Investigation of Error Probability for Grid and Random Uniform Topologies in a Variable Noise Environment

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Symbols/acronyms</td><td class="align_center">Meaning</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left"><span style="width: 24.6152ptpx;"><svg height="11.9453pt" id="M1" style="vertical-align:-3.309401pt" version="1.1" viewbox="-0.0498162 -8.6359 24.6152 11.9453" width="24.6152pt" 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"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.307,3.132)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.62,3.132)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.824,3.132)"><path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z"></path></g></svg></span></td><td class="align_center">Received signal strength power</td></tr><tr><td class="align_left"><span style="width: 33.795ptpx;"><svg height="14.0004pt" id="M2" style="vertical-align:-5.3645pt" version="1.1" viewbox="-0.0498162 -8.6359 33.795 14.0004" width="33.795pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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333V99C331 66 293 51 257 51C212 51 169 75 169 164V299C169 366 169 413 172 444C156 441 128 437 101 433C75 430 50 427 29 426V403L57 397C82 391 90 386 90 333V137C90 29 147 -12 214 -12C241 -12 262 -4 291 13S342 48 365 65V-6L371 -12C390 -7 415 1 441 8C468 15 496 21 518 24V50Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,30.296,3.132)"><path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z"></path></g></svg></span></td><td class="align_center">Transmitter output power</td></tr><tr><td class="align_left">PL(<i>d</i>)</td><td class="align_center">Path loss, which is a function of transmitter-receiver separation distance (d) in meters.</td></tr><tr><td class="align_left"><span style="width: 28.1136ptpx;"><svg height="11.9087pt" id="M3" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 28.1136 11.9087" width="28.1136pt" 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class="align_center">Probability of error</td></tr><tr><td class="align_left"><i>RSS</i></td><td class="align_center">Received signal strength</td></tr><tr><td class="align_left"><i>RSSI</i></td><td class="align_center">Received signal strength indicator</td></tr><tr><td class="align_left"><i>E</i><sub><i>b</i></sub></td><td class="align_center">Energy per bit</td></tr><tr><td class="align_left"><i>N</i><sub><i>o</i></sub></td><td class="align_center">Noise spectral density</td></tr><tr><td class="align_left"><i>B</i><sub>Noise</sub></td><td class="align_center">Noise bandwidth</td></tr><tr><td class="align_left"><i>D</i><sub>Rate</sub></td><td class="align_center">Transmission data rate</td></tr><tr><td class="align_left"><i>β</i></td><td class="align_center">Reference threshold</td></tr><tr><td class="align_left"><i>λ</i></td><td class="align_center">Weighing parameter</td></tr><tr><td class="align_left"><i>γ</i></td><td class="align_center">Spread control parameter</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Journal of Computer Networks and Communications

tab1

Table 1

Table 1: Investigation of Error Probability for Grid and Random Uniform Topologies in a Variable Noise Environment 