Certain aspects of the present disclosure relate to a technique for two-step joint demapping based on sphere decoding for log-likelihood ratio (LLR) computation related to a received multiple-input multiple-output (MIMO) signal. The first step of the proposed algorithm comprises a linear minimum mean square error (LMMSE) based detection to form soft symbol estimates of symbols being transmitted. Then, the LMMSE-based soft symbol estimates can be utilized to form a set of constellation points of a stream interfering to a stream of interest. These candidate constellation points can be then subtracted (canceled) from the received signal to improve the LLR computations of the stream of interest. After the cancellation, the maximum ratio combining (MRC) can be applied to each individual stream to form more refined soft symbol estimates as well as an effective signal-to-noise ratio (SNR) estimate. The refined outputs of the MRC can be utilized to compute LLRs of transmitted bits based on the effective SNR and the refined soft symbol estimates associated with all the candidate constellation points from the set. The LLRs of transmitted bits may be employed by a channel decoder.