5G Numerology | Subcarrier Spcaing (SCS)

In LTE, there is only type of numerology or subcarrier spacing (15 KHz), whereas in NR, multiple types of subcarrier spacing are available e.g 5G NR supports subcarrier spacing of 15, 30, 60, 120 and 240 KHz. As you see in below picture, each numerology is labled as a parameter (u, mu in Greek). The numerology (u = 0) represents subcarrier spacing of 15 kHz which is same as LTE. And as you see in the second column the subcarrier spacing other than 15KHz, for 5G NR.

 

Key Pointers:

• Unlike LTE which has only 1 subcarrier spacing (15 KHz), 5G NR has several subcarrier spacing
• In LTE, we don’t need any specific terminology to talk about the unique subcarrier spacing but in 5G NR “Numerology” indicates the “Subcarrier Spacing Type” .
• The support of multiple numerologies and multiple subcarrier spacings is the most outstanding NR feature, when compared to LTE.
• 5G NR Numerology varies from 0 to 4 indicating different types of Subcarrier spacing from 15 KHz to 240 KHz
•  Numerology-4 : 240 kHz sub-carrier spacing can be  used to provide broadcast signals at millimeter-wave
• All other Sub-carrier spacing are supported for data and signaling except 60 KHz which is for data Physical channels only
• Numerologies 0 and 1 (15/30 KHz) can be used only in FR1 (Frequency Range 1 – sub 6 GHz)
• Numerology 3 (120 KHz) can be used only in FR2 (> 24.5 GHz)
• Numerology 2 (60 KHz) can be used in both Frequency ranges FR1 and FR2.

Numerology and Channels

Not all numerology can be used for every physical channel and signals. There is a specific numerologies that are used only for a certain type of physical channels even though majority of the numerologies can be used any type of physical channels. Following list depicts which numerologies can be used for which physical channels.

• 1.25 KHz
  • PRACH with Long Preamble
• 5 KHz
  • PRACH with Long Preamble
• 15 KHz
  • PDSCH and PUSCH
  • SSB – PSS, SSS, PBCH
  • PRACH with short Preamble
• 30 KHz
  • PDSCH and PUSCH
  • SSB – PSS, SSS, PBCH
  • PRACH with short Preamble
• 60 KHz
  • PDSCH and PUSCH
  • PRACH with short Preamble
• 120 KHz
  • PDSCH and PUSCH
  • SSB – PSS, SSS, PBCH
  • PRACH with short Preamble
• 240 KHz
  • SSB – PSS, SSS, PBCH

Numerology Information within RRC message

5G NR is very dynamic in terms of Numerology selection, different numerology (Subcarrier Spacing) can be used depending upon situation and purpose. The subcarrier spacing for different situation and purpose is defined in various RRC messages as listed below.

• Master Information Block (MIB)
  • IE: subCarrierSpacingCommon
  • Purpose: It defines the Subcarrier spacing (SCS) for SIB1, MSG2/4 for initial access and System Information (SI) messages
• BandwidthPart-Config
  • IE: subcarrierSpacing
  • Purpose: It defines the SCS to be used in particular BWP and applied to at least PDCCH, PDSCH and corresponding DMRS
• LogicalChannelConfig
  • IE:allowedSubCarrierSpacing
• ReferenceSignalConfig
  • IE:subcarrierSpacing
• CSI-RS-ResourceConfig-Mobility
  • IE: subcarrierSpacing
  • Purpose: It is the subcarrier spacing of CSI-RS
• RACH-ConfigCommon
  • IE: msg2-SubcarrierSpacing, msg3-SubcarrierSpacing and rar-SubcarrierSpacing
• ServingCellConfigCommon
  • IE: subcarrierSpacingCommon
  • Purpose: It is the subcarrier spacing for SIB1, MSG2/4 for initial access and SI-messages, its values 15, and 30 kHz are applicable for carrier frequencies < FR1 and 60 and 120 kHz are applicable for carrier frequencies > FR2
  • IE: subcarrierSpacingSSB
  • Purpose:Subcarrier spacing of SSB. Used only for non-initial access (e.g. SCells, PCell of SCG).
    If the field is absent the UE shall assume the default value of the band.
• UE Capability
  • IE: supportedSubcarrierSpacingDL 
  • Purpose: It defines the supported sub-carrier spacing for DL by the UE indicating the UE supports simultaeous reception with same or different numerologies in CA.

Why different Numerologies are required ?

You must have a question in your mind why multiple Numerology is required for 5G NR design. At high level, we can say that 5G NR have cover a very wide range of  frequency e.g, sub 3 Ghz, sub 6 Ghz and mmWave over 25 Ghz and each frequency range have its own charcterisitics in term of propagation, doppler, inter sysmbol etc. So,  it is hard to support the complete frequency range with single numerology (SCS) without sacrificing too much of efficiency or performance.

Keypoints

• In OFDM, number of subcarrier that can be obtained from a specific frequency range is directly related to spectrum efficiency (how many bits can be transmitted per Hz per second). The more subcarriers we can get into a frequency range (i.e, the lower subcarrier spacing we use), the more data you can transmit or recieve
• The OFDM symbol and SCS have inverse relationship, Narrow subcarrier spacing means longer OFDM symbol length. With longer OFDM symbol, we can can have more room for Cyclick Prefic. With longer CP,  we can get large cell radius and more tolerable to fading channel
• In lower frequency bands, like Sub-3GHz, Sub-6 GHz, we don’t have wider spectrum. So to get as many subcarriers as possible in these limited spectrum, we need to use subcarrier spacing as small as possible. That’s why we use small subcarrier spacing like 15 Khz, 30 Khz, 60 Khz in lower bands
• When operating in very high frequency like mmWave, as carrier frequency gets higher, the degree of frequency drift by moving transmitter or reciever gets higher i.e, Doppler spread gets wider as carrier frequency gets higher. To tolerate this kind of wide range of frequency drift (or shift), we need to use wider subcarrier spacing. So 3GPP provided option to use very wide subcarrier spacing like 120 Khz or 240 Khz
• As frequency goes higher, the degree of phase noise would increase. So we need to implement more sophisticated mechanism for phase noise estimation and correction. It is easier to implement this kind mechanism with wider subcarrier spacing

Calculating Maximum Bandwidth for a Numerology 

To calculated the Maximum bandwidth for each Numerology in 5G, lets take some backgroud from LTE.

The Maximum bandwidth in LTE dependent on the parameters NFFT which is the size of the FFT and the Subcarrier spacing. so in LTE NFFT=2048 and SCS = 15KHz and with this you used to get 30.72MHz as the sampling Freq (15K*2048). This sampling freq limits the bandwidth that the UE can scan for a channel. So the maximum was chosen to be 20MHz.

Now taking the same logic we can identify the maximum Bandwidth in 5G as well.

In case of 5G,  the selection of subcarrier spacing and size of FFT depending on multiple factor one of which is the support of larger bandwidths.First the size of FFT in 5G NR is kept at 4096. next the SCS in 5G varies as per the table below. so the Sampling freq for 5GNR for each numerology is given below which will restrict the maximum bandwidth for each SCS.

• SCS=15KHz, Sampling frequency of 61.44MHz which will restrict the maximum bandwidth to around 50MHz
• SCS=30MHz, Sampling frequency of 122.88MHz which will restrict the maximum bandwidth to around 100MHz

So on so forth. calculated values for all Numerology in the table below.

Calculating the minimum bandwidth  for a Numerology 
Have you ever wondered how is the Minimum bandwidth defined in 5G as well as for each Numerology? we will start with the same technique to give a background of LTE and then move on to 5G. The most important and minimum information that LTE system needs to transmit is the Broadcast channel, PSS and SSS.

Now in LTE, PSS/SSS/PBCH take 72 Subcarriers and each RB consist of 12 Subcarriers, so you need minimum of 6RB’s bandwidth. This in turn makes the minimum Bandwidth in LTE to be 6RB’s which is 6*12*15KHz = 1.08Mhz add the Guard band to it and you will get the Minimum Bandwidth to be 1.4MHz

Coming back to 5G now, using the same analogy, PSS/SSS/PBCH is the most important and minimum information which the system needs to radiate.PSS/SSS/PBCH is combined in 5G and called SSB. SSB takes up 240 Subcarriers in 5G. Now each RB’s is made up of 12 so we need 20RB’s to radiate SSB block.

So the minimum bandwidth required to radiate SSB is 20RB’s. The point now to be noted is that the total bandwidth calculation will depend on the Subcarrier spacing which is different in 5G as compared to LTE. The below table provides the minimum Bandwidth that is required for each Subcarrier spacing of SSB.

So the minimum BW possible in 5G is 5MHz. One additional point here to be noted is that if you have 5G Bandwidth of 5Mhz then you can deploy only Subcarrier spacing of 15KHz and the same logic can be applied to other bandwidths and Subcarrier spacings.

Note that in 5G you can have different Subcarrier spacing for data and control channel.

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