In　this　paper,　we　propose　a　permutation　index　differential　chaos　shift　keying　with　the　noise　reduction　(NR-PI-DCSK)　to　alleviate　the　negative　effect　of　the　additive　noise　and　fading　interference.　Instead　of　sending　a　beta-length　chaotic　sequence　as　the　reference　in　the　conventional　PI-DCSK,　the　transmitter　of　NR-PI-DCSK　generates　beta/R　chaotic　samples　and　repeats　R　times,　which　serve　as　the　reference　sequence.　The　permuted　copy　of　the　reference　is　used　to　carry　the　data　given　the　predefined　permutation　index.　After　the　correlation　and　averaging　of　these　R　chaotic　segments　at　the　receiver,　the　variance　of　noise　and　fading　can　be　greatly　reduced　and　the　performance　is　improved.　Then,　we　derive　the　analytical　BER　expressions　for　the　multipath　fading　channels,　which　are　verified　by　the　consistent　simulations.　The　results　show　that　the　proposed　NR-PI-DCSK　can　achieve　up　to　3　dB　performance　gain　over　the　conventional　PI-DCSK　in　different　wireless　fading　channels.　In　addition,　the　performance　advantage　of　the　proposed　NR-PI-DCSK　is　also　demonstrated　in　a　typical　UWB　channel　by　simulations.　More　importantly,　the　proposed　scheme　maintains　almost　the　same　low　transceiver　complexity　as　the　conventional　ones,　since　it　only　requires　the　correlators.　Thus,　the　NR-PI-DCSK　can　be　seen　as　a　promising　candidate　for　low-cost　short-range　IoT　communications.