Network Coherence Time Matters - Aligned Image Sets and the Degrees of\n Freedom of Interference Networks with Finite Precision CSIT and Perfect CSIR

This work obtains the first bound that is provably sensitive to network\ncoherence time, i.e., coherence time in an interference network where all\nchannels experience the same coherence patterns. This is accomplished by a\nnovel adaptation of the aligned image sets bound, and settles various open\nproblems noted previously by Naderi and Avestimehr and by Gou et al. For\nexample, a necessary and sufficient condition is obtained for the optimality of\n1/2 DoF per user in a partially connected interference network where the\nchannel state information at the receivers (CSIR) is perfect, the channel state\ninformation at the transmitters (CSIT) is instantaneous but limited to finite\nprecision, and the network coherence time is T_c= 1. The surprising insight\nthat emerges is that even with perfect CSIR and instantaneous finite precision\nCSIT, network coherence time matters, i.e., it has a DoF impact.\n