DVB-T2 employs multiple antenna techniques and error protection coding as part of its key technologies that enhance its performance and increase the capacity by 30% over its predecessor. It defines MISO space diversity technique as an optional part in the transmission chain along with combining LDPC with BCH codes in a Bit-Interleaved Coding and Modulation (BICM) scheme to achieve high performance. Using iterative receiver between the MISO detector and the decoder can approximate the optimal receiver performance. In this paper, we propose to use a modified soft K-Best List Sphere Decoder (KB-LSD) that iteratively uses the soft output LLR from LDPC decoder to calculate a prior LLR of the Maximum A Posterior Probability (MAP) of each transmitted symbol as a cost function of each child in the tree to decode the MISO SFBC to reach near optimal soft output MAP detection. We adapt the number of K paths chosen by the KB-LSD and the number of LDPC iterations according to the channel quality to achieve optimum receiver performance with reduced complexity of the system.