Resource Allocation with Limited Feedback and Joint Coding Scheme for Wireless Multi-antenna Multicast System

Abstract

In conventional multicast scheme (CMS), the total throughput of multicast group is constrained by the user with the worst channel quality. In order to overcome this problem of limited throughput, we introduce a resource allocation algorithm by exploiting layered coding combined with erasure correction coding for multicast services in the downlink of OFDMA-based multi-antenna system. To reduce the feedback overhead of uplink, we design a novel transmission scheme with limited feedback. Then, we formulate the joint subcarrier and power allocation problem for the data of base layer and enhancement layers, which is shown to be NP hard. Hence, in order to reduce the computational complexity, we propose a three-phase suboptimal algorithm. The algorithm is designed to maximize the system throughput while at the same time guarantee the quality of services (QoS) requirements of all multicast groups. It is composed of precoding scheme, proportional fairness subcarrier allocation algorithm and modified water-filling power allocation algorithm with QoS guarantees (MWF-Q). To further decrease the complexity of MWF-Q, a power allocation algorithm with increased fixed power allocation algorithm with QoS guarantees is introduced. Simulation results show that the proposed algorithms based on limited feedback scheme significantly outperform CMS and any other existing algorithm with full feedback. Moreover, the proposed scheme can efficiently reduce 50 % of the full feedback overhead.

Appendix

Let $X_{opt}$ denote the optimal solution to the problem (15). Due to the relaxation, the matrix $X_{opt}$ obtained by solving the SDP problem will not be rank-one in general. If it is, then the optimal weight vector can be straightforwardly recovered from it by finding the principal eigenvector corresponding to the only nonzero eigenvalue. However, because of the SDP relaxation step, i.e., relaxation of the rank-one constraint, the matrix $X_{opt}$ may not be rank-one in general. Then, a randomization approach can be used to obtain an approximate solution to the original problem. A common idea of the approach is based on randomization: using $X_{opt}$ to generate a set of candidate weight vectors $\{{{\mathop {\varvec{\omega }}\limits ^\smile }}_l\}_{l=1}^R$, from which the “best” solution will be selected. Here, $R$ is the number of randomizations used.

In application to our problem, the randomization algorithm can be modified as follows. First, we calculate the eigendecomposition of $X_{opt} = U\Sigma U^{H}$ and the candidate precoding vector ${\mathop {\varvec{\omega }}\limits ^\smile }_l ={\varvec{U}}\varvec{\Sigma }^{1/2}{\varvec{e}}_{{\varvec{l}}}$ is selected as a candidate vector, where ${\varvec{U}}$ is an unitary matrix of eigenvectors, $\varvec{\Sigma }$ is a diagonal matrix of eigenvalues, and $e_{l}$ is a random vector whose elements are independent random variables uniformly distributed on the unit circle in the complex plane. i.e., $\left[ {e_l } \right] _i =e^{j\theta _{l,t} }$, where the $\theta _{l,t}$ are independent and uniformly distributed on $[0, 2\pi ]$. Second, among the feasible candidates ${\mathop {\varvec{\omega }}\limits ^\smile }_l$, the “best” of these randomly generated weight vectors chosen as the precoding vector $\omega _{g,n}$.

$$\begin{aligned} \varvec{\omega } _{g,n} =\arg \mathop {\max }\limits _{\varvec{\omega }_{g,n} \in \{{\mathop {\varvec{\omega }}\limits ^\smile }_l\}_{l=1s}^R } \mathop {\min }\limits _{k\in \mathcal{K }_g } \frac{\left| {\omega _{g,n}^H \bar{{H}}_{g,k,n} \left| {g_{g,k} (n)} \right| } \right| ^{2}}{\sigma _{g,k,n}^2 } \end{aligned}$$

(37)