1578:
105:
63:
22:
1348:. 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
746:
854:
413:
1526:
524:
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278:. 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
226:
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:
231:
134:
1377:, for the duration in which the channel does not vary significantly, merely multiplying the received demodulated symbols by the inverse of
227:
866:
1598:
741:{\displaystyle \mathbf {z} ={\begin{bmatrix}x&\ldots &x&x&x&x&\ldots &x\end{bmatrix}}^{\textsf {T}}.}
297:
uses cyclic prefixes to combat multipath by making channel estimation easy. As an example, consider an OFDM system that has
214:
It repeats the end of the symbol so the linear convolution of a frequency-selective multipath channel can be modeled as
174:
156:
49:
849:{\displaystyle \mathbf {h} ={\begin{bmatrix}h_{0}&h_{1}&\ldots &h_{L_{2}-1}\end{bmatrix}}^{\textsf {T}}}
127:
79:
422:(IDFT) of the message symbol, followed by a cyclic prefixing. Let the symbol obtained by the IDFT be denoted by
408:{\displaystyle \mathbf {d} ={\begin{bmatrix}d_{0}&d_{1}&\ldots &d_{N-1}\end{bmatrix}}^{\textsf {T}}}
35:
1575:
222:. This approach accommodates simple frequency domain processing, such as channel estimation and equalization.
1301:
419:
219:
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117:
1547:
1521:{\displaystyle {\begin{bmatrix}d_{0}&d_{1}&\ldots &d_{N-1}\end{bmatrix}}^{\textsf {T}}}
208:
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1329:
1307:
1136:
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519:{\displaystyle \mathbf {x} ={\begin{bmatrix}x&x&\ldots &x\end{bmatrix}}^{\textsf {T}}}
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8:
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286:, and thus, preserve this property in the part of the symbol after the cyclic prefix.
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76:
Needs a more accessible introduction, especially the second bullet point.
1563:, by David Tse and Pramod Viswanath, Cambridge University Press (2005).
1205:. Hence, taking the discrete Fourier transform of these values, we get
246:
A cyclic prefix is often used in conjunction with modulation to retain
247:
980:{\displaystyle y=\sum _{l=0}^{L-1}hz\quad 0\leq m\leq N-L_{1}-2}
267:
259:
218:, which in turn may transform to the frequency domain via a
294:
860:
Then, the convolution with this channel, which happens as
254:
channels. It is well known that sinusoidal signals are
230:
systems, however the cyclic prefix is now also used in
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systems. Therefore, if the channel is assumed to be
317:subcarriers. The message symbol can be written as:
274:, then a sinusoid of infinite duration would be an
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1197:
1147:
1125:
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1004:
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848:
740:
555:
518:
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309:
1576:the significance of cyclic prefix in OFDM systems
1590:
126:but its sources remain unclear because it lacks
751:Assume that the channel is represented using
418:The OFDM symbol is constructed by taking the
1428:
1413:
530:Prefixing it with a cyclic prefix of length
72:needs attention from an expert in Technology
50:Learn how and when to remove these messages
1441:and hence, the estimate of actual symbols
1512:
1188:
1187:
840:
729:
510:
399:
175:Learn how and when to remove this message
157:Learn how and when to remove this message
282:of the channel appear as though it were
1591:
1561:Fundamentals of Wireless Communication
82:may be able to help recruit an expert.
234:systems to improve the robustness to
98:
56:
15:
13:
420:inverse discrete Fourier transform
14:
1610:
1568:
31:This article has multiple issues.
1599:Quantized radio modulation modes
1334:
1312:
1141:
1086:
1064:
998:
990:results in the received symbols
762:
574:
433:
328:
103:
61:
20:
1183:
1045:{\displaystyle L_{1}\geq L_{2}}
942:
563:, the OFDM symbol obtained is:
39:or discuss these issues on the
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1:
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195:refers to the prefixing of a
1341:{\displaystyle \mathbf {d} }
1319:{\displaystyle \mathbf {x} }
1148:{\displaystyle \mathbf {z} }
1093:{\displaystyle \mathbf {h} }
1071:{\displaystyle \mathbf {z} }
1005:{\displaystyle \mathbf {y} }
241:
7:
1531:
1126:{\displaystyle m\geq L_{1}}
74:. The specific problem is:
10:
1615:
1302:discrete Fourier transform
1260:{\displaystyle Y=H\cdot X}
220:discrete Fourier transform
211:from the previous symbol.
1548:Intersymbol interference
1406:yields the estimates of
209:intersymbol interference
112:This article includes a
556:{\displaystyle L_{1}-1}
141:more precise citations.
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80:WikiProject Technology
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1434:{\displaystyle \{X\}}
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1574:A short tutorial on
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1054:circular convolution
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284:circular convolution
216:circular convolution
1581:2023-10-05 at the
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189:telecommunications
114:list of references
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1399:{\displaystyle H}
1370:{\displaystyle H}
1293:{\displaystyle X}
1198:{\displaystyle x}
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310:{\displaystyle N}
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137:this article by
128:inline citations
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118:related reading
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1569:External links
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1540:
1538:Guard interval
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1120:
1116:
1112:
1109:
1100:at the values
1088:
1066:
1052:, this is the
1039:
1035:
1031:
1026:
1022:
1012:. Now only if
1000:
988:
987:
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272:time-invariant
264:time-invariant
256:eigenfunctions
250:properties in
243:
240:
232:single carrier
224:
223:
212:
205:guard interval
203:It provides a
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122:external links
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1133:, since here
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276:eigenfunction
273:
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239:
238:propagation.
237:
233:
229:
221:
217:
213:
210:
207:to eliminate
206:
202:
201:
200:
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194:
193:cyclic prefix
190:
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147:November 2021
140:
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70:This article
68:
59:
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38:
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18:
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1270:
989:
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153:
144:
133:Please help
125:
85:
75:
71:
47:
40:
34:
33:Please help
30:
290:Use in OFDM
280:convolution
191:, the term
139:introducing
1554:References
248:sinusoids'
88:March 2010
36:improve it
1495:−
1482:…
1243:⋅
1175:−
1111:≥
1030:≥
972:−
959:−
953:≤
947:≤
934:−
905:−
887:∑
823:−
803:…
711:−
697:…
658:−
638:−
624:…
600:−
548:−
492:−
478:…
382:−
369:…
252:multipath
242:Principle
236:multipath
42:talk page
1593:Category
1579:Archived
1532:See also
1155:becomes
1326:, i.e.
1300:is the
262:, and
135:improve
1271:where
268:linear
260:linear
197:symbol
120:, or
1078:and
295:OFDM
270:and
228:OFDM
1304:of
1185:mod
1056:of
258:of
187:In
1595::
1528:.
124:,
116:,
45:.
1585:.
1513:T
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925:z
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916:[
913:h
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767:=
763:h
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591:x
585:[
579:=
575:z
551:1
543:1
539:L
526:.
511:T
504:]
498:]
495:1
489:N
486:[
483:x
473:]
470:1
467:[
464:x
459:]
456:0
453:[
450:x
444:[
438:=
434:x
400:T
393:]
385:1
379:N
375:d
362:1
358:d
350:0
346:d
339:[
333:=
329:d
305:N
178:)
172:(
160:)
154:(
149:)
145:(
131:.
90:)
86:(
52:)
48:(
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