csi acquisition for fdd-based massive mimo systems

CSI Acquisition for FDD-based Massive MIMOSystems: Exploiting Sparsity and

Multidimensionality of the Wireless Channel

Andre L. F. de Almeida

Group of Wireless Communication Research-GTELFederal University of Ceara - UFC

November 18, 2014

Andre L. F. de Almeida CPqD 2014 1 / 39

Acknowledgements

Daniel Costa Araujo (PhD student)

Samuel Tumelero Valduga (PhD student)


Scaling up MIMO systems


Testebed for Massive MIMO


Outline

1 Overview on Massive MIMO

2 Massive MIMO:TDD vs FDD

3 CSI Aquisition in FDD Massive MIMO

4 Multidimensional Channel Estimation

5 Conclusion


Overview on Massive MIMO

Scaling up the number of antennas

Massive MIMO concept

Massive MIMO is an emerging technology that scales up the number of antennas byorders of magnitude and achieving larger arrays than the current state-of-the-art[Marzetta, 2010] [Rusek et al., 2013]. This means:

to deploy hundreds, or even thousands, of antennas at the BS;

cheap power amplifier can be employed in the BS;

the BS is capable to create extremely narrow beamformers;

Motivation: Why should we scale up the number of antennas?

the mobile data traffic will be 13 × more than 2012.

2/3 of the total traffic will be video streaming and communications.

The most modern standard, LTE-Advanced, allows for up to 8 antenna ports at thebase station and equipment being built today has much fewer antennas than that.


Overview on Massive MIMO

MM-wave and Massive MIMO: Potential Application

Some interesting points

The power of the wireless signal in millimeter-wave attenuates quickly. This restrictsthe range of the area to be covered.

There is a considerable amount of free spectrum around 60 GHz.

Very-large arrays are shrunk when using MM-waves transmission.

56 57 58 59 60 61 62 63 64 65 66

North America

Europe

Australia

Korea

Japan

Figure : Unlicensed Frequency Spectrum - GHz


Massive MIMO:TDD vs FDD

Limiting Factor in TDD

BS1

h1,1

BS2

h2,2h1,2

h2,1

Figure : TDD scenario

Issues

Pilot Contamination

Channel Reciprocity



Limiting Factor in TDD: Solutions

Channel Reciprocity: Solution

This is still an open issue.

Pilot Contamination: Some proposed Solutions

The allocation of pilot waveforms

Blind channel estimation techniques

Cooperative transmission



Limiting Factor in FDD scenario

Channel

Feedback Channel

Issues

Pilot overhead

Feedback overhead



Limiting Factor in FDD scenario: Solutions

Pilot Overhead

Compressive Sensing

Adaptive channel estimation (Low complexity)

Multidimensionality of the Channel

Feedback Overhead

Compressive Sensing

Matrix Completion


CSI Aquisition in FDD Massive MIMO

A Very Brief Overview in Compressive Sensing

Definition

Compressive sensing theory asserts that one can recover certain signals and images fromfar fewer samples or measurements than traditional methods [Donoho, 2006] [Candes,2006].

Φ ∈ CN×NΨ ∈ CM×N × b ∈ CN×1y =

M < N

Figure : Compressive sensing idea.



Fundamental Result

m ≥ Cµ2(Φ,Ψ)K log(N) (1)

µ(Φ,Ψ) is the mutual coherence between the matrices Φ and Ψ.

K is the number of non-zero entries in N × 1 vector b.

C is a positive constant.

The smaller the mutual coherence is, the fewer samples are needed.



mm-Wave and Massive MIMO

Channel Characterization

Short range communication.

Sparsity in the delay domain.

Applications typically do not involve high-velocity users (indoor scenarios).

Channel Estimation

LOS channel environment could allow for channel estimation based on direction-of-arrival(DOA) estimation. Compressed sensing can be a very useful tool to apply such idea.



mm-Wave and Massive MIMO: Some results

Scenario Description

60 GHz indoor channel.

OFDM modulation.

Multiple antennas at the UE.

The problem

We address the problem of estimating beamforming directions on the downlink in a 60GHZ indoor channel.



FDD Scenario

Scatter

Scatter

UEBS

Figure : Downlink transmission



Related Work

Compressive Sensing Based Methods in Communication Systems

W.U. Bajwa, J. Haupt, A.M. Sayeed, and R. Nowak, “Compressed channel sensing: Anew approach to estimating sparse multipath channels,” Proc. of the IEEE, vol. 98, no.6, pp. 1058–1076, 2010

Estimation techniques in MM-waves Channel

D. Ramasamy, S. Venkateswaran, and U. Madhow, “Compressive tracking with1000-element arrays:A framework for multi-gbps mm wave cellular downlinks,” Proc.Allerton, pp. 690–697, 2012.

D. Ramasamy, S. Venkateswaran, and U. Madhow, “Compressive adaptation of largesteerable arrays,” Proc. ITA, pp. 234–239, 2012.



Our Proposal

Coarse

EstimationRefinement

Figure : Block Diagram of Channel Estimation Method



System Model

Received Signal

yr(k, l) =

Np∑n=1

βnvR(θR,n, φR,n)vHT (θT,n, φT,n)s(k, l)e−2πτnl∆f + z(k, l)

Steering Vector Model

[vγ(θγ,n, φγ,n)]i = e(ωxxi+ωyyi), γ ∈ {R, T} (2)

Variables Description

ωx = 2πdλ

cos (θγ,n) cos (φγ,n);

ωy = 2πdλ

cos (θγ,n) sin (φγ,n);

xi and yi defining the spatial position of the i-th antenna element on the plane x− y;

d is the inter-element antenna spacing;

λ is the wavelength.



Channel Estimation: Coarse Estimation

Coarse


Figure : Coarse Estimation stage



Coarse Estimation

Probing directions

p = maxp

∑k

∑l

‖wHp yr(k, l)‖, p = 1, . . . , P, (3)

rp(k, l) = sT (k, l)V∗TFpb(l) + zp(k, l), (4)

where

VT = [vT (θT,1, φT,1), . . . , vT (θT,Np , φT,Np)] ;

Fp is a diagonal matrix whose n-th diagonal element is given by[Fp]n,n = wH

p vR(θR,n, φR,n);

b(l) = [β1e−2πτ1l∆f , . . . , βNpe

−2πτNp l∆f ]T ;

zp(k, l) = wHp z(k, l).

Stacking spatial samples into a vector

rp(l) = STl V∗TFpb(l) + zp(l), (5)



Coarse Estimation: Angle of Departure

Compressive Sensing Estimation

min ‖bfilt(l)‖1 s.t ‖rp(l)− STl UTbfilt(l)‖22 < σ2. (6)

where UT is a Fourier matrix and bfilt(l) = Fpb(l).

UEBS

Figure : Coarse Estimation



Refinement of the Angles

Coarse


Figure : Refinement stage



Refinement of the Estimates: Angle of Arrival

Refinement Problem

[ωrefR,x(l), ωref

R,y(l)] = arg max(ωR,x,ωR,y) ∈ R2

J(ωR,x, ωR,y, l)

where J(ωR,x, ωR,y, l).=

K∑k=1

|wH(ωR,x, ωR,y)y(k, l)|2, (7)

Comments

w(ωR,x, ωR,y) is the steering vector associated with the pair (ωR,x, ωR,y).

The final estimates are given by averaging over the L subcarriers, i.e.

ωrefR,x = (1/L)

L∑l=1

ωrefR,x(l), and ωref

R,y = (1/L)L∑l=1

ωrefR,y(l).



Refinement of the Estimates: Angle of Departure

Refinement Problem

[ωrefT,x(l), ωref

T,y(l)] = arg maxωT,x,ωT,y

|vH(ωT,x, ωT,y)S∗l ybeam(l)|2, (8)

where ybeam(l) =

yT (0, l)...

yT (K − 1, l)

w∗(ωrefR,x, ω

refR,y)

Comments

As for the receive spatial frequencies, the final estimates of ωrefT,x and ωref

T,y are obtainedby averaging over the L subcarriers.



Refinement of the Estimates:Figure

UEBS

Figure : Estimation after the refinement



Summarizing

Estimate coarsely angles of arrival

Estimate coarsely angles of departure

Refine angles of arrival

Refine angles of departure

Fed back the angles of departure to the BS



Simulation Parameters: part I

Table : Simulation Parameters

Environment Indoor (LOS)

Carrier Frequency 60 GHz

Multiplexing Scheme OFDM

Subcarrier Bandwidth 360 kHz

Number of Subcarriers 512

System Bandwidth 0.18 GHz

Number of pilots Subcarriers 32

FFT size 1024

Payload period 1.389 µs

Cyclic prefix 347.22 ns

OFDM symbol period 3.1252 µs

Maximum Tx Power per AN 2 mW

Thermal Noise Level −174 dBm/Hz



Simulation Parameters: part II

Table : Simulation Parameters

Noise Figure 6 dB

Number of Tx Antennas 64

Number of Rx Antennas 16

Distance Between the Antennas λ/2

UE speed 1 m/s



Throughput

Throughput

The proposed algorithms are evaluated using Shannon’s capacity formula by consideringthree beamforming schemes as follows:

SVD-based beamforming: derived from the right singular vector of thefrequency-dependent channel matrix (i.e. each subcarrier has different beamformingweights). Perfect knowledge of the full instantaneous channel matrix is assumed;

Steering vector-based beamforming: designed from the only knowledge of theestimated spatial frequencies, i.e. [v(ωT,x, ωT,y)]i = e(ωT,xxi+ωT,yyi);

Round-phase beamforming: The design of the steering vector is constrained to fourdifferent predefined phases only. Specifically, the phases associated with each entry ofthe steering vector are rounded to the closest phase among the four ones.



Figure : Office Environment



0 5 10 151

1.2

1.4

1.6

1.8

2

2.2x 10

9

Time [s]

thro

ug

hp

ut

nOFDMsym=20; Time Interval=0.1s,LOS

SVD per subcarrier

Steering Vector

Round−phase

Figure : System throughput (bps) for three types of beamforming. The timeinterval between two consecutive blocks is 0.1s and the number of OFDMsymbols is 20.



0 5 10 151

1.2

1.4

1.6

1.8

2

2.2x 10

9

Time [s]

thro

ug

hp

ut

nOFDMsym=5; Time Interval=0.1s,LOS

Steering Vector

Round−phase

SVD per subcarrier

Figure : System throughput (bps) for three types of beamforming.



Overhead

Number of OFDM Symbols/subcarrier Overhead

20 0.0039 %

5 9.74× 10−4 %



Conclusion

Our Considerations

Low-complexity channel estimator for massive MIMO systems.

Two-stage solution that combines coarse estimation of Tx/Rx spatial directionsfollowed by a refinement stage that exploits channel sparsity.

The proposed method achieves a quite low pilot overhead while ensuring veryaccurate channel estimates.

The steering vector based precoder has a similar throughput performance comparedto the SVD-based one, being a good solution from a hardware implementationviewpoint.


Multidimensional Channel Estimation

Sparsity in a Multidimensional Space

Motivation

So far the sparsity has been taken into account only in the spatial dimension. However,the concept can be extended for other dimensions: delay and Doppler.

Compressive Sensing in Multidimensional Problems

The channel is jointly estimated based on the sparsity of angular, delay and Dopplerdomains.

More freedom to reduce the number of pilots in the time-frequency grid.

Tensor Algebra can be a very useful theory to develop new methods of estimationtechniques based on sparsity, and with reduced complexity.


Multidimensional Channel Estimation

Compressed sensing in a tensor representation

Φ2 Ψ2Φ1Ψ1

Φ3

Ψ3

Tensor A Tensor B

Tensor Compressed Sensing

Formulation

A = B ×1 Ψ1Φ1 ×2 Ψ2Φ2 ×3 Ψ3Φ3 (9)


Conclusion

Conclusion

Final Considerations

Massive MIMO: key enabling technology for beyond LTE cellular systems.

Sparsity is a key solution to channel estimation in FDD massive MIMO systems

Exploiting channel multidimensionality can further reduce the pilot overhead in TFselective propagation.


Conclusion

THANK YOU !!!


csi acquisition for fdd-based massive mimo systems

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