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
2614764375 2287503382 2963907957 1999509241
In this paper, we provide an analytical framework to analyze heterogeneous downlink millimeter-wave (mm-wave) cellular networks consisting of @math tiers of randomly located base stations (BSs), where each tier operates in an mm-wave frequency band. Signal-to-interference-plus-noise ratio (SINR) coverage probability is derived for the entire network using tools from stochastic geometry. The distinguishing features of mm-wave communications, such as directional beamforming, and having different path loss laws for line-of-sight and non-line-of-sight links are incorporated into the coverage analysis by assuming averaged biased-received power association and Nakagami fading. By using the noise-limited assumption for mm-wave networks, a simpler expression requiring the computation of only one numerical integral for coverage probability is obtained. Also, the effect of beamforming alignment errors on the coverage probability analysis is investigated to get insight on the performance in practical scenarios. Downlink rate coverage probability is derived as well to get more insights on the performance of the network. Moreover, the effect of deploying low-power smaller cells and the impact of biasing factor on energy efficiency is analyzed. Finally, a hybrid cellular network operating in both mm-wave and @math -wave frequency bands is addressed. 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. Deploying sub-6-GHz network together with millimeter wave (mm-wave) is a promising solution to simultaneously achieve sufficient coverage and high data rate. In heterogeneous networks, the traditional coupled access, i.e., users are constrained to be associated with the same base station in both downlink and uplink, is no longer optimal, and the concept of downlink and uplink decoupling (DUDe) has recently been proposed. In this paper, we analyze the coverage probability and area throughput for both the downlink and uplink of sub-6-GHz mm-wave cellular networks with decoupled access. Compared with the existing works, we take uplink power control and mm-wave interference into account. Using the tools from stochastic geometry, the expressions of signal-to-interference-plus-noise ratio coverage probability, user-perceived rate coverage probability and the area throughput are derived. The impact of decoupled access and different small cells (SCells) is investigated. In particular, analytical results reveal that with decoupled access, UEs are more likely to be associated with SCells in uplink when the network is sparse, and the uplink traffic will be offloaded from sub-6-GHz SCells to mm-wave SCells when the network is dense. Moreover, the dense deployment of mm-wave SCells rather than sub-6-GHz SCells is more reasonable, and the DUDe is a key factor in improving the performance of dense cellular networks with multi-band. In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.