Two-Dimensional Multiple-Snapshot Grid-Free Compressive Beamforming Using Alternating Direction Method of Multipliers

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Approach to solve equation (<a href="https://static.hindawi.com/articles/sv/volume-2020/1310805/figures/#EEq4" target="_blank">4</a>)</td><td class="align_center" colspan="3"><svg height="15.8234pt" id="M150" style="vertical-align:-3.2337pt" version="1.1" viewbox="-0.0498162 -12.5897 112.929 15.8234" width="112.929pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M162 -163V703H102V-163H162ZM309 -163V703H249V-163H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.841,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 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-163V703H249V-163H309Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,85.586,3.132)"><path d="M493 503C489 551 484 614 483 650H43V622C120 616 128 611 128 525V126C128 40 120 34 40 28V0H312V28C221 34 213 40 213 126V307H316C407 307 412 296 424 227H453V420H424C412 355 407 346 316 346H213V584C213 613 216 616 246 616H322C398 616 419 607 436 579C449 559 455 539 464 499L493 503Z"></path></g><g transform="matrix(.013,0,0,-0.013,90.916,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,96.277,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,102.517,0)"><path d="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,108.084,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> × 100%</td><td class="align_center" colspan="3">Consuming time</td></tr><tr class="thead"><td class="align_center">2000 Hz</td><td class="align_center">3000 Hz</td><td class="align_center">4000 Hz</td><td class="align_center">2000 Hz</td><td class="align_center">3000 Hz</td><td class="align_center">4000 Hz</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">IPM based SDPT3 solver</td><td class="align_center">2.11%</td><td class="align_center">1.75%</td><td class="align_center">1.03%</td><td class="align_center">6.25 s</td><td class="align_center">8.12 s</td><td class="align_center">6.04 s</td></tr><tr><td class="align_left">ADMM based algorithm</td><td class="align_center">2.15%</td><td class="align_center">2.47%</td><td class="align_center">1.14%</td><td class="align_center">0.98 s</td><td class="align_center">1.00 s</td><td class="align_center">1.00 s</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>DOA estimation error corresponding to Figure <a href="../fig6/">6</a> and consuming time of IPM based SDPT3 solver and ADMM based algorithm.</div>

Shock and Vibration

tab2

Table 2

Table 2: Two-Dimensional Multiple-Snapshot Grid-Free Compressive Beamforming Using Alternating Direction Method of Multipliers 