Virtual MIMO Beamforming and Device Pairing Enabled by Device-to-Device Communications for Multidevice Networks

<div>Average normalized throughput of the cluster of radius <svg height="11.6399pt" id="M359" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 43.5785 11.6399" width="43.5785pt" 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="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"><path d="M452 282C452 397 389 451 302 451C268 451 227 441 188 422C95 377 24 281 24 154C24 65 70 -12 173 -12C240 -12 297 16 342 52C418 113 452 201 452 282ZM359 282C359 163 308 66 247 39C237 35 225 32 212 32C151 32 114 79 114 157C114 301 180 380 223 398C240 405 250 408 265 408C315 408 359 369 359 282Z" id="g50-112"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="476" vert-adv-y="476"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,13.379,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,24.642,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.882,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,37.122,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg> m located at <svg height="12.5794pt" id="M360" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 45.8359 12.5794" width="45.8359pt" 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="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M452 282C452 397 389 451 302 451C268 451 227 441 188 422C95 377 24 281 24 154C24 65 70 -12 173 -12C240 -12 297 16 342 52C418 113 452 201 452 282ZM359 282C359 163 308 66 247 39C237 35 225 32 212 32C151 32 114 79 114 157C114 301 180 380 223 398C240 405 250 408 265 408C315 408 359 369 359 282Z" id="g50-112"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="476" vert-adv-y="476"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,15.628,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.891,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,33.131,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,39.371,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg> m as a function of the cluster center SNR <svg height="9.39034pt" id="M361" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.1307 9.39034" width="11.1307pt" 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="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z" id="g113-239"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="539" vert-adv-y="539"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.162,3.132)"><path d="M452 282C452 397 389 451 302 451C268 451 227 441 188 422C95 377 24 281 24 154C24 65 70 -12 173 -12C240 -12 297 16 342 52C418 113 452 201 452 282ZM359 282C359 163 308 66 247 39C237 35 225 32 212 32C151 32 114 79 114 157C114 301 180 380 223 398C240 405 250 408 265 408C315 408 359 369 359 282Z" id="g50-112"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="476" vert-adv-y="476"></glyph.data></g></svg> when <svg height="11.7782pt" id="M362" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 27.7324 11.7782" width="27.7324pt" 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="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="494" vert-adv-y="494"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.055,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.318,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>, <svg height="11.8174pt" id="M363" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 37.7757 11.8174" width="37.7757pt" 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="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="839" vert-adv-y="839"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"><path d="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z" id="g50-85"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="673" vert-adv-y="673"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.084,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,31.346,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>, and <svg height="11.927pt" id="M364" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 37.6935 11.927" width="37.6935pt" 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="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="839" vert-adv-y="839"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"><path d="M636 22C611 29 589 38 560 74C536 104 518 134 495 173L430 300C518 328 592 392 592 492C592 555 563 594 528 618C491 643 435 650 377 650H140L131 618C222 610 223 601 208 518L137 136C121 43 116 40 27 32L18 0H295L300 32C212 40 206 42 223 138L248 279H296C334 279 350 272 369 230C393 174 413 140 441 94C482 24 523 1 626 -8L636 22ZM497 480C497 422 468 374 417 343C387 324 353 315 304 315H255L298 556C303 583 309 598 319 603C331 610 348 613 367 613C448 613 497 573 497 480Z" id="g50-83"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="654" vert-adv-y="654"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.001,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,31.264,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>.</div>

Mobile Information Systems

fig2

Figure 2

Figure 2: Virtual MIMO Beamforming and Device Pairing Enabled by Device-to-Device Communications for Multidevice Networks 