Difference between revisions of "Aufgaben:Exercise 4.3: Subcarrier Mapping"

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{{quiz-Header|Buchseite=Mobile Kommunikation/Die Anwendung von OFDMA und SC-FDMA in LTE
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{{quiz-Header|Buchseite=Mobile_Communications/The_Application_of_OFDMA_and_SC-FDMA_in_LTE
  
 
}}
 
}}
  
  
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[[File:EN_Mob_A_4_3.png|right|frame|Two SC-FDMA&ndash [arrangements]]
+
[[File:EN_Mob_A_4_3.png|right|frame|Two SC–FDMA arrangements]]
−
The diagram shows two transmission schemes that play a role in connection with  ''Long Term Evolution''  (LTE). These block diagrams are referred here neutrally as "arrangement  $\rm A$” or "arrangement  $\rm B$".
+
The diagram shows two transmission schemes that play a role in connection with  Long Term Evolution  $\rm (LTE)$.  These block diagrams are referred here neutrally as  "arrangement  $\rm A$"  or  "arrangement  $\rm B$".
 
* The light grey blocks represent the transition from the time to the frequency domain.
 
* The light grey blocks represent the transition from the time to the frequency domain.
 
* The dark grey blocks represent the transition from the frequency to the time domain.
 
* The dark grey blocks represent the transition from the frequency to the time domain.
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We refer here to the following links:
 
We refer here to the following links:
  
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* [[Signal_Representation/Diskrete_Fouriertransformation_(DFT)#Von_der_kontinuierlichen_zur_diskreten_Fouriertransformation|Diskrete Fouriertransformation]]   ⇒   „DFT” ,
+
* [[Signal_Representation/Discrete_Fourier_Transform_(DFT)#Von_der_kontinuierlichen_zur_diskreten_Fouriertransformation|Discrete Fourier Transform]]   ⇒   $\rm DFT$,
  
−
* [[Signal_Representation/Diskrete_Fouriertransformation_(DFT)#Inverse_Diskrete_Fouriertransformation|Inverse Diskrete Fouriertransformation]]   ⇒   „IDFT” .
+
* [[Signal_Representation/Discrete_Fourier_Transform_(DFT)#Inverse_Discrete_Fourier_Transform|Inverse Discrete Fourier Transform]]   ⇒   $\rm IDFT$.
  
  
−
Für die Stützstellenanzahl von DFT und IDFT werden mit  $K = 12$  und  $N = 1024$  realistische Zahlenwerte angenommen.
+
For the number of interpolation points of DFT and IDFT, realistic numerical values of  $K = 12$  and  $N = 1024$  are assumed.
−
*Der Wert  $K = 12$  ergibt sich aus der Tatsache, dass durch das  ''Subcarrier–Mapping''  die Symbole auf eine gewisse Bandbreite „gemappt” werden. Der kleinste adressierbare Block ist bei LTE  $180 \ \rm kHz$. Mit dem Unterträgerabstand von  $15 \ \rm kHz$ ergibt sich  $K = 12$.
+
*The value  $K = 12$  results from the fact that the symbols are "mapped" to a certain bandwidth by the  "subcarrier mapping".  The smallest addressable block for LTE is  $180 \ \rm kHz$.  With  the subcarrier spacing of  $15 \ \rm kHz$   the value  $K = 12$  results.
−
*Mit der Stützstellenanzahl  $N$  der IDFT $($bei Anordnung   $\rm A)$  können somit bis zu  $J = N/K$  Nutzer gleichzeitig bedient werden. Für das  ''Subcarrier–Mapping''  gibt es mit DFDMA, IFDMA und LFDMA drei verschiedene Ansätze.
+
*With the number  $N$  of interpolation points of the IDFT $($with arrangement $\rm A)$ , up to  $J = N/K$  users can thus be served simultaneously.  For subcarrier mapping, there are three different approaches with DFDMA, IFDMA and LFDMA.
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*Die beiden ersten Nutzer sind in der Grafik grün bzw. türkis eingezeichnet. In der Teilaufgabe '''(5)''' sollen Sie entscheiden, ob die Skizze für DFDMA, IFDMA oder LFDMA gilt.
+
*The first two users are shown in green and turquoise in the diagram.  In subtask  '''(5)'''  you are to decide whether the sketch applies to DFDMA, IFDMA or LFDMA.
  
  
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''Hinweis:''  
+
''Note:''  
−
*Die Aufgabe gehört zum Kapitel  [[Mobile_Communications/Die_Anwendung_von_OFDMA_und_SC-FDMA_in_LTE|Anwendung von OFDMA und SC-FDMA in LTE]].
+
*The task belongs to the chapter  [[Mobile_Communications/The_Application_of_OFDMA_and_SC-FDMA_in_LTE|The Application of OFDMA and SC-FDMA in LTE]].
  
  
−
===Fragebogen===
+
===Questions===
  
 
<quiz display=simple>
 
<quiz display=simple>
  
−
{Wofür gelten die skizzierten Anordnungen auf der Angabenseite?
+
{What do the outlined arrangements in the information section apply to?
 
|type="()"}
 
|type="()"}
−
- Für den LTE–Downlink,
+
- For the LTE downlink,
−
+ für den LTE–Uplink.
+
+ for the LTE uplink.
  
−
{Welche Einheiten sind auf der Angabenseite dargestellt?
+
{Which units are shown in the information section?
 
|type="[]"}
 
|type="[]"}
−
+ Anordnung &nbsp;$\rm A$&nbsp; zeigt den Sender des LTE–Uplinks.
+
+ Arrangement &nbsp;$\rm A$&nbsp; shows the transmitter of the LTE uplink.
−
+ Anordnung &nbsp;$\rm B$&nbsp; zeigt den Empfänger des LTE–Uplinks.
+
+ Arrangement &nbsp;$\rm B$&nbsp; shows the receiver of the LTE uplink..
−
- Beide Modelle gelten für Sender und Empfänger gleichermaßen.
+
- Both models apply equally to the transmitter and receiver.
  
−
{Welche nicht eingezeichneten Blöcke sind noch erforderlich?
+
{Which blocks not shown are still required?
 
|type="[]"}
 
|type="[]"}
−
+ Vor Anordnung &nbsp;$\rm A$&nbsp; benötigt man einen Seriell–Parallel–Wandler.
+
+ Before arrangement &nbsp;$\rm A$&nbsp; you need a serial-parallel converter.
−
+ Nach Anordnung &nbsp;$\rm B$&nbsp; benötigt man einen Parallel–Seriell–Wandler.
+
+ After arrangement &nbsp;$\rm B$&nbsp; you need a parallel-serial converter.
  
  
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{Wie viele Nutzer&nbsp; $(J)$&nbsp; kann man mit&nbsp; $K = 12$&nbsp; und&nbsp; $N = 1024$&nbsp; gleichzeitig bedienen?
+
{How many users&nbsp; $(J)$&nbsp; can be served simultaneously with&nbsp; $K = 12$&nbsp; and&nbsp; $N = 1024$&nbsp;?
 
|type="{}"}
 
|type="{}"}
 
$J \ = \ $ { 85 3% }
 
$J \ = \ $ { 85 3% }
  
−
{Welches Mapping liegt der Grafik auf der Angabenseite zugrunde?
+
{Which mapping is the graphic in the information section based on?
 
|type="()"}
 
|type="()"}
 
- Distributed Mapping&nbsp; (DFDMA),
 
- Distributed Mapping&nbsp; (DFDMA),
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+ Localized Mapping&nbsp; (LFDMA).
 
+ Localized Mapping&nbsp; (LFDMA).
  
−
{Welche DFT (IDFT) lassen sich als FFT (IFFT) realisieren?
+
{Which DFT (IDFT) can be realised as FFT (IFFT)?
 
|type="[]"}
 
|type="[]"}
−
- Die DFT im linken Bereich von Anordnung &nbsp;$\rm A$.
+
- The DFT in the left area of arrangement &nbsp;$\rm A$.
−
+ Die IDFT im rechten Bereich von Anordnung &nbsp;$\rm A$.
+
+ The IDFT in the right-hand area of arrangement &nbsp;$\rm A$.
−
+ Die DFT im linken Bereich von Anordnung &nbsp;$\rm B$.
+
+ The DFT in the left-hand area of arrangement &nbsp;$\rm B$.
−
- Die IDFT im rechten Bereich von Anordnung &nbsp;$\rm B$.
+
- The IDFT in the right-hand area of arrangement &nbsp;$\rm B$.
  
 
</quiz>
 
</quiz>
  
−
===Musterlösung===
+
===Solution===
 
{{ML-Kopf}}
 
{{ML-Kopf}}
  
−
'''(1)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 2</u>:
+
'''(1)'''&nbsp; <u>Proposed solution 2</u> is correct:
−
*Beide Anordnungen zeigen ''Single Carrier Frequency Division Multiple Access'' (SC–FDMA), erkennbar an den DFT– und IDFT–Blöcken.  
+
*Both arrangements show "Single Carrier Frequency Division Multiple Access"&nbsp; $\text{(SC–FDMA)}$, recognisable by the DFT and IDFT blocks.  
−
*Der Vorteil gegenüber ''Orthogonal Frequency Division Multiple–Access'' (OFDMA) ist das günstigere ''Peak–to–Average Power–Ratio'' (PAPR).  
+
*The advantage over "Orthogonal Frequency Division Multiple–Access"&nbsp; $\text{(OFDMA)}$&nbsp; is the more favourable Peak–to–Average Power–Ratio&nbsp; $\text{(PAPR)}$.  
−
*Ein großes PAPR führt dazu, dass man die Verstärker unterhalb der Sättigungsgrenze und damit bei schlechterem Wirkungsgrad betreiben muss, um zu starke Signalverzerrungen zu verhindern.  
+
*A large PAPR means that the amplifiers must be operated below the saturation limit and thus at poorer efficiency in order to prevent excessive signal distortion.
−
*Ein niedrigeres PAPR bedeutet gleichzeitig eine längere Batterielaufzeit, ein für Smartphones äußerst wichtiges Kriterium.  
+
*A lower PAPR also means longer battery life, an extremely important criterion for smartphones.
−
*Deshalb wird SC–FDMA im LTE–Uplink eingesetzt. Für den Downlink ist der hier genannte Aspekt weniger bedeutend.
+
*This is why SC-FDMA is used in the LTE uplink.&nbsp; For the downlink, the aspect mentioned here is less significant.
  
  
  
−
'''(2)'''&nbsp;  Richtig sind die <u>Lösungsvorschläge 1 und 2</u>:
+
'''(2)'''&nbsp;  <u>Proposed solutions 1 and 2 </u>are correct:
−
*Während bei OFDMA die zu übertragenden Datensymbole direkt die verschiedenen Unterträger erzeugen, wird bei SC–FDMA ein Block von Datensymbolen mittels DFT zuerst in den Frequenzbereich transformiert.  
+
*While in OFDMA the data symbols to be transmitted directly generate the various subcarriers, in SC-FDMA a block of data symbols is first transformed into the frequency domain using DFT.  
−
*Um mehrere Nutzer übertragen zu können, muss $N > K$ gelten. Ein Eingangsblock eines Nutzers besteht somit aus $K$ Bit. Damit ist offensichtlich, dass die Anordnung &nbsp;$\rm A$&nbsp; für den Sender gilt.  
+
*To be able to transmit multiple users, $N > K$ must apply.&nbsp; An input block of a user thus consists of $K$ bits.&nbsp; It is thus obvious that arrangement&nbsp;$\rm A$&nbsp; applies to the transmitter.  
−
*Die Anordnung &nbsp;$\rm B$&nbsp; beschreibt dagegen den Empfänger des LTE–Uplinks und nicht den Sender.
+
*Arrangement &nbsp;$\rm B$,&nbsp; on the other hand, describes the receiver of the LTE uplink and not the transmitter.
  
  
 +
'''(3)'''&nbsp;  <u>Both statements</u> are correct:
 +
*The measures are necessary to be able to process a continuous bit stream at the transmitter,
 +
*or to ensure a continuous bit stream at the receiver as well.
  
−
'''(3)'''&nbsp;  <u>Beide Aussagen</u> sind zutreffend:
 
−
*Die Maßnahmen sind erforderlich,  um einen kontinuierlichen Bitstrom am Sender verarbeiten zu können bzw. auch beim Empfänger einen kontinuierlichen Bitstrom zu gewährleisten.
 
  
 +
'''(4)'''&nbsp; The DFT also generates&nbsp; $K$&nbsp; spectral values from&nbsp; $K$&nbsp; input values.
 +
*The subcarrier mapping does not change anything.
 +
*Further users also occupy&nbsp; $K$&nbsp; (bits) of the total of&nbsp; $N$&nbsp; (bits).
 +
*Thus&nbsp; $J = N/K = 1024/12 = 85.333$  &nbsp; &rArr; &nbsp;  $J \ \underline{= 85}$&nbsp; users can be supplied.
  
  
−
'''(4)'''&nbsp; Die DFT erzeugt aus $K$ Eingangswerten ebenfalls $K$ Spektralwerte.
+
'''(5)'''&nbsp; <u>Proposed solution 3</u> is correct:
−
*Durch das ''Subcarrier–Mapping'' ändert sich dadurch nichts.  
+
*The graph conforms to the current 3gpp specification, which provides for "Localized Mapping".
−
*Durch weitere Nutzer werden ebenfalls jeweils $K$ (Bit)  der insgesamt $N$  (Bit) belegt.
+
*Here, the&nbsp; $K$&nbsp; modulation symbols are assigned to adjacent subcarriers.
−
*Damit können $J = N/K = 1024/12 = 85.333$  &nbsp; &rArr; &nbsp; $J \ \underline{= 85}$ Nutzer versorgt werden.
 
  
  
  
−
'''(5)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 3</u>:
+
'''(6)'''&nbsp; <u>Solutions 2 and 3</u> are correct:
−
*Die Grafik entspricht der derzeitigen 3gpp–Spezifikation, die ''Localized Mapping'' vorsieht.
+
*The realisation of DFT or IDFT as an (inverse) "Fast Fourier Transform" is only possible if the number of interpolation points is a power of two.
−
*Hierbei werden die $K$ Modulationssymbole benachbarten Unterträgern zugeordnet.
+
*For example, for&nbsp; $N = 1024$, but not for&nbsp; $K = 12$.
−
 
 
−
 
 
−
 
 
−
'''(6)'''&nbsp; Richtig sind die <u>Lösungsvorschläge 2 und 3</u>:
 
−
*Die Realisierung von DFT bzw. IDFT als (inverse) ''Fast Fourier Transform'' ist nur möglich, wenn die Stützstellenzahl eine Zweierpotenz ist.  
 
−
*Also zum Beispiel für $N = 1024$, nicht aber für $K = 12$.
 
  
 
{{ML-Fuß}}
 
{{ML-Fuß}}
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[[Category:Exercises for Mobile Communications|^4.3 Use of OFDMA and SC-FDMA
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[[Category:Mobile Communications: Exercises|^4.3 Use of OFDMA and SC-FDMA
  
 
^]]
 
^]]

Latest revision as of 13:43, 17 November 2022


Two SC–FDMA arrangements

The diagram shows two transmission schemes that play a role in connection with  Long Term Evolution  $\rm (LTE)$.  These block diagrams are referred here neutrally as  "arrangement  $\rm A$"  or  "arrangement  $\rm B$".

  • The light grey blocks represent the transition from the time to the frequency domain.
  • The dark grey blocks represent the transition from the frequency to the time domain.


We refer here to the following links:


For the number of interpolation points of DFT and IDFT, realistic numerical values of  $K = 12$  and  $N = 1024$  are assumed.

  • The value  $K = 12$  results from the fact that the symbols are "mapped" to a certain bandwidth by the  "subcarrier mapping".  The smallest addressable block for LTE is  $180 \ \rm kHz$.  With  the subcarrier spacing of  $15 \ \rm kHz$   the value  $K = 12$  results.
  • With the number  $N$  of interpolation points of the IDFT $($with arrangement $\rm A)$ , up to  $J = N/K$  users can thus be served simultaneously.  For subcarrier mapping, there are three different approaches with DFDMA, IFDMA and LFDMA.
  • The first two users are shown in green and turquoise in the diagram.  In subtask  (5)  you are to decide whether the sketch applies to DFDMA, IFDMA or LFDMA.




Note:


Questions

1

What do the outlined arrangements in the information section apply to?

For the LTE downlink,
for the LTE uplink.

2

Which units are shown in the information section?

Arrangement  $\rm A$  shows the transmitter of the LTE uplink.
Arrangement  $\rm B$  shows the receiver of the LTE uplink..
Both models apply equally to the transmitter and receiver.

3

Which blocks not shown are still required?

Before arrangement  $\rm A$  you need a serial-parallel converter.
After arrangement  $\rm B$  you need a parallel-serial converter.

4

How many users  $(J)$  can be served simultaneously with  $K = 12$  and  $N = 1024$ ?

$J \ = \ $

5

Which mapping is the graphic in the information section based on?

Distributed Mapping  (DFDMA),
Interleaved Mapping  (IFDMA),
Localized Mapping  (LFDMA).

6

Which DFT (IDFT) can be realised as FFT (IFFT)?

The DFT in the left area of arrangement  $\rm A$.
The IDFT in the right-hand area of arrangement  $\rm A$.
The DFT in the left-hand area of arrangement  $\rm B$.
The IDFT in the right-hand area of arrangement  $\rm B$.


Solution

Solution

(1)  Proposed solution 2 is correct:

  • Both arrangements show "Single Carrier Frequency Division Multiple Access"  $\text{(SC–FDMA)}$, recognisable by the DFT and IDFT blocks.
  • The advantage over "Orthogonal Frequency Division Multiple–Access"  $\text{(OFDMA)}$  is the more favourable Peak–to–Average Power–Ratio  $\text{(PAPR)}$.
  • A large PAPR means that the amplifiers must be operated below the saturation limit and thus at poorer efficiency in order to prevent excessive signal distortion.
  • A lower PAPR also means longer battery life, an extremely important criterion for smartphones.
  • This is why SC-FDMA is used in the LTE uplink.  For the downlink, the aspect mentioned here is less significant.


(2)  Proposed solutions 1 and 2 are correct:

  • While in OFDMA the data symbols to be transmitted directly generate the various subcarriers, in SC-FDMA a block of data symbols is first transformed into the frequency domain using DFT.
  • To be able to transmit multiple users, $N > K$ must apply.  An input block of a user thus consists of $K$ bits.  It is thus obvious that arrangement $\rm A$  applies to the transmitter.
  • Arrangement  $\rm B$,  on the other hand, describes the receiver of the LTE uplink and not the transmitter.


(3)  Both statements are correct:

  • The measures are necessary to be able to process a continuous bit stream at the transmitter,
  • or to ensure a continuous bit stream at the receiver as well.


(4)  The DFT also generates  $K$  spectral values from  $K$  input values.

  • The subcarrier mapping does not change anything.
  • Further users also occupy  $K$  (bits) of the total of  $N$  (bits).
  • Thus  $J = N/K = 1024/12 = 85.333$   ⇒   $J \ \underline{= 85}$  users can be supplied.


(5)  Proposed solution 3 is correct:

  • The graph conforms to the current 3gpp specification, which provides for "Localized Mapping".
  • Here, the  $K$  modulation symbols are assigned to adjacent subcarriers.


(6)  Solutions 2 and 3 are correct:

  • The realisation of DFT or IDFT as an (inverse) "Fast Fourier Transform" is only possible if the number of interpolation points is a power of two.
  • For example, for  $N = 1024$, but not for  $K = 12$.

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