Method for calculating the PN generator mask to obtain a...

Details Method for calculating the PN generator mask to obtain a... Method for calculating the PN generator mask to obtain a...

1999-09-14

2003-04-29

Olms, Douglas (Department: 2732)

Multiplex communications

Communication over free space

Having a plurality of contiguous regions served by...

C370S203000

Reexamination Certificate

active

06556555

ABSTRACT:

BACKGROUND OF THE INVENTION
In a code division multiple access (CDMA) cellular telephone system, the different forward and reverse link transmitter waveforms are modulated by unique pseudorandom noise (PN) code sequences that provide identification of the base stations for the forward link and identification of the mobile stations for the reverse link. The PN code sequence that is uniquely assigned to a transmitter (base station or mobile station) is a different phase shift (offset) of a reference sequence, as illustrated in
FIG. 1
(numeral
100
). In
FIG. 1
, each of the base stations (denoted as having offsets A, B, C, D, E, F, and G) transmits signals modulated by PN code
1
with a unique assigned offset, and each mobile station (denoted as having offsets a, b, c, . . . , q, r) transmits signals modulated by PN code
2
with a unique assigned offset. The present invention discloses a method of generating these unique assigned offsets of any PN code relative to a given reference sequence.
It is well known in the literature, as in
CDAM Systems Engineering Handbook
, that periodic binary PN sequences are generated using linear feedback shift registers (LFSRs). There are two basic LFSR configurations: the “simple shift register generator” (SSRG) and the “modular shift register generator” (MSRG). Diagrams of these two LFSR configurations for n-stage shift registers are shown as
201
and
301
in
FIGS. 2 and 3
, respectively, in which the coefficients {c
i
, i=1, 2, . . . , n−1} assume, values 0 or 1 and indicate the feedback connections necessary for each configuration to produce at the output of the LFSR (
203
or
303
) some shift of the sequence described by the PN sequence-generating characteristic polynomial
f(x)=1
+c
1
x+c
2
x
2
+c
3
x
3
+ . . . +c
n−1
x
n−1
+x
n
, c
i
=0 or 1  (1a)
where, as described in the book
Shift Register Sequences
, the polynomial represents the recursion or the successive 0 or 1 valued outputs of the register, {a
k
}, given by
a
k
=c
1
a
k−1
+c
2
a
k−2
+ . . . +c
n−1
a
k−n+1
+a
k−n
, c
i
=0 or 1  (1b)
The output sequence from the LFSR can be denoted a
0
, a
1
, a
2
, . . . , and this sequence can be represented as a polynomial, a(x), that is,
a
0
, a
1
, a
2
, . . . ⇄a(x)=a
0
+a
1
x+a
2
x+ . . .   (1c)
It is also described in
CDMA Systems Engineering Handbook
, that the power series for output sequence a(x) is obtained by dividing a binary polynomial, g(x), of degree less than n, by the characteristic polynomial, f(x), of degree n:
a
⁢
(
x
)
=
g
⁢
(
x
)
f
⁢
(
x
)
,
 g(x)=g
0
+g
1
x+g
2
x
2
+ . . . +g
n−1
x
n−1
, g
i
=0 or 1  (1d)
Excluding the case of g(x)=0, there are 2
n
−1 possible numerator polynomials of degree less than n. For a PN sequence, which has period P=2
n
−1, each of the possible numerator polynomials corresponds uniquely to one of the possible “phase shifts” for the periodic sequence, and each one corresponds uniquely to one of the nonzero initial loadings of the LFSR. The terms of the sequence a(x) can be calculated by “long division,” given g(x). When the numerator polynomial is g(x)=1, the resulting sequence of 1/f(x) is the reference sequence for the PN code. The phase shifts of the PN sequence are measured with respect to this reference sequence.
For example, let the characteristic polynomial of a PN sequence be f(x)=1+x+x
3
and consider two cases of the numerator polynomial, g(x)=1+x and g(x)=1. By long division for case of g(x)=1+x we find that
a
⁡
(
x
)
=
1
+
x
1
+
x
+
x
3
=
1
+
x
3
+
x
4
+
x
5
+
x
7
+
x
10
+
x
11
+
x
12
⁢
…
→
(
1
,
0
,
0
,
1
,
1
,
1
,
0
)
,
(
1
,
0
,
0
,
1
,
1
,
1
,
0
)
,
(
1
,
1
,
1
,
0
,
1
,
0
,
0
)
,
(
1
,
0
,
…
)
,
…
(1e)
in which the parentheses are used to indicate periods of the sequence having P=2
n
−1=7 bits since n=3. For the case of g(x)=1, the long division becomes the reference sequence:
a
⁡
(
x
)
=
1
1
+
x
+
x
3
=
1
+
x
+
x
2
+
x
4
+
x
7
+
x
8
+
x
9
+
x
11
⁢
…
→
(
1
,
1
,
1
,
0
,
1
,
0
,
0
)
,
(
1
,
1
,
…
)
,
…
(1f)
In this example, the sequence for numerator polynomial g(x)=1+x is shifted three bits to the right compared to the reference sequence. The number of bits shifted is predicted from g(x) when it is expressed as a power of x, reduced to a polynomial of degree less than n by the modular calculation, denoted “modulo f(x)” (or sometimes “mod f(x)” for short) given by
g(x)=x
3
modulo f(x)=x
3
modulo (1+x+x
3
)=1+x  (2a)
The power of x in the expression x
3
modulo f(x) denotes the number of bits being shifted relative to the reference sequence of 1/f(x). It is now established that a given sequence can always be represented by either a power of x or by a polynomial.
The initial state of the shift register contents in
FIGS. 2 and 3
is denoted by the vector (R
1
, R
2
, . . . , R
n
), which is also represented as the polynomial s
0
(x), as follows:
(R
1, R
2
, . . . , R
n
)⇄s
0
(x)=R
1
+R
2
x+R
3
x
2
+ . . . +R
n
x
n−1
, R
i
=0 or 1  (2b)
Implied but not shown in
FIGS. 2 and 3
are connections for various timing and control signals, such as the clock pulses that control the advancement of the LFSR's shift register.
Elements
202
and
302
of
FIGS. 2 and 3
show the outputs of the shift register stages being selectively modulo-2 added in the phase shift networks (PSNs), with the selection determined by the “mask” vector (m
0
, m
1
, . . . , m
n−1
), where each component takes the values 0 or 1. As described in
Shift Register Sequences
, the bit-by-bit modulo-2 addition of two or more sequences that are different shifts of a PN sequence produces another shift of the sequence at the output of the PSN (
204
or
304
).
The prior art regarding PN code masks includes U.S. Pat. Nos. 4,460,992; 5,103,459; 5,416,797; and 5,737,329 which describe means which are disclosed for implementing CDMA communications systems in which transmissions to or from several mobile receivers are multiplexed using PN codes that are shifts of the same PN code sequence. In these patents, the shifts are obtained using masks. However, these patents do not describe how the masks are calculated. U.S. Pat. Nos. 5,228,054 and 5,532,695 describe means for making PN code masks work in conjunction with the lengthening of the sequence by insertion, but also do not indicate how the masks are calculated and implemented. In the system disclosed in U.S. Pat. No. 5,034,906, delayed PN sequences are obtained by timing techniques rather than masks. In the system disclosed in U.S. Pat. No. 5,519,736, a master PN sequence generated by an MSRG is modified by feed-forward circuits and stored masks to produce N modified versions of the master PN sequence for CDMA multiplexing, but the method for determining the masks and the feed-forward circuit connections is not disclosed.
The relationship between the sequence at the input of an SSRG and the sequence at the output of a PSN for a special LFSR loading was recognized in a paper by W. A. Davis, entitled “Automatic delay changing facility for delayed m-sequences” (
Proc. IEEE
, June 1966), which suggested using an MSRG to calculate the mask for the special case of the loading. Also, in the book
Direct Sequence Spread Spectrum Techniques
, it is noted that a particular mask causes the sequence at the output of the PSN to be delayed k bits from the sequence at the input of the SSRG for any sequence shift at the input.
Regarding the algebra of PN code masks, for both the SSRG and the MSRG implementations of a PN sequence, the particular phase of the sequence at the output of the shift

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