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Abstract-In this paper we assess how coordination among base stations can be exploited to improve downlink capacity in fourth generation (4G) cellular networks. We focus on heterogeneous networks where low-power pico cells are deployed within the coverage area of an existing macro network with the aim of offloading traffic from the (potentially congested) macro cells to low-power cells. Firstly, we describe an enhanced inter-cell interference coordination scheme which is shown to achieve a significant capacity gain in such deployments by leveraging a loose coordination among neighbor base stations. Secondly, we explore how a tighter coordination among base stations can be exploited to further improve the network capacity. Even though the schemes described in this paper apply to long term evolution (LTE) wireless networks, we point out that most of the findings and conclusions we draw apply to any cellular network.

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Variable step-size LMS (VSLMS) algorithms are a popular approach to adaptive filtering, which can provide improved performance while maintaining the simplicity and robustness of conventional fixed step-size LMS. Here, we examine the stability of VSLMS with uncorrelated stationary Gaussian data. Most VSLMS described in the literature use a data-dependent step-size, where the step-size either depends on the data before the current time (prior step-size rule) or through the current time (posterior step-size rule). It has often been assumed that VSLMS algorithms are stable (in the sense of mean-square bounded weights), provided that the step-size is constrained to lie within the corresponding stability region for the LMS algorithm. For a single tap filter, we find exact expressions for the stability region of VSLMS over the classes of prior and posterior step-sizes and show that the stability region for prior step-size coincides with that of fixed step-size, but the region for posterior step-size is strictly smaller than for fixed step-size. For the multiple tap case, we obtain bounds on the stability regions with similar properties. The approach taken here is a generalization of the classical method of analyzing the exponential stability of the weight covariance equation for LMS. Although it is not possible to derive a weight covariance equation for general data-dependent VSLMS, the weight variances can be upper bounded by the solution of a linear time-invariant difference equation, after appropriately dealing with certain nonlinear terms. For prior step-size (like fixed step-size), the state matrix is symmetric, whereas for posterior step-size, the symmetry is lost, requiring a more detailed analysis. The results are verified by computer simulations.

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