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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. DRAFT 2) Biased User Association: Associating users to the BSs with the maximum downlink received power may not be the optimal strategy in a HetNet, because in this case most users would tend to connect to high-power macro BSs, thus causing overloading. Although dynamic approaches to user association is possible, this paper adopts the simple and effective cell range expansion scheme, also known as biased user association [3], [9], where each BS is assigned a bias factor, and each user is associated with the BS that provides the maximum received power weighted by its bias. By setting a larger bias towards low-power BSs, traffic can be effectively offloaded to them. (See Fig. 1 as an illustration of a 2-tier network with biased association.) Note that the bias factors are assigned differently across the tiers but are kept the same within a tier, as BSs within a tier are expected to have approximately the same load.The bias should be properly designed such that all users receive adequate quality of service, i.e., it should achieve a tradeoff between signal quality from the users' perspective and load balancing from the BSs' perspective.3) Spectrum Allocation: This paper considers both spectrum sharing and orthogonal spectrum partition among tiers. Spectrum sharing is more bandwidth efficient, but it exacerbates the inter-tier interference problem, especially when cell range expansion is applied. In the downlink, users offloaded to small cells experience large interference from macro cells; in the uplink with p...

A compact sequential-phase (SP) feed for circularly polarized sequential-rotation (SR) arrays is presented. Unlike traditional SP feed using multiple segments for impedance transformations, the presented SP feed employs only a single-stage transition where the transmission line width is uniform, making the whole SP feed very compact and neat in layout. The radial design of SP-feed lines to antenna elements may further facilitate the optimization work in adjusting the element spacing. Two miniature square SP feeds of the sizes 4 and 3 8 are given and compared. Experimental prototypes were built and verified with measured results. The proposed compact SP feed can be extended to 2 2 feeding networks, and is very suitable for large-scale printed CP arrays.

Novel biodegradable nanoelastomers are synthesized. They can self-assemble and generate morphologies in nanometric, micrometric, or bulk scale with tunable properties. They are smart biodegradable materials with potential applications.

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