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. perhaps relay BSs [5]. Heterogeneity is expected to be a key feature of 4G cellular networks, and an essential means for providing higher end-user throughput [6], [7] as well as expanded indoor and cell-edge coverage. The tiers of BSs are ordered by transmit power with tier 1 having the highest power. Due to differences in deployment, they also in general will have differing path loss exponents and spatial density (e.g. the number of BSs per square kilometer). Finally, in order to provide relief to the macrocell network -which is and will continue to be the main bottleneck -lower tier base stations are expected to be designed to have a bias towards admitting users [6], since their smaller coverage area usually results in a lighter load. For example, as shown in Fig. 1, a picocell may claim a user even though the macrocell signal is stronger to the user. The goal of this paper is to propose and develop a model and analytical framework that successfully characterizes the signal-to-noise-plus-interference ratio (SINR) -and its derivative metrics like outage/coverage and data rate -in such a HCN with arbitrary per-tier association biases. A. Motivation and Related WorkThe SINR statistics over a network are, unsurprisingly, largely determined by the locations of the base stations (BSs). These locations are usually unknown during the design of standards or even a specific system, and even if they are known they vary significantly from one city to the next. Since the main aspects of the system must work across a...

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In this letter, we propose an overlaid hybrid division duplex (HDD) concept for cellular systems which divides a cell into inner and outer regions and utilizes the merits of both time division duplex (TDD) and frequency division duplex (FDD). The proposed system can take advantage of both TDD and FDD without handover between two duplex schemes. Moreover, it is shown that the proposed HDD system outperforms the conventional TDD or FDD system with mobile relay stations when the synchronization issue is considered in orthogonal frequency division multiple access systems. Thus, the proposed overlaid HDD can be considered as a new framework for future cellular systems.

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