ft. Therefore, f in Eq. 12.5 needs to be multiplied by 2. As shown in Figure 12.49, the highest Doppler shift is experienced by the UE that is in the middle of the two cells that are pointing towards each other (cell from eNodeB A and from eNodeB B). Table 12.2 based on [11] shows the high-speed scenario 1 and 3 parameters and the resulting required supported Doppler shift. Note that the Doppler shift requirements in Table 12.2 and Doppler shift trajectories are applicable for all bands. The UE travelling Maximum UE travelling with Doppler shift speed v Doppler shift + Af Minimum eNodeB A Doppler shift Doppler shift -Af Maximum Doppler shift Doppler shift + Af -1000 -1500 eNodeB B Time (s) Railway track Figure 12.49 Parameters for signal arrival angle O calculation and the Doppler shift trajectories for high-speed scenario 1 LTE Small Cell Optimization Table 12.2 Parameters for high-speed train condition Value Parameter Scenario 1 Scenario 3 Ds (m) D min (m) V (km/h) f (Hz) speed, V, in Table 12.2 is derived for band 1 and in case lower frequency band is used then the corresponding speed needs to be calculated using Eq. 12.6. The lower the used frequency band the higher the speed for the same Doppler shift. In case the high-speed support for physical random access channel is taken into use the length of Zadoff-Chu sequence, N zc, for preamble generation is defined according to [3] based on the restricted set of cyclic shift length, Ncs. The preambles generated based on restricted set of Ncs provide protection against Doppler shift which destroys the zero autocorrelation property of unrestricted generated preambles. The restricted set preambles are generated by masking some of the cyclic shift positions in order to retain acceptable false alarm rate while maintaining high detection performance even for very high speed UEs. Therefore, the number of cyclic shifts generated from one Zadoff-Chu root sequence is greatly limited compared to the unrestricted set. The supported cell ranges for restricted set are shown in 