QoS and energy-efficiency aware scheduling and resource allocation scheme in LTE-A uplink systems

Abstract

With the fast evolution of the wireless communications, the energy consumption of mobile network and the data flow in the network are increasing. Thus, it is very important to increase the Energy Efficiency (EE) and reduce packet loss rate. This article surveys the scheduling and resource allocation algorithm to reduce packet loss rate while increasing EE in the uplink of Long Term Evolution-Advanced system. Here, new framework that refers previous value as an optimization value of the optimization problem solving process is proposed. Furthermore, the mathematical model of the process is defined as NP-Hard problem and the new solving method is proposed. We propose a user priority metric, considering that the demand for packet loss rate and packet delay are different according to the Quality of Service (QoS) Class Identifier (QCI). For Guaranteed Bit Rate (GBR) and Non-GBR services, the proposed algorithm uses the user priority metric taking into account not only the uplink buffer status, but also the different characteristics of packet loss mechanism and energy efficiency, to select users in scheduling. To demonstrate the advantage of the proposed scheme, simulations are carried out in various size of cells like Femto cell, Pico cell, Micro cell and others and the study results are compared for the effectiveness of proposed methods. Simulation results show that the proposed algorithm enhances EE, as well as, QoS provision for different types of services.

Appendix

Proof of Theorem 1

To prove, we should examine the Hessian matrix for the function ${F}_{u}\left(P,B,\kappa ,\varphi \right)$ [17, 21].

Considering that $P=\{{P}_{u,c}\},B=\{{B}_{u,c}\}$ and the linear combination of convex functions (or concave functions) is also a convex function (or concave function), the Hessian matrix of $F_{u} \left( {P,B,\kappa ,\varphi } \right)$ as follows:

So,

$$ {\mathcal{H}}\left( {P,B} \right) = \left( {\begin{array}{*{20}c} {\frac{{\partial^{2} F_{u} }}{{\partial \left( {P_{u,c} } \right)^{2} }}} & {\frac{{\partial^{2} F_{u} }}{{\partial P_{u,c} \partial B_{u,c} }}} \\ {\frac{{\partial^{2} F_{u} }}{{\partial {\text{B}}_{{{\text{u}},{\text{c}}}} \partial {\text{P}}_{{{\text{u}},{\text{c}}}} }}} & {\frac{{\partial^{2} {\text{F}}_{{\text{u}}} }}{{\partial \left( {{\text{B}}_{{{\text{u}},{\text{c}}}} } \right)^{2} }}} \\ \end{array} } \right). $$

(A-1)

And

$$ {\mathcal{H}}_{11} = \frac{{\partial^{2} {\text{F}}_{{\text{u}}} }}{{\partial \left( {{\text{P}}_{{{\text{u}},{\text{c}}}} } \right)^{2} }} = - {\upkappa }_{{\text{u}}} \cdot {\text{w}}_{{\text{u}}} \cdot \frac{{{\text{G}}_{{{\text{u}},{\text{c}}}}^{2} \cdot {\text{B}}_{{{\text{u}},{\text{c}}}} }}{{\left( {{\text{B}}_{{{\text{u}},{\text{c}}}} \cdot {\text{N}}_{{\text{g}}} + {\text{P}}_{{{\text{u}},{\text{c}}}} \cdot {\text{G}}_{{{\text{u}},{\text{c}}}} } \right)^{2} \cdot \ln 2}} < 0, $$

(A-2)

$$ {\mathcal{H}}_{12,21} = \frac{{\partial^{2} {\text{F}}_{{\text{u}}} }}{{\partial {\text{P}}_{{{\text{u}},{\text{c}}}} \partial {\text{B}}_{{{\text{u}},{\text{c}}}} }} = \frac{{\partial^{2} {\text{F}}_{{\text{u}}} }}{{\partial {\text{B}}_{{{\text{u}},{\text{c}}}} \partial {\text{P}}_{{{\text{u}},{\text{c}}}} }} = {\upkappa }_{{\text{u}}} \cdot {\text{w}}_{{\text{u}}} \cdot \frac{{{\text{G}}_{{{\text{u}},{\text{c}}}}^{2} \cdot {\text{P}}_{{{\text{u}},{\text{c}}}} }}{{\left( {{\text{B}}_{{{\text{u}},{\text{c}}}} \cdot {\text{N}}_{{\text{g}}} + {\text{P}}_{{{\text{u}},{\text{c}}}} \cdot {\text{G}}_{{{\text{u}},{\text{c}}}} } \right)^{2} \cdot \ln 2}} > 0,{ } $$

(A-3)

$$ {\mathcal{H}}_{22} = \frac{{\partial^{2} {\text{F}}_{{\text{u}}} }}{{\partial \left( {{\text{B}}_{{{\text{u}},{\text{c}}}} } \right)^{2} }} = - {\upkappa }_{{\text{u}}} \cdot {\text{w}}_{{\text{u}}} \cdot \frac{{{\text{G}}_{{{\text{u}},{\text{c}}}}^{2} \cdot \left( {{\text{P}}_{{{\text{u}},{\text{c}}}} } \right)^{2} }}{{\left( {{\text{B}}_{{{\text{u}},{\text{c}}}} \cdot {\text{N}}_{{\text{g}}} + {\text{P}}_{{{\text{u}},{\text{c}}}} \cdot {\text{G}}_{{{\text{u}},{\text{c}}}} } \right)^{2} \cdot {\text{B}}_{{{\text{u}},{\text{c}}}} \cdot \ln 2}} < 0, $$

(A-4)

Considering that, the Hessian matrix ${\mathcal{H}}$ is a negative symmetric matrix, which means that Eq. (26) is a concave function with respect to the variables P, B. This completes the proof.