CSI Acquisition for FDD-based Massive MIMO Systems
-
Upload
cpqd -
Category
Technology
-
view
495 -
download
8
description
Transcript of 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)
Andre L. F. de Almeida CPqD 2014 2 / 39
Scaling up MIMO systems
Andre L. F. de Almeida CPqD 2014 3 / 39
Testebed for Massive MIMO
Andre L. F. de Almeida CPqD 2014 4 / 39
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
Andre L. F. de Almeida CPqD 2014 5 / 39
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.
Andre L. F. de Almeida CPqD 2014 6 / 39
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
Andre L. F. de Almeida CPqD 2014 7 / 39
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
Andre L. F. de Almeida CPqD 2014 8 / 39
Massive MIMO:TDD vs FDD
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
Andre L. F. de Almeida CPqD 2014 9 / 39
Massive MIMO:TDD vs FDD
Limiting Factor in FDD scenario
Channel
Feedback Channel
Issues
Pilot overhead
Feedback overhead
Andre L. F. de Almeida CPqD 2014 10 / 39
Massive MIMO:TDD vs FDD
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
Andre L. F. de Almeida CPqD 2014 11 / 39
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.
Andre L. F. de Almeida CPqD 2014 12 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 13 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 14 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 15 / 39
CSI Aquisition in FDD Massive MIMO
FDD Scenario
Scatter
Scatter
UEBS
Figure : Downlink transmission
Andre L. F. de Almeida CPqD 2014 16 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 17 / 39
CSI Aquisition in FDD Massive MIMO
Our Proposal
Coarse
EstimationRefinement
Figure : Block Diagram of Channel Estimation Method
Andre L. F. de Almeida CPqD 2014 18 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 19 / 39
CSI Aquisition in FDD Massive MIMO
Channel Estimation: Coarse Estimation
Coarse
EstimationRefinement
Figure : Coarse Estimation stage
Andre L. F. de Almeida CPqD 2014 20 / 39
CSI Aquisition in FDD Massive MIMO
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)
Andre L. F. de Almeida CPqD 2014 21 / 39
CSI Aquisition in FDD Massive MIMO
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
Andre L. F. de Almeida CPqD 2014 22 / 39
CSI Aquisition in FDD Massive MIMO
Refinement of the Angles
Coarse
EstimationRefinement
Figure : Refinement stage
Andre L. F. de Almeida CPqD 2014 23 / 39
CSI Aquisition in FDD Massive MIMO
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).
Andre L. F. de Almeida CPqD 2014 24 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 25 / 39
CSI Aquisition in FDD Massive MIMO
Refinement of the Estimates:Figure
UEBS
Figure : Estimation after the refinement
Andre L. F. de Almeida CPqD 2014 26 / 39
CSI Aquisition in FDD Massive MIMO
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
Andre L. F. de Almeida CPqD 2014 27 / 39
CSI Aquisition in FDD Massive MIMO
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
Andre L. F. de Almeida CPqD 2014 28 / 39
CSI Aquisition in FDD Massive MIMO
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
Andre L. F. de Almeida CPqD 2014 29 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 30 / 39
CSI Aquisition in FDD Massive MIMO
Figure : Office Environment
Andre L. F. de Almeida CPqD 2014 31 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 32 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 33 / 39
CSI Aquisition in FDD Massive MIMO
Overhead
Number of OFDM Symbols/subcarrier Overhead
20 0.0039 %
5 9.74× 10−4 %
Andre L. F. de Almeida CPqD 2014 34 / 39
CSI Aquisition in FDD Massive MIMO
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.
Andre L. F. de Almeida CPqD 2014 35 / 39
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.
Andre L. F. de Almeida CPqD 2014 36 / 39
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)
Andre L. F. de Almeida CPqD 2014 37 / 39
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.
Andre L. F. de Almeida CPqD 2014 38 / 39
Conclusion
THANK YOU !!!
Andre L. F. de Almeida CPqD 2014 39 / 39