Base station selection and resource allocation in macro–femtocell networks under noisy scenario

Abstract

In this paper, we address the problem of optimizing resources for downlink transmission in a macro–femtocell network under non-dense femtocell deployment. In the literature, some approaches perform bandwidth or power optimization depending on the air interface technology and others optimize both types of resources, but only in femtocell network. However, the following limitations can be noticed: (1) Equal distribution of transmitted power among all subcarriers, even if they are not used, leads to resource underutilization, (2) femtocell data rates are reduced in order to minimize the interference from femto base stations to macro users, and (3) the impact of noise has not been evaluated. Moreover, there is lack of optimal selection of users that can be served by femtocells. To overcome these limitations, we propose a model that finds a tradeoff between bandwidth and power to reduce the bandwidth usage per user and to minimize the impact of noise. By means of Linear Programming, our solution maximizes user satisfaction and provides optimal: serving base station, power and bandwidth for each mobile user taking into account its location and demand. Furthermore, we present a performance analysis under changes of signal to noise ratio. Simulations were conducted and a comparison with a modified version of Weighted Water Filling algorithm is presented.

Appendix: MILP BS selection and resource allocation model

For the spectrum partitioning scenario, the set of Equations from (9) to (22) are replaced by (47) to (59), including the constraints of the upper and lower bound of SNR in both tiers.

$$\max_{{\bf x, b, P}} \sum \limits_{i \in \{N\} }w_{i}^m x_i^m l_z^{mod} \sum \limits_{j =0}^{j=T}\beta_j^i 2^j \sum \limits_{i \in \{N\}}\sum \limits_{f \in \{F\}} w_{i}^f x_i^f l_f^{mod} \sum \limits_{j =0}^{j=T}\beta_j^i 2^j , $$

(47)

subject to

$$B_C \sum \limits_{i \in \{N\}}\sum \limits_{j =0}^{j=T}\beta_j^i 2^j \leq B, $$

(48)

$$x_{i}^m + \sum \limits_{f \in \{F\}}x_i^f \leq 1; \quad i \in N, $$

(49)

$$\sum \limits_{i \in \{N\}}x_{i}^f\leq N^f; \quad f \in {F}, $$

(50)

$$\sum \limits_{i \in \{N\}} P_i^m \leq P_m^{Total}, $$

(51)

$$m_k \left(\frac{P_i^m }{PL_{i}^m N_0}\right) +a_k \geq l_z^{mod} x_{i}^m; \quad i \in N, k\in K, $$

(52)

$$x_{i}^m\, SNR_{min}^k \leq \left( \frac{P_i^m}{PL_{i}^m N_0} \right) \leq SNR_{max}^k x_{i}^m; \quad i \in N, k\in K, $$

(53)

$$m_k \left(\frac{P_i^f}{PL_{i}^f N_0}\right) +a_k \geq l_f^{mod} x_{i}^f ;\quad i \in N, f\in F, $$

(54)

$$x_{i}^f\, SNR_{min}^k \leq \left(\frac{P_i^f}{PL_{i}^f N_0}\right ) \leq SNR_{max}^k x_{i}^f; \quad i \in N, f \in F, $$

(55)

$$B_C \sum \limits_{j =0}^{j=T}\beta_j^i 2^j \leq x_i^m \frac{S_i}{ l_z^{mod}} + \sum \limits_{f \in \{F\}} x_i^f\frac{S_i}{ l_f^{mod}}; \quad i \in N, f \in F, $$

(56)

$$B_C \sum \limits_{j =0}^{j=T}\beta_j^i 2^j \leq B\left( \sum \limits_{f \in \{F\}}x_i^f +x_i^m\right); \quad i \in N, $$

(57)

$$P_i^m \leq P_z^{max} x_i^m; \quad i \in N, $$

(58)

$$P_i^f\leq P_f^{max} x_i^f ;\quad i \in N, f \in F. $$

(59)