Introduction to Numerology


Numerology corresponds to one subcarrier spacing in the frequency domain. NR supports a flexible numerology with a range of subcarrier spacings, based on scaling a baseline subcarrier spacing of 15 kHz. By scaling a reference subcarrier spacing by an integer N, different numerologies can be defined.

Need for Multiple Numerologies

  1. In order to support the wide range of deployment scenarios, from large cells with sub-1 GHz carrier frequency up to mm-wave deployments with very wide spectrum allocations, NR supports a flexible OFDM numerology with subcarrier spacings ranging from 15 kHz up to 240 kHz with a proportional change in cyclic prefix duration.
  2. Also, having a single numerology for all scenarios is not efficient and probably not possible at all.

These were the primary motives to have multiple numerologies

For the lower range of carrier frequencies, from below 1 GHz up to a few GHz, the cell sizes can be relatively large and a cyclic prefix capable of handling the delay spread expected in these type of deployments, a couple of microseconds, is necessary. Consequently, a subcarrier spacing in the LTE range or somewhat higher, in the range of 15-30 kHz, was needed.

For higher carrier frequencies approaching the mm-wave range, implementation limitations such as phase noise become more critical, calling for higher subcarrier spacings. At the same time, the expected cell sizes are smaller at higher frequencies because of the more challenging propagation conditions. The extensive use of beamforming at high frequencies also helps reduce the expected delay spread. Hence, for these types of deployments a higher subcarrier spacing, and a shorter cyclic prefix are suitable.

Different Numerologies

The numerology is based on exponentially scalable sub-carrier spacing Δf = 2µ × 15 kHz with µ = {0,1,3,4} for PSS, SSS and PBCH and µ = {0,1,2,3} for other channels. Normal CP is supported for all sub-carrier spacings, Extended CP is supported for µ=2 (60kHz). 12 consecutive sub-carriers form a Physical Resource Block (PRB). Up to 275 PRBs are supported on a carrier.

With the increase in numerology, the number of slots increase within the subframe, leading to increase in the number of symbols sent in a given time. So effectively, an OFDM symbol is shortened by half in the next higher numerology. Scaling by powers of two is beneficial as it maintains the symbol boundaries across numerologies, which simplifies mixing different numerologies on the same carrier.

Supported Transmission Numerologies
Supported Transmission Numerologies

Reference: 3GPP TS 38.300 version 15.9.0 Release 15 (

15 kHz subcarrier spacing was selected as the baseline for NR. From the baseline subcarrier spacing, subcarrier spacings ranging from 15 kHz up to 240 kHz with a proportional change in cyclic prefix duration as shown in Table below are derived. Note that 240 kHz is supported for the SS block only and not for regular data transmission.

Subcarrier spacings supported by NR
Subcarrier spacings supported by NR

NR time domain structure consist of 10ms radio frame divided into 10 subframes each of 1ms. A subframe is in turn divided into slots consisting of 14 OFDM symbols each, which means that the duration of the slot in milliseconds is dependent on the numerology. For the 15 kHz subcarrier spacing, an NR slot has a structure that is identical to the structure of an LTE subframe, which is deliberately kept like this considering coexistence of LTE with NR.

Below figure shows the frame, subframe and slot structure for different numerologies:

Frame, Subframe and Slot Structure for different numerologies
Frame, Subframe and Slot Structure for different numerologies

As shown above, the capacity is same between all carrier spacings if the bits/Hz is used as a unit. The carrier spacing is increased but the number of symbols per time unit increases with the higher numerology. Above figure just tries to show this for 15 and 30 kHz subcarrier spacing. The number of subcarriers is reduced by half but the number of slots per symbol per time unit is doubled.

Advantages of Numerology:

  • One of the services in 5G is URLLC, ultra reliable low latency communication and the objective is to have a latency of less than 1ms, which means that scheduling interval must be reduced below 1ms for these types of services. Fortunately, with the support of different numerologies, it is rather simple to reduce the time as the slot time is decreased with higher numerology. This functionality is used to support flexible TTI (Transmission Time Interval), which gives scheduler in base station, a chance to decide how often it will be taking scheduling decision. Figure below, shows how TTI can be scaled with numerology, but as the URLLC service is scheduled for release 16, the numbers should be seen as examples of possible TTI values.
Flexible TTI
Flexible TTI
  • In 5G NR, UE can be configured to only monitor a part of total transmission bandwidth called Bandwidth Part (BWP). There were 2 major reasons behind using BWP instead of whole bandwidth:
    • The wide transmission bandwidth used in some cases might cause the UE to consume too much power from battery.
    • There may also be some UE categories that cannot receive the full bandwidth due to reduced complexity (machine type communication) in order to reduce the cost of the device.

But in 5G NR, the UE can be configured with up to 4 BWPs where only one can be active at a time in the 1st release. Different BWPs can be of different numerologies, which can be used to reduce the latency for certain services. If a device is capable of simultaneous reception of multiple bandwidths parts, it is in principle possible to, on a single carrier, mix transmissions of different numerologies for a single device, although release 15 only supports a single active bandwidth part at a time.

In the downlink, a device is not assumed to be able to receive downlink data transmissions, more specifically the PDCCH or PDSCH, outside the active bandwidth part. The numerology of the PDCCH and PDSCH are restricted to the numerology configured for the bandwidth part. So, in release 15, a device can only receive one numerology at a time as multiple bandwidth parts cannot be simultaneously active. A device is not expected to monitor downlink control channels while doing measurements outside the active bandwidth part.  In the uplink, a device transmits PUSCH and PUCCH in the active uplink bandwidth part only.

  • Since a slot is defined as a fixed number of OFDM symbols, a higher subcarrier spacing (At higher carrier frequency) leads to a shorter slot duration which could be used to support lower-latency transmission, but since the cyclic prefix also shrinks when increasing the subcarrier spacing, it is not a feasible approach in all deployments. Therefore, NR supports a more efficient approach to low latency by allowing for transmission over a fraction of a slot, sometimes referred to as “mini-slot” transmission. Such transmissions can also preempt an already ongoing slot-based transmission to another device, allowing for immediate transmission of data requiring very low latency.
  • NR will also have the capability to operate with mixed numerology on the same RF carrier and will have an even higher flexibility than LTE in terms of frequency domain scheduling and multiplexing of devices within a base station RF carrier.

Disadvantage of Numerology:

  • The flexibility provided by multi-numerology system comes at the cost of additional interference, known as inter-numerology interference (INI). Apart from causing the loss of orthogonality among subcarriers of different numerologies in frequency domain, mixed numerologies also cause difficulty in achieving symbol alignment in time domain. With the same sampling rate, an OFDM symbol of one numerology does not perfectly align with the symbol of another numerology, which makes synchronization within the frame difficult. Researches are ongoing to minimize the effect of INI.