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.
For a wireless multi-tier heterogeneous network with orthogonal spectrum allocation across tiers, we optimize the association probability and the fraction of spectrum allocated to each tier so as to maximize rate coverage. In practice, the association probability can be controlled using a biased received signal power. The optimization problem is non-convex and we are forced to explore locally optimal solutions. We make two contributions in this paper: first, we show that there exists a relation between the first derivatives of the objective function with respect to each of the optimization variables. This can be used to simplify numerical solutions to the optimization problem. Second, we explore the optimality of the intuitive solution that the fraction of spectrum allocated to each tier should be equal to the tier association probability. We show that, in this case, a closed-form solution exists. Importantly, our numerical results show that there is essentially zero performance loss. The results also illustrate the significant gains possible by jointly optimizing the user association and the resource allocation. In heterogeneous cellular networks (HCNs), it is desirable to offload mobile users to small cells, which are typically significantly less congested than the macrocells. To achieve sufficient load balancing, the offloaded users often have much lower SINR than they would on the macrocell. This SINR degradation can be partially alleviated through interference avoidance, for example time or frequency resource partitioning, whereby the macrocell turns off in some fraction of such resources. Naturally, the optimal offloading strategy is tightly coupled with resource partitioning; the optimal amount of which in turn depends on how many users have been offloaded. In this paper, we propose a general and tractable framework for modeling and analyzing joint resource partitioning and offloading in a two-tier cellular network. With it, we are able to derive the downlink rate distribution over the entire network, and an optimal strategy for joint resource partitioning and offloading. We show that load balancing, by itself, is insufficient, and resource partitioning is required in conjunction with offloading to improve the rate of cell edge users in co-channel heterogeneous networks. Two-tier networks, comprising a conventional cellular network overlaid with shorter range hotspots (e.g. femtocells, distributed antennas, or wired relays), offer an economically viable way to improve cellular system capacity. The capacity-limiting factor in such networks is interference. The cross-tier interference between macrocells and femtocells can suffocate the capacity due to the near-far problem, so in practice hotspots should use a different frequency channel than the potentially nearby high-power macrocell users. Centralized or coordinated frequency planning, which is difficult and inefficient even in conventional cellular networks, is all but impossible in a two-tier network. This paper proposes and analyzes an optimum decentralized spectrum allocation policy for two-tier networks that employ frequency division multiple access (including OFDMA). The proposed allocation is optimal in terms of area spectral efficiency (ASE), and is subjected to a sensible quality of service (QoS) requirement, which guarantees that both macrocell and femtocell users attain at least a prescribed data rate. Results show the dependence of this allocation on the QoS requirement, hotspot density and the co-channel interference from the macrocell and femtocells. Design interpretations are provided. The deployment of femtocells in a macrocell network is an economical and effective way to increase network capacity and coverage. Nevertheless, such deployment is challenging due to the presence of inter-tier and intra-tier interference, and the ad hoc operation of femtocells. Motivated by the flexible subchannel allocation capability of OFDMA, we investigate the effect of spectrum allocation in two-tier networks, where the macrocells employ closed access policy and the femtocells can operate in either open or closed access. By introducing a tractable model, we derive the success probability for each tier under different spectrum allocation and femtocell access policies. In particular, we consider joint subchannel allocation, in which the whole spectrum is shared by both tiers, as well as disjoint subchannel allocation, whereby disjoint sets of subchannels are assigned to both tiers. We formulate the throughput maximization problem subject to quality of service constraints in terms of success probabilities and per-tier minimum rates, and provide insights into the optimal spectrum allocation. Our results indicate that with closed access femtocells, the optimized joint and disjoint subchannel allocations provide the highest throughput among all schemes in sparse and dense femtocell networks, respectively. With open access femtocells, the optimized joint subchannel allocation provides the highest possible throughput for all femtocell densities. We study joint spectrum allocation and user association in heterogeneous cellular networks with multiple tiers of base stations. A stochastic geometric approach is applied as the basis to derive the average downlink user data rate in a closed-form expression. Then, the expression is employed as the objective function in jointly optimizing spectrum allocation and user association, which is of non-convex programming in nature. A computationally efficient Structured Spectrum Allocation and User Association (SSAUA) approach is proposed, solving the optimization problem optimally when the density of users is low, and near-optimally with a guaranteed performance bound when the density of users is high. A Surcharge Pricing Scheme (SPS) is also presented, such that the designed association bias values can be achieved in Nash equilibrium. Simulations and numerical studies are conducted to validate the accuracy and efficiency of the proposed SSAUA approach and SPS.