Verified Bit and Power Allocation for MIMO Systems: A Comparison of SVD Based Techniques With GMD

Abstract

Methods with result verification have been applied in different practical contexts, for example, in such diverse areas as robotics, computer graphics, or chemistry. Such methods help to verify the result of a computer simulation, additionally taking into account possibly present bounded uncertainty in a deterministic way. Modeling and simulation of multiple-input multiple-output (MIMO) systems has not received much attention from this angle. Nowadays, increasing the capacity of communication links by using the MIMO mechanism is an essential part of various wireless communication standards.

In this paper, we consider the channel separation stage in the overall modeling and simulation process for MIMO systems and compare the singular value decomposition (SVD) and the geometric mean decomposition (GMD) based approaches from the point of view of the achievable bit error ratio (BER) under good and poor scattering conditions. As a special focus, we use interval methods to verify the result and to deal with the appearing epistemic uncertainty. Additionally, we consider resource allocation in detail, which mostly makes sense only for the SVD approach since the goal of the GMD based one is to avoid it. However, this has been studied only asymptotically until now and needs confirmation. We propose a combined analytical-numerical approach to simulate resource allocation relying on verified techniques. The theoretical results are illustrated and the comparison is performed using simulated data for an uncorrelated and a correlated MIMO system with four receiving and four transmitting antennas.