Degrees of freedom of bursty multiple access channels with a relay

We investigate the role of relays in multiple access channels (MACs) with bursty user traffic, where intermittent data traffic restricts the users to bursty transmissions. Specifically, we examine a K-user bursty MIMO Gaussian MAC with a relay, where bursty traffic of each user is governed by a Bernoulli random process. As our main result, we characterize the degrees of freedom (DoF) region. To this end, we extend noisy network coding, in which relays compress-and-forward, to achieve the DoF cut-set bound. From this result, we establish the necessary and sufficient condition for attaining collision-free DoF performances. Also, we show that relays can provide a DoF gain which scales to some extent with additional relay antennas. Our results have practical implications in various scenarios of wireless systems, such as the Internet of Things (IoT) and media access control protocols.