# Patent

## Title
Frame identifier

## Abstract

Method and system for determining the number of one or more of a sequence of M+1 consecutive OFDM frames from analysis of the designated preambles of two or more consecutive frames (m=0, 1, . . . , M; M≧1). An overlap function OF(m;k) is formed for each frame with a sequence of selected reference signals indexed by k (k=1, 2, . . . , K), dependent upon the frame number m and the index k, and a phase (sequence location corresponding to largest amplitude of overlap function) is determined. An Mth-order phase difference is computed that corresponds to frame number of one of the M+1 frames. A consistency check is provided for the phase numbers.

## Background
FIELD OF THE INVENTION
This invention relates to discrimination between different communication signal frames, using pseudo-noise signals to determine which frame is present.
BACKGROUND OF THE INVENTION
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.
SUMMARY OF THE INVENTION
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.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates a sequence of N1 consecutive frames used in the invention
FIG. 2 illustrates two major components of a frame, with component lengths L1, and M1, processed by the invention.
FIG. 3 is a graphical view of an correlation or overlap function computed from a basic pseudo-noise signal used in the invention.
FIGS. 4A, 4B and 4C are graphical views of correlation function maxima computed using different index values.
FIG. 5 graphically illustrates how overlap functions for two consecutive frame preambles would appear.



DESCRIPTION OF BEST MODES OF THE INVENTION
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 FIG. 1. Each frame fn includes a pseudo-noise preamble or post-amble PN(t;n) (referred to collectively as a “designated pre-amble” herein) of length N1 bits or symbols (“units”), followed by or preceded by an OFDM sequence OFDM(t;n) that includes data that are being transmitted, as illustrated in FIG. 2. In one embodiment of the invention, discussed here as an example, N1=253, N1′ (=min value ≧N1 of form 2P1)=255, L1=378 and M1=3780.
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 FIG. 3: (1) small negative (or positive values) of C(n,m), except within a small band of indices m given by mc1≦m≦mc2; (2) C(n,m) rising monotonically, but not necessarily linearly, to a sharply defined peak as m increases to a central value, m→mc; (3) C(n,m) decreasing monotonically, but not necessarily linearly, to small negative (or positive) values as m increases, beyond mc, with m→mc2, with mc1>mc>mc2. Optionally, the correlation function C(n;m) is periodic in the index m, with period equal to N1 or related to N1.

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 FIGS. 4A, 4B and 4C. Except for effects of the presence of noise, one peak will always have an amplitude equal to C(max) and each of the other (subsidiary) peaks will have a reduced amplitude, no larger than C(max;sub) (<C(max)).
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 FIG. 3, as a function of the unknown frame index m, and each overlap function OF(m;k) will have a maximum peak value and a corresponding peak value location or phase, m=mc(k).

FIG. 5 graphically illustrates how the overlap functions OF(m;k) would appear in a preferred embodiment in which the correlation function in FIG. 3 is linear in the region mc1≦mc2 for each such function. Each overlap function will manifest a main peak, of height approximately equal to C(max), and one or two subsidiary peaks or lesser amplitude with maximum peak value(s) C(max;sub)<C(max). Ideally, the main peak will have the value C(max), except for the presence of noise, where the main peak may have a reduced value, at least equal to C(max;red), with C(max;sub)<C(max;red)<C(max). Optionally, the system applies a threshold criterion and determines only the location of any main peak whose amplitude C(peak) satisfies

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




  
    
      
        
          
            
              
                
                  Δ
                  2
                
                ⁡
                
                  (
                  m
                  )
                
              
              =
              
              ⁢
              
                
                  
                    Δ
                    1
                  
                  ⁡
                  
                    (
                    
                      m
                      +
                      1
                    
                    )
                  
                
                -
                
                  
                    Δ
                    1
                  
                  ⁡
                  
                    (
                    m
                    )
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  φ
                  ⁡
                  
                    (
                    
                      m
                      +
                      2
                    
                    )
                  
                
                -
                
                  2
                  ⁢
                  
                    φ
                    ⁡
                    
                      (
                      
                        m
                        +
                        1
                      
                      )
                    
                  
                
                +
                
                  φ
                  ⁡
                  
                    (
                    m
                    )
                  
                
              
            
          
        
      
    
    
      
        (
        10
        )
      
    
  




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





  
    
      
        
          
            
              Δ
              ⁢
              
                
              
            
            Q
          
          ⁢
          
            (
            m
            )
          
        
        =
        
          
            ∑
            
              q
              =
              0
            
            Q
          
          ⁢
          
            
          
          ⁢
          
            
              (
              -
              )
            
            ⁢
            q
            ⁢
            
              {
              
                
                  
                    Q
                    !
                  
                  /
                  
                    
                      (
                      
                        Q
                        -
                        q
                      
                      )
                    
                    !
                  
                
                ⁢
                
                  q
                  !
                
              
              }
            
            ⁢
            
              
                φ
                ⁡
                
                  (
                  
                    m
                    +
                    q
                  
                  )
                
              
              .
            
          
        
      
    
    
      
        (
        15
        )
      
    
  




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





  
    
      
        
          LC
          ⁡
          
            (
            m
            )
          
        
        =
        
          
            ∑
            
              p
              =
              1
            
            P
          
          ⁢
          
            
          
          ⁢
          
            
              c
              ⁡
              
                (
                p
                )
              
            
            ⁢
            
              
                Δ
                p
              
              ⁡
              
                (
                m
                )
              
            
            ⁢
            
              
            
            ⁢
            
              (
              
                P
                ≥
                2
              
              )
            
          
        
      
    
    
      
        (
        17
        )
      
    
  




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.








TABLE 1







Frame Numbers; Phases; Phase Differences














Frame No.
φ(m)
Δ1(m)
Δ2(m)
Δ3(m)
Δ4(m)


















0
0
0
−1
4
−12



1
−1
−1
3
−8
20



2
1
2
−5
12
−28



3
−2
−3
7
−16
36



4
2
4
−9
20
−44



5
−3
−5
11
−24
52



6
3
6
−13
28
−60



7
−4
−7
15
−32
68



8
4
8
−17
36
−76



9
−5
−9
19
−40
84



10
5
10
−21
44
−92



11
−6
−11
23
−48
100



12
6
12
−25
52
−108



13
−7
−13
27
−56
116



14
7
14
−29
60
−124



15
−8
−15
31
−64
132



16
8
16
−33
68
−140



17
−9
−17
35
−72
148



18
9
18
−37
76
−156



19
−10
−19
39
−80
164



20
10
20
−41
84
−172



21
−11
−21
43
−88
180



22
11
22
−45
92
−188



23
−12
−23
47
−96
196



24
12
24
−49
100
−204



25
−13
−25
51
−104
212



26
13
26
−53
108
−220



27
−14
−27
55
−112
228



28
14
28
−57
116
−236



29
−15
−29
59
−120
244



30
15
30
−61
124
−252



31
−16
−31
63
−128
260



32
16
32
−65
132
−268



33
−17
−33
67
−136
276



34
17
34
−69
140
−284



35
−18
−35
71
−144
292



36
18
36
−73
148
−300



37
−19
−37
75
−152
308



38
19
38
−77
156
−316



39
−20
−39
79
−160
324



40
20
40
−81
164
−332



41
−21
−41
83
−168
340



42
21
42
−85
172
−348



43
−22
−43
87
−176
356



44
22
44
−89
180
−364



45
−23
−45
91
−184
372



46
23
46
−93
188
−380



47
−24
−47
95
−192
388



48
24
48
−97
196
−396



49
−25
−49
99
−200
404



50
25
50
−101
204
−412



51
−26
−51
103
−208
420



52
26
52
−105
212
−428



53
−27
−53
107
−216
436



54
27
54
−109
220
−444



55
−28
−55
111
−224
452



56
28
56
−113
228
−460



57
−29
−57
115
−232
468



58
29
58
−117
236
−476



59
−30
−59
119
−240
484



60
30
60
−121
244
−492



61
−31
−61
123
−248
500



62
31
62
−125
252
−508



63
−32
−63
127
−256
516



64
32
64
−129
260
−524



65
−33
−65
131
−264
532



66
33
66
−133
268
−540



67
−34
−67
135
−272
548



68
34
68
−137
276
−556



69
−35
−69
139
−280
564



70
35
70
−141
284
−572



71
−36
−71
143
−288
580



72
36
72
−145
292
−588



73
−37
−73
147
−296
596



74
37
74
−149
300
−604



75
−38
−75
151
−304
612



76
38
76
−153
308
−620



77
−39
−77
135
−312
628



78
39
78
−157
316
−636



79
−40
−79
159
−320
644



80
40
80
−161
324
−652



81
−41
−81
163
−328
660



82
41
82
−165
332
−668



83
−42
−83
167
−336
676



84
42
84
−169
340
−684



85
−43
−85
171
−344
692



86
43
86
−173
348
−700



87
−44
−87
175
−352
708



88
44
88
−177
356
−716



89
−45
−89
179
−360
724



90
45
90
−181
364
−732



91
−46
−91
183
−368
740



92
46
92
−185
372
−748



93
−47
−93
187
−376
756



94
47
94
−189
380
−764



95
−48
−95
191
−384
772



96
48
96
−193
388
−780



97
−49
−97
195
−392
788



98
49
98
−197
396
−796



99
−50
−99
199
−400
804



100
50
100
−201
404
−812



101
−51
−101
203
−408
820



102
51
102
−205
412
−828



103
−52
−103
207
−416
836



104
52
104
−209
420
−844



105
−53
−105
211
−424
852



106
53
106
−213
428
−860



107
−54
−107
215
−432
868



108
54
108
−217
436
−876



109
−55
−109
219
−440
884



110
55
110
−221
444
−892



111
−56
−111
223
−448
900



112
56
112
−225
452
−908



113
−57
−113
227
−456
916



114
57
114
−229
460
−924



115
−58
−115
231
−464
932



116
58
116
−233
468
−940



117
−59
−117
235
−472
948



118
59
118
−237
476
−956



119
−60
−119
239
−480
964



120
60
120
−241
484
−972



121
−61
−121
243
−488
980



122
61
122
−245
492
−988



123
−62
−123
247
−496
996



124
62
124
−249
500
−1003



125
−63
−125
251
−503
1006



126
63
126
−252
503
−1003



127
−63
−126
251
−500
996



128
62
125
−249
496
−988



129
−62
−124
247
−492
980



130
61
123
−245
488
−972



131
−61
−122
243
−484
964



132
60
121
−241
480
−956



133
−60
−120
239
−476
948



134
59
119
−237
472
−940



135
−59
−118
235
−468
932



136
58
117
−233
464
−924



137
−58
−116
231
−460
916



138
57
115
−229
456
−908



139
−57
−114
227
−452
900



140
56
113
−225
448
−892



141
−56
−112
223
−444
884



142
55
111
−221
440
−876



143
−55
−110
219
−436
868



144
54
109
−217
432
−860



145
−54
−108
215
−428
852



146
53
107
−213
424
−844



147
−53
−106
211
−420
836



148
52
105
−209
416
−828



149
−52
−104
207
−412
820



150
51
103
−205
408
−812



151
−51
−102
203
−404
804



152
50
101
−201
400
−796



153
−50
−100
199
−396
788



154
49
99
−197
392
−780



155
−49
−98
195
−388
772



156
48
97
−193
384
−764



157
−48
−96
191
−380
756



158
47
95
−189
376
−748



159
−47
−94
187
−372
740



160
46
93
−185
368
−732



161
−46
−92
183
−364
724



162
45
91
−181
360
−716



163
−45
−90
179
−356
708



164
44
89
−177
352
−700



165
−44
−88
175
−348
692



166
43
87
−173
344
−684



167
−43
−86
171
−340
676



168
42
85
−169
336
−668



169
−42
−84
167
−332
660



170
41
83
−165
328
−652



171
−41
−82
163
−324
644



172
40
81
−161
320
−636



173
−40
−80
159
−316
628



174
39
79
−157
312
−620



175
−39
−78
155
−308
612



176
38
77
−153
304
−604



177
−38
−76
151
−300
596



178
37
75
−149
296
−588



179
−37
−74
147
−292
580



180
36
73
−145
288
−572



181
−36
−72
143
−284
564



182
35
71
−141
280
−556



183
−35
−70
139
−276
548



184
34
69
−137
272
−540



185
−34
−68
135
−268
532



186
33
67
−133
264
−524



187
−33
−66
131
−260
516



188
32
65
−129
256
−508



189
−32
−64
127
−252
500



190
31
63
−125
248
−492



191
−31
−62
123
−244
484



192
30
61
−121
240
−476



193
−30
−60
119
−236
468



194
29
59
−117
232
−460



195
−29
−58
115
−228
452



196
28
57
−113
224
−444



197
−28
−56
111
−220
436



198
27
55
−109
216
−428



199
−27
−54
107
−212
420



200
26
53
−105
208
−412



201
−26
−52
103
−204
404



202
25
51
−101
200
−396



203
−25
−50
99
−196
388



204
24
49
−97
192
−380



205
−24
−48
95
−188
372



206
23
47
−93
184
−364



207
−23
−46
91
−180
356



208
22
45
−89
176
−348



209
−22
−44
87
−172
340



210
21
43
−85
168
−332



211
−21
−42
83
−164
324



212
20
41
−81
160
−316



213
−20
−40
79
−156
308



214
19
39
−77
152
−300



215
−19
−38
75
−148
292



216
18
37
−73
144
−284



217
−18
−36
71
−140
276



218
17
35
−69
136
−268



219
−17
−34
67
−132
260



220
16
33
−65
128
−252



221
−16
−32
63
−124
244



222
15
31
−61
120
−236



223
−15
−30
59
−116
228



224
14
29
−57
112
−220



225
−14
−28
55
−108
212



226
13
27
−53
104
−204



227
−13
−26
51
−100
196



228
12
25
−49
96
−188



229
−12
−24
47
−92
180



230
11
23
−45
88
−172



231
−11
−22
43
−84
164



232
10
21
−41
80
−156



233
−10
−20
39
−76
148



234
9
19
−37
72
−140



235
−9
−18
35
−68
132



236
8
17
−33
64
−124



237
−8
−16
31
−60
116



238
7
15
−29
56
−108



239
−7
−14
27
−52
100



240
6
13
−25
48
−92



241
−6
−12
23
−44
84



242
5
11
−21
40
−76



243
−5
−10
19
−36
68



244
4
9
−17
32
−60



245
−4
−8
15
−28
52



246
3
7
−13
24
−44



247
−3
−6
11
−20
36



248
2
5
−9
16
−28



249
−2
−4
7
−12
20



250
1
3
−5
8
−12



251
−1
−2
3
−4
4



252
0
1
−1
0
4

## Claims

1. A method for determining a number of a frame in a sequence of two or more frames, the method comprising:
receiving a sequence of at least M+1 consecutive OFDM frames, each frame having an index m, having a designated preamble wherein the designated preamble has a selected length N1 and an associated pseudo-noise signal PN(t;m) (m=0, . . . , M; M≧1);
providing an overlap function OF(m;k) of the designated preambles with each of a sequence of selected reference signals, indexed by k=1, 2, . . . , K where K is a selected integer, and determining a phase φ(m) corresponding to a location of a maximum amplitude of the overlap functions OF(m;k) for each of the M+1 designated preambles of the sequence of at least M+1 consecutive OFDM frames;
forming a selected pth order phase difference of the phases φ(m); and
comparing the pth order difference with a selected table of pth order phase differences to determine a frame number of at least one frame of M+1 consecutive OFDM frames, the frame number uniquely identifying the at least one frame in the M+1 consecutive OFDM frames.

2. The method of claim 1, further comprising choosing p=1 and choosing said first-order phase difference to be Δ1(m)=φ(m+1)−φ(m).

3. The method of claim 1, further comprising choosing p=3 and choosing said third-order phase difference to be Δ3(m)=φ(m+3)−3φ(m+2)+3φ(m+1)−φ(m).

4. The method of claim 1, further comprising choosing p to be an odd integer.

5. The method of claim 1, further comprising forming a linear combination


P



LC(m)=Σc(p)·Δp(m)(P≧2)



p=1


where c(p) are selected coefficients, at least one of which is non-zero; and
comparing the linear combination value LC(m) with a selected table of linear combination values to determine a frame number of at least one of the M+1 frames.

6. The method of claim 1, further comprising providing at least two of said pseudo-noise signals, PN(t;m1) and PN(t;m2), as translations of each other through a relation PN(t;m2)=PN(t+Δt(m1,m2)m1), where Δt(m1,m2) is a selected time difference depending upon at least one of said indices m1 and m2.

7. The method of claim 1, further comprising
computing a first order sum Σ1(m=φ(m+1)+φ(m) for at least one index number m; and
when the sum Σ1(m) is not equal to at least one of the numbers +1 and −1, adjusting a value of at least said phases φ(m) and φ(m+1) so that the sum Σ1(m) is equal to one of the numbers +1 and −1.

8. The method of claim 1, further comprising choosing at least one of said selected reference signals to be an m-sequence.