Exact SER Analysis of DFrFT-Based QPSK OFDM System over Frequency Selective Rayleigh Fading Channel with CFO

<div>SER versus SNR for 16-point DFrFT-based OFDM QPSK transmission over a 2-tap equal power delay profile frequency selective Rayleigh fading channel with <svg height="8.55521pt" id="M180" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 36.0575 8.55521" width="36.0575pt" 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="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z" id="g113-227"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="424" vert-adv-y="424"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.145,0)"><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,-0.013,20.408,0)"><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" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.648,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,29.612,0)"><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></svg> at different values of the normalized CFO standard deviation <svg height="9.4347pt" id="M181" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 17.2753 9.4347" width="17.2753pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="565" vert-adv-y="565"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M610 0V27L347 666L316 657L46 26V0H610ZM504 54H116L310 537L504 54Z" id="g50-133"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="654" vert-adv-y="654"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.707,3.132)"><path d="M405 401C405 425 369 451 305 451C246 451 170 419 123 380C63 330 24 254 24 171C24 46 87 -12 184 -12C256 -12 327 30 380 85L362 111C308 67 260 48 213 48C148 48 112 99 112 190V211L316 205L325 257L116 251C135 342 192 405 254 405C291 405 324 389 347 357C355 346 365 344 379 355C396 368 405 387 405 401Z" id="g50-227"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="429" vert-adv-y="429"></glyph.data></g></svg>.</div>

Journal of Computer Networks and Communications

fig4

Figure 4

Figure 4: Exact SER Analysis of DFrFT-Based QPSK OFDM System over Frequency Selective Rayleigh Fading Channel with CFO 