Delay Analysis of Spatially Coded MIMO-ZFBF With Retransmissions in Random Networks

For a low-mobile Poisson bipolar network and under line-of-sight/non-line-of-sight (LOS/NLOS) path-loss model, we study repetitive retransmissions (RR) and blocked incremental redundancy (B-IR). We consider spatially-coded multiple-input multiple-output (MIMO) zero-forcing beamforming (ZFBF) multiplexing system, whereby the packet success reception is determined based on the aggregate data rate across spatial dimensions of the MIMO system. Characterization of retransmission performance in this low-mobile configuration is practically important, but inherently complex due to a substantial rate correlation across retransmissions and intractability of evaluating the probability density function of aggregate data rate. Adopting tools of stochastic geometry, we first characterize the rate correlation coefficient (RCC) for both schemes. Our results show that, compared to the RR scheme, the B-IR scheme has higher RCC while its coverage probability is substantially larger. We demonstrate that the spotted contention between coverage probability and RCC causes the mean transmission delay (MTD) of B-IR to become either smaller or larger than the MTD of the RR scheme. Finally, we develop a numerical approximation of MTD, and evaluate the effective spatial throughput (EST), which is reciprocal to MTD, of the RR and B-IR schemes. Our numerical results highlight fundamental tradeoffs between densification, multiplexing gain, block length, and activity factor of nodes. We further observe that for dense networks: first, LOS component is considerably instrumental to enhance EST; second, EST of the B-IR scheme can be much higher than that of the RR scheme; third, when Doppler spread exists, it can improve MTD of B-IR, whereas it does not cast any meaningful effect on MTD of RR.