Conventional orthogonal frequency division multiple access (OFDMA) burst construction methods can only support limited numbers of connections due to the map overhead and corresponding limitations in the numbers of orthogonal resources blocks, which limits the capacity of current 4G and the following 5th generation (5G) networks. This study therefore provides a novel OFDMA burst construction algorithm and enhanced burst indexing aware algorithm (EHA), which try to maximize the throughput while considering the subchannel diversity and optimizing burst indexing issues. The EHA not only allocates the subchannels with the best channel quality for each burst, but also groups the bursts to alleviate the MAP overhead. Simulation results showed that the EHA yields two times the throughput that has been achieved using previous algorithms under a heavy load. Two contributions of the EHA are: (1) the overhead of burst indexing decreases because massive numbers of connections can be accommodated by one burst; and (2) the overall throughput increases due to that one connection with large data transferring requirements can be split and distributed into several bursts and placed on the subchannels with good channel quality to adopt better modulation coding scheme (MCS), if the saved bandwidth in this burst construction is more than the increased overhead of burst indexing.