Modulation Methods/Further OFDM Applications - Revision history

Guenter at 16:36, 23 January 2023

2023-01-23T16:36:56Z

Guenter at 15:30, 19 January 2023

2023-01-19T15:30:36Z

Hwang at 12:36, 19 January 2023

2023-01-19T12:36:15Z

Hwang at 12:35, 19 January 2023

2023-01-19T12:35:07Z

Hwang at 12:33, 19 January 2023

2023-01-19T12:33:41Z

Hwang at 12:28, 19 January 2023

2023-01-19T12:28:45Z

Hwang at 12:21, 19 January 2023

2023-01-19T12:21:48Z

Hwang at 12:20, 19 January 2023

2023-01-19T12:20:48Z

Hwang at 12:19, 19 January 2023

2023-01-19T12:19:22Z

Hwang at 12:06, 19 January 2023

2023-01-19T12:06:22Z

@@ Line 50: / Line 50: @@
 An asymmetrical signal space constellation allows hierarchical source coding.&nbsp; In poor transmission conditions,&nbsp; only the quadrant can be detected instead of the exact signal space point.&nbsp; Reception is thus still possible,&nbsp; albeit with&nbsp; (greatly)&nbsp; reduced image quality.
-[[File:EN_Mod_T_5_8_S2b_neu.png|right|frame| Net bit rates for DVB-T. Source: &nbsp; https://en.wikipedia.org/wiki/DVB-T#Technik '''KORREKTUR: coding rate, guard interval''']]
+[[File:EN_Mod_T_5_8_S2_neu.png|right|frame| Net bit rates for DVB-T. Source: &nbsp; https://en.wikipedia.org/wiki/DVB-T#Technik]]
 The table from WIKIPEDIA shows some resulting data rates for DVB-T depending on the channel coding rate &nbsp;$R_{\rm C}$&nbsp; and the duration &nbsp;$T_{\rm G}$&nbsp; of the guard interval.&nbsp; The relative code redundancy is &nbsp;$1 - R_{\rm C}$.&nbsp; This means that the larger the coding rate &nbsp;$R_{\rm C}$,&nbsp; the less redundancy is added.

@@ Line 51: / Line 51: @@
 [[File:EN_Mod_T_5_8_S2b_neu.png|right|frame| Net bit rates for DVB-T. Source: &nbsp; https://en.wikipedia.org/wiki/DVB-T#Technik '''KORREKTUR: coding rate, guard interval''']]
-The table from WIKIPEDIA shows some resulting data rates for DVB-T depending on the channel coding rate &nbsp;$R_{\rm C}$&nbsp; and the duration &nbsp;$T_{\rm G}$&nbsp; of the guard interval.&nbsp; The relative code redundancy is &nbsp;$1 - R_{\rm C}$.&nbsp; This means that the larger the code rate '''KORREKTUR: coding rate''' &nbsp;$R_{\rm C}$,&nbsp; the less redundancy is added.
+The table from WIKIPEDIA shows some resulting data rates for DVB-T depending on the channel coding rate &nbsp;$R_{\rm C}$&nbsp; and the duration &nbsp;$T_{\rm G}$&nbsp; of the guard interval.&nbsp; The relative code redundancy is &nbsp;$1 - R_{\rm C}$.&nbsp; This means that the larger the coding rate &nbsp;$R_{\rm C}$,&nbsp; the less redundancy is added.
 The numerical values can be interpreted as follows:
@@ Line 115: / Line 115: @@
 This leads to a different formula representation.&nbsp; For a clear distinction between the two approaches,
 [[File:P_ID1658__Mod_T_5_8_S4_neu.png |right|frame|DMT spectrum]]
-*we will use&nbsp; "OFDM"&nbsp; in the following only for a bandpass '''KORREKTUR: band-pass''' system,
+*we will use&nbsp; "OFDM"&nbsp; in the following only for a band-pass  system,
 *while the term&nbsp; "DMT"&nbsp; always refers to a baseband system.

@@ Line 2: / Line 2: @@
 {{Header
 |Untermenü=Multiple Access Methods
-|Vorherige Seite=Further OFDM Applications
+|Vorherige Seite=OFDM for 4G Networks
 |Nächste Seite=
 }}

@@ Line 142: / Line 142: @@
 :$$\begin{align*}s_\nu  & = \sum\limits_{\mu = 0}^{N - 1} {S (\mu \cdot f_0 ) \cdot {\rm{e} }^{ {\rm{j \hspace{0.03cm}\cdot \hspace{0.03cm}2 \pi } }  \hspace{0.03cm}\cdot \hspace{0.03cm} \nu \hspace{0.03cm}\cdot \hspace{0.03cm}\mu /{N} } } =S( 64 \cdot f_0 ) \cdot {\rm{e} }^{ {\rm{j \hspace{0.03cm}\cdot \hspace{0.03cm}2 \pi } } \hspace{0.03cm}\cdot \hspace{0.03cm} \nu \hspace{0.03cm}\cdot \hspace{0.03cm}64 /512} + S( 448 \cdot f_0 ) \cdot {\rm{e} }^{ {\rm{j \hspace{0.03cm}\cdot \hspace{0.03cm}2 \pi } }  \hspace{0.03cm}\cdot \hspace{0.03cm} \nu \hspace{0.03cm}\cdot \hspace{0.03cm}448 /512} = \\ & = {1}/ {2} \cdot (a + {\rm{j} } \cdot b ) \cdot {\rm{e} }^{ {\rm{j \hspace{0.03cm}\cdot \hspace{0.03cm}2 \pi } }  \hspace{0.03cm}\cdot \hspace{0.03cm} \nu \hspace{0.03cm}\cdot \hspace{0.03cm}64 /512} + {1}/{2} \cdot (a - {\rm{j} } \cdot b ) \cdot {\rm{e} }^{ {\rm{j \hspace{0.03cm}\cdot \hspace{0.03cm}2 \pi } }  \hspace{0.03cm}\cdot \hspace{0.03cm} \nu \hspace{0.03cm}\cdot \hspace{0.03cm}448 /512}.\end{align*}$$
-'''(2)''' &nbsp; Applying &nbsp;[[Signal_Representation/Calculating_With_Complex_Numbers#Darstellung_nach_Betrag_und_Phase|$\text{Euler's theorem}$]]&nbsp; to this,&nbsp; we get:
+'''(2)''' &nbsp; Applying &nbsp;[[Signal_Representation/Calculating_with_Complex_Numbers#Representation_by_magnitude_and_phase|$\text{Euler's theorem}$]]&nbsp; to this,&nbsp; we get:
 :$$s_\nu   = \frac{a + {\rm{j} } \cdot b } {2}  \cdot \left[ {\rm{cos} } ( 2\pi \cdot  \frac{ {64} } { {512} }\cdot \nu  ) + {\rm{j} } \cdot {\rm{sin} } ( 2\pi \cdot  \frac{ {64} } { {512} }\cdot \nu  ) \right] + \frac{a - {\rm{j} } \cdot b } {2}  \cdot \left[ {\rm{cos} } ( 2\pi \cdot  \frac{ {448} } { {512} }\cdot \nu  ) + {\rm{j} } \cdot {\rm{sin} } ( 2\pi \cdot  \frac{ {448} } { {512} }\cdot \nu  )\right],$$
 :&nbsp;where:

@@ Line 115: / Line 115: @@
 This leads to a different formula representation.&nbsp; For a clear distinction between the two approaches,
 [[File:P_ID1658__Mod_T_5_8_S4_neu.png |right|frame|DMT spectrum]]
-*we will use&nbsp; "OFDM"&nbsp; in the following only for a bandpass system,
+*we will use&nbsp; "OFDM"&nbsp; in the following only for a bandpass '''KORREKTUR: band-pass''' system,
 *while the term&nbsp; "DMT"&nbsp; always refers to a baseband system.

@@ Line 95: / Line 95: @@
 :*either for&nbsp; "upstream"&nbsp; $($transmission into the network, &nbsp;$32$ bins, &nbsp;$\text{138 kHz)}$&nbsp;
 :*or for&nbsp; "downstream"&nbsp; $($transmission out of the network, &nbsp;$192$ bins, &nbsp;$\text{828 kHz)}$.&nbsp;
-*All ADSL lines from&nbsp; "Deutsche Telekom"&nbsp; are switched according to theeither "ADSL-over-ISDN"either standard,&nbsp; so that parallel operation with ISDN is possible.&nbsp; For this purpose,&nbsp; the frequency range up to &nbsp;$\text{138 kHz}$&nbsp; is not used for ADSL and the corresponding bins are set to zero.
+*All ADSL lines from&nbsp; "Deutsche Telekom"&nbsp; are switched according to the "ADSL-over-ISDN" standard,&nbsp; so that parallel operation with ISDN is possible.&nbsp; For this purpose,&nbsp; the frequency range up to &nbsp;$\text{138 kHz}$&nbsp; is not used for ADSL and the corresponding bins are set to zero.
 *"ADSL-over-ISDN"&nbsp; and not&nbsp; "ADSL-over-POTS"&nbsp; is also used for analog connections,&nbsp; although this wastes precisely that frequency range which has a particularly favorable&nbsp; (low)&nbsp; cable attenuation.

@@ Line 50: / Line 50: @@
 An asymmetrical signal space constellation allows hierarchical source coding.&nbsp; In poor transmission conditions,&nbsp; only the quadrant can be detected instead of the exact signal space point.&nbsp; Reception is thus still possible,&nbsp; albeit with&nbsp; (greatly)&nbsp; reduced image quality.
-[[File:EN_Mod_T_5_8_S2b_neu.png|right|frame| Net bit rates for DVB-T. Source: &nbsp; https://en.wikipedia.org/wiki/DVB-T#Technik]]
+[[File:EN_Mod_T_5_8_S2b_neu.png|right|frame| Net bit rates for DVB-T. Source: &nbsp; https://en.wikipedia.org/wiki/DVB-T#Technik '''KORREKTUR: code rate, guard interval''']]
 The table from WIKIPEDIA shows some resulting data rates for DVB-T depending on the channel coding rate &nbsp;$R_{\rm C}$&nbsp; and the duration &nbsp;$T_{\rm G}$&nbsp; of the guard interval.&nbsp; The relative code redundancy is &nbsp;$1 - R_{\rm C}$.&nbsp; This means that the larger the code rate &nbsp;$R_{\rm C}$,&nbsp; the less redundancy is added.