chronization signals; this may even change between any two subframes. Each NB-IoT subframe spans over one PRB (i.e., 12 subcarriers) in the frequency domain and 1 ms in the time domain. The NPSS and NSSS are used by an NB-IoT UE to perform cell search, which includes time and frequency synchronization, and cell identity detection. Since the legacy LTE synchronization sequences occupy six PRBs, they could not be reused for NB-IoT, thus a new design was introduced. The NPSS is transmitted in the fifth subframe of every 10 ms frame, using the last 11 OFDM symbols in the subframe. The NPSS detection is one of the most computationally intensive operations from a UE perspec- tive. To allow efficient implementation of NPSS detection, NB-IoT uses a hierarchical sequence. The signal itself consists of a single length-11 Zadoff-Chu (ZC) sequence that is either directly mapped to the 11 lowest subcarriers (the 12th subcarrier is null in the NPSS) or is inverted before the mapping process. After successful detection of the NPSS, an NB- IoT UE is able to determine the frame boundaries of a downlink transmission. For each of the 11 NPSS OFDM symbols in a subframe, either p or p is transmitted, where p is the base sequence generated based on a length-11 ZC sequence with root index 5. Each of the length-11 ZC sequence is mapped to the lowest 11 subcarriers within the NB-IoT PRB. The sequence di(n) used for the NB primary synchronization signal is generated from a fre- quency domain ZC sequence according to di(n) = S(1)e-jrun(n+1)/11; n=0, 1, 10, where the ZC root sequence index u=5 and S(1) for different symbol indices l is given as [S(3) S(13)] normal cyclic prefix [2]. The structure of NPSS is illustrated in Fig. 6.9. 6.3.3 Narrowband Secondary Synchronization Signal The NSSS has 20 ms periodicity and is transmitted in the ninth subframe of every other frame and uses the last 11 OFDM symbols. The NSSS spans 132 resource elements and comprises a length-132 frequency domain ZC sequence, with each element mapped to a resource ele