Diversity-Multiplexing Tradeoff in OFDMA Systems: An H-Matching Approach

OFDMA is a promising technique because it is capable of improving the transmission reliability and efficiency of multi-user wireless communications. However, previous works on the performance of OFDMA did not properly consider the fundamental relationship between multiplexing and diversity in OFDMA systems. As a comprehensive performance metric, the diversity-multiplexing tradeoff will be applied in this paper to evaluate the subcarrier allocation scheme. The OFDMA system will be formulated into a correlated random bipartite graph model, in which, whether the edges occur or not depends on the distribution of the channel fading. The \mathcal{H}-matching method, which is used to determine the maximum collection of vertex-disjoint copies of a fixed sub-graph \mathcal{H} contained in a given graph, will then be developed to address the optimal subcarrier allocation problem. Theoretical analysis will show that the proposed \mathcal{H}-matching method achieves the optimal outage performance at a given target multiplexing gain, which implies that the optimal diversity-multiplexing tradeoff can be achieved by only allocating subcarriers. Although the \mathcal{H}-matching problem is NP-complete, the proposed Random Rotation and Expansion based Hopcroft-Karp (R^2EHK) algorithm can still achieve the asymptotically optimal outage performance (i.e., optimal diversity-multiplexing tradeoff) with a sub-linear complexity. Furthermore, the channel state information needed is only one bit per subcarrier. Simulation results will verify the theoretical analysis and will show that the performance loss of the R^2EHK algorithm is negligible compared to the exhaustive search method. In addition, it is also shown that the R^2EHK algorithm has at least a 2 dB SNR gain compared to the interleaved subcarrier allocation with water-filling power allocation in IEEE 802.16 standards.