A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM 1 Contributions and Proposals of UPC - Department 1 NEWCOM Antonio Pascual Iserte

A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM 1

Contributions and Proposals of UPC - Department 1

NEWCOM

Antonio Pascual Iserte

Universitat Politècnica de Catalunya

Barcelona, 9 March 2005


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

Outline








Outline


Robustness

Robust Designs:• They take into account the errors in the CSI

• Sources of errors in the CSI for MIMO channels:o Estimation noiseo Channel variabilityo Quantization of the channel estimate (feedback)

Robustness Strategies:• Bayesian approach: statistical solution

• Maximin approach: best worst-case


Robustness Strategies

f: cost function to minimize, B: TX, A: RX

Bayesian Design• Best statistical mean value

Maximin Design• Optimization of the worst-case


Maximin Robust Transmitter - MIMO

OSTBC + power allocation + beamforming:

Receiver: linear operations


SNR:

Notation:• ErrorError in the channel estimate:

o Convex uncertainty region:

• BeamformersBeamformers: estimated eigenmodes of

• Power distributionPower distribution:

• Cost functionCost function to maximize:

Notation


Problem Formulation and Solution

Maximin robust design:

The problem can be solved using standard software packages for convex optimization problems:


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…


Uncertainty Regions (II)

• Also vector quantization…

• In general… any error that can be modeled by a convex uncertainty region


Robust Adaptive Modulation








Outline


Limited Feedback

Introduction:• Design of the feedback strategy:

Transmitter Receiver

Feedback Channel Quantization

channel estimate

???

B bits of feedback


Limited Feedback - MIMO Channels (I)

Scalar Quantization (SQ):• Direct quantization of the channel:

o Non-iterative: uniform vs. non-uniformo Iterative quantization: delta modulation

• Quantization of the strongest eigenvectors:o Direct quantizationo Quantization in a parameterized space (e.g. the set of

orthonormal vectors)


Limited Feedback - MIMO Channels (II)

Vector Quantization (VQ):

• Distortion measure:o SuboptimumSuboptimum: distortion = error in the channel estimateo OptimumOptimum: distortion = system performance

• Transmitter architecture:

F

(linear precoder)

STC

(space-time code)

B bits of feedback

N = 2B: F1, … , FN


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


Illustrative Results








Outline


Other Robust Designs

Extensions of the robust designs:

• Other transmitter architectures

• Multiuser scenarios

• Limited channel knowledge:o Only gaino Only phase

• Different degrees of knowledge at the transmitter and the receiver

• Robustness against implementation errors


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 metricchannel quality metric for interface between the physical/link and higher layers

o MIMO channel capacityo maximum eigenvalue of the MIMO channel matrixo others… ???

Documents

A. Pascual Contributions and Proposals of UPC to Department 1 - NEWCOM 1 Contributions and Proposals of UPC - Department 1 NEWCOM Antonio Pascual Iserte