We study the effects of instantaneous feedback of channel topology on the degrees of freedom (DoF) of the bursty MIMO X channel, where the four transmitter-receiver links are intermittently on-and-off, governed by four independent Bernoulli (p) random sequences, and each transmitter and receiver are equipped with M and N antennas, respectively. We partially characterize this channel: The sum DoF is characterized when p ≤ [1/2] or when [min(M,N)/(mm(M,N))] ≤ [2/3]. In the remaining regime, the lower bound is within 5.2% of the upper bound. Strictly higher DoF is achieved by coding across channel topologies. In particular, codes over as many as 5 topologies are proposed to achieve the sum DoF of the channel when p ≤ [1/2]. A transfer function view of the network is employed to simplify the code design and to elucidate the fact that these are space-time codes, obtained by interference alignment over space and time. A full version of this paper is accessible at: https://arxiv.org/abs/1805.02527.

We study the sum degrees of freedom (DoF) of the bursty MIMO X channel without feedback, where the four transmitter-receiver links are intermittently ON and OFF, controlled by four Bernoulli random sequences which may be arbitrarily correlated, subject to a symmetry assumption: The two direct-links have the same level of burstiness, modeled by Ber(pd), and so do the cross-links, modeled by Ber(pc). The sum DoF is fully characterized in the regime where (pc/pd) is small, i.e., below a certain threshold, and is partially characterized in the other regime where (pc/pd) is above the threshold. The achievability is proved with a combination of Han-Kobayashi strategy and interference alignment, which can achieve strictly higher DoF than interference alignment alone. The converse proof employs a channel-state-sequence pairing technique. We highlight that burstiness of the channel disrupts the network topology, turning the MIMO X channel into a network with time-varying topology. This fundamental difference has striking ramifications. In particular, various interference alignment schemes that achieve the DoF of non-bursty MIMO X channels become suboptimal on the bursty channels. The reciprocity between the forward and the reverse links is lost, and the sum DoF does not saturate when the ratio between the transmitter and the receiver antennas exceeds (2/3).

We investigate the degrees of freedom (DoF) of the symmetric bursty MIMO X channel without feedback, where the presence of the two cross links is governed by a Bernoulli pcrandom state. The sum DoF is characterized for most of the antenna-burstiness configurations, except the case where pc> 0.5 and the ratio of the number of transmit and receive antennas is between 2/3 and 3/2. When pc≤ 0.5, the sum DoF of the bursty MIMO X channel is equal to that of the interference channel, and hence cross-link messaging does not help. When pc> 0.5, cross-link messaging is necessary, and we showed that simple interference alignment schemes suffice to achieve the sum DoF. For the case where the characterization of DoF remains open, we propose a combination of Han-Kobayashi coding and interference alignment that achieves higher DoF than interference alignment alone. This is in sharp contrast to the non-bursty case where interference alignment alone is DoF-optimal.