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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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. 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. UTRAN long term evolution is currently being standardized in 3GPP with the aim of more than twice the capacity over high-speed packet access. The chosen multiple access for uplink is single carrier FDMA, which avoids the intra-cell interference typical of CDMA systems, but it is still sensitive to inter-cell interference. As a result, the role of the power control becomes decisive to provide the required SINR, while controlling at the same time the interference caused to neighboring cells. This is the target of the fractional power control (FPC) algorithm lately approved in 3GPP. This paper evaluates in detail the impact of a FPC scheme on the SINR and interference distributions in order to provide a sub-optimal configuration tuned for both interference- and noise-limited scenarios. Two-tier femtocell networks- comprising a conventional cellular network plus embedded femtocell hotspots- offer an economically viable solution to achieving high cellular user capacity and improved coverage. With universal frequency reuse and DS-CDMA transmission however, the ensuing cross-tier interference causes unacceptable outage probability. This paper develops an uplink capacity analysis and interference avoidance strategy in such a two-tier CDMA network. We evaluate a network-wide area spectral efficiency metric called the operating contour (OC) defined as the feasible combinations of the average number of active macrocell users and femtocell base stations (BS) per cell-site that satisfy a target outage constraint. The capacity analysis provides an accurate characterization of the uplink outage probability, accounting for power control, path loss and shadowing effects. Considering worst case interference at a corner femtocell, results reveal that interference avoidance through a time-hopped CDMA physical layer and sectorized antennas allows about a 7x higher femtocell density, relative to a split spectrum two-tier network with omnidirectional femtocell antennas. A femtocell exclusion region and a tier selection based handoff policy offers modest improvements in the OCs. These results provide guidelines for the design of robust shared spectrum two-tier networks. Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wyner-type model, or via complex system level simulations that often do not provide insight into why various trends are observed. This paper proposes a novel middle way using point processes that is both accurate and also results in easy-to-evaluate integral expressions based on the Laplace transform of the interference. We assume mobiles and base stations are randomly placed in the network with each mobile pairing up to its closest base station. Compared to related recent work on downlink analysis, the proposed uplink model differs in two key features. First, dependence is considered between user and base station point processes to make sure each base station serves a single mobile in the given resource block. Second, per-mobile power control is included, which further couples the transmission of mobiles due to location-dependent channel inversion. Nevertheless, we succeed in deriving the coverage (equivalently outage) probability of a typical link in the network. This model can be used to address a wide variety of system design questions in the future. In this paper we focus on the implications for power control and show that partial channel inversion should be used at low signal-to-interference-plus-noise ratio (SINR), while full power transmission is optimal at higher SINR. Uplink power control is a key radio resource management function. It is typically used to maximize the power of the desired received signals while limiting the generated interference. This paper presents the 3GPP long term evolution (LTE) power control mechanism, and compares its performance to two reference mechanisms. The LTE power control mechanism constitutes of a closed loop component operating around an open loop point of operation. Specifically, the open loop component has a parameterized fractional path loss compensation factor, enabling a trade-off between cell edge bitrate and cell capacity. The closed-loop component can be limited to compensate for long-term variations, enabling fast channel quality variations to be utilized by scheduling and link adaptation. Simulation results indicate that the LTE power control mechanism is advantageous compared to reference mechanisms using full path loss compensation and SINR balancing. The fractional pathless compensation can improve the cell-edge bitrate and or the capacity with up to 20 while at the same time battery life time is improved. The fast SINR balancing closed loop mechanism performs poorly at high load since it does not utilize the link adaptation and the full link performance capability in LTE.