s an even integer) where N is an integer, which denotes the length of the Zadoff-Chu sequence. It is easily verified that xu(n)is periodic with period N; i.e.,xu(n) = xu(n+N), An. In other word, the sequence index is prime relative to N. For a fixed value of u, the Zadoff-Chu sequence has an ideal periodic auto-correlation property (i.e., the periodic auto-correlation is zero for all time shifts other than zero). For different values of index u, 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 ofl/Vbetween any two sequences regardless of time shift. The Zadoff-Chu sequences are a subset of Constant Amplitude Zero Autocorrelation (CAZAC) sequences. The properties of Zadoff-Chu sequences can be summarized as follows [125]: 1. They are periodic with period N if N is a prime number; i.e., Xu (n + N) = u(n) 2. Given N is a prime number, the DFT of a Zadoff-Chu sequence is another Zadoff-Ch sequence conjugated and time- scaled multiplied by a constant factor; i.e., Xu[k] x*(vk)X,[0]where V is the multiplicative inverse of modulo N. It can be shown thatx(vk) x*(k)ein(1-v)k/N. 3. The autocorrelation of a prime-length Zadoff-Chu sequence with a cyclically shifted version of itself also yields zero auto-correlation sequence; i.e., it is non-zero only at one instant which corresponds to the cyclic shift 0. 4. The cross correlation between two prime-length Zadoff-Chu sequences; i.e., different u, is constant and equal to1/VN 5. The Zadoff-Chu sequences have low PAPR. CHAPTER 9 The IEEE 802.16m Physical Layer (Part I) UL Resource Block Demodulation Reference Sounding Reference Signals Signals -One SC-FDMA Slot- One SC-FDMA Symbol One SC-FDMA Subframe FIGURE 9-73 Uplink physical resource blocks and reference signals Table 9-22 Information Content of DCI Format 1 [108] Number of Bits in Information Type PDCCH Usage Resource allocation header Indicates whether resource allocatio