suits for long range propagation through underwater acoustic channels but also enables simple detection at the receiver as will be discussed further below assume that a1 all information symbols are phase modulated with unit magnitude i e d n 1 u2200 n at the transmitter information symbols d n 39 s are first demultiplexed into m independent data sequences which are then forwarded to the corresponding branches of dd encoding and ds spreading at each say the ith branch data symbols d i n are first dd encoded into coded symbols u i n by using two recursions u i n u i n u2212 1 v i n n 0 1 v i n v i n u2212 1 d i n n 0 1 these two recursions reveal that dd coding is nothing but a repetition of single differential sd coding it is well known that sd coding makes possible to forgo phase tracking at symbol detection by repeating sd coding dd coding enables symbol detection without the need of tracking not only phase shifts but also doppler shifts as we will discuss later note that under assumption a1 there will be no divergence in signal power due to recursions after.