A Novel Chaos Based ASK OOK Communication System

Transcription

1 A Novel Chaos Based ASK OOK Communication Sstem Banislav Jovic Defence echnolog Agenc New Zealand Defence Foce Auckland, New Zealand Abstact his pape poposes the novel boadband chaos and chip based noncoheent amplitude shift keing (ASK on off keing (OOK communication sstems. hei theoetical pobabilit of eo expessions ae deived and confimed with the coesponding empiical bit eo ate (BER simulations demonstating that the match the BER pefomance of the taditional naowband sstem. he supeioit of the newl poposed boadband sstems ove the taditional naowband sstems is then demonstated in the pesence of naowband intefeence. his is a paticulal impotant find as the taditional naowband ASK OOK sstems ae known to be highl susceptible to intefeence. Finall, it is demonstated that the intefeence pefomance of the poposed chaos based sstem can be futhe impoved b optimising chaos based signals fo BER using the downhill simplex algoithm. Kewods-Chaos; communications; ASK-OOK; intefeence; I. INRODUCION In chaotic communication sstems a message signal diectl modulates a boadband chaotic signal [1]-[3]. Howeve, it is also possible to indiectl utilise a chaotic signal [4][5] to modulate a sinusoidal signal and thus ceate a constant envelope chaos based signal [5]. he chaos based signal ma then be futhe modulated b a bina message signal to fom a boadband amplitude shift keing (ASK on off keing (OOK communication sstem as poposed in this pape. he ASK OOK communication sstems find use in adio fequenc identification (RFID devices as well as in medical applications such as endoscop [6], among othe. Howeve, the taditional naowband sine based ASK OOK sstems [7], whee bits ae epesented b no signal and bits 1 b a sinusoidal caie, ae highl sensitive to intefeence [6]. heefoe, the motivation fo the use of the boadband chaos and chip based caie signals in place of a naowband sinusoidal caie signal within the ASK OOK sstems stems fom the fact that boadband signals ae moe esistant to intefeence than naowband signals. In Section II, a novel boadband chaos based ASK OOK sstem is poposed and its theoetical pobabilit of eo expession deived and confimed b the coesponding empiical BER. Section III poposes the novel boadband chip based ASK OOK sstem and demonstates its matching BER pefomance to that of the chaos based sstem and the taditional naowband sstem. In Section IV, it is demonstated that that the novel chaos based ASK OOK sstem offes inceased esistance to the naowband intefeence when compaed to the taditional naowband sine based caie and the novel boadband chip based caie sstems. Finall, Section IV also shows that the novel boadband chaos based sstem can be optimised to futhe impove its BER in the pesence of naowband intefeence. II. CHAOS BASED ASK-OOK SYSEM he poposed boadband chaos based ASK OOK communication sstem is shown in Fig. 1 whee a bina signal m modulates a continuous chaos based signal. A sstematic appoach of geneating continuous time signals b chaos geneatos was poposed in [4]. he concept was used in [5] to geneate the sinusoidal chaos based signals fo ada applications. A chaos based signal, simila to that of [5], is geneated hee fo the application within the novel communication sstem b modulating the sinusoidal caie of (1: π t s( Asin whee : [ t, 1... t < 7ξ ( ] (1 7ξ ( b a chaotic signal (. he chaos based signal, (, is then modulated b a bina message signal, (, as expessed b (: {, 1} x ( m( s( whee: m( ( Finall, the modulated signal of (, (, is tansmitted ove the additive white Gaussian noise (AWGN channel, as illustated in Fig. 1. m Modulato ansmitte x n AWGN Channel x Bandpass filte Envelope detecto Receive hesholding unit Figue 1. he noncoheent chaos based ASK-OOK wieless communication sstem in an AWGN channel. m Copight (c IARIA, 14. ISBN:

2 he bandpass filte of Fig. 1 filtes out all but the fequencies suounding the cente fequenc of the eceived signal,. heoeticall, the minimum bandwidth of the bandpass filte that can be implemented is equal to the bit ate (1/ Hetz, whee denotes the bit peiod. Accodingl, the bandwidth of the chaos based, that is, the tansmitted signal, must be kept within the sstem bandwidth. he total fixed numbe of samples within the chaos based caie signal was chosen to be 1, that is, 1 samples wee chosen to epesent an bit. he sample length of 1 was found to adequatel epesent a chaos based caie signal of (1 and also ield a sufficientl low numbe of samples pe bit what allowed fo elativel fast Monte Calo BER simulations. As it has not been established whethe the signal s( of (1 is chaotic, it is efeed to as a chaos based athe than a chaotic signal [5]. he chaotic map ( of (1, used to modulate (1, was poposed b Caoll in [5]: N (1 p( i ( i mod1, i ( i ( i + 1 ( i,3... N 1, + 1 ( N (1, ξ ( (1 +.5 ( 1,... M, whee p(i ae the sstem paametes. he lagest Lapunov exponent of ( was detemined to be.97 bits/iteation [5] thus poving that the poposed sstem of (3 is chaotic. Fo a sstem to be chaotic, its lagest Lapunov exponent must be geate than [8]. Fo eve chaotic sample of (3, thee is a cetain highe numbe of chaos based signal samples of (1 [5]. he numbe of chaos based signal samples pe chaotic value is highe fo highe chaotic signal values and lowe fo lowe values. he eason fo this can be obseved b examining (1 fom which it can be seen that highe ( chaotic values poduce lowe fequenc components and moe samples pe each sinusoidal ccle of the chaos based signal. Opposite is tue fo lowe ( chaotic values which poduce highe fequenc components and less samples pe sinusoidal ccle of the chaos based signal. heefoe, in contast to a linea fequenc modulated (LFM chip signal [9] whose fequenc changes lineal, fequenc components of a chaos based signal change in a chaotic fashion. he empiical distibutions of the decision vaiables of the newl poposed boadband chaos based ASK OOK sstem of Fig. 1 ae plotted in Fig. at the bit eneg to noise powe spectal densit (Eb/No atio of 1 db, demonstating the Raleigh and Rician distibution of bits and 1, espectivel. As the eneg of a naowband sinusoidal signal ( A / [8][1] is independent of its fequenc and onl (3 depends on its amplitude and signal duation, it can also be shown that the eneg expession of the sinusoidal chaos based signal of (1 is govened b the same expession. o demonstate this, (1 is fist ewitten in the fom of (4: [ f s( sin π (4 whee f 1/[7ξ ( ] denotes the changing fequenc with chaotic values. he chaos based signal eneg is then obtained b squaing and integating (4 ove the signal duation : Fequenc of occuence E ( Asin[ π f A A Raleigh distibution A dt dt ( cos[ 4π f Figue. Histogam of the eceived envelope values at the Eb/No atio of 1 db fo the novel chaos based ASK OOK sstem. B setting the signal duation of (5 equal to the bit peiod b, bit 1 eneg equal to A b / is obtained. Futhemoe, as the bits ae epesented b no signal thei eneg is zeo, esulting in an aveage eneg pe bit of E b A b / 4 [7]. heefoe, the chaos based signal eneg is identical to that of a naowband sinusoidal signal [7][1]. As the distibution of the decision vaiables and the eneg of the chaos based signal match those of the taditional naowband sine based ASK-OOK sstem [7] it is expected that the pobabilit of eo of the two sstems will be identical. he pobabilit of eo ( is obtained b consideing the distibution of the decision vaiables sampled fom the envelope at the input to the thesholding unit of Fig. 1. Accodingl, the pobabilit of eo that a bit 1 is eceived when a bit was tansmitted is obtained b integating the Raleigh pobabilit densit function epesenting bits fo the values when the decision theshold / is exceeded: σ /(σ α /(σ e ( α e d e α P dt Rician distibution ( Received envelope values at Eb/No 1 db (6 Copight (c IARIA, 14. ISBN:

3 whee denotes the vaiance (powe of the AWGN at the input of the envelope detecto, A the amplitude of the chaos based caie and the andom vaiable. he noise powe at the input to the envelope detecto is bandwidth limited b the filte of bandwidth and is thus expessed as:. Similal, the pobabilit that a bit is eceived when a bit 1 was tansmitted is obtained b integating the Rician pobabilit densit function epesenting bits 1 fo the values when the decision theshold is not exceeded: P ( α e1 σ α ( + A /(σ e A Io d 1 Q M A α, σ whee denotes the modified Bessel function of the fist kind of zeo ode. he integal tem of (7 was put into the fom of the Macum Q function [11]: $ (,"# & ('(( *+ / % (, b making the definition: -/, so that,,-/ and substituting those into the integal tem to obtain the final esult of (7. he pobabilit of eo fo equipobable bits and 1 is then detemined b finding the aveage value of (6 and (7, to obtain the exact expession fo the noncoheent chaos based ASK-OOK sstem: 1 Pe ( α e α /(σ A + 1 QM α, σ Equation (8 is plotted in Fig. 3a alongside the coesponding empiical BER cuve obtained via the Monte Calo simulation of the chaos based ASK OOK sstem of Fig. 1. It can be obseved that the two plots exhibit a pefect match and thus pove the esult of (8. Futhemoe, as expected, the esult of (8 matches the esult fo the pobabilit of eo of the taditional naowband ASK-OOK sstem whose theoetical pobabilit of eo expession was deived in [7]: A /(8σ Pe ( α.5[ e + Q( A /(σ ], whee Q denotes the Gaussian Q function. Howeve, due to a numbe of simplifing assumptions made in the deivation of [7] the final expession is somewhat inaccuate fo high levels of noise, as demonstated in Fig. 3b whee it is plotted against the moe complex but exact esult of (8 and the naowband empiical BER. As opposed to indiectl using a chaotic signal to modulate the sinusoidal caie within the chaos based ASK OOK sstem, it is also possible to use a chaotic signal diectl to epesent a bit 1 and no signal to epesent a bit. Such a sstem, temed chaotic on off keing (COOK, was poposed and investigated in [1]-[14]. Howeve, unlike sinusoidal signals, chaotic signals geneall do not have a constant envelope making a COOK sstem potentiall moe difficult and costl to implement. (7 (8 BER (b ASK-OOK theoetical (equation 6 Chip based ASK-OOK empiical Chaos based ASK-OOK empiical (a Eb/No (db Figue 3. (a. heoetical and empiical BER cuves of the newl poposed boadband sstems. (b. Magin of eo within the theoetical BER of [7]. III. CHIRP BASED ASK-OOK SYSEM B eplacing the chaos based caie signal b an LFM chip signal, a novel boadband ASK OOK sstem is poposed hee. Its novelt ove the chip based spead spectum OOK sstem of [6] is in the envelope detecto eceive achitectue, which is simple and moe cost effective than the powe detecto achitectue of [6] that was empiicall investigated in the human bod channel. he powe detecto achitectue involves squaing and integation of the eceived signal, as opposed to the envelope detecto achitectue which simpl samples the constant envelope, esulting in a lowe implementation cost. As fo the chaos based sstem, it was found hee that the decision vaiables of the poposed sstem ae also of Raleigh and Rician distibutions. Futhemoe, as the eneg of an LFM chip signal is also equal to / [9], esulting in an aveage eneg of a bit of E b A b / 4, it is eadil veifiable b epeating the deivation pesented in (6 to (8 that the pobabilit of eo of the novel chip based sstem is also govened b (8. he esult is confimed in Fig. 3a b an exact match between the empiical BER cuve and the theoetical esult of (8. IV. BER PERFORMANCE AND OPIMISAION IN HE AWGN CHANNEL WIH NARROWBAND INERFERENCE his section pesents the BER pefomance of the naowband sinusoidal and the two novel boadband sstems when subected to the sinusoidal naowband intefeence. he novel chaos based sstem is then optimised to demonstate a futhe impovement in the BER pefomance. A. BER pefomance of the ASK-OOK sstems he BER esults fo the signal to intefeence atios (SIR of, 16, 1, 1, 8 and 6 db ae plotted in Fig. 4 fom whee it can be obseved that although the naowband and the poposed boadband ASK OOK sstems exhibit matching pefomance in the AWGN channel onl, the boadband sstems exhibit supeio pefomance at all levels of intefeence. Copight (c IARIA, 14. ISBN:

4 1 1-1 SIR 6 db 1 - BER ASK-OOK theoetical BER of equation 7 (no intefeence 8 db 1-5 Sine heoetical, no intefeence Sine based ASK OOK Chip based ASK OOK 16 db Chaos based ASK OOK 1 db db 1 db Chip Optimised chaos based ASK OOK Optimised chaos Chaos Eb/No (db Figue 4. Empiical BER of the ASK OOK sstems fo vaing SIR levels. he newl poposed boadband chip based ASK OOK sstem exhibits an inceasing BER impovement ove the naowband sstem with the deceasing SIR. A futhe simila, but moe notable, impovement ove the naowband sinusoidal and the boadband chip based sstem is exhibited b the novel boadband chaos based sstem. Fo instance, at the SIR of 1 db, and the BER level of 1 ', an impovement of appoximatel.5 and.75 db can be obseved in favou of the chaos based sstem when compaed to the chip and naowband sinusoidal sstems, espectivel. he impovement inceases to appoximatel 1 and 1.5 db at the SIR level of 8 db. he bandwidth of the chip caie signal was kept the same as that of the chaos based caie signal while the naowband intefeence tone was kept nea the cente fequenc and within the sstem bandwidth. Fo the naowband sinusoidal ASK OOK sstem, the intefeence tone was geneated at the caie fequenc. B. Optimisation of the novel chaos based ASK-OOK sstem In [5], chaos based signals wee used fo ada applications whee boadband chaos based ada pulses wee optimised fo detection of specific tagets. In contast to an LFM chip signal whee onl a single unique signal can be geneated in a given bandwidth, a chaotic sstem can theoeticall poduce an infinite numbe of chaotic signals and theefoe also chaos based signals b vaing its paametes o initial conditions. B poducing a lage numbe of diffeent chaos based signals, Caoll showed [5] that it is possible to find a paticula chaos based signal that ields a high signal eflection fom one abita ada taget and a low signal eflection fom some othe abita ada taget. his was achieved b optimising chaos based signals fo a given ada taget, o a set of tagets, whose eflection chaacteistics ae known in advance. he optimisation of the chaos based ada model was achieved b emploing the downhill simplex o Nelde Mead algoithm [15]. Downhill simplex algoithm detemines the minimum of a given equation, temed minimisation equation. In case of the chaos based ada optimisation poblem the minimisation equation of [5] was based on minimising the eflection of one ada taget with espect to anothe. aking the lead of [5], it is now demonstated that the BER pefomance of the poposed chaos based ASK OOK sstem of Section II can be futhe impoved b optimising chaos based signals fo a given level of naowband intefeence. As opposed to minimising eflections fom ada tagets, the downhill simplex algoithm was used hee to minimise the BER of the communication sstem. Optimisations wee pefomed fo each SIR level investigated at an Eb/No atio coesponding to the BER 4 level of 1 of a non optimised chaos based ASK OOK sstem. Once an optimisation fo a given SIR level was complete, the sstem was evaluated with the detemined Copight (c IARIA, 14. ISBN:

5 optimum chaos based caie fo a ange of Eb/No atios and the empiical BER cuve obtained. he optimisations wee stated off with an initial andom set of paametes that poduce a non optimised chaotic signal of (3 and thus also a chaos based signal of (1. Upon evaluating the BER fo the initial set of paametes, the downhill simplex algoithm vaied the paametes and e-evaluated the BER. he pocess was epeated a lage numbe of times until a smallest local minimum (optimum BER value was detemined. he optimisations wee all nonlinea esulting in man local minima (as opposed to a definite global minimum, of which some had simila magnitudes. Nonetheless, the astingenc of the algoithm ma be impoved b stating the algoithm execution with a favouable initial set of chaotic paametes. Howeve, again, as the pocess is nonlinea, thee is no ule on how to choose initial chaotic paametes that ma enhance astingenc. An advantage of the downhill simplex algoithm ove some othe optimisation algoithms is that it does not equie deivatives [15] what educes its complexit. Othe algoithms ma also be emploed to t to futhe impove the BER pefomance [16][15]. Howeve, this is beond the scope of this pape and will not be investigated hee. he optimised empiical BER cuves fo the vaing SIR levels ae plotted in Fig. 4 on the same set of axes as the non optimised cuves. Fom the plots it can be obseved that the impovement in BER pefomance of the optimised ove non optimised chaos based ASK OOK sstem anges fom less than.1 to appoximatel.5 db at diffeent SIR levels. heefoe, although the obseved impovements ae less significant than those of subsection IV-A, the futhe widen the impovement magin ove the taditional naowband sstem and demonstate that the poposed chaos based ASK OOK sstem s BER pefomance can be futhe impoved though an optimisation pocess. V. CONCLUSIONS In this pape, two novel boadband chaos and chip based ASK OOK communication sstems wee poposed. hei theoetical pobabilit of eo expession was deived and confimed b an exact match with the coesponding empiical BER simulations. It was shown that both of the poposed novel boadband ASK OOK sstems exhibit supeio BER pefomance to the naowband sstem in the pesence of naowband intefeence, while also exhibiting a matching pefomance in the AWGN channel onl. he novel chaos based sstem was shown to exhibit the best BER pefomance with intefeence in the sstem, poviding an impovement of up to 1.5 db. Such a find is of paticula impotance fo the ASK OOK sstems, which ae taditionall known to offe little esistance to intefeence. Futhemoe, it was demonstated that the newl poposed chaos based ASK OOK sstem can be optimised using the downhill simplex algoithm to futhe impove its BER pefomance b up to.5 db in the pesence of naowband tone intefeence. REFERENCES [1] B. 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