Aufgaben:Exercise 4.4: Modulation in LTE - Revision history

Javier: Text replacement - "Category:Exercises for Mobile Communications" to "Category:Mobile Communications: Exercises"

2021-03-23T12:37:43Z

Text replacement - "Category:Exercises for Mobile Communications" to "Category:Mobile Communications: Exercises"

Guenter at 17:20, 11 March 2021

2021-03-11T17:20:50Z

Guenter at 10:14, 9 March 2021

2021-03-09T10:14:12Z

Guenter at 10:04, 9 March 2021

2021-03-09T10:04:56Z

Guenter at 10:02, 9 March 2021

2021-03-09T10:02:53Z

Guenter at 15:36, 6 February 2021

2021-02-06T15:36:56Z

Guenter at 15:20, 6 February 2021

2021-02-06T15:20:05Z

Guenter at 17:52, 5 February 2021

2021-02-05T17:52:23Z

Guenter at 17:51, 5 February 2021

2021-02-05T17:51:38Z

Guenter at 17:43, 5 February 2021

2021-02-05T17:43:37Z

← Older revision		Revision as of 12:37, 23 March 2021
Line 86:		Line 86:


−	[[Category:~~Exercises for~~ Mobile Communications\|^4.4 Physical Layer in LTE^]]	+	[[Category:Mobile Communications: Exercises\|^4.4 Physical Layer in LTE^]]

@@ Line 4: / Line 4: @@
-[[File:EN_Mob_A_4_4.png|right|frame|Throughput comparison for LTE]]
+[[File:EN_Mob_A_4_4_neu1.png|right|frame|Throughput comparison for LTE]]
 With LTE, the scheduler selects the appropriate modulation method depending on the nature of the environment and the distance of the user from the base station.&nbsp; In this task, we consider various&nbsp; [[Modulation_Methods/Quadratur%E2%80%93Amplitudenmodulation#Allgemeine_Beschreibung_und_Signalraumzuordnung|Quadrature Amplitude Modulation]]&nbsp; $\rm (QAM)$&nbsp; procedures, namely
 *$\rm 4–QAM$&nbsp; with&nbsp; $b\text{ = 2 bit/symbol}$,
@@ Line 66: / Line 66: @@
-[[File:EN_Mob_A_4_4b.png|right|frame|Throughput of the QAM versions]]
+[[File:EN_Mob_A_4_4b_neu1.png|right|frame|Throughput of the QAM versions]]
 '''(2)'''&nbsp; Compare here the two curves labeled&nbsp; $2 \  \rm bit/symbol$&nbsp; and &nbsp;$4  \ \rm bit/symbol$.
 *The point of intersection is&nbsp; $10 \cdot {\rm lg \ SNR_{1}}\hspace{0.15cm}\underline{ \approx 15 \ \rm dB}$.

@@ Line 67: / Line 67: @@
 [[File:EN_Mob_A_4_4b.png|right|frame|Throughput of the QAM versions]]
-'''(2)'''&nbsp; Compare here the two curves labeled "$2 \  \rm bit/symbol$" and "$4  \ \rm bit/symbol$".
+'''(2)'''&nbsp; Compare here the two curves labeled&nbsp; $2 \  \rm bit/symbol$&nbsp; and &nbsp;$4  \ \rm bit/symbol$.
 *The point of intersection is&nbsp; $10 \cdot {\rm lg \ SNR_{1}}\hspace{0.15cm}\underline{ \approx 15 \ \rm dB}$.
 * It follows immediately: &nbsp; The 16-QAM only results in a higher throughput than the 4-QAM if&nbsp; $10 \cdot {\rm lg \ SNR} > 15 \ \ \rm dB$.
@@ Line 73: / Line 73: @@
-'''(3)'''&nbsp; $10 \cdot {\rm  lg \ SNR_{2}}\hspace{0.15cm}\underline{ \approx 22 \ \rm dB}$&nbsp; results from the intersection of the two curves&nbsp; "$4 \ \rm bit/symbol$" and&nbsp; "$6 \ \rm bit/symbol$".
+'''(3)'''&nbsp; $10 \cdot {\rm  lg \ SNR_{2}}\hspace{0.15cm}\underline{ \approx 22 \ \rm dB}$&nbsp; results from the intersection of the two curves&nbsp; $4 \ \rm bit/symbol$&nbsp; and&nbsp; $6 \ \rm bit/symbol$.
-'''(4)'''&nbsp; From the diagram you can see that with 4-QAM&nbsp; ($2  \rm bit/symbol$)&nbsp; the throughput is (almost) zero.
+'''(4)'''&nbsp; From the diagram you can see that with 4-QAM&nbsp; $(2  \rm bit/symbol)$&nbsp; the throughput is (almost) zero.
-*In this comparison, the QPSK is identical to the 4-QAM and therefore also unsuitable.
+*In this comparison, the QPSK is identical to the 4-QAM and therefore unsuitable, too.
-*Better would be "Binary Phase Shift Keying" (BPSK), which corresponds to the lowest curve&nbsp; "$1\ \rm bit/symbol$" &nbsp; &rArr; &nbsp; <u>solution 1</u>.
+*Better would be "Binary Phase Shift Keying"&nbsp; $\rm (BPSK)$, which corresponds to the lowest curve&nbsp; $1\ \rm bit/symbol$ &nbsp; &rArr; &nbsp; <u>solution 1</u>.
 {{ML-Fuß}}

@@ Line 25: / Line 25: @@
 ''Notes:''
 *This task belongs to the chapter&nbsp; [[Mobile_Communications/Physical_Layer_for_LTE|Physical Layer for LTE]].
-*Reference is made in particular to the pages&nbsp; [[Mobile_Communications/Physical_Layer_for_LTE#Modulation_for_LTE|Modulation for LTE]]&nbsp; as well as to chapter&nbsp; [[Modulation_Methods#collapse4|Digital Modulation methods]]&nbsp; in the book „Modulation Methods”.
+*Reference is made in particular to the pages&nbsp; [[Mobile_Communications/Physical_Layer_for_LTE#Modulation_for_LTE|Modulation for LTE]]&nbsp; as well as to chapter&nbsp; [[Modulation_Methods#collapse4|Digital Modulation Methods]]&nbsp; in the book „Modulation Methods”.
 * In subtask&nbsp; '''(1)'''&nbsp; the areas &nbsp;$\rm A$, &nbsp;$\rm B$&nbsp; and &nbsp;$\rm C$&nbsp; shown in the above sketch are to be assigned to the modulation methods 4-QAM, 16-QAM and 64-QAM.
 *The literature reference [MG08] refers to: &nbsp; Myung, H.; Goodman, D.: <br>&nbsp; &nbsp; Single Carrier FDMA - A New Air Interface for Long Term Evolution. West Sussex: John Wiley & Sons, 2008.

@@ Line 6: / Line 6: @@
 [[File:EN_Mob_A_4_4.png|right|frame|Throughput comparison for LTE]]
 With LTE, the scheduler selects the appropriate modulation method depending on the nature of the environment and the distance of the user from the base station.&nbsp; In this task, we consider various&nbsp; [[Modulation_Methods/Quadratur%E2%80%93Amplitudenmodulation#Allgemeine_Beschreibung_und_Signalraumzuordnung|Quadrature Amplitude Modulation]]&nbsp; $\rm (QAM)$&nbsp; procedures, namely
-*&nbsp; 4&ndash;QAM&nbsp; with&nbsp; $b\text{ = 2 bit/symbol}$,
+*$\rm 4–QAM$&nbsp; with&nbsp; $b\text{ = 2 bit/symbol}$,
-*16&ndash;QAM&nbsp; with&nbsp; $b\text{ = 4 bit/symbol}$,
+*$\rm 16–QAM$&nbsp; with&nbsp; $b\text{ = 4 bit/symbol}$,
-*64&ndash;QAM&nbsp; with&nbsp; $b\text{ = 6 bit/symbol}$.
+*$\rm 64–QAM$&nbsp; with&nbsp; $b\text{ = 6 bit/symbol}$.
-Formally, these procedures can be described as&nbsp; $b^{2}&ndash;{\rm QAM}$.&nbsp; The signal space constellations for 16-QAM and 64-QAM are shown on the right. The bright dots indicate the 4&ndash;QAM.
+Formally, these procedures can be described as&nbsp; $b^{2}&ndash;{\rm QAM}$.&nbsp; The signal space constellations for 16-QAM and 64-QAM are shown on the right.&nbsp; The bright dots indicate the 4&ndash;QAM.
-The lower diagram from&nbsp; [MG08]&nbsp; shows for different&nbsp; $b$&nbsp; values the throughput depending on&nbsp; $10 \cdot {\rm lg \ SNR}$&nbsp; <br>with $\rm SNR$: &nbsp; &nbsp; "signal-to-noise ratio".
+The lower diagram from &nbsp; [MG08] &nbsp; shows for different&nbsp; $b$&nbsp; values the throughput depending on&nbsp; $10 \cdot {\rm lg \ SNR}$&nbsp; <br>with $\rm SNR$ &nbsp; &rArr; &nbsp; "signal-to-noise ratio".
 You can see that for a very good channel $($very large&nbsp; $\rm SNR)$&nbsp; the throughput is approximately proportional to&nbsp;$b$.

@@ Line 25: / Line 25: @@
 ''Notes:''
 *This task belongs to the chapter&nbsp; [[Mobile_Communications/Physical_Layer_for_LTE|Physical Layer for LTE]].
-*Reference is made in particular to the pages&nbsp; [[Mobile_Communications/Physical_Layer_for_LTE#Modulation_for_LTE|Modulation for LTE]]&nbsp; as well as&nbsp; [[Modulation_Methods#collapse4|Digital Modulation methods]]&nbsp; in the book „Modulation Methods”.
+*Reference is made in particular to the pages&nbsp; [[Mobile_Communications/Physical_Layer_for_LTE#Modulation_for_LTE|Modulation for LTE]]&nbsp; as well as to chapter&nbsp; [[Modulation_Methods#collapse4|Digital Modulation methods]]&nbsp; in the book „Modulation Methods”.
 * In subtask&nbsp; '''(1)'''&nbsp; the areas &nbsp;$\rm A$, &nbsp;$\rm B$&nbsp; and &nbsp;$\rm C$&nbsp; shown in the above sketch are to be assigned to the modulation methods 4-QAM, 16-QAM and 64-QAM.
-*The literature reference [MG08] refers to: &nbsp; <br>Myung, H.; Goodman, D.: Single Carrier FDMA - A New Air Interface for Long Term Evolution. West Sussex: John Wiley & Sons, 2008.
+*The literature reference [MG08] refers to: &nbsp; Myung, H.; Goodman, D.: <br>&nbsp; &nbsp; Single Carrier FDMA - A New Air Interface for Long Term Evolution. West Sussex: John Wiley & Sons, 2008.
@@ Line 37: / Line 37: @@
 {Which assignments apply in the areas  &nbsp;$\rm A$, &nbsp;$\rm B$&nbsp; and &nbsp;$\rm C$?
 |type="[]"}
-- The modulation method for area &nbsp;$\rm A$&nbsp; is 4-QAM.
+- The modulation method for area &nbsp;$\rm A$&nbsp; is&nbsp; 4-QAM.
-+ The modulation method for area &nbsp;$\rm B$&nbsp; is 16-QAM.
++ The modulation method for area &nbsp;$\rm B$&nbsp; is&nbsp; 16-QAM.
-- The modulation method for area &nbsp;$\rm C$&nbsp; is 64-QAM.
+- The modulation method for area &nbsp;$\rm C$&nbsp; is&nbsp; 64-QAM.
-{From what signal-to-noise ratio&nbsp; $(\rm SNR_{1})$&nbsp; is 16-QAM better than 4-QAM?
+{From which signal-to-noise ratio&nbsp; $(\rm SNR_{1})$&nbsp; is 16-QAM better than 4-QAM?
 |type="{}"}
 $10 \cdot \rm lg \ SNR_{1} \ = \ $ { 15 3% } $\ \rm dB$
-{From what signal-to-noise ratio $(\rm SNR_{2})$ is 64-QAM better than 16-QAM?
+{From which signal-to-noise ratio&nbsp; $(\rm SNR_{2})$&nbsp; is 64-QAM better than 16-QAM?
 |type="{}"}
 $10 \cdot \rm lg \ SNR_{2} \ = \ $ { 22 3% } $\ \rm dB$
@@ Line 51: / Line 51: @@
 {Which modulation method would be most suitable for&nbsp; $10 \cdot {\rm lg \ SNR} = 5 \ \rm dB$&nbsp;?
 |type="()"}
-+ BPSK (''Binary Phase Shift Keying''),
++ BPSK&nbsp; ("Binary Phase Shift Keying"),
-- QPSK (''Quadrature Phase Shift Keying''),
+- QPSK&nbsp; ("Quaternary Phase Shift Keying"),
-- 4–QAM.
+- 4–QAM&nbsp; ("Quadrature Amplitude Modulation").
 </quiz>
@@ Line 60: / Line 60: @@
 {{ML-Kopf}}
-'''(1)'''&nbsp;  Correct is only the <u>solution 2</u>:
+'''(1)'''&nbsp;  Correct is only the&nbsp; <u>solution 2</u>:
-*The area close to the transmitter &nbsp;$\rm A$&nbsp; usually has the best reception conditions. Here the 64-QAM modulation method can be used, which allows the highest throughput under ideal conditions, but also degrades the most when the SNR decreases.
+*The area close to the transmitter &nbsp;$\rm A$&nbsp; usually has the best reception conditions.&nbsp; Here the 64-QAM modulation method can be used, which allows the highest throughput under ideal conditions, but also degrades the most when the SNR decreases.
-*64-QAM, on the other hand, is not suitable for the remote area &nbsp;$\rm C$&nbsp;. Here it is better to use the lowest level modulation method 4-QAM.
+*64-QAM, on the other hand, is not suitable for the remote area &nbsp;$\rm C$&nbsp;.&nbsp; Here it is better to use the lowest level modulation method "4-QAM".
 [[File:EN_Mob_A_4_4b.png|right|frame|Throughput of the QAM versions]]
-'''(2)'''&nbsp; Compare here the two curves labeled "$2 \ \ \rm bit/Symbol$" and "$4 \ \ \rm bit/Symbol$".
+'''(2)'''&nbsp; Compare here the two curves labeled "$2 \  \rm bit/symbol$" and "$4  \ \rm bit/symbol$".
-*The point of intersection is $10 \cdot {\rm lg \ SNR_{1}}\hspace{0.15cm}\underline{ \approx 15 \ \rm dB}$.
+*The point of intersection is&nbsp; $10 \cdot {\rm lg \ SNR_{1}}\hspace{0.15cm}\underline{ \approx 15 \ \rm dB}$.
-* It follows immediately: The 16-QAM only results in a higher throughput than the 4-QAM if $10 \cdot {\rm lg \ SNR} > 15 \ \ \rm dB$.
+* It follows immediately: &nbsp; The 16-QAM only results in a higher throughput than the 4-QAM if&nbsp; $10 \cdot {\rm lg \ SNR} > 15 \ \ \rm dB$.
-'''(3)'''&nbsp; The result $10 \cdot {\rm  lg \ SNR_{2}}\hspace{0.15cm}\underline{ \approx 22 \ \rm dB}$ results from the intersection of the two curves „$4 \ \rm bit/Symbol$” and „$6 \ \rm bit/Symbol$”.
+'''(3)'''&nbsp; $10 \cdot {\rm  lg \ SNR_{2}}\hspace{0.15cm}\underline{ \approx 22 \ \rm dB}$&nbsp; results from the intersection of the two curves&nbsp; "$4 \ \rm bit/symbol$" and&nbsp; "$6 \ \rm bit/symbol$".
-'''(4)'''&nbsp; From the diagram you can see that with 4-QAM ($2 \ \rm bit/symbol$) the throughput is (almost) $0$.
+'''(4)'''&nbsp; From the diagram you can see that with 4-QAM&nbsp; ($2  \rm bit/symbol$)&nbsp; the throughput is (almost) zero.
 *In this comparison, the QPSK is identical to the 4-QAM and therefore also unsuitable.
-*Better would be ''Binary Phase Shift Keying'' (BPSK), which corresponds to the lowest curve "$1\ \rm bit/Symbol$" &nbsp; &rArr; &nbsp; <u>solution 1</u>.
+*Better would be "Binary Phase Shift Keying" (BPSK), which corresponds to the lowest curve&nbsp; "$1\ \rm bit/symbol$" &nbsp; &rArr; &nbsp; <u>solution 1</u>.
 {{ML-Fuß}}

@@ Line 11: / Line 11: @@
-Formally, these procedures can be described as&nbsp; $b^{2}&ndash;{\rm QAM}$.&nbsp; The signal space constellations for 16-QAM and 64-QAM are shown on the right. The yellow dots indicate the 4&ndash;QAM.
+Formally, these procedures can be described as&nbsp; $b^{2}&ndash;{\rm QAM}$.&nbsp; The signal space constellations for 16-QAM and 64-QAM are shown on the right. The bright dots indicate the 4&ndash;QAM.
-The lower diagram from&nbsp; [MG08]&nbsp; shows for different&nbsp; $b$&nbsp; values the throughput depending on&nbsp; $10 \cdot {\rm lg \ SNR}$&nbsp; <br>with $\rm SNR$: &nbsp; &nbsp; signal-to-noise ratio.
+The lower diagram from&nbsp; [MG08]&nbsp; shows for different&nbsp; $b$&nbsp; values the throughput depending on&nbsp; $10 \cdot {\rm lg \ SNR}$&nbsp; <br>with $\rm SNR$: &nbsp; &nbsp; "signal-to-noise ratio".
-You can see that for a very good channel $($very large&nbsp; $\rm SNR)$&nbsp; the throughput is approximately proportional to&nbsp;$b$&nbsp;.
+You can see that for a very good channel $($very large&nbsp; $\rm SNR)$&nbsp; the throughput is approximately proportional to&nbsp;$b$.

← Older revision		Revision as of 17:52, 5 February 2021
Line 15:		Line 15:
	The lower diagram from  [MG08]  shows for different  $b$  values the throughput depending on  $10 \cdot {\rm lg \ SNR}$  <br>with $\rm SNR$:     signal-to-noise ratio.		The lower diagram from  [MG08]  shows for different  $b$  values the throughput depending on  $10 \cdot {\rm lg \ SNR}$  <br>with $\rm SNR$:     signal-to-noise ratio.

−	You can see that for a very good channel $($~~also~~ very large  $\rm SNR)$  the throughput is approximately proportional to $b$ .	+	You can see that for a very good channel $($very large  $\rm SNR)$  the throughput is approximately proportional to $b$ .

@@ Line 5: / Line 5: @@
 [[File:EN_Mob_A_4_4.png|right|frame|Throughput comparison for LTE]]
-With LTE, the scheduler selects the appropriate modulation method depending on the nature of the environment and the distance of the user from the base station.&nbsp; In this task, we consider various QAM procedures, namely
+With LTE, the scheduler selects the appropriate modulation method depending on the nature of the environment and the distance of the user from the base station.&nbsp; In this task, we consider various&nbsp; [[Modulation_Methods/Quadratur%E2%80%93Amplitudenmodulation#Allgemeine_Beschreibung_und_Signalraumzuordnung|Quadrature Amplitude Modulation]]&nbsp; $\rm (QAM)$&nbsp; procedures, namely
-*4–QAM with&nbsp; $b\text{ = 2 bit/Symbol}$,
+*4&ndash;QAM with&nbsp; $b\text{ = 2 bit/Symbol}$,
-*16– QAM with&nbsp; $b\text{ = 4 bit/Symbol}$,
+*16&ndash;QAM with&nbsp; $b\text{ = 4 bit/Symbol}$,
-*64– QAM with&nbsp; $b\text{ = 6 bit/Symbol}$.
+*64&ndash;QAM with&nbsp; $b\text{ = 6 bit/Symbol}$.