1. University of Houston Cullen College of Engineering Electrical & Computer Engineering Capacity Scaling in MIMO Wireless System Under Correlated Fading --by Chen-Nee Chuah, David N. C. Tse, Joseph M. Kahn, and Reinaldo A. Valenzuela IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 3, MARCH 2002 Presented by: Jia (Jasmine) Meng Advisor: Dr. Zhu Han Wireless Network, Signal Processing & Security Lab University of Houston, USA Oct. 1, 2009

2. University of Houston Cullen College of Engineering Electrical & Computer Engineering Outline  Introduction Concepts Existing results  System Model Assumptions Channel models  MEA Capacity and Mutual Information  Asymptotic Analysis  Simulations  Conclusions

3. University of Houston Cullen College of Engineering Electrical & Computer Engineering 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) antennas 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)

4. University of Houston Cullen College of Engineering Electrical & Computer Engineering Introduction-- Existing Results  If the fades between pairs of transmit-receive antennas 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

5. University of Houston Cullen College of Engineering Electrical & Computer Engineering System Model  Linear and time-invariant channel use the following discrete-time equivalent model: is the signal transmitted by the i-th transmitter is the signal received by the i-th receiver is the noise received by the i-th receiver is the path gain from the j-th transmitter to the i-th receiver

6. University of Houston Cullen College of Engineering Electrical & Computer Engineering 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.

7. University of Houston Cullen College of Engineering Electrical & Computer Engineering 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.

8. University of Houston Cullen College of Engineering Electrical & Computer Engineering MEA Capacity and Mutual Information (I)  Capacity with water filling power allocation MEA capacity with optimal power allocation is

9. University of Houston Cullen College of Engineering Electrical & Computer Engineering MEA Capacity and Mutual Information (II)  Mutual information with equal-power allocation MEA capacity with optimal power allocation is

10. University of Houston Cullen College of Engineering Electrical & Computer Engineering 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.

11. University of Houston Cullen College of Engineering Electrical & Computer Engineering 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:

12. University of Houston Cullen College of Engineering Electrical & Computer Engineering Asymptotic Analysis -- Correlated Fading (II)

13. University of Houston Cullen College of Engineering Electrical & Computer Engineering 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

14. University of Houston Cullen College of Engineering Electrical & Computer Engineering Simulation  Multipath, Rayleigh fading channel simulation  Verify the correlations @ both sides  Verify the feasibility of multiply the correlations  Show strength of the correlations @ different antenna distances  Show channel capacity @ different antenna distributions

15. University of Houston Cullen College of Engineering Electrical & Computer Engineering SHOW: Channel Correlation

16. University of Houston Cullen College of Engineering Electrical & Computer Engineering Average & Asymptotic Capacity Vs. n for in-line & broadside case Correlated Independent

17. University of Houston Cullen College of Engineering Electrical & Computer Engineering 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.

18. University of Houston Cullen College of Engineering Electrical & Computer Engineering

19. University of Houston Cullen College of Engineering Electrical & Computer Engineering 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)). BACK