Title :
Further Results on the Asymptotic Mutual Information of Rician Fading MIMO Channels
Author :
Taricco, Giorgio
Author_Institution :
Politec. di Torino, Turin, Italy
Abstract :
Rician fading multiple-input multiple-output (MIMO) channels with Kronecker-decomposable covariance structure are considered in this study to derive information measures characterizing their achievable rate. Analytic results are obtained in the asymptotic setting corresponding to infinitely many transmit and receive antennas, whose numbers approach a finite limiting ratio. More specifically, the asymptotic mean and variance of the mutual information are derived in this asymptotic regime, and it is shown that the corresponding probability distribution converges to a Gaussian distribution. All these results are based on the replica method, whose mathematical principles are discussed in this study. The ergodic capacity is also addressed by deriving an iterative water-filling algorithm yielding the capacity-achieving input covariance matrix (under an average power constraint). Resorting to the asymptotic Gaussianity of the mutual information distribution, an analytic expression of the outage capacity is derived based on the mean and variance of the mutual information. Finally, numerical results are reported to assess the level of approximation of the analytic results in comparison with those obtained by Monte Carlo simulation.
Keywords :
Gaussian channels; Gaussian distribution; MIMO communication; Monte Carlo methods; Rician channels; approximation theory; covariance matrices; iterative methods; probability; radio receivers; radio transmitters; receiving antennas; transmitting antennas; Gaussian distribution; Kronecker-decomposable covariance structure; Monte Carlo simulation; Rician fading MIMO channel; approximation level; asymptotic Gaussianity; asymptotic mean regime; asymptotic mutual information distribution; average power constraint; capacity-achieving input covariance matrix; ergodic capacity; finite limiting ratio; iterative water-filling algorithm; multiple-input multiple-output; probability distribution convergence; receiving antenna; replica method; transmitting antenna; Channel models; Covariance matrix; Fading; Mutual information; Rician channels; Vectors; Asymptotic capacity; Kronecker-decomposable (KD) covariance structure; Rician fading multiple-input multiple-output (MIMO) channels; replica method; saddlepoint approximation;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2012.2223195