International audienceThis paper investigates the widely linear processing(WLP) for the detection of circular signals such as M-aryphase shift keying (MPSK) signals, M-ary quadrature amplitudemodulation (MQAM) signals. Firstly, a unified mathematicalmodel is derived to describe the conjugate symmetry of generalMPSK/MQAM signals. In the unified model, a phase-rotation matrix(PRM) is introduced to partition the constellation of multipleinputmultiple-output (MIMO) signals into subsets. Signals in asubset share the same PRM. Secondly, a widely linear receiver isproposed in each subset for MIMO detection. To avoid repetitiveWLP in each subset, a widely linear sphere decoder (WLSD)is further proposed for MIMO systems. WLSD transforms thetraditional SD searching for a true transmitted vector into ashrunk one by searching for the corresponding phase-rotationvector
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