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This paper presents a new approach to soft detection of spatial data streams in multiple input multiple output (MIMO) channels in slow fading channels. We focus on high spectral efficiency bit interleaved coded modulation (BICM) MIMO OFDM system where, after serial to parallel conversion and per antenna coding, spatial data streams are simultaneously transmitted by using an antenna array. We propose a detection algorithm based on a combination of linear and non linear detection techniques. The proposed algorithm orders spatial streams as per V-BLAST ordering and then uses linear detectors like MMSE or zero forcing (ZF) to detect the streams which have seen good channel realizations and therefore enjoy higher signal-to-noise-ratios (SNRs). These streams, after being detected, are subsequently stripped off leading to max log MAP detection of the streams which have seen comparatively poor realizations of the channel and consequently have lower SNRs. Unlike maximum likelihood (ML) detection, whose complexity is huge due to the need for enumerating all possible combinations of the transmitted constellation points, the proposed method has low complexity and moreover has a fully parallel structure suitable for the implementation in parallel hardware. Numerical examples illustrate the performance of proposed algorithm for slow fading 3times3 and 4times4 complex MIMO channels in comparison to linear and max log MAP detection.