Amplitude Zero Autocorrelation Lab Report

II. PRIMARY SYNCHRONIZATION SIGNAL

PSS GENERATION
The PSS is chosen from a class of the polyphase Zadoff-
Chu (ZC) sequences [2, 3], which satisfy a Constant
Amplitude Zero Autocorrelation (CAZAC) property. A ZC sequence is a complex-valued mathematical sequence which exhibits the useful property that cyclically shifted versions of it is orthogonal to each other.
The sequence used for the primary synchronization signal is generated from a frequency-domain ZC sequence according to the equation,

N
ZC u ZC = e πun n+1
NZC
−j
; n = 0,1,2 ... , N ZC − 1

Where N ZC = 63, is the length of the sequence, u is the root index selected from the set {25, 29, 34}.
This set of roots for the ZC sequences was chosen to obtain good periodic autocorrelation
Monte Carlo simulations using 10000 trials were used to estimate the probability of detection for a range of noisy channels, for each scheme.

PSS DETECTION PROBABILITY
The probability of PSS detection using both the schemes is shown in Figure 11.
Figure 11. PSS Detection Probability.
Thus the physical layer identity detected from the received
PSS is 1.
IV. SECONDARY SYNCHRONIZATION SIGNAL


SSS DETECTION
Figure 6 shows Block Diagram for SSS Detector. It uses the following blocks: Sign Filter, Deinterleaving, De-scrambling,
Correlator and Extraction process.
SSS GENERATION
The physical layer cell identity group can be extracted from the SSS. The sequence used for the SSS is an interleaved concatenation of two length-31 bi-level sequences. The sequence is scrambled with a scrambling sequence, c(n)
(2)
which is dependent on N ID . The SSS differs between slot 0 and slot 10 according to the following equations [2], m 0

s 0 d 2n =

d 2n + 1 = s 1 s 1 s 0 m 1 m 1 m 0 n . c 0 n ... in slot 0

n . c 0 n ... in slot 10 m 0 n . c 1 n . z 1 n . c 1 n m . z 1 1
(n) ... in slot 0
(n) ... in slot 10

  where 0 ≤ n ≤
Extraction process is performed using Decision Dictionary,
(1)
which links the values of m 0 and m 1 to N ID .
The transmitted SSS is received as shown in Figure 7.
Figure 7. Transmitted and Received SSS
(1)
(2)
Figure 5. SSS with N ID =1 and N ID =1
The User Equipment (UE) is unaware of the subframe index of the received SSS. Thus the binary sequence s e n is extracted from the even part of received SSS according to
Block Diagram. The sequence s e n thus obtained is shown in
Figure 8.

Figure 9. SSS detection using Linear Correlation
Figure 11 shows that the probability of PSS detection is same for linear and circular correlation schemes up to SNR of
6 dB. As SNR reduces, linear correlation proves to be more effective than circular correlation.

Figure 10. SSS detection using Circular Correlation
SSS DETECTION PROBABILITY
The probability of SSS detection is shown in Figure 12.
The result shows that the schemes are equally effective till a
BER of 15%. The performance of Linear Correlation scheme degrades rapidly as compared to Circular Correlation scheme for channels with higher AWGN. The probability of detection for circular correlation scheme does not fall below 0.9 even for a BER of 40%. Thus circular correlation is superior to