can you please explain what will be the effect of noise in a practical system? can we multiply the PN sequence directly and then pass it through a low pass filter?
With direct sequence spread spectrum (DSSS), each bit in the original signal is represented by multiple bits in the transmitted signal, using a spreading code. The spreading code spreads the signal across a wider frequency band in direct proportion to the number of bits used. Therefore, a 10-bit spreading code spreads the signal across a frequency band that is 10 times greater than a 1-bit spreading code.
One technique with direct sequence spread spectrum is to combine the digital information stream with the spreading code bit stream using an exclusive-OR (XOR). Stallings DCC8e Figure 9.6 shows an example. Note that an information bit of one inverts the spreading code bits in the combination, while an information bit of zero causes the spreading code bits to be transmitted without inversion. The combination bit stream has the data rate of the original spreading code sequence, so it has a wider bandwidth than the information stream. In this example, the spreading code bit stream is clocked at four times the information rate.
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Spread spectrum signal for digital communication Direct Sequence Spread spectrum signal Sarbjeet Singh
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OBJECTIVE 5.1 Concept of Spread Spectrum Why Spread specturm used for..! spread spectrum- Family..! Direct Sequence spread spectrumApplications DS spread Spectrum
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Spread-spectrum (SS) communications technology was first described on paper by an actress and a musician! In 1941, Hollywood actress Hedy Lamarr and pianist George Antheil described a secure radio link to control torpedos and received U.S. patent #2.292.387. It was not taken seriously at that time by the U.S. Army and was forgotten until the 1980s, when the came alive, and has become increasingly popular for applications that involve radio links in hostile environments.
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This is based on Shannon and Hartley channel-capacity theorem. C = B Log2 (1+ S/N) ...(1)C is the channel capacity in bits per second (bps)B is the required channel bandwidth in HzS/N is the signal-to-noise power ratio C here is which represents the amount of information allowed by the communication channel, also represents the desired performance. Bandwidth (B) is the price to be paid, because frequency is a limited resource. S/N ratio expresses the environmental conditions or the physical characteristics (obstacles, présence of jam mers, interférences, etc.).
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Modify the above equation (1) by changing the log base from 2 to e (the Napierian number). C/B = (1/Ln2) Ln(1+S/N) = 1.443 Ln(1+S/N)...(2) Applying the MacLaurin series development for Ln(1+x) = x – x2/2 + x3/3 – x4/4 + ...+ (-1)k+1xk/k +...:Therefore C/B = 1.443 (S/N – 1/2 (S/N)2 + 1/3 (S/N)3 - ...) S/N is usually low for spread-spectrum applications. (As just mentioned, the signal power density can be even below the noise level.) Assuming a noise level such that S/N <<1, Shannons expression becomes simply: C/B= 1.433 S/N Or N/S B/C To send error-free information for a given noise-to-signal ratio in the channel, therefore, we need only perform the fundamental SS signal- spreading operation: increase the transmitted bandwidth. That principle seems simple and evident, but its implementation is complexæmainly because spreading the baseband forces the electronics to act and react accordingly, making necessary the spreading and despreading operations.
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Definition: Spread Spectrum Spread spectrum is an RF communications system in which the baseband signal bandwidth is intentionally spread over a larger bandwidth by injecting a higher-frequency signal, which occurs when a key is attached to the communication channel. As a direct consequence, energy used in transmitting the signal is spread over a wider bandwidth, and appears as noise. The ratio (in dB) between the spread baseband and the original signal is called processing gain. Typical SS processing gains run from 10dB to 60dB. By doing so, signal become less susceptible to electrical noise and interferes less with other radio signals. Spread spectrum provides 11 Mbps capacity links.
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SPREAD SPECTRUMTECHNIQUE To apply an SS technique, simply inject the corresponding SS code somewhere in the transmitting chain before the antenna. The effect is to diffuse the information in a larger bandwidth. Conversely, you can remove the SS code) at a point in the receive chain before data retrieval. The effect of a de spreading operation is to reconstitute the information in its original bandwidth. Obviously, the same code must be known in advance at both ends of the transmission channel.
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qSpread spectrum is characterized by: wide bandwidth low power 8
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Why Spread Spectrum..?Advantages:• Resists intentional and non-intentional interference• Has the ability to eliminate or alleviate the effect of multipath interference• Can share the same frequency band (overlay) with other users• Privacy due to the pseudo random code sequence (code division multiplexing)Disadvantages:• Bandwidth inefficient• Implementation is somewhat more complex.
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Spread Spectrum Technology - Family •Direct Sequence (DS) - A carrier is modulated by a digital code sequence in which bit rate is much higher than the information signal bandwidth. • Frequency Hopping (FH) - A carrier frequency is shifted in discrete increments in a pattern dictated by a code sequence. • Time Hopping (TH) - Bursts of the carrier signal are initiated at times dictated by a code sequence. • Hybrid Systems - Use of combination of the above.
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It is combination of data signal and higher data rate bit sequence of transmitter-Processing gain/ chipping code each bit is represented by multiple bits using a spreading code this spreads signal across a wider frequency band has performance similar to FHSS
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Transmitter end stage1: consist of binary PSK modulator. stage2: consist of multiplier/ modulator with data and PN sequence inputs. Receiver end satge1: consist of multiplier with received signal and local PN sequence. stage2: consist of demodulator or coherent detector.
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Model for analysis Transmitter Channelb(t) X m(t) m(t) r(t) Receiver C(t) i(t) r(t) X z(t) C(t)
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b(t) – message signal c(t) - Spreading code m(t) – transmitted signal – c(t)b(t) ------------(1) r(t) – received signal after passing through channel i(t) – interfering signal r(t) = m(t) + i(t) ----------------------(2)z(t) - original signal recovered z(t) = r(t)c(t) -----------------(3)
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Using equ.(3),we get – z(t) = r(t)c(t) = c(t)[ m(t) + i(t)] z(t) = c(t) [ c(t) b(t) + i(t)] z(t) = c2(t) b(t) + c(t) i(t) -----------(4)Equ.(4) shows that the PN signal c(t) alternates between the levels -1 and +1 and the alterations is destroyed when squared , hence , c2(t) = 1 for all t
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Thus the equ.(4) becomes – z(t) = b(t) + c(t) i(t) -----------(5)b(t) is reproduced at the multiplier output in the receiver , the effect of interference is present ,which is removed by passing the signal through low pass filter.
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et data sequence be d(t)= modulated signal s(t)=and Spreading code c(t)=fter spreading, transmitted signal x(t)= s(t)*c(t) =t Receiver , despread signal becomes
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Processing GainThe output signal-to-noise ratio ,(SNR)o = 2Eb/jTcInput signal-to-noise ratio ,(SNR)I = (Eb/Tb)/jEliminating Eb/j between above equations, we may express the output signal to noise ratio as – (SNR)o = (2Tb/Tc)(SNR)I
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Processing GainThe spread spectrum scheme increases the bandwidth of the message signal by a factor N, called the processing gain.Processing Gain = PG = Bss/B = (Tb / Tc ) where , B is message signal bandwidth Bss is spread spectrum signal bandwidth
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Jamming MarginThe average probability of error of PSK is – Pe = (1/2)erfc(√Eb/No) -------(1)In DSSS PSK system the interference may be treated as wideband noise power spectral density , (No/2),defined by- (No/2) = jTc/2 --------(2)Signal energy per bit , Eb=P Tb --------(3)where , P is average signal power & Tb is bit duration
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Jamming MarginSignal energy bit –to-noise spectral density ratio as ( Eb/No) = (Tb / Tc) (P/j)----------(4)Reformulating equ.(4),we get- j/P = = (Tb / Tc) / ( Eb/No)-----------(5) j/P = PG / ( Eb/No)-----------(5)j/P is Jamming margin(Jamming margin)dB = (PG)dB – 10log10( Eb/No)min----(6)