Difference between revisions of "Aufgaben:Exercise 4.3: Subcarrier Mapping"
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− | {{quiz-Header|Buchseite= | + | {{quiz-Header|Buchseite=Mobile_Communications/The_Application_of_OFDMA_and_SC-FDMA_in_LTE |
}} | }} | ||
− | [[File: | + | [[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 $\rm (LTE)$. 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: | |
− | * [[ | + | * [[Signal_Representation/Discrete_Fourier_Transform_(DFT)#Von_der_kontinuierlichen_zur_diskreten_Fouriertransformation|Discrete Fourier Transform]] ⇒ $\rm DFT$, |
− | * [[ | + | * [[Signal_Representation/Discrete_Fourier_Transform_(DFT)#Inverse_Discrete_Fourier_Transform|Inverse Discrete Fourier Transform]] ⇒ $\rm IDFT$. |
− | + | 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. |
Line 29: | Line 29: | ||
− | '' | + | ''Note:'' |
− | * | + | *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]]. |
− | === | + | ===Questions=== |
<quiz display=simple> | <quiz display=simple> | ||
− | { | + | {What do the outlined arrangements in the information section apply to? |
|type="()"} | |type="()"} | ||
− | - | + | - For the LTE downlink, |
− | + | + | + for the LTE uplink. |
− | { | + | {Which units are shown in the information section? |
|type="[]"} | |type="[]"} | ||
− | + | + | + 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. |
− | { | + | {Which blocks not shown are still required? |
|type="[]"} | |type="[]"} | ||
− | + | + | + Before arrangement $\rm A$ you need a serial-parallel converter. |
− | + | + | + After arrangement $\rm B$ you need a parallel-serial converter. |
− | { | + | {How many users $(J)$ can be served simultaneously with $K = 12$ and $N = 1024$ ? |
|type="{}"} | |type="{}"} | ||
$J \ = \ $ { 85 3% } | $J \ = \ $ { 85 3% } | ||
− | { | + | {Which mapping is the graphic in the information section based on? |
|type="()"} | |type="()"} | ||
- Distributed Mapping (DFDMA), | - Distributed Mapping (DFDMA), | ||
Line 64: | Line 64: | ||
+ Localized Mapping (LFDMA). | + Localized Mapping (LFDMA). | ||
− | { | + | {Which DFT (IDFT) can be realised as FFT (IFFT)? |
|type="[]"} | |type="[]"} | ||
− | - | + | - 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 $\rm B$. |
</quiz> | </quiz> | ||
− | === | + | ===Solution=== |
{{ML-Kopf}} | {{ML-Kopf}} | ||
− | '''(1)''' | + | '''(1)''' <u>Proposed solution 2</u> 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)''' | + | '''(2)''' <u>Proposed solutions 1 and 2 </u>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)''' <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. | ||
− | |||
− | |||
+ | '''(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)''' <u>Proposed solution 3</u> 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)''' <u>Solutions 2 and 3</u> 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 $K = 12$. | |
− | |||
− | |||
− | |||
− | '''(6)''' | ||
− | * | ||
− | * | ||
{{ML-Fuß}} | {{ML-Fuß}} | ||
Line 118: | Line 116: | ||
− | [[Category: | + | [[Category:Mobile Communications: Exercises|^4.3 Use of OFDMA and SC-FDMA |
^]] | ^]] |
Latest revision as of 13:43, 17 November 2022
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:
- Discrete Fourier Transform ⇒ $\rm DFT$,
- Inverse Discrete Fourier Transform ⇒ $\rm IDFT$.
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:
- The task belongs to the chapter The Application of OFDMA and SC-FDMA in LTE.
Questions
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 $K = 12$.