Nu = 5 * (FUL – 1850.1 MHz)

Description

The parameter 'II', more accurately represented by the formula Nu = 5 * (FUL – 1850.1 MHz), is a critical definition within the 3GPP UTRA (UMTS Terrestrial Radio Access) specifications, specifically for the Time Division Duplex (TDD) mode, also known as TD-CDMA. This formula is used to calculate the nominal UTRA Absolute Radio Frequency Channel Number (UARFCN) for the uplink carrier in certain TDD frequency bands. The variable 'Nu' represents this nominal channel number, while 'FUL' is the actual uplink carrier frequency expressed in MHz. The constant '1850.1 MHz' serves as a reference frequency, and the multiplier '5' defines the channel raster, or the spacing between consecutive channel numbers, in terms of frequency (each step in Nu corresponds to a 0.2 MHz change in frequency). This formula applies specifically to the 1900 MHz frequency band (Band I for UTRA TDD as per some regional plans). In operation, network planners use this formula to assign a unique channel number to each carrier frequency deployed. This channel number is then used within signaling messages and network configuration instead of the raw frequency value, simplifying system design and ensuring unambiguous identification. The UE uses knowledge of this mapping to tune its receiver to the correct frequency when instructed by the network to use a specific channel number. The formula is a fundamental part of the physical layer frequency definition, ensuring all network elements have a consistent and standardized way to refer to radio carriers.

Purpose & Motivation

The purpose of this formula is to provide a standardized, unambiguous method for identifying radio carrier frequencies in UTRA TDD systems. Using raw frequency values in signaling and configuration is prone to rounding errors and implementation differences. By defining a linear mapping between a integer channel number (Nu) and the physical frequency, 3GPP ensures interoperability. The formula solves the problem of how to efficiently signal frequency information between the network and the UE within protocol messages, which have limited bit fields. The historical context is the need for a common numbering scheme across all UTRA modes (FDD and TDD) for efficient network management and UE implementation. The specific constants (1850.1 MHz reference and multiplier of 5) were chosen to provide a convenient integer channel number for the designated frequency band, aligning with the channel raster and band plan. It addresses the limitation of ad-hoc frequency identification, providing a clean, mathematical relationship essential for automated network planning, cell selection, and handover procedures.