Barker sequences are dispersive sequences. There are 6 Barker Sequences. They have very good autocorrelation properties. ∑ + = n n S n S N K ) ( ) ( 1 ) ( τ τ BARKER SEQUENCES ∑ + = n n S n S N K ) ( ) ( 1 ) ( τ τ BARKER SEQUENCES Example for N=5 1 1/5 0 1 2 3 4 Autocorrelation function SEQUENCE LENGTH (N) BARKER SEQUENCE 3 + + − 4 + + − + 5 + + + − + 7 + + + − − + − 11 + + + − − − + − − + − 13 + + + + + − − + + − + − + BARKER SEQUENCES BARKER SEQUENCES CODER FOR N = 5 ( + + + − + ) + + + + DELAY LINE OR bipolar signal BARKER SEQUENCES DECODER FOR N = 5 ( + + + − + ) + + + + ∑ DECISION UNIT DELAY LINE BARKER SEQUENCES If sequence x=(x0, x1,..., xN-1) is Barker’s sequence, then sequences: • (negation of original sequence) • (reverse original sequence) are also Barker’s sequences. ) , ,..., ( 0 1 1 x x x x N − = ) ,..., , ( 1 1 0 − − − − = N x x x x GOLD SEQUENCES PPG 1 PPG 2 CLOCK INITIAL SELECTOR + EXOR GOLD SEQUENCE FREQUENCY HOPPING SPREAD SPECTRUM FHSS is one of the two variants of spread spectrum system – a technique which enables coexistence of multiple devices in same area (the other is DSSS). FHSS relies on spreading spectrum of information signal through use hopping frequencies as frequencies of carrier signals. The choice of frequency from set of available frequencies is done by pseudorandom way. FREQUENCY HOPPING SPREAD SPECTRUM PNG × WIDEBAND BPF m (t) MODULATOR FSK x (t) FREQUENCY SYNTHESIZER TRANSMITTER s (t) FREQUENCY HOPPING SPREAD SPECTRUM PNG × WIDEBAND BPF DEMODULATOR FSK FREQUENCY SYNTHESIZER RECEIVER NARROWBAND BPF PN SEQUENCE SYNCHRONIZATION SYMBOL TIMING RECOVERY s (t) + noise BINARY OUTPUT ≈ m (t) FREQUENCY HOPPING SPREAD SPECTRUM There are two types of FHSS: •Fast FHSS, in which one bit is transmitted on many frequencies •Slow FHSS, in which many bits are transmitted on one frequency FREQUENCY HOPPING SPREAD SPECTRUM FAST FHSS t f f0 t TCh TN 0 1 1 f0+Δf Δf f0+(J-1)Δf JΔf f0+2Δf FREQUENCY HOPPING SPREAD SPECTRUM FAST FHSS • T N/TCh1 , where TN is duration of bit in information signal and TCh is chip time • FFHSS bandwidth B = JΔf, where Δf = 1/ T Ch and J is number of available frequencies • processing gain PG = bandwidth of wideband signal / bandwidth of digital information signal = Ch N N T JT T f
… with all possible code words and we obtain
ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING
Several different types of multicarrier systems exist. Here we
consider Orthogonal Frequency Division Multiplexing (OFDM).
OFDM is a block modulation scheme that transmits a block of N
source symbols in parallel by using N sub-carriers.
The sub-carrier spacing is chosen so the waveforms…
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