On the Performance of MMSE Channel Estimation in Massive MIMO Systems over Spatially Correlated Rician Fading Channels

<div>NMSE vs. the ULA interelement spacing, given in terms of <span class="nowrap"><svg height="9.49473pt" id="M217" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 7.30254 9.49473" width="7.30254pt" 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"></path></g></svg>,</span> considering <svg height="11.7782pt" id="M218" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 34.0872 11.7782" width="34.0872pt" 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="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 336C212 421 189 448 159 448C126 448 75 412 23 327L48 306C83 354 103 371 115 371C125 371 134 360 144 334C185 224 192 64 183 -19C146 -100 116 -202 110 -244L125 -261C154 -259 208 -234 222 -220C222 -194 225 -84 235 -23C247 -3 273 36 308 79C379 165 478 288 478 372Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.148,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.411,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,27.651,0)"><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"></path></g></svg> dB in the UL of an M-MIMO system where the BS employs <svg height="8.8423pt" id="M219" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 46.6662 8.8423" width="46.6662pt" 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="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.439,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.702,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,33.942,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,40.182,0)"><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"></path></g></svg> antennas across a range of correlated fading channels, parameterized by <span class="nowrap"><svg height="9.25986pt" id="M220" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -9.01432 13.2658 9.25986" width="13.2658pt" 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="M771 669C722 624 660 598 616 598C593 598 565 610 530 629C460 664 429 678 388 678C284 678 211 602 211 527C211 453 270 401 350 401C418 401 468 443 501 508L483 517C450 464 405 431 352 431C288 431 252 473 252 525S306 626 370 626C398 626 435 612 472 592C525 563 556 548 596 548C607 548 623 550 632 553L633 550C510 448 474 360 391 210C314 77 264 16 181 16C121 16 79 48 75 79H77C84 68 97 66 106 66C134 66 150 90 150 115C150 144 130 165 103 165C63 165 40 130 40 91C40 38 96 -15 183 -15C301 -15 418 42 546 321C553 310 560 306 580 306C619 306 620 284 620 275C620 211 535 149 535 70C535 21 581 -12 628 -12C689 -12 755 40 830 132L811 147C736 61 680 18 642 18C621 18 610 29 610 52C610 93 686 163 686 232C686 263 673 286 638 321V323C721 350 782 402 849 522C876 570 898 630 916 646H917C918 613 943 601 962 601C990 601 1004 621 1004 646C1004 674 981 687 953 687C900 687 834 608 741 471C684 385 650 354 609 346C596 358 582 360 567 360C627 465 677 573 784 653L771 669Z"></path></g></svg>.</span></div>

Wireless Communications and Mobile Computing

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Figure 3

Figure 3: On the Performance of MMSE Channel Estimation in Massive MIMO Systems over Spatially Correlated Rician Fading Channels 