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Weak Convergence and Rate of Convergence of MIMO Capacity Random Variable

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2 Author(s)
Raghavan, V. ; Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI ; Sayeed, A.M.

Recent works on the distribution function of the capacity of independent and identically distributed (i.i.d.) and semicorrelated narrowband channels show that the outage capacity computed using a Gaussian approximation is close to the true outage capacity even for few antennas. Motivated by physical scattering considerations, we study a multi-antenna channel model with independent entries that are not necessarily identically distributed and show the weak convergence of capacity to a Gaussian random variable. The channel model considered in this paper subsumes well-studied cases like the i.i.d. and separable correlation models and thus we generalize previous results on weak convergence of multi-antenna capacity. Using recent results from random matrix theory, we also study the rate of convergence of ergodic capacity of i.i.d. channels to its limit value. Employing a well-known conjecture from random matrix theory, we establish tight results for the rate of convergence and show a dependence of this rate on signal-to-noise ratio

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Information Theory, IEEE Transactions on  (Volume:52 ,  Issue: 8 )