Aufgaben:Exercise 5.6Z: Single-Carrier and Multi-Carrier System - Revision history

Guenter at 11:00, 10 January 2022

2022-01-10T11:00:42Z

Guenter at 10:58, 10 January 2022

2022-01-10T10:58:02Z

Guenter at 10:52, 10 January 2022

2022-01-10T10:52:16Z

Guenter: Guenter moved page Aufgaben:Exercise 5.6Z: Single and Multiple Beam System to Aufgaben:Exercise 5.6Z: Single-Carrier and Multi-Carrier System

2022-01-10T10:44:28Z

Guenter moved page Exercise 5.6Z: Single and Multiple Beam System to Exercise 5.6Z: Single-Carrier and Multi-Carrier System

Hwang at 09:33, 20 December 2021

2021-12-20T09:33:24Z

Hwang at 09:33, 20 December 2021

2021-12-20T09:33:11Z

Guenter at 15:53, 14 December 2021

2021-12-14T15:53:07Z

Guenter: Guenter moved page Aufgaben:Aufgabe 5.6Z: Einträger–und Mehrträgersystem to Aufgaben:Exercise 5.6Z: Single and Multiple Beam System

2021-12-14T15:51:41Z

Guenter moved page Aufgabe 5.6Z: Einträger–und Mehrträgersystem to Exercise 5.6Z: Single and Multiple Beam System

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

2021-03-23T12:50:31Z

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

Javier: Text replacement - "[[Modulationsverfahren" to "[[Modulation_Methods"

2020-07-09T12:56:36Z

Text replacement - "[[Modulationsverfahren" to "[[Modulation_Methods"

@@ Line 59: / Line 59: @@
-'''(2)'''&nbsp;  In contrast,&nbsp; the multi-carrier system is based on&nbsp; $\rm (16–QAM)$  &nbsp; ⇒  &nbsp; <u>solution 4</u>.
+'''(2)'''&nbsp;  In contrast,&nbsp; the multi-carrier system is based on&nbsp; $\rm 16–QAM$  &nbsp; ⇒  &nbsp; <u>solution 4</u>.
@@ Line 65: / Line 65: @@
 :$$T = N \cdot {\rm{log}_2}\hspace{0.04cm}(M) \cdot T_{\rm{B}}.$$
 *Because of &nbsp;$R_{\rm{B}} = 1 \ \rm Mbit/s$,&nbsp; the bit duration for BPSK is equal to&nbsp; $T_{\rm{B}} = 1 \ \rm &micro; s$.
-*From this,&nbsp; the symbol duration of the single-carrier system with&nbsp; $N = 1$&nbsp; and&nbsp; $M = 2$ is:
+*From this,&nbsp; the symbol duration of the single-carrier system with&nbsp; $N = 1$&nbsp; and&nbsp; $M = 2$&nbsp; is:
 :$$ T_{\rm{SC}} = 1 \cdot {\rm{log}_2}\hspace{0.04cm}(2) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 1\,\,{\rm &micro; s}}.$$
@@ Line 75: / Line 74: @@
 '''(5)'''&nbsp;  <u>Solution 2</u>&nbsp; is correct because:
-::At large symbol duration,&nbsp; the relative fraction extending from the predecessor symbol into the symbol under consideration and thus causing intersymbol interference&nbsp; $\rm (ISI)$&nbsp; is smaller than at small symbol duration.
+*At large symbol duration,&nbsp; the relative fraction extending from the predecessor symbol into the symbol under consideration and thus causing intersymbol interference&nbsp; $\rm (ISI)$&nbsp; is smaller than at small symbol duration.
 {{ML-Fuß}}

@@ Line 56: / Line 56: @@
 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;  From the diagram on the information page, it is immediately apparent that the single-carrier system is based on binary phase modulation&nbsp; $\rm (BPSK)$&nbsp; &nbsp; ⇒  &nbsp; <u>solution 2</u>.
+'''(1)'''&nbsp;  From the diagram on the front page,&nbsp; it is immediately apparent that the single-carrier system is based on&nbsp; "binary phase modulation"&nbsp; $\rm (BPSK)$&nbsp; ⇒  &nbsp;<u>solution 2</u>.
-'''(2)'''&nbsp;  In contrast, the multi-carrier system is based on &nbsp; $\rm (16–QAM)$  &nbsp; ⇒  &nbsp; <u>solution 3</u>.
+'''(2)'''&nbsp;  In contrast,&nbsp; the multi-carrier system is based on&nbsp; $\rm (16–QAM)$  &nbsp; ⇒  &nbsp; <u>solution 4</u>.
-'''(3)'''&nbsp;  In general, for an OFDM system with&nbsp; $N$ carriers&nbsp; and&nbsp; $M$&nbsp; signal space points, the symbol duration is:
+'''(3)'''&nbsp;  In general,&nbsp; for an OFDM system with&nbsp; $N$&nbsp; carriers&nbsp; and&nbsp; $M$&nbsp; signal space points,&nbsp; the symbol duration is:
 :$$T = N \cdot {\rm{log}_2}\hspace{0.04cm}(M) \cdot T_{\rm{B}}.$$
 *Because of &nbsp;$R_{\rm{B}} = 1 \ \rm Mbit/s$,&nbsp; the bit duration for BPSK is equal to&nbsp; $T_{\rm{B}} = 1 \ \rm &micro; s$.
-*From this, the symbol duration of the single-carrier system with&nbsp; $N = 1$&nbsp; and&nbsp; $M = 2$ is:
+*From this,&nbsp; the symbol duration of the single-carrier system with&nbsp; $N = 1$&nbsp; and&nbsp; $M = 2$ is:
 :$$ T_{\rm{SC}} = 1 \cdot {\rm{log}_2}\hspace{0.04cm}(2) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 1\,\,{\rm &micro; s}}.$$
-'''(4)'''&nbsp;  Similarly, for the multi-carrier system with&nbsp; $N = 32$&nbsp; and&nbsp; $M = 16$, we obtain:
+'''(4)'''&nbsp;  Similarly,&nbsp; for the multi-carrier system with&nbsp; $N = 32$&nbsp; and&nbsp; $M = 16$,&nbsp; we obtain:
 :$$T_{\rm{MC}} = 32 \cdot {\rm{log}_2}\hspace{0.04cm}(16) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 128\,\,{\rm &micro; s}}.$$
-'''(5)'''&nbsp;  <u>Solution 2</u> is correct because:
+'''(5)'''&nbsp;  <u>Solution 2</u>&nbsp; is correct because:
-::At large symbol duration, the relative fraction extending from the predecessor symbol into the symbol under consideration and thus causing impulse interference (ISI) is smaller than at small symbol duration.
+::At large symbol duration,&nbsp; the relative fraction extending from the predecessor symbol into the symbol under consideration and thus causing intersymbol interference&nbsp; $\rm (ISI)$&nbsp; is smaller than at small symbol duration.
 {{ML-Fuß}}

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1660__Z_5_6.png|right|frame|Two signal space assignments]]
+[[File:P_ID1660__Z_5_6.png|right|frame|Signal space assignments for&nbsp; $\rm SC$&nbsp; (above),&nbsp;  $\rm MC$&nbsp; (bottom)]]
 In this exercise, a comparison is to be made between
-*a single-carrier system &nbsp;$(N = 1)$&nbsp; &rArr; &nbsp; ''Single–Carrier''&nbsp; $\rm (SC)$ and
+*a single-carrier&nbsp; $\rm (SC)$&nbsp; system &nbsp;$(N = 1)$,&nbsp;  and
-*a multi-carrier system with &nbsp;$N = 32$&nbsp; carriers &rArr; &nbsp; ''Multi–Carrier''&nbsp; $\rm (MC)$.
+*a multi-carrier&nbsp; $\rm (MC)$&nbsp; system with &nbsp;$N = 32$&nbsp; carriers.
-For both transmission systems (see diagram), a data bit rate of &nbsp;$R_{\rm B} = 1 \ \rm Mbit/s$&nbsp; is required in each case.
+For both transmission systems&nbsp; (see diagram),&nbsp; a data bit rate of &nbsp;$R_{\rm B} = 1 \ \rm Mbit/s$&nbsp; is required in each case.
 Notes:
 *The exercise belongs to the chapter&nbsp; [[Modulation_Methods/Allgemeine_Beschreibung_von_OFDM|General Description of OFDM]].
 *Reference is also made to the chapter&nbsp;    [[Modulation_Methods/Quadratur%E2%80%93Amplitudenmodulation|Quadrature Amplitude Modulation]].

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1660__Z_5_6.png|right|frame|Two signal spaces assignments]]
+[[File:P_ID1660__Z_5_6.png|right|frame|Two signal space assignments]]
 In this exercise, a comparison is to be made between
 *a single-carrier system &nbsp;$(N = 1)$&nbsp; &rArr; &nbsp; ''Single–Carrier''&nbsp; $\rm (SC)$ and

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Modulationsverfahren/Allgemeine Beschreibung von OFDM
+{{quiz-Header|Buchseite=Modulation_Methods/General_Description_of_OFDM
 }}
-[[File:P_ID1660__Z_5_6.png|right|frame|Zwei Signalraumbelegungen]]
+[[File:P_ID1660__Z_5_6.png|right|frame|Two signal spaces assignments]]
-In dieser Aufgabe soll ein Vergleich erfolgen zwischen
+In this exercise, a comparison is to be made between
-*einem Einträgersystem &nbsp;$(N = 1)$&nbsp; &rArr; &nbsp; ''Single–Carrier''&nbsp; $\rm (SC)$ und
+*a single-carrier system &nbsp;$(N = 1)$&nbsp; &rArr; &nbsp; ''Single–Carrier''&nbsp; $\rm (SC)$ and
-*einem Mehrträgersystem mit &nbsp;$N = 32$&nbsp; Trägern &rArr; &nbsp; ''Multi–Carrier''&nbsp; $\rm (MC)$.
+*a multi-carrier system with &nbsp;$N = 32$&nbsp; carriers &rArr; &nbsp; ''Multi–Carrier''&nbsp; $\rm (MC)$.
-Für beide Übertragungssysteme (siehe Grafik) wird jeweils eine Datenbitrate von &nbsp;$R_{\rm B} = 1 \ \rm Mbit/s$&nbsp; gefordert.
+For both transmission systems (see diagram), a data bit rate of &nbsp;$R_{\rm B} = 1 \ \rm Mbit/s$&nbsp; is required in each case.
@@ Line 16: / Line 16: @@
-''Hinweise:''
+''Notes:''
-*Die Aufgabe gehört zum  Kapitel&nbsp; [[Modulation_Methods/Allgemeine_Beschreibung_von_OFDM|Allgemeine Beschreibung von OFDM]].
+*The exercise belongs to the chapter&nbsp; [[Modulation_Methods/Allgemeine_Beschreibung_von_OFDM|General Description of OFDM]].
-*Bezug genommen wird auch auf das Kapitel&nbsp;    [[Modulation_Methods/Quadratur%E2%80%93Amplitudenmodulation|Quadratur-Amplitudenmodulation]].
+*Reference is also made to the chapter&nbsp;    [[Modulation_Methods/Quadratur%E2%80%93Amplitudenmodulation|Quadrature Amplitude Modulation]].
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Welches Mapping verwendet das Einträgersystem?
+{Which mapping does the single-carrier system use?
 |type="()"}
 - ASK,
@@ Line 32: / Line 32: @@
 - 16-QAM
-{Welches Mapping verwendet das Mehrträgersystem?
+{Which mapping does the multi-carrier system use?
 |type="()"}
 - ASK,
@@ Line 39: / Line 39: @@
 + 16-QAM
-{Berechnen Sie die Symboldauer &nbsp;$T_{\rm SC}$&nbsp; des Einträgersystems.
+{Calculate the symbol duration &nbsp;$T_{\rm SC}$&nbsp; of the single-carrier system.
 |type="{}"}
 $T_{\rm SC} \ = \ $ { 1 3% } $\ \rm &micro; s$
-{Berechnen Sie die Symboldauer &nbsp;$T_{\rm MC}$&nbsp; des Mehrträgersystems.
+{Calculate the symbol duration &nbsp;$T_{\rm MC}$&nbsp; of the multi-carrier system.
 |type="{}"}
 $T_{\rm MC} \ = \ $ { 128 3% } $\ \rm &micro; s$
-{Welche der folgenden Aussagen treffen zu?
+{Which of the following statements is true?
 |type="()"}
-- Die Impulsinterferenzen sind unabhängig von der Symboldauer &nbsp;$T$.
+- The intersymbol interferences are independent of the symbol duration &nbsp;$T$.
-+ Die Impulsinterferenzen nehmen mit steigender Symboldauer &nbsp;$T$&nbsp; ab.
++ The intersymbol interferences decrease with increasing symbol duration &nbsp;$T$.&nbsp;
-- Die Impulsinterferenzen nehmen mit steigender Symboldauer  &nbsp;$T$&nbsp; zu.
+- The intersymbol interferences increase with increasing symbol duration  &nbsp;$T$.&nbsp;
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;  Aus der Grafik auf der Angabenseite erkennt man sofort, dass das Einträgersystem auf binärer Phasenmodulation&nbsp; $\rm (BPSK)$&nbsp; basiert  &nbsp; ⇒  &nbsp; <u>Lösungsvorschlag 2</u>.
+'''(1)'''&nbsp;  From the diagram on the information page, it is immediately apparent that the single-carrier system is based on binary phase modulation&nbsp; $\rm (BPSK)$&nbsp; &nbsp; ⇒  &nbsp; <u>solution 2</u>.
-'''(2)'''&nbsp;  Dagegen basiert das Mehrträgersystem auf &nbsp; $\rm (16–QAM)$  &nbsp; ⇒  &nbsp; <u>Lösungsvorschlag 3</u>.
+'''(2)'''&nbsp;  In contrast, the multi-carrier system is based on &nbsp; $\rm (16–QAM)$  &nbsp; ⇒  &nbsp; <u>solution 3</u>.
-'''(3)'''&nbsp;  Allgemein gilt bei einem OFDM&ndash;System mit&nbsp; $N$ Trägern&nbsp; und&nbsp; $M$&nbsp; Signalraumpunkten für die Symboldauer:
+'''(3)'''&nbsp;  In general, for an OFDM system with&nbsp; $N$ carriers&nbsp; and&nbsp; $M$&nbsp; signal space points, the symbol duration is:
 :$$T = N \cdot {\rm{log}_2}\hspace{0.04cm}(M) \cdot T_{\rm{B}}.$$
-*Wegen &nbsp;$R_{\rm{B}} = 1 \ \rm Mbit/s$&nbsp; ist die Bitdauer bei der BPSK gleich&nbsp; $T_{\rm{B}} = 1 \ \rm &micro; s$.
+*Because of &nbsp;$R_{\rm{B}} = 1 \ \rm Mbit/s$,&nbsp; the bit duration for BPSK is equal to&nbsp; $T_{\rm{B}} = 1 \ \rm &micro; s$.
-*Daraus ergibt sich für die Symboldauer des Einträgersystems mit&nbsp; $N = 1$&nbsp; und&nbsp; $M = 2$:
+*From this, the symbol duration of the single-carrier system with&nbsp; $N = 1$&nbsp; and&nbsp; $M = 2$ is:
 :$$ T_{\rm{SC}} = 1 \cdot {\rm{log}_2}\hspace{0.04cm}(2) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 1\,\,{\rm &micro; s}}.$$
-'''(4)'''&nbsp;  In gleicher Weise erhält man für das Mehrträgersystem mit&nbsp; $N = 32$&nbsp; und&nbsp; $M = 16$:
+'''(4)'''&nbsp;  Similarly, for the multi-carrier system with&nbsp; $N = 32$&nbsp; and&nbsp; $M = 16$, we obtain:
 :$$T_{\rm{MC}} = 32 \cdot {\rm{log}_2}\hspace{0.04cm}(16) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 128\,\,{\rm &micro; s}}.$$
-'''(5)'''&nbsp;  Richtig ist der <u>Lösungsvorschlag 2</u>, weil:
+'''(5)'''&nbsp;  <u>Solution 2</u> is correct because:
-::Bei großer Symboldauer ist der relative Anteil, der vom Vorgängersymbol ins betrachtete Symbol hineinreicht und damit Impulsinterferenzen (ISI) bewirkt, kleiner als bei kleiner Symboldauer.
+::At large symbol duration, the relative fraction extending from the predecessor symbol into the symbol under consideration and thus causing impulse interference (ISI) is smaller than at small symbol duration.
 {{ML-Fuß}}

← Older revision		Revision as of 15:53, 14 December 2021
Line 83:		Line 83:


−	[[Category:Modulation Methods: Exercises\|^5.5 ~~Allgemeine Beschreibung von~~ OFDM^]]	+	[[Category:Modulation Methods: Exercises\|^5.5 General Description of OFDM^]]

← Older revision		Revision as of 12:50, 23 March 2021
Line 83:		Line 83:


−	[[Category:~~Aufgaben zu Modulationsverfahren~~\|^5.5 Allgemeine Beschreibung von OFDM^]]	+	[[Category:Modulation Methods: Exercises\|^5.5 Allgemeine Beschreibung von OFDM^]]