### QPSK equation:-

The meaning of QPSK is that the carrier signal takes on different phases Π/4, 3Π/4, 5Π/4 and 7Π/4 based on incoming di-bit combination or symbol.

* = 0, elsewhere, where i = 1,2,3,4.*

E_{b} and T_{b} are the bit energy and bit-interval , E_{s} and T_{s} are the energy per symbol and symbol duration. T_{s }= 2 T_{b} .

The carrier frequency f_{c} = n_{c} /T_{s}. where n_{c} is a fixed integer.

each possible value of phase corresponds to a unique di-bit. then the foregoing phase values to represent the gray encoded set of di-bits 11,01,10 and 00, where only a single bit is changed from one di-bit to the next.

QPSK equation can be represented in another format as follows

* = 0, elsewhere ,where i=0,1,2,3.*

The above two equations are same, there is a change in i values. alternately the equation can be represented as follows.

, *where i= 1,2,3,4.*

The above equation can be expanded cos(A+B). There are two orthogonal functions Φ_{1}(t) and Φ_{2}(t) where

Let and

then the resultant equation is: .

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