  We consider the opportunistic multiuser diversity in the multiuser two-way
amplify-and-forward (AF) relay channel. The relay, equipped with multiple
antennas and a simple zero-forcing beam-forming scheme, selects a set of two
way relaying user pairs to enhance the degree of freedom (DoF) and consequently
the sum throughput of the system. The proposed channel aligned pair scheduling
(CAPS) algorithm reduces the inter-pair interference and keeps the signal to
interference plus noise power ratio (SINR) of user pairs relatively
interference free in average sense when the number of user pairs become very
large. For ideal situations, where the number of user pairs grows faster than
the system signal to noise ratio (SNR), the DoF of $M$ per channel use can be
achieved when $M$ is the relay antenna size. With a limited number of pairs,
the system is overloaded and the sum rates saturate at high signal to noise
ratio (SNR) though modifications of CAPS can improve the performance to a
certain amount. The performance of CAPS can be further enhanced by
semi-orthogonal channel aligned pair scheduling (SCAPS) algorithm, which not
only aligns the pair channels but also forms semi-orthogonal inter-pair
channels. Simulation results show that we provide a set of approaches based on
(S)CAPS and modified (S)CAPS, which provides system performance benefit
depending on the SNR and the number of user pairs in the network.
