university of houston cullen college of engineering electrical & computer engineering capacity...

University of HoustonCullen College of EngineeringE

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Capacity Scaling in MIMO Wireless System Under Correlated Fading--by Chen-Nee Chuah, David N. C. Tse, Joseph M. Kahn, and Reinaldo A. ValenzuelaIEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 3, MARCH 2002

Presented by: Jia (Jasmine) MengAdvisor: Dr. Zhu Han

Wireless Network, Signal Processing & Security LabUniversity of Houston, USA

Oct. 1, 2009


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Outline

Introduction Concepts Existing results

System Model Assumptions Channel models

MEA Capacity and Mutual Information Asymptotic Analysis Simulations Conclusions


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Introduction -- Concepts

Channel Capacity (Bits/ Channel Use)is the tightest upper bound on the amount of information that can be reliably transmitted over a communications channel.

MIMO & Multiple-element arrays (MEAs) Single-user, point-to-point links, use multiple (n) anten

nas at both transmitter and receiver side, (n,n)-MEA system

Increases the channel capacity significantly Capacity Scaling

Normalize channel capacity with respect to the number of transmitter/receiver pair (n)


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Introduction-- Existing Results If the fades between pairs of transmit-receive ant

ennas are i.i.d., the average channel capacity of a MEAs system that uses n antennas paires is approximately n times higher than that of a single-antenna pair system for a fixed bandwidth and overall transmitted power.

Recap (1) i.i.d. channel assumption(2) Channel capacity grows linearly in the # of antenna pair n

HOWEVER i.i.d. does not always hold This paper discusses under a more general case,

the channel capacities under the correlated fading


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System Model

Linear and time-invariant channel use the following discrete-time equivalent model:

ix is the signal transmitted by the i-th transmitter

iy is the signal received by the i-th receiver

iz is the noise received by the i-th receiver

ijh is the path gain from the j-th transmitter to the i-th receiver


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Transmitter Power Allocation Strategies

1) H is known only to the receiver but not the transmitter. Power is distributed equally over all transmitting antennas in this case.

2) H is known at both the transmitter and receiver, so that power allocation can be optimized to maximize the achievable rate over the channel.


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Channel Model-- Assumptions

H is considered as quasi-static, and average total power and noise variance won’t change during communication;

H changes when the receiver moves; The associated capacity and mutual information

and for each specific realization of H can be viewed as random variables;

We are interested in study the statistics of these random variables, specifically the averages of capacity and mutual information.

nC nI

totP 0N W

nC nI


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MEA Capacity and Mutual Information (I)

Capacity with water filling power allocation MEA capacity with optimal power allocation is


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MEA Capacity and Mutual Information (II)

Mutual information with equal-power allocation MEA capacity with optimal power allocation is


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Asymptotic Analysis--Independent Fading

Both the capacity and the mutual information and depends on H only through the empirical distribution (CDF) of the eigenvalues.

Conclusions: At high SNR, it is well known that the water-filling and

the constant power strategies yield almost the same performance

At low SNR, the water-filling strategy shows a significant performance gain over the constant-power strategy.

n

( )nC H

( )nI H


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Asymptotic Analysis -- Correlated Fading (I)

Each of the are assumed to be complex, zero-mean, circular symmetric Gaussian random variables with variance . The are jointly Gaussian with the following covariance structure:

ijH

2[| | ] 1ijE H


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Asymptotic Analysis -- Correlated Fading (II)


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Asymptotic Analysis

Analyze the capacity and mutual information@ high and low SNR

No analytical expression for C @ low SNR @ high SNR, C I

@ low SNR, mutual information is I_highSNR+ capacity penalty at both sides


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Simulation

Multipath, Rayleigh fading channel simulation Verify the correlations @ both sides Verify the feasibility of multiply the correlations Show strength of the correlations @ different ant

enna distances Show channel capacity @ different antenna distr

ibutions


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SHOW: Channel Correlation


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Average & Asymptotic Capacity Vs. n for in-line & broadside case

Correlated

Independent


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Conclusions

The model of multiply the correlation @ both sides is feasible

Fading correlation can significantly reduce MEA system capacity and mutual information

Capacity and mutual information still scale linearly with n, while the rate of growth is different.

The rate of growth of is reduced by correlation over the entire range of SNRs, while that for is reduced by correlation at high SNR but is increased at low SNR.

nInC


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Empirical distribution function

In statistics, an empirical distribution function is a cumulative probability distribution function that concentrates probability 1/n at each of the n numbers in a sample.

Let X1, …, Xn be iid real random variables with the cdf F(x). The empirical distribution function F- n(x) is a step function defined by

where I(A) is the indicator of event A. For fixed x, I(Xi ≤ x) is a Bernoulli random variable with

parameter p = F(x), hence nF- n(x) is a binomial random variable with mean nF(x) and variance nF(x)(1 − F(x)).

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