Admission Control and Scheduling Algorithm for Multi-carrier Systems

Abstract

LTE-Advanced aims to provide a transmission bandwidth of 100 MHz by using carrier aggregation to aggregate LTE Rel. 8 carriers. In order to increase the system capacity, resource allocation becomes a very good tool, and, in the context of the existence of multiple component carriers in LTE-Advanced becomes a complex optimization problem. This paper proposes a Multi-Carrier Scheduling Algorithm that takes into account the user’s QoS requirements and also targets the maximization of the user throughput. The algorithm is evaluated in a scenario with both macro and femto base stations (i.e. a HetNet scenario) that respects the 3GPP specifications. Numerical results show that this algorithm has better performances than the traditional round robin and proportionally fair resource scheduling algorithms.

Appendices

Appendix 1: Proof of Convexity of the Optimization Problem

From the optimization problem in Sect. 3 the following utility function is obtained:

$$\begin{aligned} -u(x_{11},x_{12},...,x_{1N_c},x_{21},...,x_{N_cN_c})= -\sum _{c=1}^{N_c}\sum _{u=1}^{N} w_{cu}x_{cu} \end{aligned}$$

(17)

where each weight $w_{cu}$ is the ratio between the estimated throughput of user $u$ and the historical average data rate for the same user.

$$\begin{aligned} w_{cu}=\frac{c_uD_uT_u}{R_u} \end{aligned}$$

(18)

where $T_u$ represents the potentially achievable data rate and $R_u$ the historical average data rate.

$T_u$ is calculated with the help of the following equation:

$$\begin{aligned} T_u=\sum _n \log _2 \left( 1+{A_t}_{c,u}^n \cdot SINR_{c,u}^n \right) =\sum _n \log _2 \left( 1+{A_t}_{c,u}^n \cdot \frac{P_{TX,c,u}^n \cdot |h_{c,u}^n|^2}{\sigma ^2 + \sum _{j\ne c}^C P_j^n \cdot |h_{j,u}^n|^2}\right) \end{aligned}$$

(19)

The historical average data rate is calculated as in the following equation:

$$\begin{aligned} R_{u,t}=\gamma \cdot R_{u,t-1} + (1-\gamma )\cdot T_{u,t-1} \end{aligned}$$

(20)

It is obvious that $T_u$ depends only on the SINR experienced by the user $u$ attached to cell $c$. At the moment (the current TTI) the scheduler makes its decision, all the received powers, as well as the channel gains are constants. We can therefor say that $C_1 = \sum _n \log _2 \left( 1+{A_t}_{c,u}^n \cdot \frac{P_{TX,c,u}^n \cdot |h_{c,u}^n|^2}{\sigma ^2 + \sum _{j\ne c}^C P_j^n \cdot |h_{j,u}^n|^2}\right) = const.$ Likewise, the historical average data rate is also a constant, since it depends on the average data rate, and the experienced throughput in the last TTI. Consequently, $C_2 = R_u = const.$

By rewriting Eq. 17, we obtain:

$$\begin{aligned} -u(x_{11},x_{12},...,x_{1N_c},x_{21},...,x_{N_cN_c})=-\sum _{c=1}^{N_c}\sum _{u=1}^{N} f^{cu} \end{aligned}$$

(21)

Where $f^{cu}$ is an affine function:

$$\begin{aligned} \begin{aligned} f^{cu}(x) = b + x \cdot a \\ a = \frac{C_1}{C_2}, b=0, x=x_{cu} \end{aligned} \end{aligned}$$

(22)

Since an affine function is also a convex function and since the sum of convex functions preserves the convexity of the function [16], we obtain that $-u(x_{11},x_{12},...,x_{1N_c},x_{21},...,x_{N_cN_c})$ is a convex function.

Appendix 2: Proof of the Upper Bound for Number of Users of the Cell

Considering Eq. 12 and knowing that

$$\begin{aligned} x-1 < [x] \le x \end{aligned}$$

(23)

we obtain

$$\begin{aligned} N_{users_{k_{cu}}} \le \frac{N_{PRB_c}}{N_{PRB_{min_{k_u}}}} \end{aligned}$$

(24)

From Eq. 10, considering also that the component carriers have equal bandwidths ($N_{PRB_c} = N_{PRB} \forall c \in \{1,...,N_c\}$), we obtain:

$$\begin{aligned} N_{users_{k_u}}&\le \sum _{c=1}^{N_c} N_{users_{k_{cu}}} \le \sum _{c=1}^{N_c} \frac{N_{PRB_{c}}}{N_{PRB_{min_{k_u}}}} \nonumber \\&=\frac{1}{N_{PRB_{min_{k_u}}}} \cdot \sum _{c=1}^{N_c} N_{PRB_c} = \frac{N_c \cdot N_{PRB}}{N_{PRB_{min_{k_u}}}} = \frac{N_{PRB_{tot}}}{N_{PRB_{min_{k_u}}}} \end{aligned}$$

(25)