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.
Eb and Tb are the bit energy and bit-interval , Es and Ts are the energy per symbol and symbol duration. Ts = 2 Tb .
The carrier frequency fc = nc /Ts. where nc 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 Φ1(t) and Φ2(t) where
then the resultant equation is: .
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