Research of AltBOC modulation

Research of AltBOC ModulationQin Changlu ,Lv Jing,Li YangzhiInstitute of Communications Engineering, PLA University of Science and Technology210007 Nanjing ChinaAbstract—When the modulation method of AltBOC was justpromoted,the Galileo E5 signal’s envelope will not be constant ifit brings one pilot component in upper and lower bandseparately.ThatmayinfluencetheHPA’spowerefficiency.Galileo navigation system takes PRN codes to modulatenew 4-level subcarriers instead of 2-level subcarriers then obtaina equivalent 8-PSK AltBOC broad band modulation.But it’sarduous to understand the complicated modulation way whichmultiplexes 4 navigation signal components.And themathematical formulations are not easy to comprehend.So,in thepaper,the author has researched constant envelope modulation’scharacteristics and detailed 8-PSK AltBOC principles bydescribing phase jumping rule of the E5 signal’s Fresnelplot.Then presents how the modulation method forms a envelopeconstant 4-code multiplexed signal.coherence,another way called AltBOC(Alternative BOC)modulating E5a and E5b signals on the same carrierE5(1191.795MHz) comes out.(Fig.1)dACACA 'dBCBCB 'Figure 1.Transmit block of E5 AltBOC modulationKeywords- AltBOC; constant envelope; subcarrierI.There were two signal carriers called E5a(1176.45MHz) andE5b(1207.14MHz) at the period of Galileo signal plan haven’tbeen settled.But the two bands are so close that require theOMUX filter having a very sharp characteristic.Besides,thefilter could bring high propagation delays and timeinstability[1].So they need to be combined and then transmittedwith one carrier.Since every signal is composed of a pilot and data channel itwould have been a method that multiplex 4-code wide bandsignal[2].

If we just use the reference of the simplest 2-codeAltBOC way to implement 4-code modulation,there will be aproblem that the 4-code signals envelope no moreconstant.This doesn’t allow us to use the HPA at saturation.Fortunately a 4-code constant envelope modulation calledequivalent 8-PSK AltBOC was promoted .But themodulation’s principle is very obscure to understand.Afterhaving researched the 2-code AltBOC signal’s phase pointsjumping rule on Fresnel plot,we finds out the way how twosignals being vector summed can form a constantenvelope.Finally using the same theory and changing thesubcarriers to search two phase constellations having thecharacter like 2-code AltBOC,we gives the method of 4-codeconstant envelope modulation called 8-PSK AltBOC.II.III.INTRODUCTIONALTBOC MODULATIONA.

Single Side Band SubcarrierFirst,it gives two basic waveforms of BOC subcarrier.(fs isthe subcarrier’s frequence)(1)SCB ,cos (t ) = sign(cos 2π f s t )(2)SCB ,sin (t ) = sign(sin 2π f s t )Then Use them building a 4-phase single side band(SSB)subcarrier SC4,SSB and its conjugate SC4,SSB*.1(3)SC4, SSB (t ) =(SCB ,cos (t ) + jSCB ,sin (t ))21(4)SC4, SSB* (t ) =(SCB,cos (t ) − jSCB,sin (t ))2It can be written as (5),and its phase point in Fresnel plotjumps π /2 every Ts/4 as can be seen from Fig.2.The index “1”means its initial phase.(Ts is the subcarrier period)j (π+ i ⋅π)⎧42S C 4,SSB (t ) = e⎪⎨i ⋅ T s (i + 1) ⋅ T s,]⎪ t m o d Ts ∈ [44⎩SC4, SSB (t )SC4, SSB* (t )MODULATION METHODS OF E5 BAND SIGNALSGalileo navigation system E5 signal has two ways ofmodulation.The first one modulates E5a and E5b separatelyforming two QPSK channels.For the need of transmitting awide band signal with one carrier frequency and debasing therequirement of OMUX to ensure signal’s phaseFigure 2.Phase jumping plots of 4-phase SSB subcarrier and itsconjugate(5)B.

2 code AltBOCWhen just transmitting E5a and E5b datapath signals,define2-code AltBOC as:(6)s (t ) = C A (t ) ⋅ SC4, SSB* (t ) + CB (t ) ⋅ SC4, SSB (t )、beingtheE5aandE5bsinglesidebandPRNcodes.C A CBPhase oscillation of 2-code AltBOC is the vector sum resultof the points of SC4,SSB jumping anti-clockwise and SC4,SSB*jumping clockwise in two 4-phase plots.If the 2 codes areequal,the vector sum phase point will oscillatehorizontally.When they are different, there will be a verticaloscillation.The code value -1 means to circumgyrate thebeginning point of SC4,SSB or SC4,SSB* for π anti-clockwise inthe phase plot.(Fig.3)•• SC4,SSB* (t)•Here,the impact of [CA (t ) + jC ' A (t )] and [CB (t ) + jC ' B (t )]which modulate each SSB can be regard as having moved theinitialphasepointforacertainphase( π / 4,3π / 4,5π / 4or7π / 4 ) chosen by the value of eachcode being 1 or -1.Thus the 4 codes have determined the vectorsumed phase point of the two subcarrier.Principle illustrated inFig.2 and Fig.3 and Fig.5 gives the 4-code multiplexed signal’sphase plot:3•4•5••2••06•••18•7••••Figure 5.

Non-constant envelope 4-code AltBOC phase plotFigure 3. Subcarrier and 2-code AltBOC phase jumping in one TsTwo problems turn out:1) When the number of the value 1 (or -1)taken by the 4-codeC A , C A ' , CB , C B ' is even,the vector summed phase of the twosubcarrier being circumgyrated by a certain angle separatelywill oscillate diagonally.The amplitude is not same with theoscillations along horizontal and vertical.(Fig.6, 4-code alltakes 1 as a example)Base on (6) and Fig.3 can obtain 2-code AltBOC phasejumping rule in the Fresnel plot.•••••••••SC4 ,S SBS C(t )*4 ,S S BS (t )(t )Figure 6.

4-code AltBOC diagonal phase oscillationSC4, SSB (t )SC4, SSB* (t )2) When the number of the value 1 (or -1)taken by the 4-codeC A , C A ' , CB , C B ' is odd, the vector summed phase of the twosubcarrier being circumgyrated by a certain angle separatelywill oscillate horizontally or vertically,and occurs aphenomenon that the phase may resort at “0” point with zeroamplitude for Ts/4.Let C A , C A ' , CB , C B ' take -1,1,1,1 forinstance:Figure 4.

Phase jumping rule of 2-code AltBOC••C. 4-code AltBOC4-code double band modulation of E5a and E5b composedof two pilot channels and two data channels thus in either bandis 2-code modulation.(7)s(t ) = [CA (t ) + jC' A (t )]SC4SSB* (t ) + [CB (t ) + jC' B (t )]SC4, SSB (t )•••••••SC4 ,SSB(t )SC*4 ,SSB(t )Figure 7. 4-code AltBOC vertical oscillation cross zero pointThe corresponding phase function as follows:1SC8, SSB（t）=2 P1SC 38, SSB（t）=[ scE 5 − S (t ) + jscE 5 − S (t − Ts , E 5 / 4)]12 P2[ scE 5 − p (t ) + jscE 5 − p (t − Ts , E 5 / 4)](10)(11)Where P1 = (2 + 2) / 4 , P2 = (2 − 2) / 4 (let the envelopenormalized);Figure 8. The phenomenon of zero amplitudeObviously,here we see the phenomenon of non-constantenvelope we don’t expect to have since the satellite payload’sHPA can’t working at saturation,so AltBOC modulation needssome improve to transmit signals with constant envelope.IV.MAKE THE ALTBOC SIGNAL’S ENVELOPE CONSTANTOnce insert two pilot channels to form 4-code AltBOC theenvelope is no more constant.The reason is that the impact of[CA (t ) + jC ' A (t )] and [CB (t ) + jC ' B (t )] is not correlated.Contrastwith 2-code AltBOC constant envelope modulation may find ifthe beginning point of two 4-phase constellation plot of the twosubcarrier been circumgyrated have a difference of π / 2 ,afterbeing vector summed,the amplitude of horizontal(vertiacal)and diagonal oscillation will be equal and the phase point withzero amplitude will disappear.As code and data don’t haveorder, focus has been taken on the subcarrier format.Decompose the original subcarrier’s phase point ofSC4, SSB (t ) as two vertical vectors according to the rule ofhaving a angle between them of θ = π / 8 .It brings two new8-phase subcarrier and every phase’s interval is Ts/8.(Fig.9)Define the new single side band subcarrier and productsubcarrier as:ππ（j+ i⋅ )⎧84S C 8 , S S（⎪B t） = e⎨i ⋅ T s ( i + 1) ⋅ T s⎪ t m o d Ts ∈ [,]88⎩5π3π（j−⋅i)⎧84⎪ S C 3 8 , S S（B t） = e⎨i ⋅ T s ( i + 1) ⋅ T s⎪ t m o d Ts ∈ [,]88⎩SC4,SSB (t)θ(8)(9)SC4,SSB (t)θ = π /8Figure 9.

Decompose of SC4,SSB(t)They also can be written as:waveforms sampled from cosine function that mapping to theprojection of phase point on the coordinate axes.So the originalSSB conjugate SC4, SSB* (t ) can be decomposed as2 P1 SC8, SSB* (t ) and2 P2 SC 38, SSB* (t ) in the same way.Let’s recall the 2-code AltBOC,the two 4-phaseconstellations’ phase points after being vector summed in somemanner will be a constant envelope modulation.So at first usethe new 8-phase SSB subcarrier and product subcarrier to forma 4-phase constellation.(the same with 2 P1 SC8, SSB* (t ) and2 P2 SC 38, SSB* (t ) ,only have a difference of clockwise)+2PSC（）t1 8,SSB2P2 SC38,SSB（t）Figure 10.

Vector sum of the new 8-phase SSB and product subcarrier2 P1 SC8, SSB* (t )+2 P2 SC 38,SSB* (t )Figure 11. Vector sum of 8-phase SSB and product subcarrier conjugatesθ2PSC（）t18,SSBscE 5− S (t ) , scE 5− p (t ) are 4-level subcarrier2P2 SC38,SSB（t）Now consider the influence of PRN code.We know that theimpact of the 4-code can be regard as having moved the initialphase point for a certain phase.For the purpose that the resultdoesn’t have zero amplitude,the initial phase of the two 4phase constellations could not be the same or have a differenceof π .So 4-code must chang the initial phase point of2 P1 SC8, SSB（t） 2 P2 SC 38, SSB（t） 2 P1 SC4,SSB* (t )2 P SC 3*(t )28, SSB,,,in a particular rule to ensure that,the two 4-phase constellationscomposedby2 P1 SC8, SSB（t） ,2 P2 SC 38, SSB（t） or+2 P1 SC4, SSB (t ) , 2P2 SC3(t) will not have a moment that thephases are the same or have a difference of π .Hence,in theinterest of coming into two 4-phase constellations describedabove define:*8,SSB*11*(CA (t) + j ⋅ CA '(t)) ⋅ 2PSC(CB (t) + j ⋅ CB '(t)) ⋅ 2PSCt +（）18,SSB (t) +18,SSB2 22 211*(CB (t) + j ⋅ CB '(t)) ⋅ 2P2 SC38,SSB（）t(CA (t) + j ⋅ CA '(t)) ⋅ 2P2 SC38,SSB (t)2 22 2C A = C A '⋅ CB ⋅ CB ' , C A ' = C A ⋅ CB ⋅ CB ' ,CB = C A ⋅ C A '⋅ CB ' , CB ' = C A ⋅ C A '⋅ CB .Figure 12.

Oscillation along diagonalBesides,define 4-code modulation as follows:sE 5 (t ) =12 2(C A (t ) + j ⋅ C A '(t ))[ scE 5− S (t ) − jscE 5− S (t − Ts , E 5 / 4)] +1(CB (t ) + j ⋅ CB '(t ))[ scE 5− S (t ) + jscE 5− S (t − Ts , E 5 / 4)] +2 21(C A (t ) + j ⋅ C A '(t ))[ scE 5− P (t ) − jscE 5− P (t − Ts , E 5 / 4)] +2 212 2When the number of value 1 (or -1)taken by the 4-codeC A , C A ' , CB , C B ' is odd,the circumgyrated angle of singleside band subcarrier and product subcarrier by(C A (t ) + j ⋅ C A '(t )) and (C A (t ) + j ⋅ C A '(t )) have a difference ofπ .So as for (CB (t ) + j ⋅ CB '(t )) and (CB (t ) + j ⋅ CB '(t )) .They+formed two 4-phase constellations separately with initial phasedifference of π / 2 .In this case,the result signal’s phaseoscillates along vertical or horizontal.For instance:+TABLE II.(CB (t ) + j ⋅ CB '(t ))[ scE 5− P (t ) + jscE 5− P (t − Ts , E 5 / 4)]（12）(C A (t ) + j ⋅ C A '(t )) and (C A (t ) + j ⋅ C A '(t )) have determinedthe initial point of the first clockwise jumping 4-phaseconstellation and they must be equal or have a angle ofπ .

(CB (t ) + j ⋅ CB '(t )) and (CB (t ) + j ⋅ CB '(t )) do the samewith the second anti-clockwise 4-phase constellation.When the number of value 1 (or -1)taken by the 4-codeC A , C A ' , CB , C B ' is even,the circumgyrated phases of sigleside band subcarrier and product subcarrier by(C A (t ) + j ⋅ C A '(t )) and (C A (t ) + j ⋅ C A '(t )) are the same.So asfor (CB (t ) + j ⋅ CB '(t )) and (CB (t ) + j ⋅ C B '(t )) .After beingvector summed,the 4-code formed two 4-phase constellationsseparately with initial phase difference of π / 2 .In thiscase,the final signal’s phase oscillates along diagonal.Forinstance:TABLE I.THE NUMBER OF 4-CODE BEING 1 IS ODD FOR INSTANCEcodeCACA 'CBCB 'CACA 'CBCB 'valueangle1-111-11-1-1turnsto:7π / 4Now,thephaseπ /4jumpingof3π / 4sE 5 (t )5π / 4+11*(CA (t) + j ⋅ CA '(t)) ⋅ 2PSC（）(CB (t) + j ⋅ CB '(t)) ⋅ 2PSCt +18,SSB (t) +18,SSB2 22 211*(CA (t) + j ⋅ CA '(t)) ⋅ 2P2 SC38,SSB (t)(CB (t) + j ⋅ CB '(t)) ⋅ 2P2 SC38,SSB（）t2 22 2Figure 13.