" I know what you are thinking about" is not a compound sentence because a compound sentence contains two Independent Clauses joined by a coordinator. ( and, but , or etc...)
>>> ID clause + coordinator + ID clause <<< [ ID = Independent Clause]
e.g. I love you and you love me:)
" I know what you are thinking about" can be a Simple Sentence or " a Complex sentence.
We can say this sentence is a Simple sentence because it contains only one Independent Clause.
Sentence Structure :
-- I + know + what you are thinking about.
Subj + VT + Obj [ noun clause] = 1 ID { Simple Sentence}
Noun clauses perform the same functions in sentences that nouns do. So it can be "object" in this sentence.
OR
We can say this sentence is a Complex sentence because it contains only one Independent Clause and one or more dependent clauses (Dependent clauses are also called subordinate clauses and begin with noun clause markers such as:
that
if, whether
Wh-words: how, what, when, where, which, who, whom, whose, why
Wh-ever words: however, whatever, whenever, wherever, whichever, whoever, whomever
Sentence Structure
---- I + know + what you are thinking about.
Independent + Subordinate Clause as a noun clause - Marker = what
---------= 1 ID + 1 DC { Complex Sentence }
Anyway , the type of this sentence depends on individual consideration. And I think communication is the most important when we speak.