
W9310
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To ensure good system performance, the PN sequences and UW must be selected with care.
Guidelines for choosing the PN sequences and UW are presented below.
PN Sequence Selection
The four PN sequences are used to represent a di-bit symbol in the W9310. To ensure the
transmitted symbol is decoded correctly at the receiver, follow the principles below when choosing the
four PN sequences.
1. The four PN sequences should be orthogonal to each other. Two PN sequences A and B are
orthogonal to each other if
a.b
0
i
∑
=
(6)
where PN sequence A = [A31, A30, A29, ..., A1, A0], a1 = -1 for Ai = 0, and ai = 1 for Ai = 1. A similar
relation holds for B.
2. The PN sequences should be even, i.e., each sequence should have the same number of zeros
and ones.
3. The PN sequences should not have more than four consecutive identical bits.
With the three criteria outlined above, it is possible to generate a large set of valid PN sequences.
Two additional and optional criteria can be used to further identify PN sequences for reduced self-
and cross-interference.
1. The auto-correlation side lobes of the PN sequences should be at least 4 less than the auto-
correlation of the main lobe.
2. The cross-correlation of PN sequences between sets (one set being the four orthogonal PN
sequences for one spread spectrum W9310) should also be at least 4 less than the auto-correlation
of the main lobe.
UW Selection
The UW is used in the receiver in full-duplex mode to establish synchronization. To avoid
interference, the UW must be chosen such that it has a good auto-correlation and cross-correlation
properties. The auto-correlation of a sequence A, denoted by S
N
, is defined as
S
a.a
N
i N
=
∑
(7)
where L is the length of the sequence A, -L < N < L, N
≠
0, ai = -1 for i < 0, and ai = ai-22 for i
≥
L. A
"window" version of S
N
can also be defined according to Eq. (7) with the exception that 0 < N < W,
where W is the window size. The desired auto-correlation property is that the maximum value of the
auto-correlation S
N
(with or without the window where the window size is the size of the detection
window, WSL) be less than L - 2
×
T, where T is the allowable number of UW errors programmed into
the W9310.
The cross-correlation of two sequences A and B, denoted by R
N
, is defined as
R
a.b
N
i N
=
∑
(8)