143 mimo feedback final
Post on 18-Nov-2015
229 Views
Preview:
DESCRIPTION
TRANSCRIPT
-
Linear Precoding in MIMO Wireless Systems
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego
Acknowledgement: Y. Isukapalli, L. Yu, J. Zheng, J. Roh
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 1 / 48
-
Outline
1 Promise of MIMO Systems
2 Point to Point MIMO
3 Limited Feedback MIMO Systems
4 MIMO-OFDM
5 Multi-User MIMO
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 2 / 48
-
Outline
1 Promise of MIMO Systems
2 Point to Point MIMO
3 Limited Feedback MIMO Systems
4 MIMO-OFDM
5 Multi-User MIMO
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 3 / 48
-
Multiple Input Multiple Output (MIMO) Systems
A system with multiple antennas at the transmitter and multipleantennas at the receiver.
Enables Spatio-Temporal processing and the goal is to exploitthe spatial dimension to increase system throughput
Multi-Input Multi-Output System
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 4 / 48
-
Textbooks
Introduction to Space-Time Wireless Communications, A.Paulraj, R. Nabar and D. Gore, Cambridge University Press
Fundamentals of Wireless Communications, D. Tse and P.Vishwanath
Space-Time Coding, H. Jafarkhani
MIMO Wireless Communications, Edited by Biglieri, Calderbank,et al
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 5 / 48
-
Benefits of MIMO Systems
Increased Network Capacity
Improved Signal Quality
Increased Coverage
Lower Power Consumption
Higher Data Rates
These requirements are often conflicting. Need balancing tomaximize system performance
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 6 / 48
-
Technical Rationale
Spatial Diversity to Combat Fading
Spatial Signature for Interference Management
Array Gain enables Lower Power Consumption
Capacity Improvements using Spatial Multiplexing
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 7 / 48
-
Outage Capacity of MIMO SystemsCapacity of MIMO systems
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 8 / 48
-
Outline
1 Promise of MIMO Systems
2 Point to Point MIMO
3 Limited Feedback MIMO Systems
4 MIMO-OFDM
5 Multi-User MIMO
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 9 / 48
-
MIMO Channel Model
Input-Output relation for a discrete-time frequency-flat r tMIMO channel
y =
Est
Hs + n
y = [y1, y2, , yr ]T r 1 receive signal vectors = [s1, s2, , st ]T t 1 transmit signal vectorn = [n1, n2, , nr ]T r 1 noise vector at the receiverH is the r t channel matrixEs average energy over a symbol period
ni NC(0,No) with E [nnH ] = No Ir
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 10 / 48
-
MIMO Options
Channel assumed known at Receiver
Channel unknown at transmitter
Diversity Gain: Orthogonal space-time block codes, Space timetrellis codesSpatial Multiplexing: V-Blast, D-Blast
Channel known at the transmitter- Transmit precoding
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 11 / 48
-
Transmitter With Channel Knowledge
SVD of H can be expressed as
H = UVH
UHU = VHV = Ir = diag(m)
km=1, m > 0
Further, HHH is Hermitian with eigendecomposition
HHH = UUH
= diag(m)km=1, m m+1 with m = 0 for m > k and
m = 2m
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 12 / 48
-
Transmitter With Channel Knowledge Contd
Transmitted vector s = Vs
Input vector s is of dimension r 1 with E [ssH ] = t , tdiagonal
Received signal transformed to y = UHy
y =
Est
s + n
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 13 / 48
-
Transmitter With Channel Knowledge Contd
H is decomposed into k parallel sub-channels satisfying
ym =
Estmsm + nm, m = 1, 2, , k
The channels are of different quality with the gain on eachchannel determined by m
Number of channels depends on the rank of H.
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 14 / 48
-
Transmitter with Channel KnowledgeTransmitter with Channel Knowledge
sV
sH HU
rTransmitte Channel Receivern
y y~
11~s1
~n
1~y
kks~kn~
ky~
22~s2
~n
2~y
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 15 / 48
-
Capacity of a deterministic MIMO Channels
The channel capacity is given by
C = maxm
km=1
log2
[1 +
EsmNot
m
]m = E [|sm|2] is the transmit energy in the mth sub-channelk
m=1 m = t is the transmit energy constraint
Optimum power allocation across the sub-channels is obtainedas a solution to the lagrangian optimization problem
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 16 / 48
-
Optimal Power Allocation
Optimal power allocation satisfies
optm =
( Not
Esm
)+, m = 1, 2, , k
km=1
optm = t
where is a constant and (x)+ implies
(x)+ =
{x if x 00 if x < 0
optm is found iteratively by waterpouring algorithm
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 17 / 48
-
Waterpouring Solution
Waterpouring Solution
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 18 / 48
-
High SNR
At high SNR, equal power allocation is optimal
C =k
m=1
log2
[1 +
EsmNot
]
km=1
log2
[EsmNot
]= k log2
[EsNo
]+
km=1
log2
[mt
]Capacity grows linearly with k , the rank of the channel. Significant
increase in Capacity.
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 19 / 48
-
Special Cases
SIMO: H = h. Rank one and all power allocated to one mode
CSIMO = log2(1 +Esh2
No)
MISO: H = hH . Rank one and all power allocated to one mode
CMISO = log2(1 +Esh2
No)
When Channel known at Tx
CSIMO = CMISO
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 20 / 48
-
Maximum Ratio Transmission (MRT)
Input-Output relation for a r t MIMO channel
y =
Est
Hs + n
When the channel is known at the transmitter, the informationcan be used to design an optimum precoder w
The new Input-Output relation becomes
y =
Est
Hws + n
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 21 / 48
-
Maximum Ratio Transmission Contd
The receiver forms a weighted sum of the antenna outputs
y = gHy
The objective is to maximize the received SNR
=gHHw2F
tg2F
Optimal scheme is given by
w = v1, g = u1
Where, v1 and u1 are the left and right singular vectors of Hcorresponding to the maximum singular value
The scheme achieves full diversity
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 22 / 48
-
MRT Transmission: 2 2 MIMOMRT Transmission: 2x2 MIMO
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 23 / 48
-
Outline
1 Promise of MIMO Systems
2 Point to Point MIMO
3 Limited Feedback MIMO Systems
4 MIMO-OFDM
5 Multi-User MIMO
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 24 / 48
-
2
Importance of CSI Feedback
A. Improved system performance, in terms of capacity, SNR, BER, etc.Example: An MISO system with M transmit antennas and single receive antenna
NO CSIT Perfect CSIT
B. Reduced implementation complexity
Example: An MIMO system with M transmit and receive antennas,
No CSIT, capacity can be achieved by some 2-D (space-time) code
Pre-coder with perfect CSIT, system isequivalent to M parallel SISO channels
-
3
Importance of CSI Feedback
D. Greatly increase the system capacity region as well as the sum capacity
C. Enables exploitation of multi-user diversity
With CSIT, effective selection of active users and route selection can be made.
E. Improve the robustness of the communication link (QoS requirements)
Power and rate control is possible when CSIT is available and the network throughput is increased.
Example: A multi-user MISO broadcasting channel with M transmit and single receive antenna
users are not allowed to cooperate, and hencecause serious multi-userinterference.
CSI FeedbackProper pre-coding is possible, such as Zero-forcing, MMSE, etc
-
Block Diagram
Sources of feedback imperfection
Channel estimation
Channel quantization
Feedback delay
() 6 / 34
-
4
Nature of CSI FeedbackChannel state information (CSI) is a complex vector or matrix of continuous values
For example: An MIMO system with M transmit antennas and N receive antennas, .
It is not reasonable to feedback total 2MN real numbers of continuous values.
Each index represents a particular mode of the channel, which corresponds to a particular transmission strategy
Channel Quantizer
Integer Index
Adaptive Transmitter
Practical Feedback Schemes:
-
5
Considerations in Feedback Systems
A. Design of Optimal Quantizers (at the receiver) & Optimization of the Codebook?
1) The quantizer (or the encoder) should be simple as well as effective.
2) The quantizer and the codebook should be designed to match both the channel distribution and the system performance metrics, such as capacity, SNR, BER, etc.
B. Performance Analysis of Finite Rate Feedback Multiple Antenna Systems
1) To understand the effects of the finite rate feedback on the system performance, to be specific, performance metric vs feedback rate.
2) Shed insights on the choice of the feedback schemes as well as the quantizer design.
-
6
MISO Channel Quantizer
If ideal CSIT available, the transmit beamforming scheme is chosen to be:
MISO Channel System Model:
(vector)(scalar)
If only finite rate feedback is available, the beamforming vector is quantized to ,
capacity
(codebook)
capacity
-
7
Codebook Design (Optimization)
1). The capacity loss can be approximated by the following form in high resolution regimes,
2). A New Design Criterion that can minimize the system capacity loss:
Simplifications:
(MSwIP)
High SNR(MSIP)
The capacity loss due to the finite rate quantization of the beamforming vectors is:
Motivation: Minimize the capacity loss by optimizing the codebook vectors
It is a difficult problem (non-convex optimization problem)!
-
8
Codebook design using the Lloyd Algorithm
partitioning the regions
Nearest Neighborhood Condition (NNC):
For given codebook vectors
the optimum partitions are given by:
Centroid Condition (CC):
For given partitions ,
the optimal code matrices are given by:
Shifting new centers
-
9
Codebook Design Examples
-
10
MISO Capacity With Quantized Feedback
-
11
Extension to MIMO Channel Quantizer
Precoding Matrix Equal Power Allocation
MIMO Channel System Model:
Channel Model With Quantized Feedback:
-
12
Sequential Vector QuantizerA simple approach to quantize the precoding matrix:
How? Consider a unitary matrix whose first column is and the remainder columns are arbitarily chosen to satisfy . Then, has the form of
where is a orthogonormal column matrix.
-
13
The Sequential Quantization Method
Practical applications: Under consideration by the Broadband Wireless Group (802.16e)
Vector Parameterization: An orthonormal column matrix can be uniquely represented by by a set of unit-norm vectors with different dimensions, .
Statistical Property: For random channel with entries,, for , and they are statistically independent.
Quantization: For , unit-norm vector is quantized using a codebook that is designed for random unit-norm vectors In with the MSIP criterion.
-
14
Joint Quantization for MIMO Systems
Joint Quantization: by quantizing the entire precoding matrix at one shot
The codebook is designed to minimize the system mutual information rate loss
With ideal CSI Feedback With Quantized CSI Feedback
Under the high resolution assumptions, it can be approximated as
The first n eigen-valuesGeneralized Weighted Matrix Inner Product between and .
-
15
Codebook design using the Lloyd Algorithm
partitioning the regions
Shifting new centers
Nearest Neighborhood Condition (NNC):
For given code matrices ,
the optimum partitions are given by:
Centroid Condition (CC):
For given partitions ,
the optimal code matrices are given by:
-
16
Multi-mode Spatial Multiplexing
Case I: Low SNR
water level
power allocated
Case II: High SNR
water level
power allocated
Multi-mode SP transmission strategy:
1) The number of data streams n is determined by the system SNR:
2) In each mode, the simple equal power allocation over n spatial channels is employed.
Intuitive Explanation:Inverse Water-Filling Power Allocation (Optimal)
-
17
Performance of Multi-mode S-M
Ideal CSI Feedback Quantized CSI Feedback
-
18
Performance Analysis
Some Interesting Questions:
Finite Rate Effects: What is the performance (capacity, SNR, BER) versus the feedback rate ?
Mismatched Analysis: What happens if a codebook designed for one system is used in another system?
Transform Codebooks: The codebook for a particular system is transformed from another system through a linear or non-linear operation. What is the performance? & How to design?
Feedback With Error: What happens if the feedback information also suffers from error (delay)?
Quantization of Imperfect CSI: What happens if CSI to be quantized suffers from estimation error?
-
19
Capacity Loss Analysis for MISO Channels
Assume MISO channel with entries
Instantaneous Capacity (mutual information rate) Loss:
Capacity Loss: For a given codebook
Analysis is quite involved
-
Publications
1 J. C. Roh and B. D. Rao, Transmit Beamforming inMultiple-Antenna Systems with Finite Rate Feedback: A VQ-BasedApproach, IEEE Transactions Information Theory. vol. 52, no. 3,Pages: 1101-1112, Mar. 2006
2 J. C. Roh and B. D. Rao, Design and Analysis of MIMO SpatialMultiplexing Systems with Quantized Feedback, IEEE Transactionson Signal Processing, Vol. 54, no. 8, Pages. 2874-2886, Aug. 2006
3 J. C. Roh and B. D. Rao, Efficient Feedback Methods for MIMOChannels Based on Parameterizations, IEEE Transactions onWireless Communications, Pages: 282 - 292, Jan. 2007
4 J. Zheng, E. Duni, and B. D. Rao, Analysis of Multiple AntennaSystems with Finite-Rate Feedback Using High ResolutionQuantization Theory, IEEE Trans. on Signal Processing, vol.55,Issue 4,Pages: 1461 1476, April 2007.
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 25 / 48
-
Outline
1 Promise of MIMO Systems
2 Point to Point MIMO
3 Limited Feedback MIMO Systems
4 MIMO-OFDM
5 Multi-User MIMO
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 26 / 48
-
Frequency Selective Channels: MIMO-OFDM
Next generation wireless communication system uses MIMO- OFDM
MIMO-OFDM transfers a wideband frequency-selective channelinto a number of parallel narrowband flat fading MIMO channels
Benefits of OFDM
Achieves high spectral efficiency
Cyclic prefix is capable of mitigating multi-path fading
Allows for efficient FFT-based implementations and simplefrequency domain equalization
Exploits frequency diversity, in addition to time and spatialdiversity
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 27 / 48
-
MIMO-OFDM Block Diagram
MIMO-OFDM Transceiver
Binary Data
Modulation& Mapping
S/P Space-TimeProcessing
Space-TimeDecoder
& Equalizer
P/S
Binary Data
Demodulation& Demapping
IFFT Add CP P/S
IFFT Add CP P/S
FFTS/P RemoveCP
FFTS/P RemoveCP
OFDM Modulation OFDM Demodulation
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 28 / 48
-
MIMO-OFDM Signaling
The input-output relation of a broadband MIMO channel is
y [k] =
Est
Ll=0
H[l ]s[k l ] + n[k]
k - discrete time index
L - number of channel taps
t - number of transmit antennas
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 29 / 48
-
MIMO-OFDM Signaling Contd
OFDM with FFT/IFFT and CP insertion/removal operationsdecuples the frequency selective MIMO channel to a set of parallelMIMO channels as
y [l ] =
Est
H[l ]s[l ] + n[l ], l = 0, 1, ..,N 1.
N - Number of subcarriers
H[l ] - DFT Coefficient of the channel
s[l ] - data on carrier l
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 30 / 48
-
Spatial Diversity in MIMO-OFDM
Take Alamouti scheme as an example, there are two ways to realizespatial diversity
1 Coding in frequency domain, rather than in time domain
It requires that the channel remains constant over at least twoconsecutive tones
2 Coding on a per-tone basis across OFDM symbols in time
It requires that the channel remains constant during twoconsecutive OFDM symbols
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 31 / 48
-
Outline
1 Promise of MIMO Systems
2 Point to Point MIMO
3 Limited Feedback MIMO Systems
4 MIMO-OFDM
5 Multi-User MIMO
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 32 / 48
-
Multi-User MIMO
Main Issue is the utilization of the spatial degree of freedom in amulti-user environment
Resource ManagementInterference Management
Capacity of Multi-User systems
Multi-user Diversity
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 33 / 48
-
Multi-User SIMO Systems
r(t) =P
l=1
hlsl(t) + n(t)
To receive user j , can use beamformer wj
yj(t) = wHj r(t) = w
Hj hjsj(t) +
Pl=1,l 6=j
wHj hlsl(t) + wHj n(t)
The beamforming vector can be optimized for each user separately.
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 34 / 48
-
Multi-User MISO Systems
Transmitted signal
s(t) =P
l=1
wlsl(t)
Signal received by user j
rl(t) = hHj s(t) = h
Hj wjsj(t) +
Pl=1,l 6=j
hHj wlsl(t) + nj(t)
The transmit beamformers for the other users do interfere with thedesired user. Beamformers have to be jointly selected. A morechallenging problem.
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 35 / 48
-
Problem Statement
University of California, San Diego
Problem StatementConsider a multiuser MIMO beamforming network
Arbitrary Network configurations (cellular networks, multi-hop networks, etc.)Heterogeneous communication nodes with different power costs
Minimize the network power cost while satisfying the minimum SINR requirements of all links
SINR (signal to interference plus noise ratio)Joint optimization of beamforming weights and transmit powers
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 36 / 48
-
Problem Statement
University of California, San Diego
JOP:
Solved for SIMO and MISO cases for MISO problem is solved by using the virtual uplink concept
Problem Statement
LlSINR
J
ll
T
=
1 allfor subject to
)( min,,
pwpUVp
TL
L
L
TL
ww
pp
],...,[
},...,{ },...,{
],...,[ where
1
1
1
1
=
===
w
uuUvvV
p (network power vector, L: no. of links)(unit norm tx. beamforming vectors)
(unit norm rx. beamforming vectors)
(weight vector defining power costs)
T]1,...,1[== 1w
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 37 / 48
-
SINR Expression for MIMO Beamforming
University of California, San Diego
SINR Expression for MIMO BeamformingSINR (signal to interference plus noise ratio)
Problem isolation for optimal Rx. beamforming vectors UMMSE/MVDR beamforming at the receivers
No straightforward problem isolation for V
linl
Hl
lsl
Hl
liliili
Hl
llllHl
lilili
lllll np
pnpG
pGSINRuuuu
vHuvHu
=+
=+
=
2
2
||||
liiliHlli
l
l
lili
l
l
rtG
llrt
lrLllt
to fromgain link effective: ||
link ofctor weight veantenna receive : link ofctor weight veantenna transmit :
to frommatrix gain channelcomplex : link ofReceiver :
)1( link ofr Transmitte :
2vHu
uvH
=
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 38 / 48
-
SIMO problem : Cellular Uplink (Rashid-Farrokhi
et al. 98)
University of California, San Diego
SIMO problem : Cellular Uplink(Rashid-Farrokhi et al. 98)
Problem :
Joint Beamforming & Power Control Algorithm
Convergence to the global optima is established.Desirable features
MVDR beamforming : implemented using adaptive filters power control : using a simple power control loop
)(*)(
)(
)()1(
)()(
)(min)( where
)(
nl
lnl
l
lll
llj
jllj
ln
l
nn
pSINRG
npGI
l uu
up
pIp
u
=+
=
=
+
l
p
ll
ll
subject to
min,
Up
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 39 / 48
-
MISO Problem & Virtual Uplink
Concept(Rashid-Farrokhi et al. 98)
University of California, San Diego
MISO Problem & Virtual Uplink Concept(Rashid-Farrokhi et al. 98)
Dual relation between cellular downlink and uplinkVirtual uplink : uplink with reciprocal channels and noise vector 1. Optimal transmit beamforming vectors are identical to the optimal receive beamforming vectors in the virtual uplink
(a) Downlink (Primal) (b) Virtual Uplink (Dual)
11H
22H
33H HH11
HH22
HH33
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 40 / 48
-
Generalization
University of California, San Diego
GeneralizationWe generalize this idea to arbitrary multiuser MIMO networks with generalized cost function (e.g., MIMO multihop networks, energy-aware networking environment, etc.)
We derive the dual relation using the well-established duality concept in optimization theory
We take advantage of the dual relation for solving the stated problem
We developed an improved Decentralized Algorithm
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 41 / 48
-
Construction of a Dual Network
University of California, San Diego
Construction of a Dual NetworkFor any multi-user MIMO network with linear beamformers, one can construct a dual network using the following three rules:
Reverse the direction of all linksReplace any MIMO channel matrix H by HH
Use transmit beamforming vectors as receive beamforming vectors, and vice versa.
44H22H11
H
33H 55H
HH44
HH22HH11
HH33HH55
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 42 / 48
-
Duality
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 43 / 48
-
Applications to JOP
University of California, San Diego
Applications to JOPTheorem 2 suggests an iterative algorithm (Algorithm E)
Primal Network : Update p and U for fixed V, so that wTp is minimizedDual Network : Update q and V for fixed U, so that nTq is minimized
Lemma 3. In the proposed algorithm, once the solution becomes feasible, i.e., all SINR values meet or exceed the minimum requirements, it generates a sequence of feasible solutions with monotonic decreasing cost.
)(nout
)()(~ nout
nin =
)(~ nout
)()1( ~ nout
nin =+
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 44 / 48
-
Cellular Network -Downlink
University of California, San Diego
Cellular Network - DownlinkMultiple wrapped around cells (19 three-sectored cells)Same channel is reused in every cell but only in one sectorThree co-channel users per sectorPropagation exponent = 3.5, 8dB shadow fading
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 45 / 48
-
Performance Comparison
University of California, San Diego
Algorithm A, B, E and F
The proposed algorithm presents significant improvement in the complexity-performance tradeoff, thereby greatly improving practical value.
Performance Comparison
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 46 / 48
-
Current Trends
Multi-user OFDM systems
Coordinated Multi-Point Transmission (CoMP)
Cooperative MIMO
MIMO Ad-Hoc Networks
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 47 / 48
-
Summary
MIMO Systems offer unique opportunities in wirelesscommunication
Provides an opportunity to use spatial dimension to providediversity and hence reliability.
Can be used to significantly increase capacity in a rich scatteringenvironment
Bhaskar RaoCenter for Wireless CommunicationsUniversity of California, San Diego ()Linear Precoding in MIMO Wireless Systems 48 / 48
Promise of MIMO SystemsPoint to Point MIMOLimited Feedback MIMO SystemsMIMO-OFDMMulti-User MIMOlge_limited_feedback.pdfSlide Number 1Importance of CSI FeedbackImportance of CSI FeedbackNature of CSI FeedbackConsiderations in Feedback Systems MISO Channel QuantizerCodebook Design (Optimization)Codebook design using the Lloyd AlgorithmCodebook Design ExamplesMISO Capacity With Quantized FeedbackExtension to MIMO Channel QuantizerSequential Vector QuantizerThe Sequential Quantization MethodJoint Quantization for MIMO SystemsCodebook design using the Lloyd AlgorithmMulti-mode Spatial MultiplexingPerformance of Multi-mode S-MPerformance AnalysisCapacity Loss Analysis for MISO ChannelsPrevious WorkSource Coding PerspectiveIllustration of a Simple ExampleGeneral Vector Quantization Problem High Resolution AnalysisTwo Important CharacteristicsMinimization of The Distortion Some More Distortion BoundsExtensions of the Distortion AnalysisApplication to MISO SystemsOptimal MISO CSI QuantizerSimulation ResultsSimulation Results (Cont.)Simulation Results (Cont.)Mismatched CSI Quantizer (I)Simulation Results (Mismatched I)Mismatched CSI Quantizer (II)Simulation Results (Mismatched II)Application to MIMO CaseNumerical Examples (MIMO)Summary of MIMO with Quantized CSICorresponding PublicationsCorresponding Publications (Cont.)Statistics of Unconstraint Inner ProductQuantization Cell ApproximationStatistics of Inner Product with QuantizationCapacity Loss AnalysisApproximation to Capacity LossCapacity Loss: Numerical ResultsCapacity Loss: Numerical ResultsRelated PublicationsSource Coding PerspectiveA Simple Example (Motivation)Important Source Coding ResultsExtension to Feedback MIMO SystemsApplication to MISO SystemsAdditional ResultsSummary
top related