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.
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. For small cell technology to significantly increase the capacity of tower-based cellular networks, mobile users will need to be actively pushed onto the more lightly loaded tiers (corresponding to, e.g., pico and femtocells), even if they offer a lower instantaneous SINR than the macrocell base station (BS). Optimizing a function of the long-term rate for each user requires (in general) a massive utility maximization problem over all the SINRs and BS loads. On the other hand, an actual implementation will likely resort to a simple biasing approach where a BS in tier j is treated as having its SINR multiplied by a factor Aj ≥ 1, which makes it appear more attractive than the heavily-loaded macrocell. This paper bridges the gap between these approaches through several physical relaxations of the network-wide association problem, whose solution is NP hard. We provide a low-complexity distributed algorithm that converges to a near-optimal solution with a theoretical performance guarantee, and we observe that simple per-tier biasing loses surprisingly little, if the bias values Aj are chosen carefully. Numerical results show a large (3.5x) throughput gain for cell-edge users and a 2x rate gain for median users relative to a maximizing received power association. As the spectral efficiency of a point-to-point link in cellular networks approaches its theoretical limits, with the forecasted explosion of data traffic, there is a need for an increase in the node density to further improve network capacity. However, in already dense deployments in today's networks, cell splitting gains can be severely limited by high inter-cell interference. Moreover, high capital expenditure cost associated with high power macro nodes further limits viability of such an approach. This article discusses the need for an alternative strategy, where low power nodes are overlaid within a macro network, creating what is referred to as a heterogeneous network. We survey current state of the art in heterogeneous deployments and focus on 3GPP LTE air interface to describe future trends. A high-level overview of the 3GPP LTE air interface, network nodes, and spectrum allocation options is provided, along with the enabling mechanisms for heterogeneous deployments. Interference management techniques that are critical for LTE heterogeneous deployments are discussed in greater detail. Cell range expansion, enabled through cell biasing and adaptive resource partitioning, is seen as an effective method to balance the load among the nodes in the network and improve overall trunking efficiency. An interference cancellation receiver plays a crucial role in ensuring acquisition of weak cells and reliability of control and data reception in the presence of legacy signals. In this paper, we jointly consider the resource allocation and base-station assignment problems for the downlink in CDMA networks that could carry heterogeneous data services. We first study a joint power and rate allocation problem that attempts to maximize the expected throughput of the system. This problem is inherently difficult because it is in fact a nonconvex optimization problem. To solve this problem, we develop a distributed algorithm based on dynamic pricing. This algorithm provides a power and rate allocation that is asymptotically optimal in the number of mobiles. We also study the effect of various factors on the development of efficient resource allocation strategies. Finally, using the outcome of the power and rate allocation algorithm, we develop a pricing-based base-station assignment algorithm that results in an overall joint resource allocation and base-station assignment. In this algorithm, a base-station is assigned to each mobile taking into account the congestion level of the base-station as well as the transmission environment of the mobile. This paper considers optimization of the user and base-station (BS) association in a wireless downlink heterogeneous cellular network under the proportional fairness criterion. We first consider the case where each BS has a single antenna and transmits at fixed power and propose a distributed price update strategy for a pricing-based user association scheme, in which the users are assigned to the BS based on the value of a utility function minus a price. The proposed price update algorithm is based on a coordinate descent method for solving the dual of the network utility maximization problem and it has a rigorous performance guarantee. The main advantage of the proposed algorithm as compared to an existing subgradient method for price update is that the proposed algorithm is independent of parameter choices and can be implemented asynchronously. Further, this paper considers the joint user association and BS power control problem and proposes an iterative dual coordinate descent and the power optimization algorithm that significantly outperforms existing approaches. Finally, this paper considers the joint user association and BS beamforming problem for the case where the BSs are equipped with multiple antennas and spatially multiplex multiple users. We incorporate dual coordinate descent with the weighted minimum mean-squared error (WMMSE) algorithm and show that it achieves nearly the same performance as a computationally more complex benchmark algorithm (which applies the WMMSE algorithm on the entire network for BS association) while avoiding excessive BS handover. Pushing data traffic from cellular to WiFi is an example of inter radio access technology (RAT) offloading. While this clearly alleviates congestion on the over-loaded cellular network, the ultimate potential of such offloading and its effect on overall system performance is not well understood. To address this, we develop a general and tractable model that consists of M different RATs, each deploying up to K different tiers of access points (APs), where each tier differs in transmit power, path loss exponent, deployment density and bandwidth. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. The distribution of rate over the entire network is then derived for a weighted association strategy, where such weights can be tuned to optimize a particular objective. We show that the optimum fraction of traffic offloaded to maximize SINR coverage is not in general the same as the one that maximizes rate coverage, defined as the fraction of users achieving a given rate. Next-generation cellular networks will provide higher cell capacity by adopting advanced physical layer techniques and broader bandwidth. Even in such networks, boundary users would suffer from low throughput due to severe intercell interference and unbalanced user distributions among cells, unless additional schemes to mitigate this problem are employed. In this paper, we tackle this problem by jointly optimizing partial frequency reuse and load-balancing schemes in a multicell network. We formulate this problem as a network-wide utility maximization problem and propose optimal offline and practical online algorithms to solve this. Our online algorithm turns out to be a simple mixture of inter- and intra-cell handover mechanisms for existing users and user association control and cell-site selection mechanisms for newly arriving users. A remarkable feature of the proposed algorithm is that it uses a notion of expected throughput as the decision making metric, as opposed to signal strength in conventional systems. Extensive simulations demonstrate that our online algorithm can not only closely approximate network-wide proportional fairness but also provide two types of gain, interference avoidance gain and load balancing gain, which yield 20 100 throughput improvement of boundary users (depending on traffic load distribution), while not penalizing total system throughput.We also demonstrate that this improvement cannot be achieved by conventional systems using universal frequency reuse and signal strength as the decision making metric. We consider a resource management problem in a multi-cell downlink OFDMA network whereby the goal is to find the optimal combination of (i) assignment of users to base stations and (ii) resource allocation strategies at each base station. Efficient resource management protocols must rely on users truthfully reporting privately held information such as downlink channel states. However, individual users can manipulate the resulting resource allocation (by misreporting their private information) if by doing so they can improve their payoff. Therefore, it is of interest to design efficient resource management protocols that are strategy-proof, i.e. it is in the users' best interests to truthfully report their private information. Unfortunately, we show that the implementation of any protocol that is efficient and strategy-proof is NP-hard. Thus, we propose a computationally tractable strategy-proof mechanism that is approximately efficient, i.e. the solution obtained yields at least 1 2 of the optimal throughput. Simulations are provided to illustrate the effectiveness of the proposed mechanism. In order to expand the downlink (DL) coverage areas of picocells in the presence of an umbrella macrocell, the concept of range expansion has been recently proposed, in which a positive range expansion bias (REB) is added to the DL received signal strengths (RSSs) of picocell pilot signals at user equipments (UEs). Although range expansion may increase DL footprints of picocells, it also results in severe DL inter-cell interference in picocell expanded regions (ERs), because ER picocell user equipments (PUEs) are not connected to the cells that provide the strongest DL RSSs. In this paper, we derive closed-form formulas to calculate appropriate REBs for two different range expansion strategies, investigate both DL and uplink (UL) inter-cell interference coordination (ICIC) to enhance picocell performance, and propose a new macrocell-picocell cooperative scheduling scheme to mitigate both DL and UL interference caused by macrocells to ER PUEs. Simulation results provide insights on REB selection approaches at picocells, and demonstrate the benefits of the proposed macrocell-picocell cooperative scheduling scheme over alternative approaches. We consider the distributed uplink resource allocation problem in a multi-carrier wireless network with multiple access points (APs). Each mobile user can optimize its own transmission rate by selecting a suitable AP and by controlling its transmit power. Our objective is to devise suitable algorithms by which mobile users can jointly perform these tasks in a distributed manner. Our approach relies on a game theoretic formulation of the joint power control and AP selection problem. In the proposed game, each user is a player with an associated strategy containing a discrete variable (the AP selection decision) and a continuous vector (the power allocation among multiple channels). We provide characterizations of the Nash Equilibrium of the proposed game. We present a novel algorithm named Joint Access Point Selection and Power Allocation (JASPA) and its various extensions (with different update schedules) that allow the users to efficiently optimize their rates. Finally, we study the properties of the proposed algorithms as well as their performance via extensive simulations. Embedding pico femto base-stations and relay nodes in a macro-cellular network is a promising method for achieving substantial gains in coverage and capacity compared to macro-only networks. These new types of base-stations can operate on the same wireless channel as the macro-cellular network, providing higher spatial reuse via cell splitting. However, these base-stations are deployed in an unplanned manner, can have very different transmit powers, and may not have traffic aggregation among many users. This could potentially result in much higher interference magnitude and variability. Hence, such deployments require the use of innovative cell association and inter-cell interference coordination techniques in order to realize the promised capacity and coverage gains. In this paper, we describe new paradigms for design and operation of such heterogeneous cellular networks. Specifically, we focus on cell splitting, range expansion, semi-static resource negotiation on third-party backhaul connections, and fast dynamic interference management for QoS via over-the-air signaling. Notably, our methodologies and algorithms are simple, lightweight, and incur extremely low overhead. Numerical studies show that they provide large gains over currently used methods for cellular networks.