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

## TL;DR

This paper analyzes the delay performance of spatially-coded MIMO-ZFBF with retransmissions in random networks, revealing tradeoffs between coverage, delay, and throughput under different schemes and network conditions.

## Contribution

It introduces a stochastic geometry-based analysis of rate correlation and delay in MIMO-ZFBF systems with retransmissions, comparing RR and B-IR schemes.

## Key findings

- B-IR has higher rate correlation coefficient but larger coverage probability than RR.
- B-IR's mean transmission delay can be smaller or larger than RR depending on contention.
- Dense networks benefit from LOS components and Doppler spread for improved throughput.

## Abstract

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 (pdf) of aggregate data rate. Adopting tools of stochastic geometry, we firstly characterize the rate correlation coefficient (RCC) for both schemes. Our results show that, compared to RR scheme, 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 RR scheme. Finally, we develop a numerical approximation of MTD, and evaluate the effective spatial throughput (EST), which is reciprocal to MTD, of 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 1) LOS component is considerably instrumental to enhance EST; 2) EST of B-IR scheme can be much higher than that of RR scheme; 3) When Doppler spread exists, it can improve MTD of B-IR while it does not cast any meaningful effect on the MTD of RR.

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Source: https://tomesphere.com/paper/1901.11067