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:

(9.9)

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.


Products & Services
RF and Wireless Chips
RF and wireless chips are integrated circuits (IC) that are designed specifically for radio frequency (RF), microwave, and other wireless communications or data transmission applications.
Long Pass Filters and Short Pass Filters
Long pass filters transmit a wide spectral band of long wavelength radiation while blocking short wavelength radiation. Short pass filters transmit a wide spectral band of short wavelength radiation and block long wave radiation.
ZigBee® Chips
ZigBee® chips are cost-effective, standards-based, wireless networking chips that provide low data-rates, low-power consumption, security, and reliability.
Video Switchers
Video switchers control video display sequences for multiple camera systems.
Programmable Logic Controllers (PLC)
Programmable logic controllers (PLC) are the control hubs for a wide variety of automated systems and processes. They use a wide variety of inputs and outputs and provide network capability.

Topics of Interest

9.3 Downlink Frame Structure The downlink transmissions in the LTE system are scheduled on a subframe basis. A subframe of duration 1 ms consists of two slots each of duration 0.5 ms. A group of 20...

9.4 Synchronization Signals A large number of physical layer cell identities (IDs) simplify the task of network planning. This is because neighboring cells are generally required to use different...

5.1 Definitions and Basic Properties A convolution-decimation operator has at least three incarnations, depending upon the domain of the functions upon which it is defined. We have three different...

6.7 Problems A Gold sequence is constructed from a maximal sequence with characteristic polynomial 1 + x 2 + x 3. The second sequence is obtained by decimation of the maximal sequence by q = 3. (a)...

4.2 Uplink Consider the antenna array CDMA system described in (1.13). In the presence of noise, the baseband signal received at the mth receiver is given by: (4.1) The additive noise { v m( t)} is...