The two-hop MISO broadcast network with quantized delayed CSIT

We consider a downlink two-hop MISO broadcast network with a 2-antenna source communicating to 2 single-antenna destinations, assisted by 2 single-antenna intermediate relays. We investigate spectrally efficient transmission schemes and their achieved sum degrees of freedom (DoF), with quantized delayed channel state information (CSI) feedback. Assuming Grassmannian vector quantization, we study two feedback scenarios according to the feedback range limit, namely global-range feedback, i.e., the source can receive the feedback signals from both the relays and the destinations, and one-hop-range feedback, i.e., each node can only attain the feedback information of its upcoming hop. We establish a sum DoF lower bound for each case. Our results reveal that when the quantization rate at relays B_R = α₁log₂(SNR) and at destinations B_D = α₂log₂(SNR) for min{α₁, α₂} ≥ 1, the optimal sum DoF 4 over 3 can be achieved with finite-rate delayed feedback.