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116:
74:
33:
1359:. Thus, a multipath channel is converted into scalar orthogonal sub-channels in the frequency domain, thereby simplifying the receiver design considerably. The task of channel estimation is simplified, as we just need to have access to an estimate of the scalar coefficients
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289:. However, in practice, this cannot be achieved, as real signals are always time-limited. So, to mimic the infinite behavior, prefixing the end of the symbol to the beginning makes the linear
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For the cyclic prefix to serve its objectives, it must have a length at least equal to the length of the multipath channel. The concept of a cyclic prefix is traditionally associated with
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with a repetition of the end. The receiver is typically configured to discard the cyclic prefix samples, but the cyclic prefix serves two purposes:
1388:, for the duration in which the channel does not vary significantly, merely multiplying the received demodulated symbols by the inverse of
877:
185:
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60:
752:{\displaystyle \mathbf {z} ={\begin{bmatrix}x&\ldots &x&x&x&x&\ldots &x\end{bmatrix}}^{\textsf {T}}.}
90:
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uses cyclic prefixes to combat multipath by making channel estimation easy. As an example, consider an OFDM system that has
46:
225:
It repeats the end of the symbol so the linear convolution of a frequency-selective multipath channel can be modeled as
860:{\displaystyle \mathbf {h} ={\begin{bmatrix}h_{0}&h_{1}&\ldots &h_{L_{2}-1}\end{bmatrix}}^{\textsf {T}}}
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430:
230:
128:
433:(IDFT) of the message symbol, followed by a cyclic prefixing. Let the symbol obtained by the IDFT be denoted by
419:{\displaystyle \mathbf {d} ={\begin{bmatrix}d_{0}&d_{1}&\ldots &d_{N-1}\end{bmatrix}}^{\textsf {T}}}
1558:
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138:
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233:. This approach accommodates simple frequency domain processing, such as channel estimation and equalization.
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1532:{\displaystyle {\begin{bmatrix}d_{0}&d_{1}&\ldots &d_{N-1}\end{bmatrix}}^{\textsf {T}}}
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530:{\displaystyle \mathbf {x} ={\begin{bmatrix}x&x&\ldots &x\end{bmatrix}}^{\textsf {T}}}
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87:
Needs a more accessible introduction, especially the second bullet point.
1574:, by David Tse and Pramod Viswanath, Cambridge University Press (2005).
1216:. Hence, taking the discrete Fourier transform of these values, we get
257:
A cyclic prefix is often used in conjunction with modulation to retain
278:
270:
991:{\displaystyle y=\sum _{l=0}^{L-1}hz\quad 0\leq m\leq N-L_{1}-2}
305:
109:
67:
26:
229:, which in turn may transform to the frequency domain via a
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Then, the convolution with this channel, which happens as
265:
channels. It is well known that sinusoidal signals are
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systems, however the cyclic prefix is now also used in
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systems. Therefore, if the channel is assumed to be
328:subcarriers. The message symbol can be written as:
285:, then a sinusoid of infinite duration would be an
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1587:the significance of cyclic prefix in OFDM systems
137:but its sources remain unclear because it lacks
762:Assume that the channel is represented using
429:The OFDM symbol is constructed by taking the
8:
1439:
1424:
541:Prefixing it with a cyclic prefix of length
83:needs attention from an expert in Technology
61:Learn how and when to remove these messages
1452:and hence, the estimate of actual symbols
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186:Learn how and when to remove this message
168:Learn how and when to remove this message
293:of the channel appear as though it were
1572:Fundamentals of Wireless Communication
93:may be able to help recruit an expert.
245:systems to improve the robustness to
7:
431:inverse discrete Fourier transform
25:
42:This article has multiple issues.
1610:Quantized radio modulation modes
1345:
1323:
1152:
1097:
1075:
1009:
1001:results in the received symbols
773:
585:
444:
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114:
72:
31:
1194:
1056:{\displaystyle L_{1}\geq L_{2}}
953:
574:, the OFDM symbol obtained is:
50:or discuss these issues on the
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1:
206:refers to the prefixing of a
1352:{\displaystyle \mathbf {d} }
1330:{\displaystyle \mathbf {x} }
1159:{\displaystyle \mathbf {z} }
1104:{\displaystyle \mathbf {h} }
1082:{\displaystyle \mathbf {z} }
1016:{\displaystyle \mathbf {y} }
1137:{\displaystyle m\geq L_{1}}
85:. The specific problem is:
1626:
1313:discrete Fourier transform
1271:{\displaystyle Y=H\cdot X}
231:discrete Fourier transform
222:from the previous symbol.
1559:Intersymbol interference
1417:yields the estimates of
220:intersymbol interference
123:This article includes a
567:{\displaystyle L_{1}-1}
152:more precise citations.
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91:WikiProject Technology
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1445:{\displaystyle \{X\}}
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1585:A short tutorial on
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1093:
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1065:circular convolution
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295:circular convolution
227:circular convolution
1592:2023-10-05 at the
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200:telecommunications
125:list of references
1525:
1410:{\displaystyle H}
1381:{\displaystyle H}
1304:{\displaystyle X}
1209:{\displaystyle x}
853:
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321:{\displaystyle N}
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16:(Redirected from
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148:this article by
139:inline citations
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129:related reading
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1580:External links
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1549:Guard interval
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1120:
1111:at the values
1099:
1077:
1063:, this is the
1050:
1046:
1042:
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1033:
1023:. Now only if
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283:time-invariant
275:time-invariant
267:eigenfunctions
261:properties in
254:
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243:single carrier
235:
234:
223:
216:guard interval
214:It provides a
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176:
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133:external links
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1144:, since here
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287:eigenfunction
284:
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268:
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252:
250:
249:propagation.
248:
244:
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232:
228:
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221:
218:to eliminate
217:
213:
212:
211:
209:
205:
204:cyclic prefix
201:
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158:November 2021
151:
147:
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92:
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84:
81:This article
79:
70:
69:
64:
62:
55:
54:
49:
48:
43:
38:
29:
28:
19:
18:Cyclic Prefix
1281:
1000:
870:
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428:
304:
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236:
203:
197:
182:
164:
155:
144:Please help
136:
96:
86:
82:
58:
51:
45:
44:Please help
41:
301:Use in OFDM
291:convolution
202:, the term
150:introducing
1565:References
259:sinusoids'
99:March 2010
47:improve it
1506:−
1493:…
1254:⋅
1186:−
1122:≥
1041:≥
983:−
970:−
964:≤
958:≤
945:−
916:−
898:∑
834:−
814:…
722:−
708:…
669:−
649:−
635:…
611:−
559:−
503:−
489:…
393:−
380:…
263:multipath
253:Principle
247:multipath
53:talk page
1604:Category
1590:Archived
1543:See also
1166:becomes
1337:, i.e.
1311:is the
273:, and
146:improve
1282:where
279:linear
271:linear
208:symbol
131:, or
1089:and
306:OFDM
281:and
239:OFDM
1315:of
1196:mod
1067:of
269:of
198:In
1606::
1539:.
135:,
127:,
56:.
1596:.
1524:T
1517:]
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1499:d
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1474:0
1470:d
1463:[
1440:}
1437:]
1434:k
1431:[
1428:X
1425:{
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1402:k
1399:[
1396:H
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1373:k
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1367:H
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1242:H
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1227:Y
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1177:[
1174:x
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1010:y
986:2
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967:N
961:m
955:0
951:]
948:l
942:m
939:[
936:z
933:]
930:l
927:[
924:h
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908:0
905:=
902:l
894:=
891:]
888:m
885:[
882:y
867:.
852:T
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837:1
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825:L
820:h
807:1
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795:0
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784:[
778:=
774:h
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728:]
725:1
719:N
716:[
713:x
703:]
700:1
697:[
694:x
689:]
686:0
683:[
680:x
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672:1
666:N
663:[
660:x
655:]
652:2
646:N
643:[
640:x
630:]
627:1
624:+
619:1
615:L
608:N
605:[
602:x
596:[
590:=
586:z
562:1
554:1
550:L
537:.
522:T
515:]
509:]
506:1
500:N
497:[
494:x
484:]
481:1
478:[
475:x
470:]
467:0
464:[
461:x
455:[
449:=
445:x
411:T
404:]
396:1
390:N
386:d
373:1
369:d
361:0
357:d
350:[
344:=
340:d
316:N
189:)
183:(
171:)
165:(
160:)
156:(
142:.
101:)
97:(
63:)
59:(
20:)
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