Patent Grant
7324428
This invention relates to discrimination between different communication signal frames, using pseudo-noise signals to determine which frame is present.
In certain communication systems that rely upon use of pseudo-noise techniques for signal discrimination, signals are transmitted within each of a sequence of frames, with each frame including a pseudo-noise preamble or post-amble section of a selected length L1 (expressed in bits or symbols) and a data section of length L2. Where the length L1 of the pseudo-noise preamble is greater than the number N1 of distinguishable pseudo-noise signals (each of original length N1), these pseudo-noise signals must be extended to a length L1, in some manner, in order to fill in the remaining bit or symbol spaces.
What is needed in an approach that provides an identification of frame number using a computable value associated with a pseudo-noise signal associated with a preamble (or post-amble) of the frame. Preferably, this approach should provide a unique correspondence between a computable value and a frame id.
These needs are met by the invention, which provides a method and system for determining which frame is present by: (1) receiving two or more consecutive frames and computing overlap functions, OF(m;1) and OF(m;2) (e.g., correlation functions), for each of the frame preambles or post-ambles with a reference signal, where m is an offset index or integer; (2) determining the location (“phase”) of the maximum amplitude of OF(m;k) (k=1, 2) as the index m is varied; (3) forming a pth-order difference of the phases (p≧1); and (4) using the pth-order phase difference to determine a (unique) frame number that corresponds to the pth-order difference. The pth order difference can be defined in several ways to provide a unique correspondence with frame number.
A communication signal, as received and analyzed according to the invention, includes a sequence of N1 consecutive frames fn, numbered n=0, 1, 2, . . . , N1-2, N1-1, with frame numbers being repeated periodically where required, as shown in
In one embodiment of the invention, each pseudo-noise preamble PN(t;n) consists of a sequence of values (+1 or −1) and is optionally a time shifted replica of any other pseudo-noise preamble PN(t;n′) in the ensemble of pseudo-noise signals of length N1; each augmented preamble is periodic;
PN(t;n)=PN(t+Δt(n;m);m), (1)
Here the time shift value Δt(n;m) is a selected number of units that may depend upon the indices m and n. More generally, PN(t;n) need not be a time-shifted replica of PN(t;m), and the relationship is more complex. An overlap function, such as a correlation function,
C(n;m)=∫PN(t;n) PN(t;n+m)dt (m=0, ±1, ±2, . . . ), (2)
computed over a selected interval for any pair of pseudo-noise signals, PN(t;n) and P(t;n+m), behaves approximately as illustrated in
Because the number N1 (and thus length) of a PN signal used is less than the length L1 of the designated preamble, the quantity C(n;m) will have a main peak of amplitude C(max) and one or two subsidiary peaks of lesser amplitude, as indicated in
When two or more consecutive frames as received, the designated preamble PRE(t;m) for each frame is used to compute overlap functions
OF(m;k)=∫PRE(t;m) MS(t;k) dt (k=1, 2, . . . , N1′) (3)
over a discrete range, such as −[(N1)/2]int≦m≦[(N1+1)/2]int, over a corresponding continuous range, or over a selected sub-range for the N1 designated preamble signals, where MS(t;k) is a known m-sequence signal and k=1, . . . , N1 is an index that may represent a shift or translation of a single m-sequence, or {MS(t;k)} may be a collection of different m-sequences. If each of the designated preamble signals PRE(t;m) is a PN signal, each of the overlap functions will behave as illustrated in
C(peak)>Cthr=w·C(max;sub)+(1−w)·C)max;red), (4)
where w is a selected real number satisfying 0≦w≦1. This optional approach again ensures that only the maximum peak amplitude, and its corresponding phase, will be identified.
Each of the locations, m=mc(1) and m=mc(2), of the maximum peaks for the overlap functions, OF(m;k) and OF(m+1;k), of two or more consecutive frames has an associated phase φ(m), an integer or other index that ranges from −63++63 and generally has two different frames (e.g., nos 51 and 201, each with phase φ(m)=−26) that correspond to the same phase. Table 1 sets forth phases and phase differences associated with each of the 253 frames. Thus, an individual phase φ(m) cannot be used as a unique identifier for the unknown frame number m. However, a first-order phase difference
Δ1(m)=φ(m+1)−φ(m) (5)
also set forth in Table 1, varies from 0 to +126 and from −1 to −126 and is unique, if not monotonic, for each of the 253 frames.
Thus, Δ1(m) can be computed and compared against a table or data base to determine the frame number m. If Δ1(m) is negative, the frame number is odd (e.g., 1, 3, 5, . . . , 251); and if Δ1(m) is positive, the frame number is even. The frame number itself can be determined from the following:
1≦Δ1(m)≦126 and even: m=Δ1(m);
1≦Δ1(m)≦125 and odd: m=253−Δ1(m);
−126≦Δ1(m)≦−2 and even: m=253+Δ1(m);
−125≦Δ1(m)≦−1 and odd: m=−Δ1(m). (6)
Equation (6( can be expressed here as an inverse mapping m=F{Δ1(m)}.
From Table 1, one verifies that the first-order phase sums satisfy
Σ1(m)=φ(m+1)=±1, (7)
and the values +1 and −1 should alternate as m increases. These constraints can be used to check for consistency in the phases φ(m), where φ(m) is allowed to have integer and non-integer values. For example, the peaks of three consecutive overlap functions, OF(m;k) and OF(m+1;k) and OF(m+2;k) (k=unknown frame no. =1, 2, . . . ), may appear to occur at non-integer values m=m′ and m=m″ and m=m′″, such as φ(m)=6. 9 and φ(m″)=−7.4 and φ(m′″)=8.7. As a first approach, one might re-assign the indices to nearest-integer values, φ(m′)→7, φ(m″)→−7 and φ(m′″)→9. However, the sums become
Σ1(m)=φ(m′)+φ(m″)=0, (8A)
Σ1(m)=φ(m″)+φ(m′″)=+2, (8B)
each of which is clearly inconsistent with the constraints set forth in Eq. (10). One method of avoiding these inconsistencies is to (re)assign φ(m″)=−8, whereby the sums become
Σ1(m)=φ(m′)+φ(m″)=−1, (9A)
Σ1(m)=φ(m″)+φ(m′″)=+1, (9B)
which is consistent with Eq. (10). If each of two consecutive sums, Σ1(m) and Σ1(m+1), does not satisfy the constraint in Eq. (7), adjustment of the reassigned phase value φ(m+1) may satisfy each of the corresponding constraints.
Other phase differences Δn(m) may or may not provide a unique correspondence with frame number. For example, the second-order phase different
does not provide a unique correspondence because, for example
Δ2(m=124)=Δ2(m=126)=251. (11)
This is also true for the fourth-order phase difference
Δ4(m)=φ(m+4)−4φ(m+3)+6φ(m+2)+4φ(m+1)+φ(m), (12)
where, for example,
Δ4(m=122)=Δ4(m=126)=−988. (13)
However, the third order phase difference, defined by
Δ3(m)=φ(m+3)−3φ(m+2)+3φ(m+1)−φ(m), (14)
does provide a unique correspondence with frame number m. It is postulated here that a Qth-order phase difference (Q≧2), defined as
does provide a unique correspondence with frame number (only) for odd integers Q. More generally, a suitably weighted linear combination, such as
LC(m)=Δ1(m)±0.5·Δ2(m)±0.25·Δ3(m)±0.125·Δ4(m) (16)
can provide a unique correspondence, because the pair of indices at which Δ2(m) is not unique and the pair of indices at which Δ4(m) is not unique, do not coincide. More generally, a linear combination such as
may provide a unique correspondence, where at least one coefficient c(p) is non-zero. In particular, a linear combination LC(m) for which
c(1)=1, (18A)
c(p+1)/c(p)≦0.5 (p=1, . . . , P−1), (18B)
provides a unique correspondence.
| Number | Name | Date | Kind |
|---|---|---|---|
| 5444697 | Leung et al. | Aug 1995 | A |
| 6151295 | Ma et al. | Nov 2000 | A |
| 6671284 | Yonge et al. | Dec 2003 | B1 |
