From LTE for 4G Mobile Broadband: Air Interface Technologies and Performance

9.2 Zadoff ?Chu (ZC) Sequences

Zadoff Chu (ZC) sequences [2] are also used extensively in the LTE system, for example, for primary synchronization signals, uplink reference signals, uplink physical control channel (PUCCH) and random access channel. A ZC sequence of length N ZC is defined as:


where u, the sequence index, is relatively prime to N ZC (that is, the only common divisor for u and N ZC is 1). For a fixed u, the ZC 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 u, ZC sequences are not orthogonal, but exhibit low cross-correlation. If the sequence length N ZC is selected as a prime number, there are ( N ZC ? 1) different sequences with periodic cross-correlation of between any two sequences regardless of time shift.

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