Piecewise-quadratic Harmut basis functions and their application to problems in digital signal processing

In this paper, we present a hierarchical convergence scheme for multi-radio access networks via heterogeneous cooperative relaying technique, where heterogeneous cooperative relay node (HCRN) acts as the convergence gateway and provides cooperative diversity and antenna array gains. The multiple antennas are configured on base station (BS), HCRN, and destination node (DS) to achieve the antenna array gain. Considering the power consumption and implementing complexity at HCRN, only a single antenna is configured at HCRN to transmit decoded packages to the destination node (DS). A joint heterogeneous cooperative relay selection and maximal-ratio combining scheme is proposed to maximize both cooperative and multi-user diversity (MUD) gains. Tight closed-form expressions for the outage probability and average symbol error rate are derived to evaluate performances, which are related strictly to the cooperative relay selection scheme, multiple antenna configurations, and fading channels. The analytical and simulation results show that the numbers of HCRNs and DSs play identical roles in the performance improvement, while the antenna number of DS provides a more significant diversity gain. Thus, in a practical application, we should aim to achieve a high MUD gain, instead of approaching the cooperative diversity gain via deploying too many HCRNs. In addition, the antenna array gain via configuring multiple antennas in DSs is preferred because it is bigger than the MUD gain or the cooperative diversity gain. Copyright © 2009 John Wiley & Sons, Ltd. A hierarchical convergence mechanism for the heterogeneous RANs is presented, where the heterogeneous cooperative relay selection, maximal-ratio combining, multi-user diversity schemes are designed jointed. A closed-form outage probability and symbol error rate expressions and their approximated formulas are derived, and they shows that a full diversity order approximately equals to (KJND–KJ+1) can be achieved, where ND is the antenna number of destination nodes, K and J are the number of destination nodes and relay nodes, respectively. Copyright © 2009 John Wiley & Sons, Ltd.