Stochastic Geometry Analysis of Downlink Spectral and Energy Efficiency in Ultradense Heterogeneous Cellular Networks

<div>Average downlink throughput <svg height="11.8174pt" id="M180" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 16.8669 11.8174" width="16.8669pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z" id="g58-107"></path></g></svg> of a UE served by the MBS versus SINR threshold <svg height="12.7178pt" id="M181" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 7.68094 12.7178" width="7.68094pt" 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="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path></g></svg> when the SBS density ratio <span class="nowrap"><svg height="11.7782pt" id="M182" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 43.8215 11.7782" width="43.8215pt" 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></g><g transform="matrix(.013,0,0,-0.013,10.642,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,21.905,0)"><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></g><g transform="matrix(.013,0,0,-0.013,28.145,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,31.109,0)"><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></g><g transform="matrix(.013,0,0,-0.013,37.349,0)"><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></g></svg>.</span></div>

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Figure 3

Figure 3: Stochastic Geometry Analysis of Downlink Spectral and Energy Efficiency in Ultradense Heterogeneous Cellular Networks 