Difference between revisions of "Aufgaben:Exercise 5.6Z: Single-Carrier and Multi-Carrier System"

From LNTwww
m (Text replacement - "Category:Aufgaben zu Modulationsverfahren" to "Category:Modulation Methods: Exercises")
 
(7 intermediate revisions by 2 users not shown)
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|Signal space assignments for  $\rm SC$  (above),  $\rm MC$  (bottom)]]
−
In dieser Aufgabe soll ein Vergleich erfolgen zwischen
+
In this exercise, a comparison is to be made between
−
*einem Einträgersystem  $(N = 1)$  ⇒   ''Single–Carrier''  $\rm (SC)$ und
+
*a single-carrier  $\rm (SC)$  system  $(N = 1)$,  and
−
*einem Mehrträgersystem mit  $N = 32$  Trägern ⇒   ''Multi–Carrier''  $\rm (MC)$.  
+
*a multi-carrier  $\rm (MC)$  system with  $N = 32$  carriers.  
  
  
−
Für beide Übertragungssysteme (siehe Grafik) wird jeweils eine Datenbitrate von  $R_{\rm B} = 1 \ \rm Mbit/s$  gefordert.
+
For both transmission systems  (see diagram),  a data bit rate of  $R_{\rm B} = 1 \ \rm Mbit/s$  is required in each case.
  
  
  
  
−
 
+
Notes:  
−
 
+
*The exercise belongs to the chapter  [[Modulation_Methods/Allgemeine_Beschreibung_von_OFDM|General Description of OFDM]].
−
''Hinweise:''
+
*Reference is also made to the chapter     [[Modulation_Methods/Quadratur%E2%80%93Amplitudenmodulation|Quadrature Amplitude Modulation]].
−
*Die Aufgabe gehört zum  Kapitel  [[Modulation_Methods/Allgemeine_Beschreibung_von_OFDM|Allgemeine Beschreibung von OFDM]].
 
−
*Bezug genommen wird auch auf das Kapitel     [[Modulation_Methods/Quadratur%E2%80%93Amplitudenmodulation|Quadratur-Amplitudenmodulation]].
 
 
   
 
   
  
  
−
===Fragebogen===
+
===Questions===
  
 
<quiz display=simple>
 
<quiz display=simple>
−
{Welches Mapping verwendet das Einträgersystem?
+
{Which mapping does the single-carrier system use?
 
|type="()"}
 
|type="()"}
 
- ASK,
 
- ASK,
Line 32: Line 30:
 
- 16-QAM
 
- 16-QAM
  
−
{Welches Mapping verwendet das Mehrträgersystem?
+
{Which mapping does the multi-carrier system use?
 
|type="()"}
 
|type="()"}
 
- ASK,
 
- ASK,
Line 39: Line 37:
 
+ 16-QAM
 
+ 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="{}"}
 
|type="{}"}
 
$T_{\rm SC} \ = \ $ { 1 3% } $\ \rm &micro; s$
 
$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="{}"}
 
|type="{}"}
 
$T_{\rm MC} \ = \ $ { 128 3% } $\ \rm &micro; s$
 
$T_{\rm MC} \ = \ $ { 128 3% } $\ \rm &micro; s$
  
−
{Welche der folgenden Aussagen treffen zu?
+
{Which of the following statements is true?
 
|type="()"}
 
|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>
 
</quiz>
  
−
===Musterlösung===
+
===Solution===
 
{{ML-Kopf}}
 
{{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 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;  Dagegen basiert das Mehrträgersystem auf &nbsp; $\rm (16–QAM)$  &nbsp; ⇒  &nbsp; <u>Lösungsvorschlag 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;  Allgemein gilt bei einem OFDM&ndash;System mit&nbsp; $N$ Trägern&nbsp; und&nbsp; $M$&nbsp; Signalraumpunkten für die Symboldauer:
+
'''(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:
 
:$$T = N \cdot {\rm{log}_2}\hspace{0.04cm}(M) \cdot T_{\rm{B}}.$$
 
:$$T = N \cdot {\rm{log}_2}\hspace{0.04cm}(M) \cdot T_{\rm{B}}.$$
−
*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,&nbsp; the symbol duration of the single-carrier system with&nbsp; $N = 1$&nbsp; and&nbsp; $M = 2$&nbsp; is:
 
:$$ T_{\rm{SC}} = 1 \cdot {\rm{log}_2}\hspace{0.04cm}(2) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 1\,\,{\rm &micro; s}}.$$
 
:$$ T_{\rm{SC}} = 1 \cdot {\rm{log}_2}\hspace{0.04cm}(2) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 1\,\,{\rm &micro; s}}.$$
  
  
−
 
+
'''(4)'''&nbsp;  Similarly,&nbsp; for the multi-carrier system with&nbsp; $N = 32$&nbsp; and&nbsp; $M = 16$,&nbsp; we obtain:
−
'''(4)'''&nbsp;  In gleicher Weise erhält man für das Mehrträgersystem mit&nbsp; $N = 32$&nbsp; und&nbsp; $M = 16$:
 
 
:$$T_{\rm{MC}} = 32 \cdot {\rm{log}_2}\hspace{0.04cm}(16) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 128\,\,{\rm &micro; s}}.$$
 
:$$T_{\rm{MC}} = 32 \cdot {\rm{log}_2}\hspace{0.04cm}(16) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 128\,\,{\rm &micro; s}}.$$
  
  
−
'''(5)'''&nbsp;  Richtig ist der <u>Lösungsvorschlag 2</u>, weil:
+
'''(5)'''&nbsp;  <u>Solution 2</u>&nbsp; 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,&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}}
 
{{ML-Fuß}}
Line 83: Line 80:
  
  
−
[[Category:Modulation Methods: Exercises|^5.5 Allgemeine Beschreibung von OFDM^]]
+
[[Category:Modulation Methods: Exercises|^5.5 General Description of OFDM^]]

Latest revision as of 12:00, 10 January 2022

Signal space assignments for  $\rm SC$  (above),  $\rm MC$  (bottom)

In this exercise, a comparison is to be made between

  • a single-carrier  $\rm (SC)$  system  $(N = 1)$,  and
  • a multi-carrier  $\rm (MC)$  system with  $N = 32$  carriers.


For both transmission systems  (see diagram),  a data bit rate of  $R_{\rm B} = 1 \ \rm Mbit/s$  is required in each case.



Notes:


Questions

1

Which mapping does the single-carrier system use?

ASK,
BPSK,
4-QAM
16-QAM

2

Which mapping does the multi-carrier system use?

ASK,
BPSK,
4-QAM,
16-QAM

3

Calculate the symbol duration  $T_{\rm SC}$  of the single-carrier system.

$T_{\rm SC} \ = \ $

$\ \rm µ s$

4

Calculate the symbol duration  $T_{\rm MC}$  of the multi-carrier system.

$T_{\rm MC} \ = \ $

$\ \rm µ s$

5

Which of the following statements is true?

The intersymbol interferences are independent of the symbol duration  $T$.
The intersymbol interferences decrease with increasing symbol duration  $T$. 
The intersymbol interferences increase with increasing symbol duration  $T$. 


Solution

Solution

(1)  From the diagram on the front page,  it is immediately apparent that the single-carrier system is based on  "binary phase modulation"  $\rm (BPSK)$  ⇒  solution 2.


(2)  In contrast,  the multi-carrier system is based on  $\rm 16–QAM$   ⇒   solution 4.


(3)  In general,  for an OFDM system with  $N$  carriers  and  $M$  signal space points,  the symbol duration is:

$$T = N \cdot {\rm{log}_2}\hspace{0.04cm}(M) \cdot T_{\rm{B}}.$$
  • Because of  $R_{\rm{B}} = 1 \ \rm Mbit/s$,  the bit duration for BPSK is equal to  $T_{\rm{B}} = 1 \ \rm µ s$.
  • From this,  the symbol duration of the single-carrier system with  $N = 1$  and  $M = 2$  is:
$$ T_{\rm{SC}} = 1 \cdot {\rm{log}_2}\hspace{0.04cm}(2) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 1\,\,{\rm µ s}}.$$


(4)  Similarly,  for the multi-carrier system with  $N = 32$  and  $M = 16$,  we obtain:

$$T_{\rm{MC}} = 32 \cdot {\rm{log}_2}\hspace{0.04cm}(16) \cdot T_{\rm{B}}\hspace{0.15cm}\underline {= 128\,\,{\rm µ s}}.$$


(5)  Solution 2  is correct because:

  • At large symbol duration,  the relative fraction extending from the predecessor symbol into the symbol under consideration and thus causing intersymbol interference  $\rm (ISI)$  is smaller than at small symbol duration.

Retrieved from "http://en.lntwww.de/index.php?title=Aufgaben:Exercise_5.6Z:_Single-Carrier_and_Multi-Carrier_System&oldid=44652"
  • Powered by MediaWiki