PN Sequences By Dr. Ernest Simo 3.0 Some Useful PN Codes Properties Shift-and-Add Property The Modulo-2 condition of a PN Sequence with time-shift i and a time shifted version of the same PN sequence with time-shift j, yields another time shifted version of the same PN sequence with time-shift k. Ci(t-i) + Ci(t-j) = Ci(t-k) For example, consider two Time-Shifted version of the previously generated PN sequence C1(t): 1 0 0 1 1 1 0 C1(t-1)= 0 0 1 1 1 0 1 C1(t-5)= 1 0 1 0 0 1 1 + Ci-1) (C1(t-5)= 1 0 0 1 1 1 0 = Ci (t- 0) TIME-SHIFTS 0 1 2 3 4 5 6 7 TIME-SHIFTS 1   0   0   1   1   1   0   1 0   0   1   1   1   0   1   1 0   1   1   1   0   1   0   1 1   1   1   0   1   0   0   1 1   1   0   1   0   0   1   1 1   0   1   0   0   1   1   1 0   1   0   0   1   1   1   1 1   0   0   1   1   1   0   1 Once again, the sequence repeats itself after L shifts. (Here L=7). CODE: AN INTRODUCTION By Dr. Ernest Simo © 1999 DR. ERNEST SIMO - SPACE2000