MBOC The new optimized spreading modulation (797940), страница 2
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Fig. 1 shows BOC(1,1)’s resultingincrease in higher frequency power, compared to BPSK-R(1).BPSK-R(1)MBOC(6,1,1/11)-70-75BOC(1,1)-80-85-90-95-100-20The multiplexed binary offset carrier (MBOC) PSDrecommended in [2, 3] is the PSD of the entire signal (pilotand data components together), denoted MBOC(6,1,1/11), andgiven by101GSignal ( f ) = GBOC (1,1) ( f ) + GBOC (6,1) ( f )(1)1111where GBOC ( m,n) ( f ) is the unit-power PSD of a sine--15-10-505Frequency (MHz)101520Fig. 2. Unit Power PSD of BOC(1,1) and MBOC(6,1,1/11)Spreading Modulations, Showing MBOC(6,1,1/11)’sAdditional Power at Higher FrequenciesThe recommended MBOC(6,1,1/11) is a specific case of moregeneral spreading modulations that have been studiedextensively. It was selected to meet technical constraints in theAgreement [1], to retain a high degree of interoperability withreceivers that might use BOC(1,1), and to facilitateimplementation in satellites and receivers.phased BOC spreading modulation as defined in [4].
Theselection of this PSD and identification of practical ways toproduce time waveforms that implement it are based onextensive work by many individuals. Some of thesefoundational references are listed in [4 -11].885deterministic or periodic pattern. To produce aMBOC(6,1,1/11) spectrum, the spreading symbols used areBOC(1,1) spreading symbols denoted g BOC (1,1) (t ) and andSPREADING TIME SERIES ANDAUTOCORRELATION FUNCTIONA variety of time waveforms can be used to produce theMBOC(6,1,1/11) PSD described in (1). Two fundamentallydifferent approaches, time-multiplexed BOC (TMBOC) andcomposite BOC (CBOC), are described in this section, alongwith various applications of each approach.BOC(6,1) spreading symbols denoted g BOC (6,1) (t ) , with⎧sgn[sin (2πt / Tc )] 0 ≤ t ≤ Tcg BOC (1,1) (t ) = ⎨0elsewhere⎩and defined by⎧sgn[sin (12πt / Tc )] 0 ≤ t ≤ Tcg BOC (6,1) (t ) = ⎨0elsewhere⎩Denote a baseband spread spectrum waveform bys(t ) =∞∑ak = −∞kg k (t − kTc )(2)combination of spreading code chip, any data messagesymbol, and any overlay code bit, Tc is the spreading codechip rate, and { g k (t ) } are spreading symbols expressed in aA candidate TMBOC implementation for a signal with 75%power on the pilot component and 25% power on the datacomponent, could use all BOC(1,1) spreading symbols on thedata component, since data demodulation does not benefitfrom the higher frequency contributions of the BOC(6,1), andpilot component whose spreading time series comprises 29/33BOC(1,1) spreading symbols and 4/33 BOC(6,1) spreadingsymbols.
This design places all of the higher frequencycontributions in the pilot component, providing the greatestpossible benefit to signal tracking when only the pilot channelis used to this purpose, while yielding the PSDs294GPilot ( f ) = GBOC (1,1) ( f ) + GBOC (6,1) ( f )3333GData ( f ) = GBOC (1,1) ( f )(6)31GMBOC (6,1,1/11) ( f ) = GPilot ( f ) + GData ( f )44101= GBOC (1,1) ( f ) + GBOC (6,1) ( f )1111Fig. 3 next shows an example of this implementation, with theBOC(6,1) spreading symbols in locations 1, 5, 7, and 30 ofeach 33 spreading symbol locations.
This pattern could begeneral enough form so that they can be different for differentvalues of k . (Clearly, more general versions of (2) couldemploy complex-valued {a k } and g k (t ) to achieve higherorder phase modulations.)Define the spreading time series as the deterministic timeseries produced with the chip values formed by thecombination of the spreading code bits, any data messagesymbols, and any overlay code or other secondary code.
Forexample, a BPSK-R spreading time series takes on theconstant value of unity, while a BOC time series is merely therepetition of identical BOC spreading symbols. The mostgeneral case corresponds to BCS signals, whose time series isgiven by a vector s as shown in [8, 9]. According to this thespreading time series of BPSK-R in (2) is defined as∞∑ g (t − kT )kc(5)Since the pilot and data components of a signal can be formedusing different spreading time series, and the total signalpower can be divided differently between the pilot and datacomponents, many different TMBOC-based implementationsare possible.where the {a k } take on the values ± 1 as determined by thes (t ) =(4)(3)k = −∞TMBOC ImplementationIn a TMBOC spreading time series, different BOC spreadingsymbols are used for different values of k , in either aFig.
3. Example of TMBOC(6,1,4/33) Spreading Time Series, with All BOC(6,1) Spreading Symbols in the 75% PilotPower Component886repeated 310 times if the spreading code length is 10230, or124 times if the spreading code length is 4092.power split between data and pilot components, CBOCsymbols formed from the sum of 9 /11 g BOC (1,1) (t ) symbolsFor a signal with 50%/50% power split between pilot andcarrier component, a candidate TMBOC implementationwould be to use all BOC(1,1) spreading symbols on the datacomponent, and 2/11 BOC(6,1) spreading symbols on thepilot, yielding the PSDsand92GBOC (1,1) ( f ) + GBOC (6,1) ( f )1111GData ( f ) = GBOC (1,1) ( f )pilot component, with the data component remaining allg BOC (1,1) (t ) . The resulting PSDs would be the same as (7).ThenormalizedautocorrelationfunctionoftheTMBOC(6,1,4/33) spread spectrum time series, computedover infinite bandwidth and with ideal spreading codes, isillustrated in Fig.
4, along with the autocorrelation function forBOC(1,1). Observe that TMBOC(6,1,4/33)’s correlationfunction peak is narrower than that of BOC(1,1), but thewidths at values of 0.5 and at the zero crossing are virtuallythe same.GPilot ( f ) =11GMBOC (6,1,1/11) ( f ) = GPilot ( f ) + GData ( f )22101= GBOC (1,1) ( f ) + GBOC (6,1) ( f )1111(7)Yet another option for a signal with 50%/50% power splitbetween pilot and carrier component would be to place 1/11BOC(1,1) spreading symbols on both the pilot and data,yielding the PSDs101GBOC (1,1) ( f ) + GBOC (6,1) ( f )1111101GData ( f ) = GBOC (1,1) ( f ) + GBOC (6,1) ( f )111111GMBOC (6,1,1/11) ( f ) = GPilot ( f ) + GData ( f )22101= GBOC (1,1) ( f ) + GBOC (6,1) ( f )11112 /11 g BOC ( 6,1) ( t ) symbols could be used on only theGPilot ( f ) =(8)Several considerations affect the choice of specific locationsfor the BOC(6,1) spreading symbols.
If BOC(6,1) symbols areplaced in both the pilot and data components, receiverimplementation is simplest when these symbols are placed inthe same locations in both components. Also, it has beendetermined that proper placement of the BOC(6,1) symbolscan lead to improvement of the spreading codes’autocorrelation and crosscorrelation properties, compared tothese properties with all BOC(1,1) spreading symbols.Fig. 4. Normalized Autocorrelation Functions Computedover ±15 MHz BandwidthSummary of Spreading Time Series and ImplementationTable 1 summarizes the variety of implementations ofMBOC(6,1,1/11) that have been outlined:Work is underway to determine the best placement ofBOC(6,1) symbols in a L1 OS signal, accounting for theseconsiderations.
Good results have been obtained for L1C usingthe BOC(6,1) locations shown in Fig. 3, and the resultingperformance of spreading codes for L1C are reported later inthis paper.Table 1. MBOC(6,1,1/11) Possible implementationsPercentage onDataPilotpilotBOC(1,1)TMBOC(6,1,2/11)50%BOC(1,1)TMBOC(6,1,4/33)75%TMBOC(6,1,1/11) TMBOC(6,1,1/11)50%TMBOC(6,1,1/11) TMBOC(6,1,1/11)75%BOC(1,1)CBOC(6,1,2/11)50%BOC(1,1)CBOC(6,1,4/33)75%CBOC(6,1,1/11)CBOC(6,1,1/11)50%CBOC(6,1,1/11)CBOC(6,1,1/11)75%CBOC ImplementationA CBOC implementation can be based on the approachpresented in [6, 9, 11], using four-level spreading symbolsformed by the weighted sum of g BOC (1,1) (t ) andg BOC ( 6,1) ( t ) symbols.
For a 50%/50% power split betweendata and pilot components, CBOC symbols formed from thesum of10 /111/11g BOC (1,1) (t ) symbols andg BOC ( 6,1) ( t ) symbols could be used on both components,yielding the PSDs in (8). Alternatively, for the same 50%/50%887the MBOC waveforms provide lower average delays similar invalue to that of a BOC(2,2) spreading symbol.PERFORMANCE ASSESSMENTMany different performance characteristics have beenconsidered during waveform optimization.
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