hifted is referred to as a root sequence. The uth root Zadoff-Chu sequence of prime length N is defined as follows: 0<n<N- 1 (N is an odd integer) 1 (N is an even integer) where N is an integer, denoting the length of the Zadoff-Chu sequence. One can verify that u(n) is periodic with period N, that is, xu(n) = xu(n+N), In. In other words, the sequence index uis a prime relative to N. For a fixed value of the Zadoff-Chu sequence has an ideal periodic autocorrelation property (i.e., the peri- odic autocorrelation is zero for all time shifts other than zero). For different values of index the Zadoff-Chu sequences are not orthogonal, rather exhibit low cross-correlation. If the sequence length N is selected as a prime number, there are different sequences with periodic cross-correlation of /VN between any two sequences regardless of time shift. The Zadoff-Chu sequences are a subset of constant amplitude zero autocorrelation sequences. The properties of Zadoff-Chu sequences can be summarized as follows: They are periodic with period N, if N is a prime number, that is, xu(n + N) = xu(n). Given N is a prime number, the DFT of a Zadoff-Chu sequence is another Zadoff-Chu sequence con- jugated and time-scaled multiplied by a constant factor, that is, Xu[k] = where V is the multi- plicative inverse of modulo N. It can be shown that x"(vk) = x",(k)ein(1-v)k/N. The autocorrelation of a prime-length Zadoff-Chu sequence with a cyclically shifted version of itself also yields zero autocorrelation sequence, that is, it is non-zero only at one instant which corresponds to the cyclic shift zero. The cross-correlation between two prime-length Zadoff-Chu sequences, that is, different , is constant and equal to 1/VN The Zadoff-Chu sequences have low PAPR. 602 Chapter 4 PUSCH (data (data Active control PUSCH bandwidth part control SRS Comb-2 structure for two UEs General SRS/PUSCH multiplexing Figure 4.76 Example illustration of NR SRS structure in time and frequency domains [6]. Although Zadoff-Chu sequences of prime length are prefer