Reduced Complexity Power Allocation Strategies for MIMO Systems With Singular Value Decomposition

Abstract

We consider wireless multiple-input-multiple-output (MIMO) systems in fading environments, with frequency flat fading, channel state information at both transmitter and receiver sides, and linear precoding based on singular value decomposition (SVD). The optimal solution for these MIMO SVD systems, in terms of achievable rate, requires water filling to optimally allocate power to the different channel eigenmodes. Alternatively, reduced complexity power allocation methods can be employed. We propose two power allocation techniques that only require statistical knowledge of the channel matrix coefficients and do not need knowledge of the instantaneous values of the channel state. To study these power allocation methods, we introduce a new expression for the exact distribution of the eigenvalues of Wishart matrices, where the probability density function of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> th largest eigenvalue is given as a sum of terms of the form <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> δ. The expression is here used, in the context of MIMO SVD systems, to obtain the achievable rate for both zero-outage and nonzero-outage strategies. We show that low-complexity methods have performance very similar to water-filling methods.