Constellation reference. More...

Functions
function	constref (in type, in M, in varargin)

Detailed Description

Constellation reference.

This function returns regular reference constellations that can be easily parameterized.

Usage

[c, P] = constref(type, M, ROT)

Parameters

type	constellation type {'ASK','QAM','PSK','DSQ','B','C','CIRCA', 'CIRCB','CIRCULAR','COMPACT','CROSS','DODECA','DOUBLESIMPLEX','DOUBLEQPSK', 'ENNEA','FIVECIRCLE','HEPTA','HEX','HONEYCOMB','MODEM','MULTIPSK','OCTA', 'PENTA','RECTANGLE','STAR','SQUARE','SIXCIRCLE','T','TA','TB','TRI', 'V29MODEM','VORONOI','DPASK'} type can also be {'OOK','PAM','QPSK','16-QAM'} for fast reference, and is not case-sensitive.
M	constellation order (number of points/levels). M must be an integer such that: for 'ASK', M=any for 'QAM', M=4/8/16/32/60/64/256/1024/4096... for 'PSK', M=any for 'DSQ', M=8/32/128/512 for 'B', M=128 for 'C', M=8/16/32/64/128/256 for 'CIRCA', M=32/64 for 'CIRCB', M=32/64 for 'CIRCULAR', M=64 for 'COMPACT', M=16 for 'CROSS', M=16/32/64/128/512 for 'DODECA', M=16 for 'DOUBLESIMPLEX', M=4 for 'DOUBLEQPSK', M=8 for 'ENNEA', M=16 for 'FIVECIRCLE', M=128 for 'HEPTA', M=8 for 'HEX', M=16 for 'HONEYCOMB', M=16/32/64 for 'MODEM', M=8/64 for 'MULTIPSK', M=16/32 for 'OCTA', M=16 for 'PENTA', M=16 for 'RECTANGLE', M=8 for 'STAR', M=8 for 'SQUARE', M=8 for 'SIXCIRCLE', M=128 for 'T', M=16 for 'TA', M=32 for 'TB', M=32 for 'TRI', M=4/16/32/64/128 for 'V29MODEM', M=8/16 for 'VORONOI', M=64 for 'DPASK' M=4/8/16/64/256/1024... for 'OOK' M=2 for 'QPSK' M=4 for '16-QAM', M=16
ROT	constellation rotation in degrees

Return values

c	- complex constellation
P	average constellation energy (scaling factor) use c/sqrt(P) for normalization

Conventions

'QAM': Clusters for QAM are returned in the following order:

*          Q(j)
*     1  5 |  9 13
*     2  6 | 10 14
*    ------+------- I
*     3  7 | 11 15
*     4  8 | 12 16
*

'QAM' (M=8): 8-QAM returns a constellation from a subset of 16QAM. 8-Star returns a circular QAM constellation with 8 points, which is more commonly used in optics as 8QAM.

*       Q(j)
*    1   |   7
*      3 | 5
*    ----+--- I
*      4 | 6
*    2   |   8
*

'PSK': Clusters for PSK are returned in the following order (first point always has phase of 0):

*         Q(j)
*          3
*       4  |  2
*    -5----+----1- I
*       6  |  8
*          7
*

'CROSS' (M = 16/32/128/512):

*                                                                          M=128
*                                                                           Q(j)
*                                                            017 029 041 053|065 077 089 101
*          M=16                     M=32                     018 030 042 054|066 078 090 102
*          Q(j)                     Q(j)             001 009 019 031 043 055|067 079 091 103 113 121
*           |                   05 11|17 23          002 010 020 032 044 056|068 080 092 104 114 122
*        03 07 11            01 06 12|18 24 29       003 011 021 033 045 057|069 081 093 105 115 123
*     01 04 08 12 15         02 07 13|19 25 30       004 012 022 034 046 058|070 082 094 106 116 124
*    -------+---------I     ---------+---------I   -------------------------+------------------------I
*     02 05 09 13 16         03 08 14|20 26 31       005 013 023 035 047 059|071 083 095 107 117 125
*        06 10 14            04 09 15|21 27 32       006 014 024 036 048 060|072 084 096 108 118 126
*           |                   10 16|22 28          007 015 025 037 049 061|073 085 097 109 119 127
*                                                    008 016 026 038 050 062|074 086 098 110 120 128
*                                                             027 039 051 063|075 087 099 111
*                                                             028 040 052 064|076 088 100 112
* 
* 
*                                                 M=512
*                                                 Q(j)
*                   065 089 113 137 161 185 209 233|257 281 305 329 353 377 401 425
*                   066 090 114 138 162 186 210 234|258 282 306 330 354 378 402 426
*                   067 091 115 139 163 187 211 235|259 283 307 331 355 379 403 427
*                   068 092 116 140 164 188 212 236|260 284 308 332 356 380 404 428
*   001 017 033 049 069 093 117 141 165 189 213 237|261 285 309 333 357 381 405 429 449 465 481 497
*   002 018 034 050 070 094 118 142 166 190 214 238|262 286 310 334 358 382 406 430 450 466 482 498
*   003 019 035 051 071 095 119 143 167 191 215 239|263 287 311 335 359 383 407 431 451 467 483 499
*   004 020 036 052 072 096 120 144 168 192 216 240|264 288 312 336 360 384 408 432 452 468 484 500
*   005 021 037 053 073 097 121 145 169 193 217 241|265 289 313 337 361 385 409 433 453 469 485 501
*   006 022 038 054 074 098 122 146 170 194 218 242|266 290 314 338 362 386 410 434 454 470 486 502
*   007 023 039 055 075 099 123 147 171 195 219 243|267 291 315 339 363 387 411 435 455 471 487 503
*   008 024 040 056 076 100 124 148 172 196 220 244|268 292 316 340 364 388 412 436 456 472 488 504
*  ------------------------------------------------+------------------------------------------------I
*   009 025 041 057 077 101 125 149 173 197 221 245|269 293 317 341 365 389 413 437 457 473 489 505
*   010 026 042 058 078 102 126 150 174 198 222 246|270 294 318 342 366 390 414 438 458 474 490 506
*   011 027 043 059 079 103 127 151 175 199 223 247|271 295 319 343 367 391 415 439 459 475 491 507
*   012 028 044 060 080 104 128 152 176 200 224 248|272 296 320 344 368 392 416 440 460 476 492 508
*   013 029 045 061 081 105 129 153 177 201 225 249|273 297 321 345 369 393 417 441 461 477 493 509
*   014 030 046 062 082 106 130 154 178 202 226 250|274 298 322 346 340 394 418 442 462 478 494 510
*   015 031 047 063 083 107 131 155 179 203 227 251|275 299 323 347 341 395 419 443 463 479 495 511
*   016 032 048 064 084 108 132 156 180 204 228 252|276 300 324 348 342 396 420 444 464 480 496 512
*                   085 109 133 157 181 205 229 253|277 301 325 349 343 397 421 445
*                   086 110 134 158 182 206 230 254|278 302 326 350 344 398 422 446
*                   087 111 135 159 183 207 231 255|279 303 327 351 345 399 423 447
*                   088 112 136 160 184 208 232 256|280 304 328 352 346 400 424 448
*

'DODECA' (M = 16):

*         Q(j)
*         8
*     04  |  12
*   02  06|10  14
*  01-----+-----16 I
*   03  07|11  15
*     05  |  13
*         9
*

'DOUBLESIMPLEX' (M = 4):

*         Q(j)
*          2
*          |
*    ----1-+-4---- I
*          |
*          3
*

'DOUBLEQPSK' (M = 8)

*       Q(j)
*    1   |   7
*      3 | 5
*    ----+--- I
*      4 | 6
*    2   |   8
*

'DSQ' (M = 8/32/128/512)

*                           Q(j)
*                       05  13|  21  29
*       Q(j)          01  09  |17  25
*       3 |    7        06  14|  22  30
*    1    | 5         02  10  |18  26
*    -----+----- I    --------+--------- I
*       4 |    8        07  15|  23  31
*    2    | 6         03  11  |19  27
*                       08  16|  24  32
*                     04  12  |20  28
*

'ENNEA' (M = 16)

*       Q(j)
*       06|11
*   03    |    14
*  01   07|10    16
*   ------+------- I
*   02 05 08 12 15
*     04  |   13
*         09
*

'HEPTA' (M = 8):

*         Q(j)
*         3|
*      4   |  2
*    ------8----1- I
*      5   |  7
*         6|
*

'HONEYCOMB' (M = 16):

*            Q(j)
*           06|09
*      02 04  |  12 14
*    01-----07+10-----16- I
*      03 05  |  13 15
*           08|11
*

'MODEM' (M = 8):

*         Q(j)
*          |
*      1   4   7
*    ----3-+-6---- I
*      2   5   8
*          |
*

'MULTIPSK' (M = 16):

*         Q(j)
*       11 | 10
*         3|2   9
*    12 4  |  1
*    ------+------ I
*    13 5  |  8
*         6|7   16
*       14 | 15
*

'OCTA' (M = 16):

*         Q(j)
*          11
*     12  3|2  10
*       4  |  1
*    13----+-----9- I
*       5  |  8
*     14  6|7  16
*          15
*

'PENTA' (M = 16):

*         Q(j)
*      10  9  8
*          |
*   11    3| 2   7
*    ---4--1------- I
*   12    5| 6   16
*          |
*      13  14 15
*

'RECTANGLE' (M = 8):

*         Q(j)
*          |
*      1  3|5  7
*    ------+----- I
*      2  4|6  8
*          |
*

'SQUARE' (M = 8):

*         Q(j)
*      1    4    6
*           |
*    --2----+----7-- I
*           |
*      3    5    8
*

'STAR' (M = 8):

*         Q(j)
*     1    |    7
*          4
*    ---3--+--6--- I
*          5
*     2    |    8
*

'TRI' (M = 4/16):

*   M=4    Q(j)
*           2
*           |
*    -------3------- I
*        1  |  4
*           |
* 
*  M=16     Q(j)
*        04  8  12
*      02  06|10  14
*    --------+---------I
*    01  05  9  13  16
*      03  07|11  15
*

'DPASK': Clusters for DP-ASK are returned in the following order:

*    Py
*    | 4  8 12 16
*    | 3  7 11 15
*    | 2  6 10 14
*    | 1  5  9 13
*    +------------ Px
*

See also: constmap.m

Author: Robert Borkowski 15.8.2014; J�lio C�sar M. Diniz 11.03.2016

Version: v4.0

Definition in file constref.m.

Functions

Detailed Description