Estimation of DOA for Noncircular Signals via Vandermonde Constrained Parallel Factor Analysis

<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">Algorithm</td><td class="align_center">Computational complexity</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">The proposed method</td><td class="align_center"><span style="width: 195.222ptpx;"><svg height="18.3157pt" id="M270" style="vertical-align:-5.8304pt" version="1.1" viewbox="-0.0498162 -12.4853 195.222 18.3157" width="195.222pt" 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="M663 549C663 621 608 680 521 680C283 680 82 444 82 188C82 80 142 -15 258 -15C466 -15 637 203 637 396C637 502 561 542 497 542C414 542 336 469 336 362C336 331 339 284 371 232L393 242C369 289 366 322 366 347C366 448 430 506 494 506C539 506 586 470 586 396C586 266 508 157 469 118C409 57 343 15 256 15C179 15 142 78 142 150C142 331 347 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transform="matrix(.013,0,0,-0.013,174.34,0)"><path d="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z" id="g113-76"></path></g><g transform="matrix(.0091,0,0,-0.0091,184.157,-5.741)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path></g><g transform="matrix(.013,0,0,-0.013,189.104,2.0537e-05)"><path d="M364 271V272C364 550 278 798 87 953L65 927C205 795 285 542 285 271S204 -253 65 -385L87 -411C278 -259 364 -10 364 271Z" id="g119-134"></path></g></svg></span></td></tr><tr><td class="align_left">TALS-based PARAFAC</td><td class="align_center"><span style="width: 115.052ptpx;"><svg height="18.3157pt" id="M271" style="vertical-align:-5.8304pt" version="1.1" viewbox="-0.0498162 -12.4853 115.052 18.3157" width="115.052pt" 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="M663 549C663 621 608 680 521 680C283 680 82 444 82 188C82 80 142 -15 258 -15C466 -15 637 203 637 396C637 502 561 542 497 542C414 542 336 469 336 362C336 331 339 284 371 232L393 242C369 289 366 322 366 347C366 448 430 506 494 506C539 506 586 470 586 396C586 266 508 157 469 118C409 57 343 15 256 15C179 15 142 78 142 150C142 331 347 645 517 645C590 645 624 603 643 547L663 549Z" id="g198-16"></path></g><g transform="matrix(.013,0,0,-0.013,11.175,2.0537e-05)"><path d="M378 -385C239 -253 158 0 158 271S238 795 378 927L356 953C165 798 79 550 79 272V271C79 -10 165 -259 356 -411L378 -385Z" id="g119-133"></path></g><g transform="matrix(.013,0,0,-0.013,16.956,2.0537e-05)"><path d="M378 -385C239 -253 158 0 158 271S238 795 378 927L356 953C165 798 79 550 79 272V271C79 -10 165 -259 356 -411L378 -385Z" id="g119-133"></path></g><g transform="matrix(.013,0,0,-0.013,22.736,0)"><path d="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z" id="g113-76"></path></g><g transform="matrix(.0091,0,0,-0.0091,32.554,-5.741)"><path d="M290 377C321 398 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Computational complexity of the proposed algorithm and TALS-based PARAFAC.

International Journal of Antennas and Propagation

tab1

Table 1

Table 1: Estimation of DOA for Noncircular Signals via Vandermonde Constrained Parallel Factor Analysis 