CHAPTER-8 Spread Spectrum Modulation Introduction: Problem of radio transmission Solution Firstly Secondly

Transcription

1 CHAPER-8 Spread Spetrum Modulation Introdution: Initially developed for military appliations during II world war, that was less sensitive to intentional interferene or jamming y third parties. Spread spetrum tehnology has lossomed into one of the fundamental uilding los in urrent and next-generation wireless systems Prolem of radio transmission Narrow and an e wiped out due to interferene o disrupt the ommuniation, the adversary needs to do two things, (a) to detet that a transmission is taing plae and () to transmit a jamming signal whih is designed to onfuse the reeiver.. Solution A spread spetrum system is therefore designed to mae these tass as diffiult as possile. Firstly, the transmitted signal should e diffiult to detet y an adversary/jammer, i.e., the signal should have a low proaility of interept (LPI). Seondly, the signal should e diffiult to distur with a jamming signal, i.e., the transmitted signal should possess an anti-jamming (AJ) property Remedy spread the narrow and signal into a road and to protet against interferene In a digital ommuniation system the primary resoures are Bandwidth and Power. he study of digital ommuniation system deals with effiient utilization of these two resoures, ut there are situations where it is neessary to sarifie their effiient utilization in order to meet ertain other design ojetives. For example to provide a form of seure ommuniation (i.e. the transmitted signal is not easily deteted or reognized y unwanted listeners) the andwidth of the transmitted signal is inreased in exess of the minimum andwidth neessary to transmit it. his requirement is atered y a tehnique nown as Spread Spetrum Modulation.

2 he primary advantage of a Spread Spetrum ommuniation system is its aility to rejet Interferene whether it e the unintentional or the intentional interferene. he definition of Spread Spetrum modulation may e stated in two parts.. Spread Spetrum is a mean of transmission in whih the data sequene oupies a BW (Bandwidth) in exess of the minimum BW neessary to transmit it.. he Spetrum Spreading is aomplished efore transmission through the use of a ode that is independent of the data sequene. he Same ode is used in the reeiver to despread the reeived signal so that the original data sequene may e reovered. s(t) wide and r(t) wide and (t) + Noise (t) Narrow Wide Band Band (t) n(t) (t) Wide and (noise) Wide and ---- ransmitter Channel Reeiver fig: spread spetrum tehnique. (t) Data Sequene to e transmitted (Narrow Band) (t) Wide Band ode s(t) (t) * (t) (wide Band)

3 Fig: Spetrum of signal efore & after spreading PSUEDO-NOISE SEQUENCE: Generation of PN sequene: Clo Shift Shift Shift S Register S Register S SRegister3 3 Sequene Output Logi Ciruit Fig : Maximum-length sequene generator for n3 A feeda shift register is said to e Linear when the feed a logi onsists of entirely mod--address ( Ex-or gates). In suh a ase, the zero state is not permitted. he period of a PN sequene produed y a linear feeda shift register with n flip flops annot exeed n -. When the period is exatly n -, the PN sequene is alled a maximum length sequene or m-sequene. Example: Consider the linear feed a shift register as shown in fig involve three flip-flops. he input s o is equal to the mod- sum of S and S 3. If the initial state of the shift register is. hen the suession of states will e as follows.,,,,,,, he output sequene (output S 3 ) is therefore Whih repeats itself with period 3 7 (n3) Maximal length odes are ommonly used PN odes In inary shift register, the maximum length sequene is N m - hips, where m is the numer of stages of flip-flops in the shift register.

4 At eah lo pulse Contents of register shifts one it right. Contents of required stages are modulo added and fed a to input. Fig: Initial stages of Shift registers Let initial status of shift register e We an see for shift Register of length m4..at eah lo the hange in state of flip-flop is shown. Feed a funtion is modulo two of X 3 and X 4. After 5 lo pulses the sequene repeats. Output sequene is

5 Properties of PN Sequene Randomness of PN sequene is tested y following properties. Balane property. Run length property 3. Autoorrelation property. Balane property In eah Period of the sequene, numer of inary ones differ from inary zeros y at most one digit. Consider output of shift register Seven zeros and eight ones -meets alane ondition.. Run length property Among the runs of ones and zeros in eah period, it is desirale that aout one half the runs of eah type are of length, one- fourth are of length and one-eighth are of length 3 and so-on. Consider output of shift register Numer of runs Auto orrelation property Auto orrelation funtion of a maximal length sequene is periodi and inary valued. Autoorrelation sequene of inary sequene in polar format is given y R () N N n n n - Where N is length or period of the sequene and is the lag of the autoorrelation if l N R () l N N Where l is any integer. R we an also state Autoorrelation funtion as () N

6 { No. of agreements No. of disagreements in omparison of one full period } Consider output of shift register for l R () R () ( 7 8) 5 5 Yields PN autoorrelation as Range of PN Sequene Lengths Length f Shift Register, m PN Sequene Length, A Notion of Spread Spetrum:

7 An important attriute of Spread Spetrum modulation is that it an provide protetion against externally generated interfaing signals with finite power. Protetion against jamming (interfaing) waveforms is provided y purposely maing the information earing signal oupy a BW far in exess of the minimum BW neessary to transmit it. his has the effet of maing the transmitted signal a noise lie appearane so as to lend into the aground. herefore Spread Spetrum is a method of amouflaging the information earing signal. V (t) m(t).. r(t) z(t) Deisio dt n Devie (t) n(t) (t) hreshold <----ransmitter-----> --Channel Reeiver Let { K } denotes a inary data sequene. { K } denotes a PN sequene. (t) and (t) denotes their NRZ polar representation respetively. he desired modulation is ahieved y applying the data signal (t) and PN signal (t) to a produt modulator or multiplier. If the message signal (t) is narrowand and the PN sequene signal (t) is wide and, the produt signal m(t) is also wide and. he PN sequene performs the role of a Spreading Code. For ase and transmission, the produt signal m(t) represents the transmitted signal. herefore m(t) (t).(t) he reeived signal r(t) onsists of the transmitted signal m(t) plus an additive interferene noise n(t), Hene r(t) m(t) + n(t) (t).(t) + n(t)

8 + - + a) Data Signal (t) - + )Spreading Code (t) - )Produt signal or ase and transmitted signal m(t) o reover the original message signal (t), the reeived signal r(t) is applied to a demodulator that onsists of a multiplier followed y an integrator and a deision devie. he multiplier is supplied with a loally generated PN sequene that is exat replia of that used in the transmitter. he multiplier output is given y

9 Z(t) r(t).(t) [(t) * (t) + n(t)] (t) (t).(t) + (t).n(t) he data signal (t) is multiplied twie y the PN signal (t), where as unwanted signal n(t) is multiplied only one. But (t), hene the aove equation redues to Z(t) (t) + (t).n(t) Now the data omponent (t) is narrowand, where as the spurious omponent (t)n(t) is wide and. Hene y applying the multiplier output to a ase and (low pass) filter most of the power in the spurious omponent (t)n(t) is filtered out. hus the effet of the interferene n(t) is thus signifiantly redued at the reeiver output. he integration is arried out for the it interval t to provide the sample value V. Finally, a deision is made y the reeiver. If V > hreshold Value, say inary symol If V < hreshold Value, say inary symol Diret Sequene Spread Spetrum with oherent inary Phase shift Keying:- Binary data Binary PSK (t) m(t) x(t) Modulator (t) PN Code Carrier Generator a) ransmitter > Say Deision y(t) Coherent v v if v Detetor dt Devie Reeived Say Signal (t) if v < Loal PN generator Loal Carrier ) Reeiver

10 Fig: model of diret sequene spread inary PSK system(alternative form) o provide and pass transmission, the ase and data sequene is multiplied y a Carrier y means of shift eying. Normally inary phase shift eying (PSK) is used eause of its advantages. he transmitter first onverts the inoming inary data sequene { } into an NRZ waveform (t), whih is followed y two stages of modulation. he first stage onsists of a multiplier with data signal (t) and the PN signal (t) as inputs. he output of multiplier is m(t) is a wideand signal. hus a narrow and data sequene is transformed into a noise lie wide and signal. he seond stage onsists of a inary Phase Shift Keying (PSK) modulator. Whih onverts ase and signal m(t) into and pass signal x(t). he transmitted signal x(t) is thus a diret sequene spread inary PSK signal. he phase modulation θ(t) of x(t) has one of the two values and π (8 o ) depending upon the polarity of the message signal (t) and PN signal (t) at time t. Polarity of PN & Polarity of PN signal oth +, + or - - Phase Polarity of PN & Polarity of PN signal oth +, - or - + Phase π Polarity of data sequene (t) + - Polarity of PN sequene C(t) +

11 π - π he reeiver onsists of two stages of demodulation. In the first stage the reeived signal y(t) and a loally generated arrier are applied to a oherent detetor (a produt modulator followed y a low pass filter), Whih onverts and pass signal into ase and signal. he seond stage of demodulation performs Spetrum despreading y multiplying the output of low-pass filter y a loally generated replia of the PN signal (t), followed y integration over a it interval and finally a deision devie is used to get inary sequene. Signal Spae Dimensionality and Proessing Gain Fundamental issue in SS systems is how muh protetion spreading an provide against interferene. SS tehnique distriute low dimensional signal into large dimensional signal spae (hide the signal). Jammer has only one option; to jam the entire spae with fixed total power or to jam portion of signal spae with large power. Consider set of orthonormal asis funtions; φ (t) ~ φ (t) os(π ft) sin(π f t) t ( + ) otherwise t ( + ) otherwise,,...,n where is hip duration, N is numer of hips per it.

12 ransmitted signal x(t) for the interval of an information it is x(t) E ± (t) os(π ft) where, E is signal energy per it. PN Code sequene N {,, N- } with + E ransmitted ± signal x(t) is therefore N dimensional and requires N orthonormal funtions φ(t) t to represent Nit. j(t) represent interfering signal (jammer). As said jammer tries to plaes all its availale energy in exatly same N dimension signal spae. But jammer has no nowledge of signal phase. Hene tries to plae equal energy in two phase oordinates that is osine and sine As per that jammer an e represented as j(t) where (t) s(t) N N jφ (t) + ~ j ~ φ (t) j j(t)φ(t)dt,,...n t ~ j ~ j(t) φ(t)dt,,...n hus j(t) is N dimensional, twie the dimension as that of x(t). Average interferene power of j(t) J j N (t)dt j + N ~ j as jammer plaes equal energy in two phase oordinates, hene

13 N j N ~ j J N j o evaluate system performane we alulate SNR at input and output of DS/BPSK reeiver. he oherent reeiver input is u(t) s(t) + (t)j(t) and using this u(t), output at oherent reeiver v s v u(t)os(π ft)dt + v j Where v s is despread omponent of BPSK and v j of spread interferene. v s s(t) os(π f t)dt v j (t) j(t) os(π f t)dt Consider despread BPSK signal s(t) s(t) ± E os(π f t) t Where + sign is for symol - sign for symol. If arrier frequeny is integer multiple of /, wehave v s ± E Consider spread interferene omponent v j here (t) is onsidered in sequene form {,, N- } v j N N j j(t)φ (t)dt

14 With C treated as independent idential random variales with oth symols having equal proailities P(C ) P(C ) Expeted value of Random variale v j is zero, for fixed we have [ j j ] E C j j P(C ) j P(C j ) and Variane Var [ V j] N j j N J Spread fator N / Output signal to noise ratio is E (SNR) J he average signal power at reeiver input is E / hene input SNR (SNR) I E / J (SNR) (SNR) I Expressing SNR in deiels log (SNR) log (SNR) I log (PG),dB where PG

15 .3d term on right side aounts for gain in SNR due to oherent detetion.. Last term aounts for gain in SNR y use of spread spetrum. PG is alled Proessing Gain. Bit rate of inary data entering the transmitter input is R. he andwidth of PN sequene (t), of main loe is W W Proaility of error PG W R o alulate proaility of error, we onsider output omponent v of oherent detetor as sample value of random variale V V ± E + V j E is signal energy per it and V j is noise omponent

16 Deision rule is, if detetor output exeeds a threshold of zero volts; reeived it is symol else deision is favored for zero. Average proaility of error P e is nothing ut onditional proaility whih depends on random variale V j. As a result reeiver maes deision in favor of symol when symol transmitted and vie versa Random variale Vj is sum of N suh random variales. Hene for Large N it an assume Gaussian distriution. As mean and variane has already een disussed, zero mean and variane J / Proaility of error an e alulated from simple formula for DS/BPSK system P e erf E J Antijam Charateristis Consider error proaility of BPSK E P e erf N Comparing oth proailities; N J Sine it energy E P, P average signal power. We an express it energy to noise density ratio as E N P J or J PG P E / N he ratio J/P is termed jamming margin. Jamming Margin is expressed in deiels as (jamming E N margin) db (Proessing gain) db log E N min

17 Where is minimum it energy to noise ratio needed to support a presried average proaility of error. Example A pseudo random sequene is generated using a feed a shift register of length m4. he hip rate is 7 hips per seond. Find the following a) PN sequene length ) Chip duration of PN sequene ) PN sequene period Solution a) Length of PN sequene N m ) Chip duration /hip rate /7.µse ) PN sequene period N 5 x.µse.5µse Example A diret sequene spread inary phase shift eying system uses a feeda shift register of length 9 for the generation of PN sequene. Calulate the proessing gain of the system. Solution Given length of shift register m 9 herefore length of PN sequene N m Proessing gain PG / N in d log N log ( 9 ) 57d Example3 A Spread spetrum ommuniation system has the following parameters. Information it duration.4 mses and PN hip duration of µses. he average proaility of error of system is not to exeed -5. alulate a) Length of shift register ) Proessing gain ) jamming margin Solution Proessing gain PG N / 4 orresponding length of shift register m In ase of oherent BPSK For Proaility of error -5. [Referring to error funtion tale] E /N.8 herefore jamming margin (jammingmargin) db (jamming margin) (Proessinggain) db log PG db db log log E N E N min min

18 log4 log d Frequeny Hop Spread Spetrum: In a frequeny hop Spread Spetrum tehnique, the spetrum of data modulated arrier is widened y hanging the arrier frequeny in a pseudo random manner. he type of spread spetrum in whih the arrier hops randomly form one frequeny to another is alled Frequeny Hop (FH) Spread Spetrum. Sine frequeny hopping does not overs the entire spread spetrum instantaneously. We are led to onsider the rate at whih the hop ours. Depending upon this we have two types of frequeny hop.. Slow frequeny hopping:- In whih the symol rate R s of the MFSK signal is an integer multiple of the hop rate R h. hat is several symols are transmitted on eah frequeny hop.. Fast Frequeny hopping:- In whih the hop rate R h is an integral multiple of the MFSK symol rate R s. hat is the arrier frequeny will hoop several times during the transmission of one symol. A ommon modulation format for frequeny hopping system is that of M- ary frequeny shift eying (MFSK). Slow frequeny hopping:- Fig.a) Shows the lo diagram of an FH / MFSK transmitter, whih involves frequeny modulation followed y mixing. he inoming inary data are applied to an M-ary FSK modulator. he resulting modulated wave and the output from a digital frequeny synthesizer are then applied to a mixer that onsists of a multiplier followed y a and pass filter. he filter is designed to selet the sum frequeny omponent resulting from the multipliation proess as the transmitted signal. An it segments of a PN sequene drive the frequeny synthesizer, whih enales the arrier frequeny to hop over n distint values. Sine frequeny synthesizers are unale to maintain phase oherene over suessive hops, most frequeny hops spread spetrum ommuniation system use non oherent M-ary modulation system.

19 Fig a :- Frequeny hop spread M-ary Frequeny shift eying In the reeiver the frequeny hoping is first removed y mixing the reeived signal with the output of a loal frequeny synthesizer that is synhronized with the transmitter. he resulting output is then and pass filtered and susequently proessed y a non oherent M-ary FSK demodulator. o implement this M-ary detetor, a an of M non oherent mathed filters, eah of whih is mathed to one of the MFSK tones is used. By seleting the largest filtered output, the original transmitted signal is estimated. An individual FH / MFSK tone of shortest duration is referred as a hip. he hip rate R for an FH / MFSK system is defined y R Max(R h,r s ) Where R h is the hop rate and R s is Symol Rate In a slow rate frequeny hopping multiple symols are transmitted per hop. Hene eah symol of a slow FH / MFSK signal is a hip. he it rate R of the

20 inoming inary data. he symol rate R s of the MFSK signal, the hip rate R and the hop rate R n are related y R R s R / R h where log M Fast frequeny hopping:- A fast FH / MFSK system differs from a slow FH / MFSK system in that there are multiple hops per m-ary symol. Hene in a fast FH / MFSK system eah hop is a hip. Fast Frequeny Hopping Slow Frequeny Hopping Several frequeny hops Per modulation Several modulation symols per hop Shortest uninterrupted waveform in the system is that of hop Shortest uninterrupted waveform in the system is that of data symol Chip duration hop duration Chip durationit duration.

21 Fig. illustrates the variation of the frequeny of a slow FH/MFSK signal with time for one omplete period of the PN sequene. he period of the PN sequene is 4-5. he FH/MFSK signal has the following parameters: Numer of its per MFSK symol K. Numer of MFSK tones M K 4 Length of PN segment per hop 3 otal numer of frequeny hops 8

22 Fig. illustrates the variation of the transmitted frequeny of a fast FH/MFSK signal with time. he signal has the following parameters: Numer of its per MFSK symol K. Numer of MFSK tones M K 4 Length of PN segment per hop 3 otal numer of frequeny hops 8