Contributions and Proposals of
UPC - Department 1
NEWCOM
Antonio Pascual Iserte
Universitat Politècnica de Catalunya
Barcelona, 9 March 2005
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Outline
 Design of MIMO systems: a practical overview:
• MIMO robust designs
• Design of limited feedback
 Some proposals for future work:
• Other robust designs
• Impact of MIMO channels on system level aspects
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Outline
 Design of MIMO systems: a practical overview:
• MIMO robust designs
• Design of limited feedback
 Some proposals for future work:
• Other robust designs
• Impact of MIMO channels on system level aspects
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Robustness
 Robust Designs:
• They take into account the errors in the CSI
• Sources of errors in the CSI for MIMO channels:
o Estimation noise
o Channel variability
o Quantization of the channel estimate (feedback)
 Robustness Strategies:
• Bayesian approach: statistical solution
• Maximin approach: best worst-case
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Robustness Strategies
f: cost function to minimize, B: TX, A: RX
 Bayesian Design
• Best statistical mean value
 Maximin Design
• Optimization of the worst-case
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Maximin Robust Transmitter - MIMO
 OSTBC + power allocation + beamforming:
 Receiver: linear operations
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Notation
 SNR:
 Notation:
• Error in the channel estimate:
o Convex uncertainty region:
• Beamformers: estimated eigenmodes
of
• Power distribution:
• Cost function to maximize:
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Problem Formulation and Solution
 Maximin robust design:
 The problem can be solved using standard software
packages for convex optimization problems:
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Uncertainty Regions (I)
• Several sources of errors can be modeled
(a) Gaussian estimation errors (TDD)
(b) Errors from scalar quantization (FDD)
(c) Combination of both (FDD)
Quadratic convex problems…
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Uncertainty Regions (II)
• Also vector quantization…
• In general… any error that can be modeled by a
convex uncertainty region
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Robust Adaptive Modulation
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Outline
 Design of MIMO systems: a practical overview:
• MIMO robust designs
• Design of limited feedback
 Some proposals for future work:
• Other robust designs
• Impact of MIMO channels on system level aspects
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Limited Feedback
 Introduction:
• Design of the feedback strategy:
Receiver
Transmitter
channel estimate
???
Feedback Channel
Quantization
B bits of feedback
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Limited Feedback - MIMO Channels (I)
 Scalar Quantization (SQ):
• Direct quantization of the channel:
o Non-iterative: uniform vs. non-uniform
o Iterative quantization: delta modulation
• Quantization of the strongest eigenvectors:
o Direct quantization
o Quantization in a parameterized space (e.g. the set of
orthonormal vectors)
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Limited Feedback - MIMO Channels (II)
 Vector Quantization (VQ):
• Distortion measure:
o Suboptimum: distortion = error in the channel estimate
o Optimum: distortion = system performance
• Transmitter architecture:
STC
F
(space-time
code)
(linear
precoder)
B bits of feedback
N = 2B: F1, … , FN
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Limited Feedback - MIMO Channels (III)
• Precoder codebook: {F1, …, FN}
• Precoder selection function F=f (H): performance
metric (SER, MSE, SNR, mutual information, etc…)
 Example of design of the precoder codebook:
• Use a set of linear precoders F1, …, FN spanning
maximally spaced subspaces
Grassmannian packaging
• Random precoder: easier, asymptotically equivalent
to Grassmannian
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Illustrative Results
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Outline
 Design of MIMO systems: a practical overview:
• MIMO robust designs
• Design of limited feedback
 Some proposals for future work:
• Other robust designs
• Impact of MIMO channels on system level aspects
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Other Robust Designs
 Extensions of the robust designs:
• Other transmitter architectures
• Multiuser scenarios
• Limited channel knowledge:
o Only gain
o Only phase
• Different degrees of knowledge at the transmitter
and the receiver
• Robustness against implementation errors
A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM
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Impact of MIMO on System Level
 Analysis of the benefits provided by MIMO at
the system level:
• Identification of simulation scenarios
• Identification of appropriate figures of merit
• Identification of a channel quality metric for interface
between the physical/link and higher layers
o MIMO channel capacity
o maximum eigenvalue of the MIMO channel matrix
o others… ???
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