Combined Sector and Channel Hopping Schemes for Efficient Rendezvous in Directional Antenna Cognitive Radio Networks

<div>Asynchronous rendezvous between <svg height="11.9479pt" id="M720" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -8.7664 23.2125 11.9479" width="23.2125pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M409 504C401 567 396 607 392 642C354 654 312 665 266 665C137 665 60 583 60 487C60 374 161 325 225 290C300 250 355 215 355 141C355 68 311 21 235 21C131 21 86 122 71 183L41 176C48 128 61 42 68 21C78 16 93 8 118 0C142 -7 175 -15 216 -15C349 -15 438 69 438 174C438 287 344 333 265 374C186 414 138 449 138 522C138 576 172 631 249 631C336 631 363 562 380 499L409 504Z" id="g121-81"></path></g><g transform="matrix(.013,0,0,-0.013,5.927,0)"><path d="M716 650H478V622C549 617 570 605 575 566C579 535 582 493 582 401V326C582 161 537 40 393 40C269 40 205 133 205 294V521C205 611 213 617 291 622V650H33V622C111 615 120 611 120 521V272C120 154 148 80 208 34C252 0 309 -14 368 -14C434 -14 501 7 548 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38 97 32L86 0H375L382 32C285 39 277 45 296 136L324 267C329 290 337 304 350 322C420 416 479 489 523 539C582 607 595 613 668 619L679 650Z" id="g50-90"></path></g></svg> according to the combined PES-SCH scheme for <svg height="8.55521pt" id="M722" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 27.8368 8.55521" width="27.8368pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path></g><g transform="matrix(.013,0,0,-0.013,10.158,0)"><path d="M535 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138 449 138 522C138 576 172 631 249 631C336 631 363 562 380 499L409 504Z" id="g121-81"></path></g><g transform="matrix(.013,0,0,-0.013,6.162,0)"><path d="M614 175C564 76 510 21 408 21C256 21 146 149 146 336C146 488 235 629 402 629C510 629 570 586 597 480L626 488C620 541 614 582 606 638C578 643 510 665 429 665C206 665 44 527 44 316C44 157 153 -15 402 -15C474 -15 558 5 586 11C604 45 629 119 643 165L614 175Z" id="g121-65"></path></g><g transform="matrix(.013,0,0,-0.013,14.807,0)"><path d="M729 650H468V622C546 615 554 610 554 527V365H213V527C213 610 221 616 297 622V650H38V622C120 616 128 611 128 527V123C128 39 120 34 40 28V0H303V28C221 34 213 40 213 123V322H554V123C554 39 546 34 460 28V0H728V28C647 34 639 39 639 123V527C639 610 647 615 729 622V650Z" id="g121-70"></path></g><g transform="matrix(.0091,0,0,-0.0091,24.858,3.132)"><path d="M679 650H432L424 619L456 615C499 610 507 601 486 568C442 499 366 400 315 336C281 403 229 526 211 570C199 600 202 610 239 614C239 614 281 618 281 619L288 650H33L24 619C98 612 106 606 129 552L226 325C238 297 238 282 234 259L211 136C193 42 184 38 97 32L86 0H375L382 32C285 39 277 45 296 136L324 267C329 290 337 304 350 322C420 416 479 489 523 539C582 607 595 613 668 619L679 650Z" id="g50-90"></path></g></svg> is started earlier than <svg height="11.9479pt" id="M724" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -8.7664 32.5163 11.9479" width="32.5163pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M409 504C401 567 396 607 392 642C354 654 312 665 266 665C137 665 60 583 60 487C60 374 161 325 225 290C300 250 355 215 355 141C355 68 311 21 235 21C131 21 86 122 71 183L41 176C48 128 61 42 68 21C78 16 93 8 118 0C142 -7 175 -15 216 -15C349 -15 438 69 438 174C438 287 344 333 265 374C186 414 138 449 138 522C138 576 172 631 249 631C336 631 363 562 380 499L409 504Z" id="g121-81"></path></g><g transform="matrix(.013,0,0,-0.013,6.162,0)"><path 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516 42 472 36L440 32L433 0H707L716 32C627 38 622 43 581 121L455 361L629 548C685 606 696 610 775 618L782 650Z" id="g50-89"></path></g></svg> with <span class="nowrap"><svg height="12.5794pt" id="M725" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 52.222 12.5794" width="52.222pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.396,3.132)"><path d="M463 633C453 636 427 644 417 648C388 660 349 667 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Wireless Communications and Mobile Computing

fig10

Figure 10

Figure 10: Combined Sector and Channel Hopping Schemes for Efficient Rendezvous in Directional Antenna Cognitive Radio Networks 