Mm update in gr_mpsk_receiver_cc

I am reading the c++ code of

in the function: mm_error_tracking, mu is updated as [line 251]

It seems to me that omega already takes mm_error into account. Why in
updating mu, mm_error is added again?

I also checked the book “Digital Communication Receivers -
Synchronization, channel estimation, and signal processing”, where
Equation (9-39) (p 526) shows the update should be

Is this an error or my misunderstanding?


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