Asymmetric radio resource allocation scheme for OFDMA wireless networks with collaborative relays

Abstract

This work addresses the radio resource allocation problem for cooperative relay assisted OFDMA wireless network. The relays adopt the decode-and-forward protocol and can cooperatively assist the transmission from source to destination. Recent works on the subject have mainly considered symmetric source-to-relay and relay-to-destination resource allocations, which limits the achievable gains through relaying. In this paper we consider the problem of asymmetric radio resource allocation, where the objective is to maximize the system throughput of the source-to-destination link under various constraints. In particular, we consider optimization of the set of cooperative relays and link asymmetries together with subcarrier and power allocation. We derive theoretical expressions for the solutions and illustrate them through simulations. The results show clear additional performance gains through asymmetric cooperative scheme compared to the other recently proposed resource allocation schemes.

Appendices

Appendix 1

Derivation of optimal solution in (12) and (13).

For simplicity, we replace log(1 + P ⁱ _s,k γ ⁱ _s,k ) with r ₁ and log(1 + ∑ ^K _k=1 P ^j _k,d γ ^j _k,d ) with r ₂. From (7), we have

$$ \frac{T_1}{T_2} = \frac{r_2}{r_1}. $$

(21)

Then the derivative of $\mathcal{L}$ in (9) with respect to variable T ₁ is given by

$$ \begin{aligned} \frac{\partial{\mathcal{L}} }{\partial T_1}&=\frac{(T-T_1)r_1}{T^2}-\frac{(T_2)r_2}{T^2}- \mu \left(\frac{(T-T_1)r_1}{T^2}+\frac{(T_2)r_2}{T^2}\right)\\ &= \left(\frac{(T-T_1)T_2}{T^2 T_1}-\frac{(T_2)}{T^2}-\mu \left(\frac{(T-T_1)T_2}{T^2 T_1}+\frac{(T_2)}{T^2}\right)\right)r_2 . \end{aligned} $$

(22)

Since we have T = T ₁ + T ₂ and $\frac{\partial\mathcal{L} }{\partial T_1}=0,$ the (22) can be converted to:

$$ \frac{T_2}{T_1} = \frac{1+\mu}{1-\mu}, $$

(23)

and we have

$$ T_1 = \frac{1 - \mu}{2}T, $$

(24)

$$ T_2 = \frac{1 + \mu}{2}T. $$

(25)

Appendix 2

Derivation of optimal solution in (14) and (15).

For simplicity, we replace P ⁱ _s,k with P ₁ and P ^j _k,d with P _2,k . Similarly, we use G ₁ and L ₁ to replace G ⁱ _s,k and L _s,k , G _2,k and L _2,k to replace G ^j _k,d and L _k,d . First, we solve the power allocation at the transmitter. When relay selection and subcarrier allocation are done, the derivative of $\mathcal{L}$ in (9) with respect to variable P ₁ is given by

$$ \frac{\partial{\mathcal{L}} }{\partial P_1} = \left( 1- \mu\right)\frac{T_1}{T}\frac{1}{1+\frac{L_1P_1G_1}{\sigma_k^2}}\frac{L_1 G_1}{\sigma_k^2}- \lambda_s. $$

(26)

Substituting (24) into (26) and applying KKT conditions, we obtain

$$ P_1^\ast = \left\{\frac{(1-\mu)^2}{2 \lambda_s}-\frac{\sigma_k^2}{G_1L_1}\right\}^{+}. $$

(27)

Then we discuss how to achieve optimal $P_{2,k}^\ast$. The derivative of $\mathcal{L}$ respect to P _2,k is shown

$$ \frac{\partial{\mathcal{L}} }{\partial P_{2,k}}= \left(1+ \mu \right)\frac{T_2}{T}\frac{1}{1+\frac{\sum_{k=1}^{K}L_{2,k}P_{2,k}G_{2,k}}{\sigma_d^2}}\frac{L_{2,k} G_{2,k}}{\sigma_d^2}-\lambda_{k,d}. $$

(28)

By using the same scheme that shows above, we obtain

$$ \begin{aligned} P_{2,k}^\ast = & \left\{\frac{(1+\mu)^2}{2 \lambda_{k,d}}-\frac{\sigma_d^2}{G_{2,k}L_{2,k}}\right.\\ &\left.-\frac{\sum_{m=1,m \neq k}^K G_{2,m}L_{2,m}P_{2,m}}{G_{2,k}L_{2,k}}\right\}^+. \end{aligned} $$

(29)

Thus, the optimality of solution $\hbox{P}^\ast$ in (14) and (15) is proved.