Substituting eq. (2.33) into eq. (2.32), eq. (2.34) can be obtained:

E[ | x˜(n) |4 ]=E[ | x(n) |4 ]i| si(n) |4+2E2[ | x(n) |2 ]{ [ i| si(n) |2 ]2i| si(n) |4 }(2.34)+| E[ x2(n) ] |2[ | isi2(n) |2i| si(n) |4 ]

Substituting eqs. (2.29) and (2.31) into eq. (2.34), (2.35) can be obtained:

E[|x~(n)|4]=E[|x(n)|4]i|si(n)|4+2E[|x(n)2|][i|si(n)|2]22E2[|x(n)|2]i|si(n)|4+|E[x2(n)]2||isi2(n)|2|E[x2(n)]|2i|si(n)|4(2.35)=E[|x(n)|4]i|si(n)|4+2E[|x~(n)2|]2E2[|x(n)|2]i|si(n)|4+|E[x~2(n)]|2|E[x2(n)]|2i|si(n)|4

By moving the mathematical expectations of transmitted sequence and recovery sequence to both sides of the equal sign, respectively, eq. (2.36) can be obtained:

E[|x~(n)|4]2E2[|x~(n)|2]|E[x~2(

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