Exercise 4.3: Subcarrier Mapping

From LNTwww

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.




What do the outlined arrangements on the information page apply to?

For the LTE downlink,
for the LTE uplink.


Which units are shown on the information page?

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?

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  $N = 1024$ ?

$J \ = \ $


Which mapping is the graphic on the information page based on?

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


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  $\rm B$.


(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  $K = 12$.