Aufgaben:Exercise 5.8: Equalization in Matrix Vector Notation - Revision history

Guenter at 14:50, 31 January 2022

2022-01-31T14:50:10Z

Guenter at 16:49, 24 January 2022

2022-01-24T16:49:05Z

Guenter at 16:37, 24 January 2022

2022-01-24T16:37:56Z

Hwang at 10:26, 29 December 2021

2021-12-29T10:26:40Z

Hwang at 10:24, 29 December 2021

2021-12-29T10:24:04Z

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Guenter at 15:59, 14 December 2021

2021-12-14T15:59:19Z

Guenter: Guenter moved page Aufgaben:Aufgabe 5.8: Entzerrung in Matrix–Vektor–Notation to Aufgaben:Exercise 5.8: Equalization in Matrix Vector Notation

2021-12-14T15:56:25Z

Guenter moved page Aufgabe 5.8: Entzerrung in Matrix–Vektor–Notation to Exercise 5.8: Equalization in Matrix Vector Notation

Javier: Text replacement - "”" to """

2021-05-28T14:43:19Z

Text replacement - "”" to """

Javier: Text replacement - "„" to """

2021-05-28T14:42:37Z

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Javier: Text replacement - "Category:Aufgaben zu Modulationsverfahren" to "Category:Modulation Methods: Exercises"

2021-03-23T13:01:50Z

Text replacement - "Category:Aufgaben zu Modulationsverfahren" to "Category:Modulation Methods: Exercises"

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 }}
-[[File:P_ID1663__A_5_8.png|right|frame|Block diagram of OFDM transmission   '''KORREKTUR''': cyclic prefix ...]]
+[[File:EN_A_5_8.png|right|frame|Block diagram of OFDM transmission]]
 We consider the blocks of an OFDM system shown in the diagram,&nbsp; assuming a system with &nbsp;$N = 4$&nbsp; carriers and a channel with &nbsp;$L = 2$&nbsp; echoes.
 *Only a single frame is considered and for the transmission vector&nbsp; (in the time domain),&nbsp; we apply:

@@ Line 89: / Line 89: @@
-'''(3)'''&nbsp;  The vector&nbsp; ${\rm\bf{R}}$&nbsp; of spectral coefficients downstream of the channel could be calculated by DFT of the vector &nbsp; ${\rm\bf{r}}$&nbsp;, analogous to subtask&nbsp; '''(2)'''.&nbsp;
+'''(3)'''&nbsp;  The vector&nbsp; ${\rm\bf{R}}$&nbsp; of spectral coefficients after the channel could be calculated by DFT of the vector &nbsp; ${\rm\bf{r}}$,&nbsp; analogous to subtask&nbsp; '''(2)'''.&nbsp;
 *An alternative solution path is:
 :$${\rm\bf{R}} = {\rm\bf{D}} \cdot \left( {\begin{array}{*{20}c}
@@ Line 119: / Line 119: @@
-'''(5)'''&nbsp;  The equalization calculated in&nbsp; '''(4)'''&nbsp; follows the "zero forcing" approach &nbsp; &rArr; &nbsp; <u>solution 1</u>.
+'''(5)'''&nbsp;  The equalization calculated in&nbsp; '''(4)'''&nbsp; follows the&nbsp; "zero forcing"&nbsp; approach &nbsp; &rArr; &nbsp; <u>solution 1</u>.
 {{ML-Fuß}}

@@ Line 4: / Line 4: @@
 [[File:P_ID1663__A_5_8.png|right|frame|Block diagram of OFDM transmission   '''KORREKTUR''': cyclic prefix ...]]
-We consider the blocks of an OFDM system shown in the diagram, assuming a system with &nbsp;$N = 4$&nbsp; carriers and a channel with &nbsp;$L = 2$&nbsp; echoes.
+We consider the blocks of an OFDM system shown in the diagram,&nbsp; assuming a system with &nbsp;$N = 4$&nbsp; carriers and a channel with &nbsp;$L = 2$&nbsp; echoes.
-*Only a single frame is considered and for the transmission vector (in the time domain), we apply:
+*Only a single frame is considered and for the transmission vector&nbsp; (in the time domain),&nbsp; we apply:
 :$${\rm\bf{d}} = (d_0, \ d_1,\ d_2,\ d_3 ) = (+1,  -1,  +1,  -1 ).$$
 *Let the channel impulse response be described by
 :$${\rm\bf{h}} = (h_0, \ h_1,\ h_2 ) = (0, \ 0.6, \ 0.4 ).$$
-*To represent the cyclic prefix in this task, instead of the extended transmit vector with the associated transmission matrix &nbsp;${\rm\bf{H}}_{\rm ext}$,&nbsp; we use the cyclic transmission matrix
+*To represent the cyclic prefix in this task,&nbsp; instead of the extended transmission vector with the associated transmission matrix &nbsp;${\rm\bf{H}}_{\rm ext}$,&nbsp; we use the cyclic transmission matrix
 :$${\rm\bf{H}}_{\rm{C}} = \left( {\begin{array}{*{20}c} {h_0 } & {h_1 } & {h_2 } & {} \\ {} & {h_0 } & {h_1 } & {h_2 } \\ \hline {h_2 } & {} & {h_0 } & {h_1 } \\ {h_1 } & {h_2 } & {} & {h_0 } \\ \end{array}} \right).$$
-*For the spectral coefficients at the receiver, according to the Discrete Fourier Transform&nbsp; $\rm (DFT)$:
+*For the spectral coefficients at the receiver,&nbsp; according to the Discrete Fourier Transform&nbsp; $\rm (DFT)$:
 :$${\rm\bf{R}} = {\rm\bf{D}} \cdot \left( {\begin{array}{*{20}c} {H_0 } & {} & {} & {} \\ {} & {H_1 } & {} & {} \\ {} & {} & {H_2 } & {} \\ {} & {} & {} & {H_3 } \\ \end{array}} \right) ,$$
 :where the diagonal elements are to be calculated as follows:
@@ Line 24: / Line 24: @@
-''Notes:''
+Notes:
 *The exercise belongs to the chapter&nbsp; [[Modulation_Methods/Realisierung_von_OFDM-Systemen|Implementation of OFDM Systems]].
-*Reference is also made to the chapter&nbsp;  [[Signal_Representation/Discrete_Fourier_Transform_(DFT)|Discrete Fourier Transform]]&nbsp; in the book "Signal Representation".
+*Reference is also made to the chapter&nbsp;  [[Signal_Representation/Discrete_Fourier_Transform_(DFT)|Discrete Fourier Transform]]&nbsp; in the book&nbsp; "Signal Representation".
 *For the Discrete Fourier Transform (DFT) in matrix-vector notation holds:
@@ Line 36: / Line 36: @@
 <quiz display=simple>
-{Calculate the discrete reception values &nbsp;$r = (r_0, r_1, r_2, r_3)$&nbsp; in the time domain.&nbsp; Enter &nbsp;$r_0$&nbsp; and &nbsp;$r_1$&nbsp; as a check:
+{Calculate the discrete reception values &nbsp;$r = (r_0, r_1, r_2, r_3)$&nbsp; in the time domain.&nbsp; Enter &nbsp;$r_0$&nbsp; and &nbsp;$r_1$&nbsp; as a check.
 |type="{}"}
 ${\rm Re}\big[r_0\big] \ = \ $ { -0.202--0.198 }
@@ Line 50: / Line 50: @@
 ${\rm Im}\big[D_3\big] \ = \ $ { 0. }
-{Calculate the discrete spectral coefficients &nbsp;${\rm\bf{R}}= (R_0, R_1, R_2, R_3)$&nbsp; according to the channel.&nbsp; Enter &nbsp;$R_2$&nbsp; and &nbsp;$R_3$&nbsp; as a check:
+{Calculate the discrete spectral coefficients &nbsp;${\rm\bf{R}}= (R_0, R_1, R_2, R_3)$&nbsp; according to the channel.&nbsp; Enter &nbsp;$R_2$&nbsp; and &nbsp;$R_3$&nbsp; as a check.
 |type="{}"}
 ${\rm Re}\big[R_2\big] \ = \ $   { -0.202--0.198 }
@@ Line 57: / Line 57: @@
 ${\rm Im}\big[R_3\big] \ = \ $ { 0. }
-{ Determine the discrete equalizer coefficients &nbsp;${\rm\bf{e}}= (e_0, e_1, e_2, e_3)$:
+{ Determine the discrete equalizer coefficients &nbsp;${\rm\bf{e}}= (e_0, e_1, e_2, e_3)$.
 |type="{}"}
 ${\rm Re}\big[e_0\big] \ = \ $ { 1 1% }
@@ Line 71: / Line 71: @@
 |type="()"}
 + As "Zero Forcing" approach,
-- as "matched filter" approach,
+- as "Matched Filter" approach,
 - as "Minimum Mean Square Error&nbsp; $\rm (MMSE)$”approach.
 </quiz>

← Older revision		Revision as of 10:26, 29 December 2021
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−	{{quiz-Header\|Buchseite=~~Modulationsverfahren~~/~~Realisierung von OFDM-Systemen~~	+	{{quiz-Header\|Buchseite=Modulation_Methods/Implementation_of_OFDM_Systems
	}}		}}

← Older revision		Revision as of 15:59, 14 December 2021
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−	[[Category:Modulation Methods: Exercises\|^5.6 ~~Realisierung von~~ OFDM~~-Systemen~~^]]	+	[[Category:Modulation Methods: Exercises\|^5.6 Realization of OFDM Systems^]]

← Older revision	Revision as of 15:56, 14 December 2021
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← Older revision		Revision as of 14:43, 28 May 2021
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−	'''(5)'''  Die unter  '''(4)'''  berechnete Entzerrung folgt dem "Zero Forcing~~”~~–Ansatz   ⇒   <u>Antwort 1</u>.	+	'''(5)'''  Die unter  '''(4)'''  berechnete Entzerrung folgt dem "Zero Forcing"–Ansatz   ⇒   <u>Antwort 1</u>.

	{{ML-Fuß}}		{{ML-Fuß}}

← Older revision		Revision as of 14:42, 28 May 2021
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−	'''(5)'''  Die unter  '''(4)'''  berechnete Entzerrung folgt dem ~~&bdquo;~~Zero Forcing”–Ansatz   ⇒   <u>Antwort 1</u>.	+	'''(5)'''  Die unter  '''(4)'''  berechnete Entzerrung folgt dem "Zero Forcing”–Ansatz   ⇒   <u>Antwort 1</u>.

	{{ML-Fuß}}		{{ML-Fuß}}

← Older revision		Revision as of 13:01, 23 March 2021
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−	[[Category:~~Aufgaben zu Modulationsverfahren~~\|^5.6 Realisierung von OFDM-Systemen^]]	+	[[Category:Modulation Methods: Exercises\|^5.6 Realisierung von OFDM-Systemen^]]