PRECODING METHOD, TRANSMITTING DEVICE, AND RECEIVING DEVICE
A transmission scheme for transmitting a first modulated signal and a second modulated signal in the same frequency at the same time. According to the transmission scheme, a precoding weight multiplying unit multiplies a precoding weight by a baseband signal after a first mapping and a baseband signal after a second mapping and outputs the first modulated signal and the second modulated signal. In the precoding weight multiplying unit, precoding weights are regularly hopped.
1 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and
generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, using a positive real number α, as Equations 339 through 347.
Math
1
F
[
=
0
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j0
jπ
)
Equation
339
Math
2
F
[
=
1
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
2
9
π
j
(
2
9
π
+
π
)
)
Equation
340
Math
3
F
[
=
2
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
4
9
π
j
(
4
9
π
+
π
)
)
Equation
341
Math
4
F
[
=
3
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
6
9
π
j
(
6
9
π
+
π
)
)
Equation
342
Math
5
F
[
=
4
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
8
9
π
j
(
8
9
π
+
π
)
)
Equation
343
Math
6
F
[
=
5
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
10
9
π
j
(
10
9
π
+
π
)
)
Equation
344
Math
7
F
[
=
6
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
12
9
π
j
(
12
9
π
+
π
)
)
Equation
345
Math
8
F
[
=
7
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
14
9
π
j
(
14
9
π
+
π
)
)
Equation
346
Math
9
F
[
=
8
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
16
9
π
j
(
16
9
π
+
π
)
)
Equation
347
2 . The precoding method of claim 1 , further comprising:
generating coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes; and
generating a signal based on the selected modulation scheme from the coded data, wherein
the positive real number α is changed in accordance with the selected modulation scheme.
3 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and
generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, as Equations 348 through 356.
Math
10
f
[
=
0
]
=
1
2
(
j0
j0
j0
jπ
)
Equation
348
Math
11
f
[
=
1
]
=
1
2
(
j0
j0
j
2
9
π
j
(
2
9
π
+
π
)
)
Equation
349
Math
12
f
[
=
2
]
=
1
2
(
j0
j0
j
4
9
π
j
(
4
9
π
+
π
)
)
Equation
350
Math
13
f
[
=
3
]
=
1
2
(
j0
j0
j
6
9
π
j
(
6
9
π
+
π
)
)
Equation
351
Math
14
f
[
=
4
]
=
1
2
(
j0
j0
j
8
9
π
j
(
8
9
π
+
π
)
)
Equation
352
Math
15
f
[
=
5
]
=
1
2
(
j0
j0
j
10
9
π
j
(
10
9
π
+
π
)
)
Equation
353
Math
16
f
[
=
6
]
=
1
2
(
j0
j0
j
12
9
π
j
(
12
9
π
+
π
)
)
Equation
354
Math
17
f
[
=
7
]
=
1
2
(
j0
j0
j
14
9
π
j
(
14
9
π
+
π
)
)
Equation
355
Math
18
f
[
=
8
]
=
1
2
(
j0
j0
j
16
9
π
j
(
16
9
π
+
π
)
)
Equation
356
4 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and
generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 15 matrices expressed, using a positive real number α, as Equations 357 through 371.
Math
19
F
[
=
0
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j0
jπ
)
Equation
357
Math
20
F
[
=
1
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
2
15
π
j
(
2
15
π
+
π
)
)
Equation
358
Math
21
F
[
=
2
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
4
15
π
j
(
4
15
π
+
π
)
)
Equation
359
Math
22
F
[
=
3
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
6
15
π
j
(
6
15
π
+
π
)
)
Equation
360
Math
23
F
[
=
4
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
8
15
π
j
(
8
15
π
+
π
)
)
Equation
361
Math
24
F
[
=
5
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
10
15
π
j
(
10
15
π
+
π
)
)
Equation
362
Math
25
F
[
=
6
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
12
15
π
j
(
12
15
π
+
π
)
)
Equation
363
Math
26
F
[
=
7
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
14
15
π
j
(
14
15
π
+
π
)
)
Equation
364
Math
27
F
[
=
8
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
16
15
π
j
(
16
15
π
+
π
)
)
Equation
365
Math
28
F
[
=
9
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
18
15
π
j
(
18
15
π
+
π
)
)
Equation
366
Math
29
F
[
=
10
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
20
15
π
j
(
20
15
π
+
π
)
)
Equation
367
Math
30
F
[
=
11
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
22
15
π
j
(
22
15
π
+
π
)
)
Equation
368
Math
31
F
[
=
12
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
24
9
π
j
(
24
9
π
+
π
)
)
Equation
369
Math
32
F
[
=
13
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
26
15
π
j
(
26
15
π
+
π
)
)
Equation
370
Math
33
F
[
=
14
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
28
15
π
j
(
28
15
π
+
π
)
)
Equation
371
5 . The precoding method of claim 4 , further comprising:
generating coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes; and
generating a signal based on the selected modulation scheme from the coded data, wherein
the positive real number α is changed in accordance with the selected modulation scheme.
6 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and
generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 15 matrices expressed, as Equations 372 through 386.
Math
34
f
[
=
0
]
=
1
2
(
j0
j0
j0
jπ
)
Equation
372
Math
35
f
[
=
1
]
=
1
2
(
j0
j0
j
2
15
π
j
(
2
15
π
+
π
)
)
Equation
373
Math
36
f
[
=
2
]
=
1
2
(
j0
j0
j
4
15
π
j
(
4
15
π
+
π
)
)
Equation
374
Math
37
f
[
=
3
]
=
1
2
(
j0
j0
j
6
15
π
j
(
6
15
π
+
π
)
)
Equation
375
Math
38
f
[
=
4
]
=
1
2
(
j0
j0
j
8
15
π
j
(
8
15
π
+
π
)
)
Equation
376
Math
39
f
[
=
5
]
=
1
2
(
j0
j0
j
10
15
π
j
(
10
15
π
+
π
)
)
Equation
377
Math
40
f
[
=
6
]
=
1
2
(
j0
j0
j
12
15
π
j
(
12
15
π
+
π
)
)
Equation
378
Math
41
f
[
=
7
]
=
1
2
(
j0
j0
j
14
15
π
j
(
14
15
π
+
π
)
)
Equation
379
Math
42
f
[
=
8
]
=
1
2
(
j0
j0
j
16
15
π
j
(
16
15
π
+
π
)
)
Equation
380
Math
43
f
[
=
9
]
=
1
2
(
j0
j0
j
18
15
π
j
(
18
15
π
+
π
)
)
Equation
381
Math
44
f
[
=
10
]
=
1
2
(
j0
j0
j
20
15
π
j
(
20
15
π
+
π
)
)
Equation
382
Math
45
f
[
=
11
]
=
1
2
(
j0
j0
j
22
15
π
j
(
22
15
π
+
π
)
)
Equation
383
Math
46
f
[
=
12
]
=
1
2
(
j0
j0
j
24
9
π
j
(
24
9
π
+
π
)
)
Equation
384
Math
47
f
[
=
13
]
=
1
2
(
j0
j0
j
26
15
π
j
(
26
15
π
+
π
)
)
Equation
385
Math
48
f
[
=
14
]
=
1
2
(
j0
j0
j
28
15
π
j
(
28
15
π
+
π
)
)
Equation
386
7 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and
generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 18 matrices expressed, using a positive real number α, as Equations 387 through 404.
Math
49
F
[
=
0
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j0
jπ
)
Equation
387
Math
50
F
[
=
1
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
2
9
π
j
(
2
9
π
+
π
)
)
Equation
388
Math
51
F
[
=
2
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
4
9
π
j
(
4
9
π
+
π
)
)
Equation
389
Math
52
F
[
=
3
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
6
9
π
j
(
6
9
π
+
π
)
)
Equation
390
Math
53
F
[
=
4
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
8
9
π
j
(
8
9
π
+
π
)
)
Equation
391
Math
54
F
[
=
5
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
10
9
π
j
(
10
9
π
+
π
)
)
Equation
392
Math
55
F
[
=
6
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
12
9
π
j
(
12
9
π
+
π
)
)
Equation
393
Math
56
F
[
=
7
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
14
9
π
j
(
14
9
π
+
π
)
)
Equation
394
Math
57
F
[
=
8
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
16
9
π
j
(
16
9
π
+
π
)
)
Equation
395
Math
58
F
[
=
9
]
=
1
α
2
+
1
(
α
×
j0
jπ
j0
α
×
j0
)
Equation
396
Math
59
F
[
=
10
]
=
1
α
2
+
1
(
α
×
j
2
9
π
j
(
2
9
π
+
π
)
j0
α
×
j0
)
Equation
397
Math
60
F
[
=
11
]
=
1
α
2
+
1
(
α
×
j
4
9
π
j
(
4
9
π
+
π
)
j0
α
×
j0
)
Equation
398
Math
61
F
[
=
12
]
=
1
α
2
+
1
(
α
×
j
6
9
π
j
(
6
9
π
+
π
)
j0
α
×
j0
)
Equation
399
Math
62
F
[
=
13
]
=
1
α
2
+
1
(
α
×
j
8
9
π
j
(
8
9
π
+
π
)
j0
α
×
j0
)
Equation
400
Math
63
F
[
=
14
]
=
1
α
2
+
1
(
α
×
j
10
9
π
j
(
10
9
π
+
π
)
j0
α
×
j0
)
Equation
401
Math
64
F
[
=
15
]
=
1
α
2
+
1
(
α
×
j
12
9
π
j
(
12
9
π
+
π
)
j0
α
×
j0
)
Equation
402
Math
65
F
[
=
16
]
=
1
α
2
+
1
(
α
×
j
14
9
π
j
(
14
9
π
+
π
)
j0
α
×
j0
)
Equation
403
Math
66
F
[
=
17
]
=
1
α
2
+
1
(
α
×
j
16
9
π
j
(
16
9
π
+
π
)
j0
α
×
j0
)
Equation
404
8 . The precoding method of claim 7 , further comprising:
generating coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes; and
generating a signal based on the selected modulation scheme from the coded data, wherein
the positive real number α is changed in accordance with the selected modulation scheme.
9 . A precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmitting the generated precoded signals, the precoding method comprising:
selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and
generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 18 matrices expressed, as Equations 405 through 422.
Math
67
F
[
=
0
]
=
1
2
(
j0
α
×
j0
α
×
j0
jπ
)
Equation
405
Math
68
F
[
=
1
]
=
1
2
(
j0
α
×
j0
α
×
j
2
9
π
j
(
2
9
π
+
π
)
)
Equation
406
Math
69
F
[
=
2
]
=
1
2
(
j0
α
×
j0
α
×
j
4
9
π
j
(
4
9
π
+
π
)
)
Equation
407
Math
70
F
[
=
3
]
=
1
2
(
j0
α
×
j0
α
×
j
6
9
π
j
(
6
9
π
+
π
)
)
Equation
408
Math
71
F
[
=
4
]
=
1
2
(
j0
α
×
j0
α
×
j
8
9
π
j
(
8
9
π
+
π
)
)
Equation
409
Math
72
F
[
=
5
]
=
1
2
(
j0
α
×
j0
α
×
j
10
9
π
j
(
10
9
π
+
π
)
)
Equation
410
Math
73
F
[
=
6
]
=
1
2
(
j0
α
×
j0
α
×
j
12
9
π
j
(
12
9
π
+
π
)
)
Equation
411
Math
74
F
[
=
7
]
=
1
2
(
j0
α
×
j0
α
×
j
14
9
π
j
(
14
9
π
+
π
)
)
Equation
412
Math
75
F
[
=
8
]
=
1
2
(
j0
α
×
j0
α
×
j
16
9
π
j
(
16
9
π
+
π
)
)
Equation
413
Math
76
F
[
=
9
]
=
1
2
(
α
×
j0
jπ
j0
α
×
j0
)
Equation
414
Math
77
F
[
=
10
]
=
1
2
(
α
×
j
2
9
π
j
(
2
9
π
+
π
)
j0
α
×
j0
)
Equation
415
Math
78
F
[
=
11
]
=
1
2
(
α
×
j
4
9
π
j
(
4
9
π
+
π
)
j0
α
×
j0
)
Equation
416
Math
79
F
[
=
12
]
=
1
2
(
α
×
j
6
9
π
j
(
6
9
π
+
π
)
j0
α
×
j0
)
Equation
417
Math
80
F
[
=
13
]
=
1
2
(
α
×
j
8
9
π
j
(
8
9
π
+
π
)
j0
α
×
j0
)
Equation
418
Math
81
F
[
=
14
]
=
1
2
(
α
×
j
10
9
π
j
(
10
9
π
+
π
)
j0
α
×
j0
)
Equation
419
Math
82
F
[
=
15
]
=
1
2
(
α
×
j
12
9
π
j
(
12
9
π
+
π
)
j0
α
×
j0
)
Equation
420
Math
83
F
[
=
16
]
=
1
2
(
α
×
j
14
9
π
j
(
14
9
π
+
π
)
j0
α
×
j0
)
Equation
421
Math
84
F
[
=
17
]
=
1
2
(
α
×
j
16
9
π
j
(
16
9
π
+
π
)
j0
α
×
j0
)
Equation
422
10 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, using a positive real number α, as Equations 339 through 347.
Math
85
F
[
=
0
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j0
jπ
)
Equation
339
Math
86
F
[
=
1
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
2
9
π
j
(
2
9
π
+
π
)
)
Equation
340
Math
87
F
[
=
2
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
4
9
π
j
(
4
9
π
+
π
)
)
Equation
341
Math
88
F
[
=
3
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
6
9
π
j
(
6
9
π
+
π
)
)
Equation
342
Math
89
F
[
=
4
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
8
9
π
j
(
8
9
π
+
π
)
)
Equation
343
Math
90
F
[
=
5
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
10
9
π
j
(
10
9
π
+
π
)
)
Equation
344
Math
91
F
[
=
6
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
12
9
π
j
(
12
9
π
+
π
)
)
Equation
345
Math
92
F
[
=
7
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
14
9
π
j
(
14
9
π
+
π
)
)
Equation
346
Math
93
F
[
=
8
]
=
1
α
2
+
1
(
j0
α
×
j0
α
×
j
16
9
π
j
(
16
9
π
+
π
)
)
Equation
347
11 . The transmission device of claim 10 , wherein
the transmission device further generates coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes, and generates a signal based on the selected modulation scheme from the coded data, and
the positive real number a is changed in accordance with the selected modulation scheme.
12 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, as Equations 348 through 356.
Math
94
F
[
i
=
0
]
=
1
2
(
j
0
j
0
j
0
j
π
)
Equation
348
Math
95
F
[
i
=
1
]
=
1
2
(
j
0
j
0
j
2
9
π
j
(
2
9
π
+
π
)
)
Equation
349
Math
96
F
[
i
=
2
]
=
1
2
(
j
0
j
0
j
4
9
π
j
(
4
9
π
+
π
)
)
Equation
350
Math
97
F
[
i
=
3
]
=
1
2
(
j
0
j
0
j
6
9
π
j
(
6
9
π
+
π
)
)
Equation
351
Math
98
F
[
i
=
4
]
=
1
2
(
j
0
j
0
j
8
9
π
j
(
8
9
π
+
π
)
)
Equation
352
Math
99
F
[
i
=
5
]
=
1
2
(
j
0
j
0
j
10
9
π
j
(
10
9
π
+
π
)
)
Equation
353
Math
100
F
[
i
=
6
]
=
1
2
(
j
0
j
0
j
12
9
π
j
(
12
9
π
+
π
)
)
Equation
354
Math
101
F
[
i
=
7
]
=
1
2
(
j
0
j
0
j
14
9
π
j
(
14
9
π
+
π
)
)
Equation
355
Math
102
F
[
i
=
8
]
=
1
2
(
j
0
j
0
j
16
9
π
j
(
16
9
π
+
π
)
)
.
Equation
356
13 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 15 matrices expressed, using a positive real number α, as Equations 357 through 371.
Math
103
F
[
i
=
0
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
0
j
π
)
Equation
357
Math
104
F
[
i
=
1
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
2
15
π
j
(
2
15
π
+
π
)
)
Equation
358
Math
105
F
[
i
=
2
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
4
15
π
j
(
4
15
π
+
π
)
)
Equation
359
Math
106
F
[
i
=
3
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
6
15
π
j
(
6
15
π
+
π
)
)
Equation
360
Math
107
F
[
i
=
4
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
8
15
π
j
(
8
15
π
+
π
)
)
Equation
361
Math
108
F
[
i
=
5
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
12
15
π
j
(
12
15
π
+
π
)
)
Equation
362
Math
109
F
[
i
=
6
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
12
15
π
j
(
12
15
π
+
π
)
)
Equation
363
Math
110
F
[
i
=
7
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
14
15
π
j
(
14
15
π
+
π
)
)
Equation
364
Math
111
F
[
i
=
8
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
16
15
π
j
(
16
15
π
+
π
)
)
Equation
365
Math
112
F
[
i
=
9
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
18
15
π
j
(
18
15
π
+
π
)
)
Equation
366
Math
113
F
[
i
=
10
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
20
15
π
j
(
20
15
π
+
π
)
)
Equation
367
Math
114
F
[
i
=
11
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
22
15
π
j
(
22
15
π
+
π
)
)
Equation
368
Math
115
F
[
i
=
12
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
24
9
π
j
(
24
9
π
+
π
)
)
Equation
369
Math
116
F
[
i
=
13
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
26
15
π
j
(
26
15
π
+
π
)
)
Equation
370
Math
117
F
[
i
=
14
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
28
15
π
j
(
28
15
π
+
π
)
)
.
Equation
371
14 . The transmission device of claim 13 , wherein
the transmission device further generates coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes, and generates a signal based on the selected modulation scheme from the coded data, and
the positive real number α is changed in accordance with the selected modulation scheme.
15 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 15 matrices expressed, as Equations 372 through 386.
Math
118
F
[
i
=
0
]
=
1
2
(
j
0
j
0
j
0
j
π
)
Equation
372
Math
119
F
[
i
=
1
]
=
1
2
(
j
0
j
0
j
2
15
π
j
(
2
15
π
+
π
)
)
Equation
373
Math
120
F
[
i
=
2
]
=
1
2
(
j
0
j
0
j
4
15
π
j
(
4
15
π
+
π
)
)
Equation
374
Math
121
F
[
i
=
3
]
=
1
2
(
j
0
j
0
j
6
15
π
j
(
6
15
π
+
π
)
)
Equation
375
Math
122
F
[
i
=
4
]
=
1
2
(
j
0
j
0
j
8
15
π
j
(
8
15
π
+
π
)
)
Equation
376
Math
123
F
[
i
=
5
]
=
1
2
(
j
0
j
0
j
10
15
π
j
(
10
15
π
+
π
)
)
Equation
377
Math
124
F
[
i
=
6
]
=
1
2
(
j
0
j
0
j
12
15
π
j
(
12
15
π
+
π
)
)
Equation
378
Math
125
F
[
i
=
7
]
=
1
2
(
j
0
j
0
j
14
15
π
j
(
14
15
π
+
π
)
)
Equation
379
Math
126
F
[
i
=
8
]
=
1
2
(
j
0
j
0
j
16
15
π
j
(
16
15
π
+
π
)
)
Equation
380
Math
127
F
[
i
=
9
]
=
1
2
(
j
0
j
0
j
18
15
π
j
(
18
15
π
+
π
)
)
Equation
381
Math
128
F
[
i
=
10
]
=
1
2
(
j
0
j
0
j
20
15
π
j
(
20
15
π
+
π
)
)
Equation
382
Math
129
F
[
i
=
11
]
=
1
2
(
j
0
j
0
j
22
15
π
j
(
22
15
π
+
π
)
)
Equation
383
Math
130
F
[
i
=
12
]
=
1
2
(
j
0
j
0
j
24
9
π
j
(
24
9
π
+
π
)
)
Equation
384
Math
131
F
[
i
=
13
]
=
1
2
(
j
0
j
0
j
26
15
π
j
(
26
15
π
+
π
)
)
Equation
385
Math
132
F
[
i
=
14
]
=
1
2
(
j
0
j
0
j
28
15
π
j
(
28
15
π
+
π
)
)
.
Equation
386
16 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 18 matrices expressed, using a positive real number α, as Equations 387 through 404.
Math
133
F
[
i
=
0
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
0
j
π
)
Equation
387
Math
134
F
[
i
=
1
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
2
9
π
j
(
2
9
π
+
π
)
)
Equation
388
Math
135
F
[
i
=
2
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
4
9
π
j
(
4
9
π
+
π
)
)
Equation
389
Math
136
F
[
i
=
3
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
6
9
π
j
(
6
9
π
+
π
)
)
Equation
390
Math
137
F
[
i
=
4
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
8
9
π
j
(
8
9
π
+
π
)
)
Equation
391
Math
138
F
[
i
=
5
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
10
9
π
j
(
10
9
π
+
π
)
)
Equation
392
Math
139
F
[
i
=
6
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
12
9
π
j
(
12
9
π
+
π
)
)
Equation
393
Math
140
F
[
i
=
7
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
14
9
π
j
(
14
9
π
+
π
)
)
Equation
394
Math
141
F
[
i
=
8
]
=
1
α
2
+
1
(
j
0
α
×
j
0
α
×
j
16
9
π
j
(
16
9
π
+
π
)
)
Equation
395
Math
142
F
[
i
=
9
]
=
1
α
2
+
1
(
α
×
j
0
j
π
j
0
α
×
j
0
)
Equation
396
Math
143
F
[
i
=
10
]
=
1
α
2
+
1
(
α
×
j
2
9
π
j
(
2
9
π
+
π
)
j
0
α
×
j
0
)
Equation
397
Math
144
F
[
i
=
11
]
=
1
α
2
+
1
(
α
×
j
4
9
π
j
(
4
9
π
+
π
)
j
0
α
×
j
0
)
Equation
398
Math
145
F
[
i
=
12
]
=
1
α
2
+
1
(
α
×
j
6
9
π
j
(
6
9
π
+
π
)
j
0
α
×
j
0
)
Equation
399
Math
146
F
[
i
=
13
]
=
1
α
2
+
1
(
α
×
j
8
9
π
j
(
8
9
π
+
π
)
j
0
α
×
j
0
)
Equation
400
Math
147
F
[
i
=
14
]
=
1
α
2
+
1
(
α
×
j
10
9
π
j
(
10
9
π
+
π
)
j
0
α
×
j
0
)
Equation
401
Math
148
F
[
i
=
15
]
=
1
α
2
+
1
(
α
×
j
12
9
π
j
(
12
9
π
+
π
)
j
0
α
×
j
0
)
Equation
402
Math
149
F
[
i
=
16
]
=
1
α
2
+
1
(
α
×
j
14
9
π
j
(
14
9
π
+
π
)
j
0
α
×
j
0
)
Equation
403
Math
150
F
[
i
=
17
]
=
1
α
2
+
1
(
α
×
j
16
9
π
j
(
16
9
π
+
π
)
j
0
α
×
j
0
)
.
Equation
404
17 . The transmission device of claim 16 , wherein
the transmission device further generates coded data by performing error coding on data to be transmitted with use of an error coding scheme selected among a plurality of error coding schemes, and generates a signal based on the selected modulation scheme from the coded data, and
the positive real number α is changed in accordance with the selected modulation scheme.
18 . A transmission device that generates, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency bandwidth at the same time and transmits the generated precoded signals, wherein
the transmission device selects one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices and generates the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being 18 matrices expressed, as Equations 405 through 422.
Math
151
F
[
i
=
0
]
=
1
2
(
j
0
α
×
j
0
α
×
j
0
j
π
)
Equation
405
Math
152
F
[
i
=
1
]
=
1
2
(
j
0
α
×
j
0
α
×
j
2
9
π
j
(
2
9
π
+
π
)
)
Equation
406
Math
153
[
i
=
2
]
=
1
2
(
j
0
α
×
j
0
α
×
j
4
9
π
j
(
4
9
π
+
π
)
)
Equation
407
Math
154
[
i
=
3
]
=
1
2
(
j
0
α
×
j
0
α
×
j
6
9
π
j
(
6
9
π
+
π
)
)
Equation
408
Math
155
[
i
=
4
]
=
1
2
(
j
0
α
×
j
0
α
×
j
8
9
π
j
(
8
9
π
+
π
)
)
Equation
409
Math
156
[
i
=
5
]
=
1
2
(
j
0
α
×
j
0
α
×
j
10
9
π
j
(
10
9
π
+
π
)
)
Equation
410
Math
157
[
i
=
6
]
=
1
2
(
j
0
α
×
j
0
α
×
j
12
9
π
j
(
12
9
π
+
π
)
)
Equation
411
Math
158
[
i
=
7
]
=
1
2
(
j
0
α
×
j
0
α
×
j
14
9
π
j
(
14
9
π
+
π
)
)
Equation
412
Math
159
[
i
=
8
]
=
1
2
(
j
0
α
×
j
0
α
×
j
16
9
π
j
(
16
9
π
+
π
)
)
Equation
413
Math
160
[
i
=
9
]
=
1
2
(
α
×
j
0
j
π
j
0
α
×
j
0
)
Equation
414
Math
161
[
i
=
10
]
=
1
2
(
α
×
j
2
9
π
j
(
2
9
π
+
π
)
j
0
α
×
j
0
)
Equation
415
Math
162
[
i
=
11
]
=
1
2
(
α
×
j
4
9
π
j
(
4
9
π
+
π
)
j
0
α
×
j
0
)
Equation
416
Math
163
[
i
=
12
]
=
1
2
(
α
×
j
6
9
π
j
(
6
9
π
+
π
)
j
0
α
×
j
0
)
Equation
417
Math
164
[
i
=
13
]
=
1
2
(
α
×
j
8
9
π
j
(
8
9
π
+
π
)
j
0
α
×
j
0
)
Equation
418
Math
165
[
i
=
14
]
=
1
2
(
α
×
j
10
9
π
j
(
10
9
π
+
π
)
j
0
α
×
j
0
)
Equation
419
Math
166
[
i
=
15
]
=
1
2
(
α
×
j
12
9
π
j
(
12
9
π
+
π
)
j
0
α
×
j
0
)
Equation
420
Math
167
[
i
=
16
]
=
1
2
(
α
×
j
14
9
π
j
(
14
9
π
+
π
)
j
0
α
×
j
0
)
Equation
421
Math
168
[
i
=
17
]
=
1
2
(
α
×
j
16
9
π
j
(
16
9
π
+
π
)
j
0
α
×
j
0
)
.
Equation
422