Outage Analysis of Multihop Wireless Backhaul Using Millimeter Wave under Blockage Effects

<div><svg height="11.9316pt" id="M325" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 19.6006 11.9316" width="19.6006pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M262 451C169 451 38 375 38 210C38 98 121 -12 261 -12C360 -12 481 64 481 227C481 351 386 451 262 451ZM249 414C337 414 385 320 385 204C385 70 333 25 272 25C189 25 134 117 134 241C134 355 189 414 249 414Z" id="g58-109"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="519" vert-adv-y="519"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,11.278,3.132)"><path d="M527 54L498 55C459 56 451 63 451 114V445C436 442 413 438 384 435C353 432 318 430 291 429V402L328 396C361 390 370 387 370 331V101C336 70 300 54 262 54C217 54 173 78 173 166V300C173 361 173 412 176 445C160 442 132 438 105 434C77 431 52 430 29 429V402L59 395C83 390 92 385 92 331V141C92 30 150 -12 218 -12C246 -12 266 -4 295 13C324 29 346 47 370 64V-6L376 -12C396 -7 421 1 448 8C476 15 504 21 527 24V54Z" id="g58-115"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="541" vert-adv-y="541"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.092,3.132)"><path d="M303 37L293 66C280 59 256 49 231 49S173 63 173 143V396H281C294 404 298 428 287 439H173V575L158 577L92 509V439H46L17 408L22 396H92V107C92 27 128 -12 192 -12C203 -12 218 -9 237 2L303 37Z" id="g58-114"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="312" vert-adv-y="312"></glyph.data></g></svg> versus <svg height="12.7178pt" id="M326" 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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="581" vert-adv-y="581"></glyph.data></g></svg>, when <svg height="12.5794pt" id="M327" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 31.4444 12.5794" width="31.4444pt" 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="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" id="g113-99"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="469" vert-adv-y="469"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,4.992,3.132)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z" id="g50-108"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="509" vert-adv-y="509"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,13.771,0)"><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,-0.013,25.034,0)"><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>, <svg height="11.5564pt" id="M328" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 101.32 11.5564" width="101.32pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="552" vert-adv-y="552"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.806,0)"><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,-0.013,22.068,0)"><path d="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z" id="g113-124"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.58,0)"><path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="493" vert-adv-y="493"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,32.989,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g190-47"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,35.953,0)"><path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="493" vert-adv-y="493"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,42.479,0)"><path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="493" vert-adv-y="493"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,48.666,0)"><path d="M411 139C381 76 368 73 314 73H129L267 224C351 317 400 380 400 469C400 574 322 635 233 635C176 635 128 610 98 576L40 495L63 476C89 515 130 568 198 568C274 568 316 519 316 436C316 347 251 264 191 192C142 134 85 76 30 21V0H403C415 45 425 89 438 131L411 139Z" id="g190-243"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="465" vert-adv-y="465"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,54.528,0)"><path d="M465 179V225H369V632H330C227 497 124 346 29 205V179H289V107C289 37 284 33 198 26V0H454V26C374 33 369 37 369 107V179H465ZM289 225H92C156 335 222 430 287 520H289V225Z" id="g190-166"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="497" vert-adv-y="497"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,60.99,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" id="g190-45"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,68.304,0)"><path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="493" vert-adv-y="493"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,74.713,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g190-47"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,77.677,0)"><path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="493" vert-adv-y="493"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,84.204,0)"><path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="493" vert-adv-y="493"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,90.495,0)"><path d="M269 381C298 400 325 421 340 436C360 455 370 476 370 504C370 579 313 635 223 635H222C170 635 123 610 95 579L52 516L72 497C95 533 136 577 193 577C245 577 286 546 286 482C286 408 218 369 127 339L133 314C149 319 174 325 197 325C254 325 324 285 324 192C325 83 266 39 201 39C143 39 103 68 78 91C70 98 62 97 54 91C45 84 33 71 32 58C30 46 34 35 48 22C61 10 102 -12 148 -12C216 -12 410 57 410 225C410 298 357 362 269 379V381Z" id="g190-232"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="452" vert-adv-y="452"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,96.617,0)"><path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z" id="g113-126"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g></svg>, and <svg height="8.68572pt" id="M329" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 10.095 8.68572" width="10.095pt" 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="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z" id="g113-69"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="766" vert-adv-y="766"></glyph.data></g></svg> = <svg height="11.5564pt" id="M330" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 66.0533 11.5564" width="66.0533pt" 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="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z" id="g113-124"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.511,0)"><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><g transform="matrix(.013,0,0,-0.013,12.926,0)"><path d="M513 0V26C475 28 448 43 413 81C379 116 277 234 258 264C301 314 319 334 344 359C383 396 404 407 473 418V443L269 434V408C317 403 320 395 299 364C280 337 250 298 228 276C213 260 195 247 165 241V712C126 699 69 682 21 677V653C82 648 87 642 87 576V104C87 40 81 32 14 26V0H237V26C173 32 165 38 165 104V215C171 217 176 218 181 218C189 218 198 212 212 196C267 129 330 49 376 -2L513 0Z" id="g121-105"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="496" vert-adv-y="496"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.648,0)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g121-107"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.295,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" id="g113-45"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,35.438,0)"><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,-0.013,43.854,0)"><path d="M513 0V26C475 28 448 43 413 81C379 116 277 234 258 264C301 314 319 334 344 359C383 396 404 407 473 418V443L269 434V408C317 403 320 395 299 364C280 337 250 298 228 276C213 260 195 247 165 241V712C126 699 69 682 21 677V653C82 648 87 642 87 576V104C87 40 81 32 14 26V0H237V26C173 32 165 38 165 104V215C171 217 176 218 181 218C189 218 198 212 212 196C267 129 330 49 376 -2L513 0Z" id="g121-105"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="496" vert-adv-y="496"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,50.576,0)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g121-107"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,61.223,0)"><path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z" id="g113-126"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g></svg>.</div>

International Journal of Antennas and Propagation

fig8

Figure 8

Figure 8: Outage Analysis of Multihop Wireless Backhaul Using Millimeter Wave under Blockage Effects 