Topic: The figure below is a 16QAM constellation diagram of a rectangular constellation, f1(t) and f2(t) are normalized orthogonal basis functions, and each constellation point
is approximately equal.
(1) Find the average symbol energy E (average power), peak power, and minimum constellation point distance dmin of the 16QAM constellation diagram.
(2) Assuming that the 16QAM uses Gray mapping, it is known that the binary bit corresponding to s1 is 0000, and the binary bit corresponding to s4
is 0101. Try to write the binary bits corresponding to s2 and s3.
(1) E is the average of the square of the distance between each constellation point and the origin. The quadrants are symmetrical and can be
calculated according to the first quadrant : E=(18+10+10+2)/4 = 5
Emax=18
Peak-to-average ratio: Emax/E=18/5
dmin = 2
(2) Gray mapping ( Also called Gray coding) is that adjacent constellation points differ by only one bit. Note that the "
adjacent" here is based on the minimum Euclidean distance. For example, the points adjacent to s2 are s1 and s4, and there is no s3.
Under the conditions of this question, according to Gray mapping, s2 corresponds to 0100 and s3 corresponds to 0001. Or: s2 corresponds to 0010, s3 corresponds
to 0100. .
Gray coding (16-QAM)
