EE 345S Real-Time Digital Signal Processing Lab Fall 2007
EE 445S Real-Time Digital Signal Processing Lab Fall 2013 Lab 4 Generation of PN sequences Debarati Kundu and Andrew Mark Outline Pseudo Noise Sequences and Applications. Generation of Pseudo Noise Sequences. Scrambling and Descrambling. Autocorrolation Function. 2 Pseudo Noise Sequences
Special class of periodic sequence, composed of 1s and 0s, which looks like random noise But a PN sequence is deterministic Used widely in data scramblers, noise generators, calibration By convention, PN sequence is composed of chips, duration of which is much shorter than bit duration Hence, the bandwidth of PN sequence is much higher than that of the data 3 Spread Spectrum(SS) Communications and other PN sequence modulates the data, thus uses spreading the spectrum greatly. Due to this spreading, SS signals are hard to detect.
Only authorized receivers knowing the correct PN sequence can recover the SS signal from noise. More robust to jamming, interference, and multipath effects. Allows CDMA, where multiple users share the same frequency band, by appropriately choosing PN sequences having low cross correlation Enables precise timing measurement, and robust4 Simple Shift Register Generator An r-stage simple feedback shift register with one feedback tap Also
called Fibonacci implementation. Each stage stores one bit (0 or 1), called chirp. At each clock tick, contents at stage n shifts to the right to stage n+1. Additions are mod-2 additions (EX-OR) One or more intermediate stages are fed back in mod-2 addition, but final stage always fed back. 2 r 1 Proper selection ofN feedback taps yield maximal length PN sequences (m-sequences) of length 5
SSRG example y (n) y (n 1) y (n 2) y (n 3) y (n) y (n 1) y (n 3) mod 2 ([3,1]s)] n y(n) y(n-1) y(n-2) y(n-3) 0 1 1 0
0 1 1 1 1 0 2 0 1 1 1 3 1 0 1
1 4 0 1 0 1 5 0 0 1 0 6 1 0
0 1 7 1 1 0 0 6 PN Sequences for Data Long strings of 1s or 0s in the input sequence Scrambling must be randomized before transmission through a communication system. Otherwise, carrier recovery, equalization, and symbol clock tracking wont work properly.
Use a self-synchronizing data scrambler, where hk defines the scrambler connections. Modulo arithmetic! Descrambler To descramble the data, we invert the scrambling process. This is simply an FIR filter with m+1 taps that uses modulo arithmetic. Note that errors in y(n) caused by the channel will cause errors in the recovered sequence. Autocorrelation Function Let y(n) be a periodic sequence with period N. The transformed sequence is: 1,
y (n) 1, The periodic autocorrelation function is: 1 R ( n) N y (n) 1 y (n) 0 N1 y (k ) y (n k ) k 0 This sum is performed by normal addition. r N 2period 1 For maximal length sequences with 1 , for n not a multiple of N R( n) N
1 for n a multiple of N 9 An example: Waveform generated: Autocorrelation: 10 Skipped content Modular Shift Register Generator method for generating PN sequences Details on cross-correlation of PN sequences Please go through the book for the theory 11
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