Wireless MIMO Switching with Network Coding 1 arXiv:1105.1279v1 [cs.IT] 6 May 2011 Institute of Network Coding Fanggang Wang and Soung C. Liew The Chinese University of Hong Kong Index Terms I. INTRODUCTION Abstract In a generic switching problem, a switching pattern consists of a one-to-one mapping from a set of inputs to a set of outputs (i.e., a permutation). We propose and investigate a wireless switching framework in which a multi-antenna relay is responsible for switching traffic am ong a set of N stations. We refer to such a relay as a MIMO switch. With beamforming and linear detection, the MIMO switch controls which stations are connected to which other stations. Each beamforming matrix realizes a permutation pattern among the stations. We refer to the corresponding permutation matrix as a switch matrix. By scheduling a set of different switch matrices, full connectivity among the stations can be established. In this paper, we focus on “fair switching” in which equal amounts of traffic are to be delivered for all N ( N − 1) ordered pairs of stations. In particular, we investigate how the system throughput can be maximized. In general, for large N the number of possible switch matrices (i.e., permutations) is huge, making the scheduling problem combinatorially challenging. We show that for the cases of N = 4 and 5 , only a subset of N − 1 switch matrices need to be considered in the scheduling problem to achieve good throughput. We conjecture that this will be the case for large N as well. This conjecture, if valid, implies that for practical purposes, fair-switching scheduling is not an intractable problem. We also investigate MIMO switching with physical-layer network coding in this paper. We find tha t it can improve throughput appreciably. MIMO switching, relay, derangement, fairness, physical-layer network coding. Relaying in wireless networks plays a key role in various communication applications [1]. The use of relays can extend coverage as well as improve energy efficien cy [2]. In this paper, we study a set-up in which multiple stations communicate with each other via a multi-antenna relay. With beamforming, the Corresponding author ***