotating to the

same direction via

[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. 1557–1571, Apr. 2016.

RF RFH H=H H P

( ) ( )RF RF FR ,

k

H H Hk kk k

k k

i ii B∈

= = H h hp p

kBkB RF ,

H

k k H

i

Hk h

( )RFk

i p

Rotation-based precoding algorithm


Observation 3 – The channel elements corresponding to the leaked power (weak 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 pick up the weak elements


1/N

Spatial direction

Strong elementWeak element

2φ



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

Update a set that contains all adjacent elements to the elements in Pick up the element with the highest power in , and add it to Repeat such procedure until an end criteria

– Generate the RF precoder Rotate the elements in to the same direction


Baseband precoder design– Employ the maximum ratio transmission (MRT) precoding on the RF domain

channel

kBkA kB

kA kB

kB


Azimuth beam index

Elev

ation

bea

m in

dex

Azimuth beam index

Elev

ation

bea

m in

dex

Azimuth beam index

Elev

ation

bea

m in

dex

Azimuth beam index

Elev

ation

bea

m in

dex

Selected elements

Elements adjacent to selected elements



p

Hkh

q

Hkh

p q

H Hk kh h +

p

Hkh

q

Hkh

p q

H Hk kh h +

Combination without rotation

Combination with rotation



Achievable sum rate performance Observation

– The proposed PSN-based precoding can effectively overcome the power leakage problem

– The proposed PSN-based precoding can achieve near-optimal sum rate compared with the optimal FD precoding


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 leakage problem in beamspace MIMO systems with lensantenna array,” submitted to IEEE Transactions on Communications, 2017.


Contents


Our related works3






Xinyu Gao, Linglong Dai, Yuan Zhang, et al., “Fast channel trakcing for terahertz beamspace massive MIMOsystems,” IEEE Transactions Vehicular Technology, vol. 66, no. 7, pp. 5689-5696, Jul. 2017.











channel


fast


Beamspace MIMO-NOMA


Existing problems

Beamspace channel tracking– Fast-varying channel for moving users at mmWave frequencies– Real time channel estimation leads to quite high overhead– Classical Kalman filter for channel tracking Beamspace channel does not follow the one-order Markov process

– Search several candidate beams for channel tracking Beam training overhead is high


Key idea– Temporal variation law of the physical direction → Prediction– Structural properties of the beamspace channel → Priori information– Track the beamspace channel with quite low pilot overhead

Priori-aid (PA) channel tracking

Xinyu Gao, Linglong Dai, Yuan Zhang, et al., “Fast channel trakcing for terahertz beamspace massive MIMOsystems,” IEEE Transactions Vehicular Technology, vol. 66, no. 7, pp. 5689-5696, Jul. 2017.


: sampling period

Motion of the kth user

( )kd t( )2kd t +

( )1kd t +

( )k tθ ( )1k tθ +( )2k tθ +

kϕkv T

kv Taxisy −

axisx −

t

( )1t +

( )2t +

kv

( )kd t ( )k tθT kϕ: speed : direction of motion

: distance at time t : physical direction at time t

The motion of the kth user can be described by ( ) ( ){ }, , ,k k k kd t t vθ ϕ


Motion state of the kth user Target

– Predict according to ( ) ( ) ( )1 , 2 , ,k k k tθ θ θ( )1k tθ +

Solution– Define an auxiliary parameter angular speed – Define the motion state of the kth user at time t

( ) ( )/k k kt v d tλ

( ) ( ) ( ), ,T

k k k kt t tθ λ ϕ m

Proposition 1. The relationship between and is( )k tm ( )1k t +m

( ) ( )( ) ( ) ( )( ) ( )

( )( ) ( ) ( )2 2

sin cosarct1 an

cos sin 1 2 si, ,

nk k k

T

k k kk

k k k k k k k

t T t tt T t T t t

t tT t

θ λ ϕ λθ λ ϕ λ θ ϕ λ

ϕ + + + + +

+ = Θ =

m m

Corollary 1. The relationship between and is( )k tm ( )k t N+m

( ) ( )( ) ( ) ( )( ) ( )

( )( ) ( ) ( )22 2

sin cosarctan

cos sin, ,

1 2 sink k k

T

Nk k k

k

k k k k k k k

NN

t T t tt T t T t t TN

t NtN

tθ λ ϕ λθ λ ϕ λ

ϕλ θ ϕ

+ + + + +

+ = Θ =

m m

After has been estimated, can be predicted accordingly( )k tm ( )k t Nθ +


Observations– Consider the triangle with orange lines and utilize the law of sine

– Consider the triangle with red lines and utilize the law of sine

How to estimate the motion state?

( )kd t( )2kd t +

( )1kd t +

( )k tθ ( )1k tθ +

( )2k tθ +

kϕ

kv T

kv T

axisy −

axisx −

t

( )1t +

( )2t +

( ) ( )( ) ( )

( )( ) ( )

( ) ( ) ( )( ) ( )

( )( ) ( )

( )sin 1 sin 1 sin 1 sin 1

+1 ,1 sin / 2 cos sin / 2 1 cos +1

k k k k k k k kk kk k

k kk k k k k k k k

t t t t t t t tv vt td t d tT t T t T t T t

θ θ θ θ θ θ θ θλ λ

π θ ϕ θ ϕ π θ ϕ θ ϕ+ − + − + − + − = = = = = =

+ + + + − + − +

( ) ( )( ) ( )

( )( ) ( )

( ) ( ) ( )( ) ( )

( )( ) ( )

( )sin 2 sin 2 sin 2 sin 2

+2 = ,2 2 sin / 2 2 cos 2 sin / 2 2 2 cos +2

k k k k k k k kk kk k

k kk k k k k k k k

t t t t t t t tv vt tr t d tT t T t T t T t

θ θ θ θ θ θ θ θλ λ

π θ ϕ θ ϕ π θ ϕ θ ϕ+ − + − + − + − = = = = =

+ + + + − + − +


How to estimate the motion state? Solutions

– Estimate , , and by regular channel estimation– Use the observations

where – The motion state at time t can be estimated as

( )k tθ ( )1k tθ − ( )2k tθ −

( ) ( )( ) ( ) ( ) ( ) ( )

( )2 cos cos 1 sin 2

,2 sin sin 1 2 cos 2

k k k k k kk k

k k k k k k

a t b t t tt

a t b t T tθ θ θ θ

ϕ λθ θ θ ϕ − − − − = = − − − +

( ) ( ) ( ) ( )sin 1 2 , sin 2k k k k k ka t t b t tθ θ θ θ − − − − −

One step prediction– Why one step? , , and may be not accurate enough A miss is as good as a mile

– According to Proposition 1

( ) ( ) ( ), ,T

k k k kt t tθ λ ϕ m

( )k tθ ( )1k tθ − ( )2k tθ −

( ) ( ) ( )( ) ( )

sin cos1 arctan

cos sink k k

kk k k

t T tt

t T tθ λ ϕ

θθ λ ϕ

+ + = +


Priori-aid (PA) channel tracking

Regular channel estimationfor

1. Estimate by SD-based channel estimation2. Detect the physical direction according to the position of the strongest element

end

Channel Trackingfor

3. Estimate the motion state 4. Predict the physical direction 5. Detect the support of based on 6. Estimate the nonzero elements of by LS algorithm7. Form the estimated channel 8. Refine according to the position of the strongest element

end

1 3t≤ ≤

( )ek th

( )k tθ

3t >( ) ( ) ( )1 1 , 1 ,

T

k k k kt t tθ λ ϕ − − − m ( )k tθ

( )k th ( )k tθ( )k th

( )ek th

( )k tθ


Some explanations Step 2: how to detect

– Find the predefined spatial direction based on–

( )k tθ

n∗( )( )* 1 / 2 /n

n N Nψ ∗= − +

( ) ( )*=arc1

2sink

Nnt

Ndλθ

+−

Step 5: how to detect the support

– Based on , reversely compute the position of the strongest elements– Obtain the support

( )k tθ n∗( )( ) 2supp mod , , +

2 2k NV Vt n n∗ ∗ − = −

h

Step 8: why refine – Due to error, may be inaccurate, leading to the following predict imprecise– When users move nonlinearly, can be tracked adaptively

( )k tθ

( )k tθ

Step 6: how to realize LS & why it can save pilot overhead– LS can be simply realized by the selecting network of beamspace MIMO– The size of support is small, pilot overhead can be saved

( )k tθ


Simulation parameters Channel parameters

– Channel model: Saleh-Valenzuela model – MIMO configuration:– Antenna array: ULA at BS, with antenna spacing– One LoS path with gain– Length of one period

256 4,N K× = × RF 4N K= =/ 2d λ=

( )~ 0,1kβ

Motion state – User 1:– User 2:– User 3:– User 4: , (nonlinear)

( ) [ ]1 1 / 9,0.0154,3 / 4 Tπ π=m( ) [ ]2 1 / 9,0.0071, / 6 Tπ π= −m( ) [ ]3 1 2 / 9,0.0114,0 Tπ= −m( ) [ ]4 1 0,0.074, 3 / 4 Tπ= −m

Algorithms– Regular channel estimation: SD-based algorithm, pilots/period – Channel tracking: PA channel tracking, pilots/period

128Q =16Q V= =

1T =

( ) ( ) ( )4 4 416 16 , 16 ,0Tθ λ = m


Simulation results

Observations– PA channel tracking can always track the physical direction accurately– PA channel tracking can much higher accuracy– The pilot overhead can be significantly reduced (16 instead of 128)

1 5 10 15 20 25 30

-1.5

-1

-0.5

0

0.5

1

1.5

Time slot t

Phys

ical

dire

ctio

n (ra

dian

s)

Actual physical directionTracked physical direction

User 1

User 2

User 3

User 4

0 5 10 15 20 25 3010-2

10-1

100

101

SNR (dB)

NM

SE

(dB)

Conventional OMP channel estimationProposed PA channel tracking

Xinyu Gao, Linglong Dai, Yuan Zhang, et al., “Fast channel trakcing for terahertz beamspace massive MIMOsystems,” IEEE Transactions on Vehicular Technology, vol. 66, no. 7, pp. 5689-5696, Jul. 2017.


Contents


Our related works3






Bichai Wang, Linglong Dai, Zhaocheng Wang, Ning Ge, and Shidong Zhou, “Spectrum and energy efficient beamspace MIMO-NOMAfor millimeter-wave communications using lens antenna array,” IEEE Journal on Selected Areas in Communications, vol. 35, no. 10, pp.2370-2382, Oct. 2017.











channel


fast


Beamspace MIMO-NOMA


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

Existing problems


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. 74-81, Sep. 2015

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



System model- beams, users

- The set of users in the th beam is ( , )

- Beamspace channel vector between the BS and the th user in the thbeam is denoted by ,

- Uniform precoding vector for users in the th beam is

- We assume that

- After intra-beam SIC, the remaining signal received at the th user in the th beam beam can be written as

1, 2, ,2 2 2n

H H Hn n n n nS n≥ ≥ ≥h w h w h wL

i jS S∩ = ΦRF

1

N

nn

S K=

=

{1

, , , , , , , , , , ,1 1 noisedesired signal

intra-beam interferences inter-beam interferences

ˆjSm

H H Hm n m n n m n m n m n n i n i n m n j i j i j m n

i j n iy p s p s p s v

−

= ≠ =

= + + + h w h w h w1 4 4 2 4 4 3 1 4 44 2 4 4 43 1 4 4 4 2 4 4 4 3



System model

- The SINR the th user in the th beam can be represented as:

where

- The achievable rate of the th user in the th beam is

- Achievable sum rate

2

, ,2,

,

Hm n n m n

m nm n

pγ

ξ=

h w

12 2 2, , , , ,2 2

1 1

jSmH H

m n m n n i n m n j i ji j n i

p pξ σ−

= ≠ =

= + + h w h w

( ), 2 ,log 1m n m nR γ= +

RF

sum ,1 1

nSN

m nn m

R R= =

=



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

RF1,1 1,2 1,, , , N = H h h h% L



Precoding

- Precoding matrix:

- After normalizing the precoding vectors, the precoding vector for the thbeam can be written as

( ) ( )RF

1

2

†

1, , , HN

− = = = W w w w H H H H% % % % %% % %L

2

nn

n

= www%%



Power allocation

- Problem formalization:

- The objective function is non-convex

{ }

RF

,,

1 1max

n

m n

SN

m np n mR

= =

1 ,s.t. : 0, ,m nC p n m≥ ∀RF

2 ,1 1

:nSN

m nn m

C p P= =

≤

3 , min: , ,m nC R R n m≥ ∀



, ,

, ,, 2 ,0

1max max logln 2 ln 2m n m n

m n m nm n m nc a

a eR a

>

= − + +

{ }2, , , ,ˆEm n m n m n m ne s c y= −

Power allocation

- Theorem 1:

where

- The optimization problem can be reformulated as

- Iteratively optimize , , (All of the three optimization problems are convex)

{ }

RF

, ,,

, ,2 ,01 1

1max max max logln 2 ln 2

n

m n m nm n

SNm n m n

m nc ap n m

a ea

>= =

− + +

1 2 3, ,s.t. C C C


{ },m nc { },m na { },m np


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

Simulation Results


Contents


Our related works3





Future research direction


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 break the fundamental limit of beamspace MIMO

Research from our group











channel


fast


Beamspace MIMO-NOMA


Related Publications1. 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. 211-217, Apr. 2018.

2. 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. 2370-2382, Oct. 2017.

3. 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. 6010-6021, Sep. 2017.

4. Tian Xie, Linglong Dai, et al., “On the power leakage problem in beamspace MIMO systems with lens antenna array,” submitted to IEEE Transactions on Signal Processing, 2018.

5. 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, 2018.

6. Xinyu Gao, Linglong Dai, et al., “Fast channel tracking for Terahertz beamspace massive MIMO systems,” IEEE Transactions on Vehicular Technology, vol. 66, no. 7, pp. 5689-5696, Jul. 2017.

7. Wenqian Shen, Linglong Dai, et al., “Codebook design for channel feedback in lens-based millimeter-wave massive MIMO systems,” IEEE Wireless Communications Letters, 2018.

8. Xinyu Gao, Linglong Dai, et al., “Near-optimal beam selection for beamspace mmWave massive MIMO Systems,” IEEE Communications Letters, vol. 20, no. 5, pp. 1054-1057, May 2016.

Reproducible research: http://oa.ee.tsinghua.edu.cn/dailinglong/


Xiny Gao Wenqian ShenTian Xie

http://oa.ee.tsinghua.edu.cn/dailinglong/

Bichai Wang

millimeter-wave massive mimo with lens antenna array for

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