A novel approach to smart multi-cell radio resource management based on load gradient calculations

Abstract

This paper presents a novel methodology for capturing the coupling between the different cells in both the uplink and downlink directions in a Wideband Code Division Multiple Access (WCDMA) scenario. It is based on the definition and computation of the gradient of the uplink cell load factor and the downlink transmitted power, which are the two main parameters that reflect the actual cell load in the two link directions. The paper shows that the gradient is able to capture the relevant information about the spatial distribution of traffic, which has an impact on cell performance. The proposed methodology is also used as the basis for defining and evaluating new Radio Resource Management (RRM) strategies that operate at a multi-cell level.

Appendix: Method of approximation for gradient computation

The method described in Sect. 4 for the gradient computation of the uplink cell load factor and the downlink base station transmitted power gradient involves the solution of (K + 1) linear equation systems. Although the computational complexity would be feasible in real time, from a radio network engineering point of view a simpler formulation that maintains a sufficient degree of accuracy may be preferred. In this framework, this Appendix provides a method of approximation for gradient computation that can be used as an alternative to the method described in Sect. 4. Specifically, the method of approximation for Expression (22) is given by:

$$ \frac{\partial \eta_0}{\partial \eta_k}\approx \frac{S_{k,0}^{UL} \left( 1-S_{0,0}^{UL} \right)}{\left( 1-\eta_k \right)^{2}\left( 1+\mathop{\sum}\nolimits_{j=1}^K \frac{S_{j,0}^{UL}}{1-\eta_j} \right)^{2}} $$

(50)

where it has been assumed that the term in the summation in (22) that most contributes to $\partial\eta_{0}/\partial\eta_{k}$ is $\partial\eta_{k}/\partial\eta_{k} = 1$.

For the downlink direction, a similar argument can be made, therefore, the approximation of (32) is given by:

$$ \frac{\partial P_{T0}}{\partial P_{Tk}}\approx \frac{S_{0,k}^{DL}}{1-\rho S_{0,0}^{DL}} $$

(51)

In order to assess the accuracy of this approximation, various simulations were carried out in different scenarios using different traffic distributions. Various examples are shown in Figs. 1(b) and  2(b), which correspond to the uplink and downlink directions under the conditions discussed in Sect. 6.1. Notice that in both links the approximation underestimates the exact derivative due to the terms that were neglected when expressions (50) and (51) were obtained. In general, for other load conditions and spatial distributions the approximation holds quite well and errors below 10% were observed. Furthermore, as is shown in Sect. 7.1, the use of the exact or the approximate gradient has a very low impact on the performance that is observed with the gradient-based algorithms.