In this post, let us derive the theoretical bit error probability for 16PSK modulation using Gray coded mapping. For deriving the equation, we will refer material from the following posts:
(a) Symbol Error Rate for 16PSK
(b) Gray code to Binary code conversion for PSK
(c) Binary to Gray code conversion for PSK
As discussed in the previous posts, the key feature of Gray code is that adjacent symbols differ by only one bit. The 16PSK constellation with Gray mapping can be as shown in the figure below.
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