The data bits were differentially encoded. Let the data bits be
b(1) b(2) b(3) b(4) ... b(n) b(n+1) ...
where the Matlab convention of starting with index 1 (instead of index 0) has been used. Without
differential encoding, data bits b(1) and b(2)select the first OQPSK symbol, data bits b(3) and b(4)select the second OQPSK symbol, and so on. Let the differentially encoded bits be
d(1) d(2) d(3) d(4) ... d(n) d(n+1) ...
where the differential encoding rule is
d(n) = b(n) XOR ~d(n-1) d(n+1) = b(n+1) XOR d(n)
for odd values of n where ~d(n-1) means the logical complement of d(n-1). The differentially encoded bits are now used to select the OQPSK symbol as illustrated by the
bit-to-symbol mapping above. d(1) and d(2) select the first OQPSK symbol, d(3) and d(4) select the second OQPSK symbol, and so on.
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