IEEE TRANSACTIONS ON BROADCASTING, VOL. 43, NO. I , MARCH 1997 96

f1.R. Walker, CEO Pegasus Data Systeiris

Middlesex, N .J.

13aiidwidtli ellicieiicies that have riot been possible in the past are now being achieved using VPSK and VMSK modulation without the loss of sigiial power that nornially accompanies high bandwidth enicicncjr inetliods. I’lieoretically, these two methods do not losc any sigiial energy with increasing bandwidth compression EEciencies up to 15 bits/sec /1iz are now being achieved in usable hardwale with C/N ratios better tliaii that

paper explains how this is accoiriylislaed and gives a full niatheniatical aiialysis of the me tliod

obtainable usiiig FM, BPSK or QPSK. Tllis -f Il l +fm

Fig. 1, Spectrum of QPSK vs VPSK.

The niodulation inellnods with wliicli most people are fatrriliar are “ N M Line Code” nicthods. This includes FM, BPSK, QPSK, MIjSK, W S K , GMSK, QAM and any otlier nietliod that coilcentrates its bandwidth around a carrier If the data is eiicoded to kcep the iril’ot ination sidebands away fi oiri the carrier, i t is a “Biphase” inethod Marichester codiirg, and Miller (1) or MFM codiiig used for disk I ecoidiiig are exatriples of bipliase codes. No1 inally a bipliase code is used at basebarid. The two methods to be described (2) use a biphasc codc as a start point for RI;

modulation. ‘The spectrums of the the two coding methods are cornpared in Fig. 1. QPSK is a17 N1U Liiie Code method. VPSM is a “bipliasc” nietliod. Note that the bipliase spectrum stays as far as possible away li-om llie car i icr whilc Lhc NRZ Line Code specli uin

surr~ounds it. W = Sampling Rate. 1% = Data Rate. Fin = Nyquist BW.

It is well hiowii that bandwidth call be cut in hall‘ by usiiig single sideband transmission. ’This call be seen in Fig. 1 , The problem with SSB data transniission is that it is very diflicult, but not iiiipossible, to restore a carrier. If the carrier is a xiurrierical multiple of the data rate, tlieii it is possible to restore a coherent wrrier froiii the siiigle sideband. This is coniinonly done when using VPSK modulation.

Publisher Item Identifier S 0018-9316(97)02616-4

0018-9316/97$10.00 0 1997 IEEE

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‘l‘tie biplinse codes do not necessarily use tlie full bandwidth that FM or BYSK would use. WM, for example, has a spectrum that extends fi-om .25 J3K to .5 bit ratc. When transmit Led SSU with suppressed carrier, the spectiitin occupied is 1/4 that ofBPSK.-- or-- 4 bitdsedl-lz, as shown in Fig. 1. Manchester coding, uscd with ETIIJXNET at basebatid, uses the full bandwidth atid would L’ w e no inipi ovenietit in bandwidth eficiency if used at 1W

All of tlic biphase codcs are time varying, that is they have a zero crossing point that varies with time. l‘hey are polar and theoretically have liltle or no DC componeiit. If a I X coinpoilent is present, i t can be disregarded in nlost cases. Tlis is tlie ieason Manchester and MFhl or Miller codes are used for disk or tape recording - no DC component. 111 each case, thcre is a positive and a negative zero crossing that is time vnrying. ‘The decoder fits this time d i f h elice into a time aperture arid determines from the zeiu crossing time what the desired inforinatioti is. Ratlier tlian describe these IWO

wcll knowii codes. two new codes will bc dcsci ibcd thal utilize thc satiie concept.

1;iyiire 2 sliows the “cye pntterd’ for a IO, 1 1, I 2 “slip code”. A fixed apcrture code is slio-\vn i l l Fig.3.

In the slip code, the aperture is reset after each received zero crossing. With the fixed aperture code, the aperture stays fixed as showri i i i

lGg.3. ( Center +-).

Slip coding follows these iules: (10,11,12 code):

1) If there is no bit change, rcverse phase &er a IO/ I O bit period.

2) lf‘tliere is a change, wait 1/10 bit yeiiod, then reverse phase. ( I 1/ 10 period).

3) If there is a 101 in the pipeline and the count is 8, tlicii reverse the phase 12/10 bit period alter the last change.

The possible bit widths are 10/10,1 1/10 and 12/10. When encoded in this inanner and transmitted SSB-SC-FM or PM, the baadwidtli efficiency is 15.3 bits/sec./Ifz.

Assunie the upward zero crossing at tlie start has been received. The decoder has its aperture timer set to await the next zero crossing. If i t occurs 10/10 bit width later, there is a %o cha~~ge” signal and the last bit is repeated. If tlie change came at 11/10 bit width, a cliange is noted arid the output bit cliaiigcs li-om the prcvious bit. If‘ tlie crossing occurs at 12/10, then a reset is noted a d a zero followed by a onc are output. ‘I’his dvuble bit is necessaiy because the data is coiniig in slower than it it is going out of the decoder. In telecoiiiiiiuiiications, this is nornially referred to as “bit stufliiig” or “justification”.

‘I’he aperture timing is reset after each zero crossing so that the next zero crossing can be deterniined as a 10,ll or 12.

With a fixed aperiurc set (Fig. 3 ), the positive zero crossings set the timing start. Assume a 6,7( 13) code is used. The timing is set by the

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- 1 bit I

G ‘ 7 1 3

rising edge. If the faliiiig edge crosses in a 6 aperturc7 tlic sigiial is a one. If it falls in tlie 7 apeiture, tlie sigiial is a zero. ‘I’his nietliod is sclftiuiing. ‘l’iie spcctruin oftlie eye pattern is almost itietitical to a perfect 1/1 data clock. I t is 1101 neccssary to have a 6 or a 7 receive aperture. A ciossover point at the middle can be establislied so that if the negative crossing is early, it is a ow, arid if late it is a zero. Tlic apci t t i i e gatc timing is oiily of importance at the transmit elid of the system.

If it seems these zero crossings are too close to be kept apart iii red life, then compare tliein with ordinaiy PSI<. ?he 10,11,12 code sliown Iias zei o crossiiigs comparable to 2OPSK. ‘I’he 0,7( 13 ) COLIC a p p oxinialely tlial [or 1 OPSK.

’ 1 ’ 1 1 ~ slip codes a i c cxccllent fix FM subcai rier iisc where dala at I96 kb/s can be transtiiitted over ail I W bioadcast subcarrier. This is 20 times the rate presently being used. Ref. (7 ). They have soiiie advantages in terrestrial iiiicrowave use as well. A radio station reniote pickup unit has been built that traiisniits full coinpact disk quality sterco audio in a 26 IChz bandwidtfi. ‘I’lis fits an FCC 5OM-lz baridwidth allocation. (6,7,8 code) If the 10,11,12 code is used, the bandwidth required will fit a 25 K Liz a1 I oca t io n.

?’he disadvautage of the slip code inethod is the need for FIR filters for the nqrrow

bandwidth. Conventional crystal or saw fi!ters cannot be used ( excess dif’ferential gi oup delay variation) and LC filters are too broad.

l’he fixed aperture code (Fig, 3 .) is remarkable in that the specliuiii appears to be a single frequency at the data clock rate In fact, this single fiequericy can be ainplitude niodulated aml data can be transiiiittcd in the background as phase tiiotlulation. ?‘liis is being dolie over a power line niodeni operathg at 1.544 Mb/s iii accordance with FCC part 15.2h7c 1 rules.(8). Again, the data rate is at leasi 10, possibly 20 times that being achieved by iiiust

othcr powcr line or carrier currelit modems. I n this particular case the modem operates at baseband fur the coding method.“

When used at RI;, a 15,17(32) code has the saixie bandwidth efliciency as 256 QAM, ie., 8 bits/sec/l-1z.-- but -- without the powcr loss that acconyariies the use of QAM.

PHASE vs FIIEQ. MQDULA‘I‘IQN.

The two biyhase codes described are phase reversal. codcs. If the upper part of Fig. 2 is at 0 degrees arid lhc lower at I80 degrees. the phase ieverscs with each cliangc. Ttik is exactly what Iiappens with BlFX ~.r~odula!ioli. ‘I’liesc lwo codes arc tlicrefor ti l‘orni ofUPSSK niodulation in which the data is precodcd. Dif’fi.reiitia1 encoditig also precodes the data, but not in a biphase form.

If the biyhase code is applied to a balanced iiiodulator 01’ XOK gate along with a carrier, two liarrow sidebands are created. The width of the indivklual sideband call be taken from Tables 1 at~d 2.

Maiichester and MFM c m also be considered as a forin of slip code. Table 2 shows the fi-eqiiency spread when using the various slip codes.

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1,2 1VI"SK M anches ter 2 A 4 2VI"SK MFM 4,5$ 4VPSK Walker 67,s GVI'SK Walker 8,9,10 8VPSK Walker 10,11,12 LOVE'SK Walker

- C h ! Umdwidlh Y , b i t s / s e c / l l Z

2,3,1 .5 -.25 4 4,5,6 .5 -.3G 7.4 6,7,8 . 5 -.4 10.0 8,9,10 .5 -.42 12.6 10,11,12 A 5 -.435 15.3

1 ,z 1.0 - . 5 2 (SSB)

x Bit Rate

1;or the lixed ape1 lure inetliod:

Q = (t l+t2)/2(t2-t 1)= fW(f2-fl) bits/sedH_lz

Note tlie reseiiiblarice lo 1/( iiiodulation index) in FM.

'Ihe cletection Inetliod is described in detail in Kef(3 ). hiefly the overall inetliod consists of' geiierating a double sicleband signal, filtering oil' the carrier a i d one sideband, theii Iransniitting the desired sidebarid. At tlic receiver, a cotierenl carrier is created that is inixed with tlie sideband to obtaiii a pattern that rcserribies the start pattern, which is the11 litted to the apcrture detecting process to extract the inforination.

This incthod is a pliase niethod, since two phases ai e involved, A carrier is required as a start Jloillt.

Texts generally say that FM and €"I cgii be

equated, or at least converted to one another. Pegasus has patented a iiietliod to generate the spectnirn for the two codes described using frequencies instead of phases. The net speutral result is the same.

If two frequencies start in phase at a given time, but are of dilrerent frequeocies, they will be 180 degrees out of pliase at some later time. Tlus principal is used with OMSK where the l'requencies are clioscn to be 00 degrees apart li.oiii each other at a giveu time. In the biphase code inethods described here, they are cliosen to be 180 degrees at the desired time. Thus, the zero crossing effect accomplislietf by plisse iiroclulatioii can also be accomplished by fi equeiicy changiiig, or frequency'iiiodulation.

Using frequeiicy modulation there is 110 need to generate a carrier at the transmitter. The sidebatid can be geneiated directly and transmitted *it11 oiily minimal filtering to rileet ITC iegulations. For satellite use, the ItCC niask can be met with only a locked oscilhtor as a filter. Ref (9). At the receiver, the coherent carrier can be restored in the same iiiaiiiier as before.

Usiiig the frequency method, the first half of the fixed aperture is frequency a) and the secoiicl halrfre(pe1icy b). It can be seen that this results in din'erent zero crossing times when mixed with a recreated carrier, if tlie frequencies are different, 'The decoding nietliod used is: If fi-equency 1 occurs first, it is a data one. If frequency 2 occurs first, it is a data zero. hi each case tlie opposite frequvncy is used to fill the pattern.

?'Ire frequciicies i'or the two tone method are cliosen so that (for exninple) the carrier l u 64 times the data rate and the sideband tratistnitted is 65 times the data rate, then dividing the sidebarid as received by 65 will yield the data clock, which working backwards

100

is 1/64 the desired carrier.

For the fixed aperture code, selected crystal filters have been used successhlly instead of FIR filters, although with poorer BER results. It is only riecessary to know if the phase is -t- the center.

‘I’lie fixed aperture code is pailicularly applicable to communications systems with a cliiliciilt to mect FCG inask. The spectral slioulders are easier to reduce thari when using a slip code, making it easier to fit ail FCC inask. The data is self’ clocking and any ambiguity is resolved in the first bit or two. A ti ansinit/reccive of’fset in fiecluency of‘ scvcral pal ts per niillion can be tolerated.

‘I’he fiist of the two methods to bc developed and pateiited was the slip codc nietliotl. I W (2 ) This iiictliod was given the name VPSK- Variable Pliase Shift Keying- because the phase shift angle was not constant. ?‘lie ariglc iixm G to 7 in a 6,7,8 code is 30 degrees, but the mgle fiorn 7 back to 6 is less than 30 degrees. The err or angle in the calculations tlial follow is an average error airglc. I’ixcd i p t lure coding was developed w l m it was I calized that the FIR filters Cor VPSK w e ~ c surmliriies too coniplicated to be practical. U S and Forcigii patents are pentling 011 the llCW 111ethod.

l‘lie fixed aperture code is also a yhasc sliifl code, but the phase changes remain firtctl. When used at RF, with a two tone modulator, there is a great resemblance to GMSK or FSIC

In the analysis that follows, VYSK refers to using a slip code and VMSK to a fixed aperture code.

All modulation methods can be analyzed using a ~ ~ n i n i o n forinula:

Eq. 1. ‘The Universal Equation.

n i s equation relates all of the factors. The five sequential letters I70,PQM are a memory aid. N = Bitdsynibol; 0 is fix other factors such as 3/2 for FM and any correction netdcd for Viteibi or other error correction nietliods; 1’ is for power loss in modulation, which it) the case of phase or frequency modulation is -- 11 2 ;

Q is the bandwidth eficiency in bitdsec: /Ilz and l< is il factoi that occurs only with Fhf or niodulation of a bipliase type. For Variable Pliase Shifl Keying ( VPSK) and VMSK, N=l, always - only oiie bit per symbol. 0 is not used P=P ’. Q is taken from table 2 01 the fur iiiula above.

rI’lis leaves I<, l< is a phase noise irnproveriient figure that occurs when the bandwidth transrriitted ( Nyquist DW) is greater than the filkter bandwidth. For example in Fbl, a deviahii of 75 Khz for an audio signal o f 15 K1iz results in an 1% value of 5 . A 5/1 inipiovement in phase clistorlion. This faclor is indepeiident of the noise power relationship, See Best, Ref ( 5 ), pp49-57. When used with bipliase data, R is equal to:

niodulation, except that the frequency Nyquist SW,Noise BW = differences used are much smaller and can be

For the slip codes it has a value = .5 Q. For the fixed aperture code the value = Q.

decreased theoretically almost to zero. For tliis reason, the method was given tile iiariic VMSK - Very Miririiutsi Sliifl Keying.

‘Ihe lt phase noise iinprovernent occurs in

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biphase methods because the noise and digital signals do not act directly within the narrow bandwidth filter , but beat against one another. If the filter is narrow, the beat frequency lies outside the filter BW in region near zero Hz. The signal is being sampled at the data rate and the interference is at a much lower fiequency. Thus, only a sniall portion of the interference appears in each sample.

Q cnii also be defined as Sample Rnte / filter IJW. It is similar to Processing Gain (G,, 1 in spread spectrnm analysis.

The SNR at the detector for VPSK or VMSK can be obtained from Eq. 1 .:

SNI’1=(P)2QRE,/n = (P)’QI<(CNR)

= (p) ’ (2 E / n for VMSK

Q = 2.2( 2(ni+l)/n For VPSK

Q == (t I+t2)/2(t2-t 1)= fb/(n-fl) For VMSK

Q is in Bitdsecll-Iz

13 ‘n/(2(m t 1)) for VPSK P Q = 2 . 2

p = n(tZtl)/(tl+t2) for VMSK p Q 4 2

p In radians

Using 6,7,8 for VPSK ( m=6) and G,7( 13) for VMSK, the values are:

Q = 10 for VPSK

Q = 6.5 for VMSK

(PQ)’= 4.84 for VPSK I

(PQ) ’= 2.46 for VMSK

Inserting these values in the SNR equation:

SNR = 2.42 Eb/n for VPSK

SNR = 2.46 Eb/n For VMSK

SNR = I .O Eb/n for BPSK

This means that both methods are better than the theoretical BPSK value (the cornpatison standard) by 4 dB. DESI’I‘I‘E TIIE FACT TIIAT THE IrANDWIDTiI EFFICIENCY IS VERY IIIGH. VPSK loses 2 dB due to detector uncertainty. Whet her VMSK also suffers this loss or not is dependent upon the detect ion method.

Note the end results of both equations are independent of the bandwidth efficiency (b/s/r IZ).

Theoretically, both conld increase the bsndwidtli efficiency infinitely and the SNIZ. would remain the same. Compare this with QAM, where Shaiiiion’s Limit is not zero, brit increases with the value of N, reaching 20 dB for 1024QAM.

VPSK equipment is being demonstrated at 15.3 bits/sec/Hz., with a 12 dI3 CNR. This is the equivalent of 40,320 QAM which would require a CNR of 55 dB.

Note also that only MWSK and broadband FM show an SNR improvement over BI’SK. VPSK and VMSK are FM methods (SSB-SC- FM), so the 4 dB improvement should not be surprising.

Both VPSK and VMSK can be used at baseband. For example as broadcast FM- SCA signals and with power line or wired LAN modems,

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Those who haven’t followed the concept will claim that VPSK and VMS ~ l i a~ i i io~ i ’ s Limit and/or Carson’ s Rule. They do not i n either case, The references (3)(4)(6) calculate Slianiion’s limit in detail. Briefly, ~ ~ ~ ~ 1 ~ ~ 0 1 1 ’ s limit holds that if you use more than oiie bit per symbol, the power requiied ( or Sliaiinon’s Limit) rises. VPSK and VMSK arc

bit pcr symbol irietli

I’ all oiie bit per syn

Carson’s Rule and the Nyquist bandwidth are obviously not violated as will be noted from

igure 4. Fig. 4a shows the narrow baseband spectrum of a signal using VPSK. The spectrum from 0 Hz to .5 bit rate is the Nyquist Bandwidth, or the rnininiurn b ~ i ~ w ~ d t ~ i that can be used to pass the signal. Tlie point to note is that while it is there, it is not necessary to use or tranniit all of it. Figure 4b sliows the double sideband spectrum required by Carsons’s iule. If only one sidebad is used and only the part of that which contains infomation is transmitted, then Caison’s rule is observed. 4c shows the upper sideband as transmitted. 4d shows the e~~~iiva~ent signal as seen by the detector when the carrier is reinserted. 4e is the baseband signal from the detector, exactly like the signal at the stait. Carson’s Rule and the Nyquist

I ’ -SBR

.9BB ‘

Why transmit unnecessary bandwidth whe:i all it it contains is noise,?

Why are VPSK VMS different from FM with a very low i i i o d ~ l a t ~ ~ i ~ index.? A low niodulation index has a strong J, signal and weak J, sidebands. VMSK has no J, aid a strong J, sideband. When the J signal represented by a restored carrier is added, VMSK becomes the equivalent of an FM signal with a ~ ~ i o ~ ~ l a ~ i ~ n index of I .26. ‘I’his calulates to have the same post detection SNR as given above for VMSK VPSK.

The spectrum for the two methods’ is shown1 in Fig. 5. Tlie spectrum for VPSK is -26 dB at the nominal end points, (,4 and .5 BK for GVPSK). The spectauni background for VMSK is froiii 30-35 d below the peak of the single observable frequency at the celiter. Filtering is required to reduce the shoulder:;. ln both cases, over 99% of the energy is concentrated in the central peak. The lower levels beyond the peak come froni the A,, value ofthe Fourier waveforni analysis and are not necessary to recover the signal.

Figure 5 . VPSK and

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1‘ESI’ RESULT’S:

DER ineasurenients have been made using both of these “biphase” methods which confirm the theoretical analysis. Hardware is now undergoing beta testing in the field. Fig. G shows the performance of a Compact Disk stereo transmitter and receiver in both the RF and FM-SCA mode for VPSK. Note the dramatic reduction in audio noise compared to AM or narrow band FM.

SSB - FM - SC VPSK

-70 #

I I I I I I I J +io +20 +30 +40 +50 +60 +70 U80

SIN d13

Fjg.6. S/N Comparison, VPSK vs AM & FM.

CONCLUSIONS:

1) Biphase modulation codes as represented by the VPSK and VMSK rnetliods cui result in dramatic iinyrovetiieizts over otlicr inodulatioii methods in SNR, BER arid bandwidth efficiency in bitslseclI-Iz.

2) VPSK and VMSK do not lose power as other high bandwidth efficiency inethods do.

3) ‘l’he two methods offer trade off dipices

between filtering ease, bandwidth efficiency aid meeting transmission masks. VMSK is the easiest to impliment, but at a sacrifice in bandwidth emciency of 33%.

REIWUCNCES.

1) Miller, A. and Miller, W. U.S. Pats. 3,108,261 and 3,646,534.( MFM Pats.).

2) H.K. Walkcr, “High. Spccd Dah Coiiiriiiittica~iotis Syslciti Using Pliasc Shin Key Coding” U.S. Pats, 4,742,532 aid 5,185,765. ( Basic VPSK aiid “slip code” Patcnts.) U.S. and Forcigri yatcnts arc pciiding on the fixed apcjlure coding inclhod itnd thc pliantoni carrier signalling a~clliad. Licciiscs NC rcquired to usc cithcr method.

3) B. Strymk and H.R. Walker,” Iiiiprove Data Transmission Using Singlc Sideband FM With Supprcssetl Carricr”. Microwaves and RF Magazinc, Wirclcss Dcsign Supplcmenl, Nov. 1994.

4) H.R. Walker, “VPSK Modulation Transmils Digital Audio at 15 Bits/Sec./Hz”. Microwaves and RF Magazitic, Wireless Dcsigti Supplcmcnt, Dec. 1996.

5 ) R.E. 13cs1, “Phase Locked Loops ’I, Mc Graw Hill, NYC. 1084. ( Analym llic I’LL as an FM delcctor aiid the R factor).

6) H.R. Walkcr, “The Advantages of VPSK Modulatioii” Proceedings, lEEE Wescon,, San Fraiiscisco, Nov. 1995,

7) B. Sl~yzak, “VPSK Modulation on FM Subcarricrs”, Procccdings, Wirclcss Symposium, Si111ta Clara, Ca. Feb. 1997.

8) H.K.Walker, “ High Data Rale Power Line Modein Uses VMSK Modulation”, Proceedings, Wirclcss Symposium, Santa Clara, Ca. Feb. 1097,

9) H. R. Walker. ”Rcgctieralive IF Amplifiers Improve Noise Bandwidth” Microwaves mid RF Magazine, Dcc 95 and Jan 96.