Multi-antenna processing first appeared in Digital Video Broadcasting in the 2nd generation terrestrial system DVBT2 by defining an optional MISO processing based on modified version of Alamouti codes in frequency domain. Decoding methods recommended by the DVB-T2 is the linear methods ZF and MMSE. In this paper we propose to use a modified K-Best Sphere Decoder (SD), to enhance the system performance in a frequency selective time varying channel with some modification to target the reduction of the fixed K-Best SD complexity to be more suitable for hardware implementations over different platforms. The proposed modified K-Best SD that we name Adaptive K-Best SD (AKBSD) exploit the channel impulse response (CIR) to measure the channel selectivity as an indicator of the channel state. BER simulations show how the performance is enhanced when applying the AKBSD method rather than the linear methods defined by the DVB-T2 implementation guide with low extra added complexity.