Random Matrix Theory Based Resource Allocation in Correlated MIMO Systems with ARQ Feedback

Marie Zwingelstein (1) , Mérouane Debbah (2)

1 IEMN - Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520
2 Chaire Radio Flexible - Chaire Radio Flexible Alcatel-Lucent/Supélec

We consider resource allocation under partial feed-back in a spatially correlated MIMO link, when the ARQ protocol is implemented at the MAC layer. We propose a design framework, which makes use of results from random matrix theory (RMT), to find the rate as well as the input covariance matrix that maximize the long term goodput. We consider partial feedback in terms of positive/negative acknowledgment bits (ACK/NAK), which comes essentially for free since they are always present in the signaling of the upper layers. We provide explicit expressions of the long term goodput, which, in association with a RMT based approximation of the mu-tual information enable us to optimize the resource allocation problem. Interestingly, the simulations show that the asymptotic optimization analysis is still valid for MIMO sizes as small as 2x2. Index Terms—MIMO, resource allocation, random matrix theory, ARQ, partial feedback. I. BACKGROUND AND MOTIVATION R ESOURCE allocation is a widely studied subject (e.g. [1] and references therein) for which the assumptions may be of two kinds: perfect channel state information at the transmitter (CSI-T), and partial CSI-T, also known as partial feedback. Only the latest is acceptable from a practical point of view as soon as the number of degrees of freedom in the system gets large (MIMO, wideband or/and multi-user systems for example). The objective of this paper is to present a design framework to optimize the long term goodput by using the ACK/NAK bits provided by ARQ. This can be viewed as a cross-layer design in the sense that physical layer parameters are optimized based on (ARQ) information provided at the MAC layer [2]. We apply results from Random Matrix Theory (RMT) to estimate the average received SNR and determine the rate and the input covariance matrix to maximize the goodput. To the best of the authors' knowledge, RMT results have never been applied to the resource allocation problem for MIMO-ARQ systems. Importantly, general considerations about the optimal transmission scheme without perfect CSI-T (training-based methods, blind methods, error-rate based methods. . .) are out of the scope of this paper. The proposed framework can be seen as a proof of concept that acknowledgment bits can be used for the resource allocation problem in a MIMO-ARQ setup, although it is probable that optimal solutions would be, e.g., mixed training-ARQ based.

Mots clés: ARQ, MIMO, partial feedback, random matrix theory, resource allocation

Domaines: Informatique [cs]; Mathématiques [math]; Sciences de l'ingénieur [physics]

Marie Zwingelstein, Mérouane Debbah. Random Matrix Theory Based Resource Allocation in Correlated MIMO Systems with ARQ Feedback. IEEE Communications Letters, 2014, 18 (5), pp.793-796. ⟨10.1109/LCOMM.2014.031414.140214⟩. ⟨hal-01098948⟩