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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
University of HoustonCullen College of EngineeringE
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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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