The joint user association and spectrum allocation problem is studied for multi-tier heterogeneous networks (HetNets) in both downlink and uplink in the interference-limited regime. Users are associated with base-stations (BSs) based on the biased downlink received power. Spectrum is either shared or orthogonally partitioned among the tiers. This paper models the placement of BSs in different tiers as spatial point processes and adopts stochastic geometry to derive the theoretical mean proportionally fair utility of the network based on the coverage rate. By formulating and solving the network utility maximization problem, the optimal user association bias factors and spectrum partition ratios are analytically obtained for the multi-tier network. The resulting analysis reveals that the downlink and uplink user associations do not have to be symmetric. For uplink under spectrum sharing, if all tiers have the same target signal-to-interference ratio (SIR), distance-based user association is shown to be optimal under a variety of path loss and power control settings. For both downlink and uplink, under orthogonal spectrum partition, it is shown that the optimal proportion of spectrum allocated to each tier should match the proportion of users associated with that tier. Simulations validate the analytical results. Under typical system parameters, simulation results suggest that spectrum partition performs better for downlink in terms of utility, while spectrum sharing performs better for uplink with power control.
Most of the previous works on HetNets focus on the downlink. A key difference in uplink as compared to downlink is that fractional power control is often used in uplink to fully or partially compensate for the path loss, e.g., as defined in 3GPP-LTE @cite_1 . The influence of fractional power control on system performance is studied in various works, e.g., @cite_21 @cite_17 @cite_14 under regular hexagonal topology. For networks with random topology and accounting for fractional power control, @cite_6 analytically derives uplink SIR and rate distribution for single-tier networks; @cite_32 investigates uplink outage capacity for two-tier networks with shared spectrum; @cite_33 extends the analysis to multi-tier uplink networks in terms of outage probability and spectral efficiency. In this paper, the mean user utility of random multi-tier HetNets in uplink with fractional power control is analyzed and optimized.
@cite_14 @cite_33 @cite_21 @cite_1 @cite_32 @cite_6 @cite_17
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Using stochastic geometry, we develop a tractable uplink modeling paradigm for outage probability and spectral efficiency in both single and multi-tier cellular wireless networks. The analysis accounts for per user equipment (UE) power control as well as the maximum power limitations for UEs. More specifically, for interference mitigation and robust uplink communication, each UE is required to control its transmit power such that the average received signal power at its serving base station (BS) is equal to a certain threshold ρ o . Due to the limited transmit power, the UEs employ a truncated channel inversion power control policy with a cutoff threshold of ρ o . We show that there exists a transfer point in the uplink system performance that depends on the following tuple: BS intensity λ, maximum transmit power of UEs P u , and ρ o . That is, when P u is a tight operational constraint with respect to (w.r.t.) λ and ρ o , the uplink outage probability and spectral efficiency highly depend on the values of λ and ρ o . In this case, there exists an optimal cutoff threshold ρ o *, which depends on the system parameters, that minimizes the outage probability. On the other hand, when P u is not a binding operational constraint w.r.t. λ and ρ o , the uplink outage probability and spectral efficiency become independent of λ and ρ o . We obtain approximate yet accurate simple expressions for outage probability and spectral efficiency, which reduce to closed forms in some special cases. In this paper, a comprehensive study of the downlink performance in a heterogeneous cellular network (or HetNet) is conducted via stochastic geometry. A general HetNet model is considered consisting of an arbitrary number of open-access and closed-access tiers of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs within each tier have a constant transmission power, random fading factors with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability are derived for the max-SINR connectivity and nearest-BS connectivity models. Using stochastic ordering, interesting properties and simplifications for the HetNet downlink performance are derived by relating these two connectivity models to the maximum instantaneous received power (MIRP) connectivity model and the maximum biased received power (MBRP) connectivity models, providing good insights about HetNets and their downlink performance in these complex networks. Furthermore, the results also demonstrate the effectiveness and analytical tractability of the stochastic geometric approach to study the HetNet performance. Uplink power control in UTRAN Long Term Evolution consists of an open-loop scheme handled by the User Equipment and closed-loop power corrections determined and signaled by the network. In this study the difference in performance between pure open-loop and combined open and closed-loop power control has been analyzed and the different behavior of fractional vs. full path-loss compensation has been evaluated. A comprehensive system level simulation model has been used with a facility to trace a particular test user during its motion from eNodeB towards the cell border and back to its initial position. This study demonstrates the effect of distance path-loss of a test user on several physical layer performance metrics including throughput, resource allocation as well as modulation and coding scheme utilization. Simulation results in a fully loaded network show high throughput for open-loop fractional power control for the user located in the vicinity of the serving eNodeB, however, steep performance degradation has been observed when the user is moving towards the cell edge. The user throughput at the cell border can be increased by the closed-loop component. The benefit of closed-loop power control is the higher homogeneity in terms of throughput across the entire network area and the ability to automatically stabilize the network performance under different conditions like cell load and traffic distribution. In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association policies. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a particular transmit power, path loss exponent, spatial density, and bias towards admitting mobile users. For example, as compared to macrocells, picocells would usually have lower transmit power, higher path loss exponent (lower antennas), higher spatial density (many picocells per macrocell), and a positive bias so that macrocell users are actively encouraged to use the more lightly loaded picocells. In the present paper we implicitly assume all base stations have full queues; future work should relax this. For this model, we derive the outage probability of a typical user in the whole network or a certain tier, which is equivalently the downlink SINR cumulative distribution function. The results are accurate for all SINRs, and their expressions admit quite simple closed-forms in some plausible special cases. We also derive the average ergodic rate of the typical user, and the minimum average user throughput - the smallest value among the average user throughputs supported by one cell in each tier. We observe that neither the number of BSs or tiers changes the outage probability or average ergodic rate in an interference-limited full-loaded HCN with unbiased cell association (no biasing), and observe how biasing alters the various metrics.