We investigate the role of a relay in multiple access channels (MACs) with bursty user traffic, where intermittent data traffic restricts the users to bursty transmissions. As our main result, we characterize the degrees of freedom (DoF) region of a K-user bursty multi-input multi-output (MIMO) Gaussian MAC with a relay, where Bernoulli random states are introduced to govern bursty user transmissions. To that end, we extend the noisy network coding scheme to achieve the cut-set bound. Our main contribution is in exploring the role of a relay from various perspectives. First, we show that a relay can provide a DoF gain in bursty channels, unlike in conventional non-bursty channels. Interestingly, we find that the relaying gain can scale with additional antennas at the relay to some extent. Moreover, observing that a relay can help achieve collision-free performances, we establish the necessary and sufficient condition for attaining collision-free DoF. Lastly, we consider scenarios in which some physical perturbation shared around the users may generate data traffic simultaneously, causing transmission patterns across them to be correlated. We demonstrate that for most cases in such scenarios, the relaying gain is greater when the users’ transmission patterns are more correlated, hence when more severe collisions take place. Our results have practical implications in various scenarios of wireless networks such as device-to-device systems and random media access control protocols.
In terms of relaying operations, the aforementioned works mainly consider full-duplex and strictly causal relays. Most of the theories developed for full-duplex relays were shown extendable to cases where relays are half-duplex through discussions in @cite_14 which model half-duplex relays by imposing constraints such as fractions of time allowed for relays to be in either reception or transmission mode. Also, causal relaying strategies including instantaneous relaying as well as non-causal relaying strategies have been explored in @cite_11 .
@cite_14 @cite_11
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Relay channels where terminals cannot receive and transmit at the same time are modeled as being memoryless with cost constraints. Cost functions are considered that measure the power consumed in each of three sleep-listen-or-talk (SLoT) modes, as well as the fraction of time the modes are used. It is shown that strategies that have the SLoT modes known ahead of time by all terminals are generally suboptimal. It is further shown that Gaussian input distributions are generally suboptimal for Gaussian channels. For several types of models and SLoT constraints, it is shown that multi-hopping (or decode-andforward) achieves the information-theoretic capacity if the relay is geometrically near the source terminal, and if the fraction of time the relay listens to the source is lower bounded by a positive number. SLoT constraints for which the capacity claim might not be valid are discussed. Finally, it is pointed out that a lack of symbol synchronization between the relays has little or no effect on the capacity theorems if the signals are bandlimited and if independent input signals are optimal. The paper investigates the effect of link delays on the capacity of relay networks. The relay-with-delay is defined as a relay channel with relay encoding delay d isin Z of units, or equivalently, a delay of units on the link from the sender to the relay, zero delay on the links from the transmitter to the receiver and from the relay to the receiver, and zero relay encoding delay. Two special cases are studied. The first is the relay-with-unlimited look-ahead, where each relay transmission can depend on its entire received sequence, and the second is the relay-without-delay, where the relay transmission can depend only on current and past received symbols, i.e., d=0. Upper and lower bounds on capacity for these two channels that are tight in some cases are presented. It is shown that the cut-set bound for the classical relay channel, corresponding to the case where d=1, does not hold for the relay-without-delay. Further, it is shown that instantaneous relaying can be optimal and can achieve higher rates than the classical cut-set bound. Capacity for the classes of degraded and semi-deterministic relay-with-unlimited-look-ahead and relay-without-delay are established. These results are then extended to the additive white Gaussian noise (AWGN) relay-with-delay case, where it is shown that for any dles0, capacity is achieved using amplify-and-forward when the channel from the sender to the relay is sufficiently weaker than the other two channels. In addition, it is shown that a superposition of amplify-and-forward and decode-and-forward can achieve higher rates than the classical cut-set bound. The relay-with-delay model is then extended to feedforward relay networks. It is shown that capacity is determined only by the relative delays of paths from the sender to the receiver and not by their absolute delays. A new cut-set upper bound that generalizes both the classical cut-set bound for the classical relay and the upper bound for the relay-without-delay on capacity is established.