In this paper, using stochastic geometry tools, we develop a systematic 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 device in a Internet of Things (IoT) 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 ( @math wave) wireless backhaul. The @math wave channels are interference limited and mm-wave channels are noise limited; therefore, we have the meta-distribution of SIR and SNR in microwave 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 @math moment for a typical device (a) when it associates to a @math wave 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. Closed-form expressions are presented for special scenarios. The extensions of the developed framework to the @math wave-only IoT network or IoT 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.
Some recent studies analyzed the success probability of coexisting @math wave and mm-wave cellular networks. A hybrid cellular network was considered by @cite_18 to estimate the uplink-downlink coverage and rate distribution of self-backhauled mm-wave networks. @cite_5 developed an analytical model to characterize decoupled uplink and downlink cell association strategies. The authors showed the superiority of this technique compared to the traditional coupled association in a network with traditional MBSs coexisting with denser mm-wave SBSs. @cite_18 and @cite_5 modeled the fading power as Rayleigh fading to enable better tractability.
@cite_5 @cite_18
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Millimeter wave (mmWave) links will offer high capacity but are poor at penetrating into or diffracting around solid objects. Thus, we consider a hybrid cellular network with traditional sub-6 GHz macrocells coexisting with denser mmWave small cells, where a mobile user can connect to either opportunistically. We develop a general analytical model to characterize and derive the uplink and downlink cell association in the view of the signal-to-interference-and-noise-ratio and rate coverage probabilities in such a mixed deployment. We offer extensive validation of these analytical results (which rely on several simplifying assumptions) with simulation results. Using the analytical results, different decoupled uplink and downlink cell association strategies are investigated and their superiority is shown compared with the traditional coupled approach. Finally, small cell biasing in mmWave is studied, and we show that unprecedented biasing values are desirable due to the wide bandwidth. Millimeter wave (mmWave) cellular systems will require high-gain directional antennas and dense base station (BS) deployments to overcome a high near-field path loss and poor diffraction. As a desirable side effect, high-gain antennas offer interference isolation, providing an opportunity to incorporate self-backhauling , i.e., BSs backhauling among themselves in a mesh architecture without significant loss in the throughput, to enable the requisite large BS densities. The use of directional antennas and resource sharing between access and backhaul links leads to coverage and rate trends that significantly differ from conventional UHF cellular systems. In this paper, we propose a general and tractable mmWave cellular model capturing these key trends and characterize the associated rate distribution. The developed model and analysis are validated using actual building locations from dense urban settings and empirically derived path loss models. The analysis shows that, in sharp contrast to the interference-limited nature of UHF cellular networks, the spectral efficiency of mmWave networks (besides the total rate) also increases with the BS density, particularly at the cell edge. Increasing the system bandwidth does not significantly influence the cell edge rate, although it boosts the median and peak rates. With self-backhauling, different combinations of the wired backhaul fraction (i.e., the fraction of BSs with a wired connection) and the BS density are shown to guarantee the same median rate (QoS).