Spread Spectrum Modulation Dr. Teerasit Kasetkasem

Introduction

Concept of Spread-spectrum modulation It will spread the spectrum of transmitted signals into wider range. The code is used to spread the spectrum of transmitted signals Since the spectrum of transmitted signal is wider than its usual forms, spread spectrum modulation makes the signal very robust to unintentional interference or jamming.

Introduction Types of Spread-Spectrum Modulations Direct sequence spread spectrum: This means that transmitted signal is represented by a wideband code. This code transforms narrow band data into a noiselike wideband data. Frequency-hop spread spectrum: Transmitted signal keeps randomly changing its carrier frequency in wideband range

Pseudo-Noise Sequences Both types of spread-spectrum require a noiselike code which will be used to modulate with transmitted signal or control oscillator for direct sequence and frequency hopping, respectively. This noiselike sequence is called pseudo-noise sequence or PN code.

Pseudo-Noise Sequences Feedback shift registers are used.

Pseudo-Noise Sequences Output sequence depends on the length of shift-register (m), initial state and feedback logic. For m flip-flop the number of states is 2 m. The maximum length of the period of this sequence is also 2 m.

Pseudo-Noise Sequences In case that feedback logic consists entirely with modular-2 adders (XOR gate) only, the initial state cannot be all zero state. And the period of this PN sequence produced by linear feedback cannot exceed 2 m -1. When the period is exactly 2 m -1, the PN sequence is called a maximal-length sequence or m-sequence

Maximum length sequence (m =3)

Pseudo-Noise Sequences Possible states of shift registers are

Maximum length sequence (m =3)

Properties of Maximal-length Sequence In each period, the number of “1” is always one more than the number of “0”. This property is called “balance property.” Run property: ½ of sequence has one run, ¼ of sequence has two runs, 1/8 of sequence has three runs and so on. Correlation property: The autocorrelation function of a maximal-length sequence is periodic and binary values.

Properties of Maximal-length Sequence Where T b is a period of PN sequence

m=3,N=7

PN sequence For large N, m-sequence can be treated as random binary sequence.

Baseband model of spread spectrum systems Let {b k } be the binary data sequence Let {c K } be the PN sequence. Both sequences are represented by polar NRZ and are written as b(t) and c(t) Let m(t) be the modulated signal by multiplying b(t) and c(t) together or m(t)=b(t).c(t) Observe that spectrum is wider for lager N.

Bit duration Chip duration

Transmitted signal interference Received signal Despread LPF

Baseband model of spread spectrum systems The transmitted signal is disturbed by interference i(t). Received signal r(t) = m(t)+i(t) Assume that receiver has perfect synchronization. We multiply r(t) with c(t) again z(t) = c(t)r(t)= c(t)m(t)+c(t)i(t)= c 2 (t)b(t)+c(t)i(t). Since c 2 (t) =1, we have z(t) = b(t) + c(t)i(t). c(t)i(t) has a wide spectrum. Hence LPF can removed most of power of i(t).

Direct sequence Spread Spectrum with coherent BPSK (DS/BPSK) Transmitter: Receiver: Despread

Direct sequence Spread Spectrum with coherent BPSK (DS/BPSK) The transmitter of bandpass signal may modulate m(t) with BPSK. The modulated signal x(t) has wider spectrum than BPSK of b(t). But still, x(t) has either 0 or  phase. Receiver demodulate received signal y(t) with carrier to move the spectrum to baseband after passing through LPF will be recovered after despreading

Direct sequence Spread Spectrum with coherent BPSK (DS/BPSK) Since both spread spectrum and BPSK modulation are linear operation, we can switch their order to make the problem easy to solve.

Direct sequence Spread Spectrum with coherent BPSK (DS/BPSK) From the figure, we assume that the performance is limited by the interference j(t) only. Channel noise is not considered here. Received signal before coherent detector is

Direct sequence Spread Spectrum with coherent BPSK (DS/BPSK) When passing through coherent detector the output is given by

Direct sequence Spread Spectrum with coherent BPSK (DS/BPSK) It can be proven that if j(t) has average energy J V cj has mean = 0 V cj has variance = JTc/2 Hence

Direct sequence Spread Spectrum with coherent BPSK (DS/BPSK) We have Or 3dB gain is from the use of coherent detector 10log N gain is from the use of spread spectrum. Hence we call spread factor as processing gain (PG)

Frequency-Hop Spread Spectrum Frequency of carrier keeps changing according to PN sequence. Since the carrier frequency is not constant the spectrum of transmitted signal is spread out. FH usually uses with M-ary FSK called FH/MFSK

Frequency-Hop Spread Spectrum R s is the symbol rate. R h is the hop rate. There are two kinds of FH Slow-FH R s = NR h. This means that symbol rate is higher than Hop rate. Several symbols are transmitted over one hop frequency Fast-FH R h = NR s. This means that hop are is higher than symbol rate. The carrier frequency will change or hop several times during the transmission of one symbol.

Slow-FH The shortest tone duration of FH/MFSK is called chip rate Slow FH: where Example FH/MFSK Number of bits per MFSK K =2 Number of MFSK tones M = 2 K = 4 Length of PN segmentation per hop k = 3 Total number of frequency hops 2 k = 8

Slow-FH

Slow-FH Assume that j(t) decide to spread its energy J over entire hop range. It acts like AWGN with PSD N 0 /2 where N 0 =J/W c. where W c is the bandwidth of FH. Energy-to-noise spectral density ratio: P/J is the jamming margin. Hence PG=W c /R s =2 k or (PG) dB  3k

Fast-FH

There two approaches to make the decision Majority vote: For a given symbol of MFSK, each decision will be make for different frequency hops and the majority will be considered as the right one. Optimum approach: Signals from all frequency hops of a given symbol is combined through some statistical method and the decision is made based on the combined signal