Unambiguous Processing Techniques of Binary Offset Carrier Modulated Signals - Global Navigation Satellite Systems: Signal,Theory and Applications - page 68

positive values could pass the threshold). In consideration of the shape of BOC ACF, it is
desirable that the envelop of R B/L be zigzag and symmetric with respect to τ= . Moreover, 0

( )

2
B/L R should be zero in order to ensure that the magnitude of main peak is unaffected
after the subtracting.

As explained in the previous section, the above constraints of the CCF shape can be
translated into the restriction on r via (19). The constraint

( )

R

2
B/L 00

= is equivalent to

r = 0 (24)

0

and the axial symmetry of R means

B/L

r = r − (25)

i i

The requirement of zigzag shape can be realized through making adjacent

r have opposite

sign, that is

rr < 0, i > 0

⎨

(26)

ii + 1

rr < 0, i < 0

⎩

ii − 1

Actually, under the restrictions of (24) and (26), (25) can be simplified to

r = − r − (27)

i i

because by (20) and (24) we have

M /2 − 1 M /2 − 1

1

∑

()

i

∑

()

i − M /2

r + r = − 1 d + − 1 d

M /2 − M /2 i + M /2 i

M

i = 0 i = 0

1 ⎛

M /2 − 1 M − 1

⎞

∑∑

()

iM − /2

(28)

= + − 1 d

⎜ ⎟ i

M

⎝ ⎠

i = 0 i = M /2

1

M − 1

∑

()

i

= − 1 dr = = 0

i 0

M

i = 0

so that r =− r − . Then using (26), we obtain (27).

M /2 M /2

5.3 Step 3 - UVS establishment

Substituting (20) into (24), (26) and (27), after some straightforward algebraic simplification,
we have the set of inequalities constraints on the elements of

d :

⎧

k

∑

()

i

− 1 d > 0, k = 0, 1, ,

M

− 1

⎪

i 2

i = 0

(29)

dd = , k = 0, 1, ,

M

− 1

⎨
⎪

k Mk −− 1

2

M − 1

∑

dM

2

=

i

⎩

i = 0

Note that the last term in (29) is the energy normalization constraint of SCS waveform. So
that the UVS can be represented as