This　paper　presents　a　novel　multi-carrier　differential　chaos　shift　keying　modulation　with　permutation　index　(PI-MC-DCSK)　over　wireless　multipath　fading　channels,　since　the　conventional　multi-carrier　DCSK　(MC-DCSK)　suffers　from　low　spectral　efficiency　and　loss　of　system　performance.　In　this　system,　the　predefined　subcarriers　can　carry　multiple　data　bits　according　to　permutation　indexes,　while　only　a　single　subcarrier　is　used　as　the　chaotic　reference　and　shared　by　data　subcarriers.　Thus,　the　transmission　energy　is　saved　and　the　data　rate　can　be　enhanced.　Moreover,　the　low　cross-correlation　property　of　permuted　chaotic　sequences　is　exploited　in　PI-MC-DCSK　to　effectively　suppress　inter-subcarrier　interference.　The　theoretical　analysis　and　consistent　simulation　results　show　that　the　proposed　system　can　obtain　significant　performance　gains　of　more　than　2　dB　than　the　conventional　MC-DCSK　over　Rayleigh　multipath　channels.　This　performance　gain　can　be　up　to　4　dB　in　typical　ultra-wideband　(UWB)　channels,　which　proves　its　feasibility　in　practical　applications.　Therefore,　this　new　design　can　be　viewed　as　a　low-complexity　solution　for　chaos-based　wireless　communications,　such　as　short-range　Internet　of　Things　(IoT)　applications　of　transmitted-reference　communications.　©　2014　IEEE.