(Updated) preamble for FDMA

A wireless device that distinguishes between multiple piconets, the wireless device comprising:

• a preamble component operable to provide a preamble for a wireless orthogonal frequency division modulation transmission;
• and
• a correlator component operable to distinguish a wireless transmission based on the preamble,
• wherein the preamble component reads the preamble out of a memory area, the preamble further defined as proportional to the following ordered sequence of 128 bi-phase values:
• Sequence Element
• Value
• C1
• 1
• C2
• 1
• C3
• 1
• C4
• −1
• C5
• −1
• C6
• −1
• C7
• 1
• C8
• −1
• C9
• 1
• C10
• 1
• C11
• 1
• C12
• −1
• C13
• −1
• C14
• −1
• C15
• 1
• C16
• −1
• C17
• 1
• C18
• 1
• C19
• 1
• C20
• −1
• C21
• −1
• C22
• −1
• C23
• 1
• C24
• −1
• C25
• −1
• C26
• −1
• C27
• −1
• C28
• 1
• C29
• 1
• C30
• 1
• C31
• −1
• C32
• 1
• C33
• 1
• C34
• 1
• C35
• 1
• C36
• −1
• C37
• −1
• C38
• −1
• C39
• 1
• C40
• −1
• C41
• 1
• C42
• 1
• C43
• 1
• C44
• −1
• C45
• −1
• C46
• −1
• C47
• 1
• C48
• −1
• C49
• 1
• C50
• 1
• C51
• 1
• C52
• −1
• C53
• −1
• C54
• −1
• C55
• 1
• C56
• −1
• C57
• −1
• C58
• −1
• C59
• −1
• C60
• 1
• C61
• 1
• C62
• 1
• C63
• −1
• C64
• 1
• C65
• 1
• C66
• 1
• C67
• 1
• C68
• −1
• C69
• −1
• C70
• −1
• C71
• 1
• C72
• −1
• C73
• −1
• C74
• −1
• C75
• −1
• C76
• 1
• C77
• 1
• C78
• 1
• C79
• −1
• C80
• 1
• C81
• 1
• C82
• 1
• C83
• 1
• C84
• −1
• C85
• −1
• C86
• −1
• C87
• 1
• C88
• −1
• C89
• 1
• C90
• 1
• C91
• 1
• C92
• −1
• C93
• −1
• C94
• −1
• C95
• 1
• C96
• −1
• C97
• −1
• C98
• −1
• C99
• −1
• C100
• 1
• C101
• 1
• C102
• 1
• C103
• −1
• C104
• 1
• C105
• 1
• C106
• 1
• C107
• 1
• C108
• −1
• C109
• −1
• C110
• −1
• C111
• 1
• C112
• −1
• C113
• −1
• C114
• −1
• C115
• −1
• C116
• 1
• C117
• 1
• C118
• 1
• C119
• −1
• C120
• 1
• C121
• −1
• C122
• −1
• C123
• −1
• C124
• 1
• C125
• 1
• C126
• 1
• C127
• −1
• C128
• 1.

A wireless device that distinguishes between multiple piconets, the wireless device comprising:

• a preamble component operable to provide a preamble for a wireless orthogonal frequency division modulation transmission;
• and
• a correlator component operable to distinguish a wireless transmission based on the preamble,
• wherein the preamble component reads the preamble out of a memory area, the preamble formed by transforming an ordered sequence of 128 bi-phase values to enhance a spectral energy density of the preamble, the 128 bi-phase values defined as proportional to:
• Sequence Element
• Value
• C1
• 1
• C2
• 1
• C3
• 1
• C4
• −1
• C5
• −1
• C6
• −1
• C7
• 1
• C8
• −1
• C9
• 1
• C10
• 1
• C11
• 1
• C12
• −1
• C13
• −1
• C14
• −1
• C15
• 1
• C16
• −1
• C17
• 1
• C18
• 1
• C19
• 1
• C20
• −1
• C21
• −1
• C22
• −1
• C23
• 1
• C24
• −1
• C25
• −1
• C26
• −1
• C27
• −1
• C28
• 1
• C29
• 1
• C30
• 1
• C31
• −1
• C32
• 1
• C33
• 1
• C34
• 1
• C35
• 1
• C36
• −1
• C37
• −1
• C38
• −1
• C39
• 1
• C40
• −1
• C41
• 1
• C42
• 1
• C43
• 1
• C44
• −1
• C45
• −1
• C46
• −1
• C47
• 1
• C48
• −1
• C49
• 1
• C50
• 1
• C51
• 1
• C52
• −1
• C53
• −1
• C54
• −1
• C55
• 1
• C56
• −1
• C57
• −1
• C58
• −1
• C59
• −1
• C60
• 1
• C61
• 1
• C62
• 1
• C63
• −1
• C64
• 1
• C65
• 1
• C66
• 1
• C67
• 1
• C68
• −1
• C69
• −1
• C70
• −1
• C71
• 1
• C72
• −1
• C73
• −1
• C74
• −1
• C75
• −1
• C76
• 1
• C77
• 1
• C78
• 1
• C79
• −1
• C80
• 1
• C81
• 1
• C82
• 1
• C83
• 1
• C84
• −1
• C85
• −1
• C86
• −1
• C87
• 1
• C88
• −1
• C89
• 1
• C90
• 1
• C91
• 1
• C92
• −1
• C93
• −1
• C94
• −1
• C95
• 1
• C96
• −1
• C97
• −1
• C98
• −1
• C99
• −1
• C100
• 1
• C101
• 1
• C102
• 1
• C103
• −1
• C104
• 1
• C105
• 1
• C106
• 1
• C107
• 1
• C108
• −1
• C109
• −1
• C110
• −1
• C111
• 1
• C112
• −1
• C113
• −1
• C114
• −1
• C115
• −1
• C116
• 1
• C117
• 1
• C118
• 1
• C119
• −1
• C120
• 1
• C121
• −1
• C122
• −1
• C123
• −1
• C124
• 1
• C125
• 1
• C126
• 1
• C127
• −1
• C128
• 1.

A wireless device that distinguishes between multiple piconets, the wireless device comprising:

• a preamble component operable to provide a preamble for a wireless orthogonal frequency division modulation transmission;
• and
• a correlator component operable to distinguish a wireless transmission based on the preamble,
• wherein the preamble component reads the preamble out of a memory area, the preamble further defined as proportional to the following ordered sequence of 128 values:
• Sequence Element
• Value
• C′1
• 0.9574
• C′2
• 0.5270
• C′3
• 1.5929
• C′4
• −0.2500
• C′5
• −0.2536
• C′6
• −0.3023
• C′7
• 1.2907
• C′8
• −0.4258
• C′9
• 1.0012
• C′10
• 1.7704
• C′11
• 0.8593
• C′12
• −0.3719
• C′13
• −1.3465
• C′14
• −0.7419
• C′15
• 1.5350
• C′16
• −1.2180
• C′17
• 0.6955
• C′18
• 1.7204
• C′19
• 0.1643
• C′20
• −0.3347
• C′21
• −1.7244
• C′22
• −0.7447
• C′23
• 1.1141
• C′24
• −1.3541
• C′25
• −0.7293
• C′26
• 0.2682
• C′27
• −1.2401
• C′28
• 1.0527
• C′29
• 0.1199
• C′30
• 1.1496
• C′31
• −1.0544
• C′32
• 1.3176
• C′33
• 0.8400
• C′34
• 1.3980
• C′35
• 1.1147
• C′36
• −0.4732
• C′37
• −1.7178
• C′38
• −0.8477
• C′39
• 1.5083
• C′40
• −1.4364
• C′41
• 0.3853
• C′42
• 1.5673
• C′43
• 0.0295
• C′44
• −0.4204
• C′45
• −1.4856
• C′46
• −0.8404
• C′47
• 1.0111
• C′48
• −1.4269
• C′49
• 0.3033
• C′50
• 0.7757
• C′51
• −0.1370
• C′52
• −0.5250
• C′53
• −1.1589
• C′54
• −0.8324
• C′55
• 0.6336
• C′56
• −1.2698
• C′57
• −0.7853
• C′58
• −0.7031
• C′59
• −1.1106
• C′60
• 0.6071
• C′61
• 0.7164
• C′62
• 0.8305
• C′63
• −1.2355
• C′64
• 1.1754
• C′65
• 0.5859
• C′66
• 0.3053
• C′67
• 0.2408
• C′68
• −0.6744
• C′69
• −0.2361
• C′70
• −0.8133
• C′71
• 0.9201
• C′72
• −1.0841
• C′73
• −0.8036
• C′74
• −0.3105
• C′75
• −1.0514
• C′76
• 0.7644
• C′77
• 0.7301
• C′78
• 0.9788
• C′79
• −1.1305
• C′80
• 1.3257
• C′81
• 0.7801
• C′82
• 0.7867
• C′83
• 1.0996
• C′84
• −0.5623
• C′85
• −1.2227
• C′86
• −0.8223
• C′87
• 1.2074
• C′88
• −1.2338
• C′89
• 0.2957
• C′90
• 1.0999
• C′91
• −0.0201
• C′92
• −0.5194
• C′93
• −1.2284
• C′94
• −0.9215
• C′95
• 0.7941
• C′96
• −1.4128
• C′97
• −0.8528
• C′98
• −0.6973
• C′99
• −1.2477
• C′100
• 0.6246
• C′101
• 0.7687
• C′102
• 0.7966
• C′103
• −1.2809
• C′104
• 1.1023
• C′105
• 0.4250
• C′106
• −0.1614
• C′107
• 0.7547
• C′108
• −0.6696
• C′109
• −0.3920
• C′110
• −0.7589
• C′111
• 0.6701
• C′112
• −0.9381
• C′113
• −0.7483
• C′114
• −0.9659
• C′115
• −0.9192
• C′116
• 0.3925
• C′117
• 1.2864
• C′118
• 0.6784
• C′119
• −1.0909
• C′120
• 1.1140
• C′121
• −0.6134
• C′122
• −1.5467
• C′123
• −0.3031
• C′124
• 0.9457
• C′125
• 1.9645
• C′126
• 1.4549
• C′127
• −1.2760
• C′128
• 2.2102.

A wireless device that distinguishes between multiple piconets, the wireless device comprising:

• a preamble component operable to provide a preamble for a wireless orthogonal frequency division modulation transmission;
• and
• a correlator component operable to distinguish a wireless transmission based on the preamble,
• wherein the preamble component forms the preamble as a 128-length sequence by spreading a first sequence of 16 ordered bi-phase values with a second sequence of 8 ordered bi-phase values, the first sequence specified as proportional to:
• a1
• a2
• a3
• a4
• a5
• a6
• a7
• a8
• a9
• a10
• a11
• a12
• a13
• a14
• a15
• a16
• 1
• 1
• 1
• −1
• 1
• 1
• 1
• −1
• 1
• −1
• 1
• 1
• −1
• 1
• −1
• −1
• and the second sequence specified as proportional to:
• b1
• b2
• b3
• b4
• b5
• b6
• b7
• b8
• 1
• 1
• 1
• −1
• −1
• −1
• 1
• −1.

A wireless device that distinguishes between multiple piconets, the wireless device comprising:

• a preamble component operable to provide a preamble for a wireless orthogonal frequency division modulation transmission;
• and
• a correlator component operable to distinguish a wireless transmission based on the preamble,
• wherein the correlator component comprises a first spreader and a second spreader, and distinguishes the wireless transmission containing the preamble by spreading at least a portion of the wireless transmission with a first sequence of ordered bi-phase values through the first spreader, and by spreading the output of the first spreader with a second sequence of ordered bi-phase values through the second spreader, the output of the second spreader providing an indication of the presence of the preamble in the wireless transmission, the first sequence specified as proportional to:
• b1
• b2
• b3
• b4
• b5
• b6
• b7
• b8
• 1
• 1
• 1
• −1
• −1
• −1
• 1
• −1
• and the second sequence specified as proportional to:
• a1
• a2
• a3
• a4
• a5
• a6
• a7
• a8
• a9
• a10
• a11
• a12
• a13
• a14
• a15
• a16
• 1
• 1
• 1
• −1
• 1
• 1
• 1
• −1
• 1
• −1
• 1
• 1
• −1
• 1
• −1
• −1.

A method for determining a K-length wireless message preamble for a fixed frequency interleaving piconet, comprising:

• identifying K-length hierarchical sequences having a zero mean;
• identifying K-length hierarchical sequences having first side lobes of an autocorrelation less than a first threshold;
• calculating a cross-correlation for K-length hierarchical sequences with other time frequency interleaved preambles;
• and
• selecting a K-length hierarchical sequence having the autocorrelation greater than a second threshold, a cross-correlation with other time frequency interleaved preambles less than a third threshold, zero mean, and first side lobes of the autocorrelation less than the first threshold.

A circuit for a wireless transmitter, the circuit comprising:

• a spreader to spread a first sequence with a second sequence to generate a 128-length sequence, the first sequence selected from one of an 8-length sequence and a 16-length sequence, the second sequence selected from the other of the 16-length sequence and the 8-length sequence, wherein the 8-length sequence is proportional to:
• b1
• b2
• b3
• b4
• b5
• b6
• b7
• b8
• 1
• 1
• 1
• −1
• −1
• −1
• 1
• −1
• and the 16-length sequence is proportional to:
• a1
• a2
• a3
• a4
• a5
• a6
• a7
• a8
• a9
• a10
• a11
• a12
• a13
• a14
• a15
• a16
• 1
• 1
• 1
• −1
• 1
• 1
• 1
• −1
• 1
• −1
• 1
• 1
• −1
• 1
• −1
• −1.
• and wherein the wireless transmitter transmits a message containing a 128-length orthogonal frequency division modulation preamble based on the 128-length sequence.