| Summary: | Using stochastic geometry tools, we develop a systematic framework to characterize the meta distributions of the downlink SIR/SNR and data rate of the typical device in a cellular network with coexisting sub-6GHz and millimeter wave (mm-wave) spectrums. Macro base-stations (MBSs) transmit on sub-6GHz channels (which we term “microwave” channels), whereas small base-stations (SBSs) communicate with devices 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. To derive the meta distribution of SIR/SNR, we characterize the conditional success probability (CSP) (or equivalently reliability) and its b<sup>th</sup> moment for the typical device (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). 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 derived. Closedform expressions are presented for special scenarios. The extensions of the developed framework to the μwave-only network or mm-wave only 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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