- A novel iteratively detected Sphere Packing (SP) modulation aided Orthogonal Frequency Division Multiplexing (OFDM) scheme is proposed, which we refer to as the SPOFDM arrangement. The advocated SP-OFDM system outperforms conventional OFDM dispensing with SP. As its upperbound performance limit, the Discrete Input Continuous Output Memoryless Channel (DCMC) capacity of this system is formulated. In order to maximize the DCMC channel capacity, a SP-to- OFDM-sub-carrier mapper (SPTSCM) is contrived, which is capable of providing an approximately 0.3bit/s/Hz DCMC capacity benefit, by employing a variety of different SPTSCM arrangements. Additionally, the proposed SP-OFDM scheme exhibits a DCMC capacity advantage of 0.8bit/s/Hz over the conventional equivalent-throughput Gray Mapping (GM) and Anti-Gray Mapping (AGM) based QPSK-OFDM schemes. Furthermore, the performance of the SP-OFDM system can be improved by serially concatenated convolutional coding relying on iterative extrinsic info...