Based on the assumption of continuous fading

a multiple symbol differential approximate automatic sphere decoding（MSDAASD） algorithm was developed by incorporating a recursive form of an approximate maxi-mum-likelihood（ML） metric into automatic sphere decoding.The proposed algorithm is suitable for arbitrary unitary constellations and eliminates the error floor caused by in multiple symbol differential sphere decoding（MSDSD） with quasi-static channel assumption.Compared with decision-feedback detection under the same assumption

MSDAASD achieves similar performance of ML detection with much lower complexity at moderate to high signal-to-noise ratios.