The Meta Distributions of the SIR/SNR and Data Rate in Coexisting Sub-6GHz and Millimeter-wave Cellular Networks
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We develop a stochastic geometry framework to characterize the meta distributions of the downlink signal-to-interference-ratio (SIR)/signal-to-noise-ratio (SNR) and data rate of a typical blackoutdoor user in a coexisting sub-6GHz and millimeter wave (mm-wave) cellular network. Macro base-stations (MBSs) transmit on sub-6GHz channels (which we term "microwave" channels), whereas small base-stations (SBSs) communicate with users on mm-wave channels. The SBSs are connected to MBSs via a microwave (μwave) wireless backhaul. The μwave channels are interference limited and mm-wave channels are noise limited; therefore, we have the meta-distribution of SIR and SNR in μwave and mm-wave channels, respectively. To model the line-of-sight (LOS) nature of mm-wave channels, we use Nakagami-m fading model. We first characterize the association probabilities of a typical user to a μwave MBS, a LOS mm-wave SBS and a non-LOS (NLOS) mm-wave SBS. Then, we characterize the conditional success probability (CSP) (or equivalently reliability) and its b-th moment for a typical user (a) when it associates to a μwave MBS for direct transmission and (b) when it associates to a mm-wave SBS for dual-hop transmission (backhaul and access transmission). We then characterize the exact as well as approximate expressions for the meta distributions. Performance metrics such as the mean and variance of the local delay (network jitter), mean of the CSP (coverage probability), and variance of the CSP are studied. Closed-form expressions are presented for special scenarios. The extensions of the developed framework to the μwave-only network or networks where SBSs have mm-wave backhauls are discussed. Numerical results validate the analytical results. Insights are extracted related to the reliability, coverage probability, and latency of the considered network.
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