AN2254 Freescale Semiconductor / Motorola, AN2254 Datasheet - Page 2

• Manufacturer Part Number: AN2254
• Description: Scrambling Code Generation for WCDMA
• Manufacturer: Freescale Semiconductor / Motorola

Pseudo-Random Sequences
1
Pseudo-random sequences or PN codes are sequences of 1s and 0s generated by an algorithm so that the resulting
numbers look statistically independent and uniformly distributed. A random signal differs from a pseudo-random
signal in that a random signal cannot be predicted. A pseudo-random signal is not random at all; it is a
deterministic, periodic signal that is known to both the transmitter and the receiver. Even though the signal is
deterministic, it appears to have the statistical properties of sampled white noise. To an unauthorized listener, it
appears to be a truly random signal.
1.1 Randomness Properties
CDMA systems achieve their multiple access capability using large sets of sequences with three basic properties
that are applied to a periodic binary sequence as a test for the appearance of randomness [2]:
1.2 Generating Pseudo-Random Sequences
Pseudo-random binary codes are typically generated using a system of linear feedback shift registers (LFSRs). The
LFSR generators produce a sequence that depends on the number of stages, the feedback tap connections, and the
initial conditions. The output sequences can be classified as either maximal length (m-sequence) or nonmaximal
length. The m-sequences have the property that for an n-stage LFSR the sequence repetition period in clock pulses,
p, is as shown in Equation 1.
Thus, if the sequence length is less than the maximum period of (2
length sequence. In fact, all the m-sequences are generated by primitive polynomials of degree n over Galois Field
2 (GF(2)).
2
In a CDMA scheme, all users transmit on the same frequency and are differentiated by their unique scrambling
codes. The receiver correlates the received signal with a synchronously generated replica of the scrambling code to
recover the original information-bearing signal. The third-generation partnership project (3GPP) specifications
define how these uplink complex scrambling codes are generated. Part of the process in the transmitter, in addition
2
Pseudo-Random Sequences
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Scrambling Codes for WCDMA
Balance Property. In each period of the sequence, the number of binary 1s must differ from the
number of binary 0s by at most one digit. In other words, the sequences are balanced so that each
element of the sequence alphabet occurs with equal frequency.
Run Property. A run is defined as a sequence of the same binary digit. The appearance of a different
binary digit marks the start of a new run. The length of the run is the number of digits in the run. For
the randomness run property, in each period, about one-half the runs of each binary digit should be of
length 1, about one-fourth of length 2, one-eighth of length 3, and so on.
Correlation Property. Random sequences are often described in terms of their correlation properties.
A scrambling sequence in a CDMA system must have small off-peak autocorrelation values to allow
for rapid sequence acquisition at the receiver and to minimize self interference due to multipath
acquisitions. Furthermore, the cross correlations are small enough among such sequences at all delays
to minimize multiple-access interference.
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
P = 2n–1
n
–1), the sequence is classified as a nonmaximal
Freescale Semiconductor
Equation 1