PN Sequences and Generators
Application: IS-95 uses two PN generators to spread the signal power uniformly over the physical bandwidth of about 1.25 MHz. The PN spreading on the reverse link also provides near-orthogonality of and; hence, minimal interference between, signals from each mobile. This allows universal reuse of the band of frequencies available, which is a major advantage of CDMA and facilitates soft and softer handoffs.
 The flip-flop circuits when used in this way is called a shift register since each clock pulse applied to the flip-flops causes the contents of each flip-flop to be shifted to the right. The feedback connections provide the input to the left-most flip-flop. With N binary stages, the largest number of different patterns the shift register can have is 2N. However, the all-binary-zero state is not allowed because it would cause all remaining states of the shift register and its outputs to be binary zero. The all-binary-ones state does not cause a similar problem of repeated binary ones provided the number of flip-flops input to the module 2 adder is even. The period of the PN sequence is therefore 2N-1, but IS-95 introduces an extra binary zero to achieve a period of 2N, where N equals 15.
Starting with the register in state 001 as shown, the next 7 states are 100, 010, 101, 110, 111, 011, and then 001 again and the states continue to repeat. The output taken from the right-most flip-flop is 1001011 and then repeats. With the three stage shift register shown, the period is 23-1 or 7.
The PN sequence in general has 2N/2 binary ones and [2N/2]-1 binary zeros. As an example, note that the PN sequence 1001011 of period 23-1 contains 4 binary ones and 3 binary zeros. Furthermore, the number of times the binary ones and zeros repeat in groups or runs also appear in the same proportion they would if the PN sequence were actually generated by a coin tossing experiment.
The flip-flops which should be tapped-off and fed into the module 2 adder are determined by an advanced algebra which has identified certain binary polynomials called primitive irreducible or unfactorable polynomials. Such polynomials are used to specify the feedback taps. For example, IS-95 specifies the in-phase PN generator shall be built based on the characteristic polynomial
PI(x) = x15 + x13 + x9 + x8 + x7 + x5 + 1 (1)
Now visualize a 15 stage shift register with the right-most stage numbered zero and the successive stages to the left numbered 1, 2, 3 etc., until the left-most stage is numbered 14. Then the exponents less than 15 in Eq. (1) tell us that stages 0, 5, 7, 8, 9, and 13 should be tapped and summed in a module 2 adder. The output of the adder is then input to the left-most stage. The shift register PN sequence generator is shown below. 
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