Analytical comparison of power allocation methods in MIMO systems with singular value decomposition

We investigate high spectral efficiency wireless multiple-input multiple-output (MIMO) systems in fading en- vironments. We assume frequency flat fading, channel state information at both the transmitter and receiver sides, and linear precoding based on singular value decomposition (SVD). For this MIMO SVD scenario, the optimal solution in terms of achievable rate requires water-filling to optimally allocate the power to the different channel eigenmodes. Alternatively, reduced complexity power allocation methods can be employed, where the allocation is based on statistical expectations of functions related to the singular values of the channel gain matrix. In this paper we study these power allocation methods, by using the exact distribution of an arbitrary (ordered) eigenvalue of Wishart matrices, with the probability density function of the ℓth largest eigenvalue given as a sum of terms xβ e−xδ . We derive expressions for the achievable rate for both zero-outage and non-zero-outage strategies. We show that, often, the low-complexity methods have performance very similar to water-filling methods.