All about Ultra Narrow Band Modulation - assembled from the papers presented by the experts.

3/8/2013 Update.

This Site is dedicated to the understanding of Ultra Narrow Band Modulation.  


Ultra Narrow Band Modulation has been found to result from previously unused modulation and filter combinations

- The components of the Fourier spectrum are separable if Negative group delay filters are used -

It has now been applied to several practical applications that meet FCC Regulations and is now being used in commercially available products.

Various technical papers are posted here in .pfd format. Some important new information has been added to show circuitry and results not previously revealed.

The Textbook and nearly all of the files are now undergoing constant revision. Extensive changes have been made to the Textbook Chapter 7  ---- The Series Emitter Filter with Feedback is used presently.

Chapter 18 has been added.

Files [2] and [3] have been added to show new data - including Radar and other AM pulse applications..

This textbook is a non-commercial educational item for use by students and engineers worldwide.

It summarizes the work of many authors who have each contributed small to significant amounts of material. Credit is given where appropriate. In its present form, a great deal of latitude is allowed in reproducing copyrighted material from other sources, and in the language used for explanation. The source is noted where it is of significance.

Numerous references from peer review papers and patents are given in the Preface to the Textbook available below. Applicable patents are also listed.

The Ultra Narrow Band Textbook

Preface               Contains a list of over 70 published papers and other           information

Chapter 1            Baseband Coding

Chapter 2            Modulation Methods

Chapter 3            Filter Effects

Chapter 4            Filters with Group Delay      

Chapter 5            Bipolar Phase Shift Keying and Coded BPSK

Chapter 6            Abrupt Phase Change Modulation Methods

Chapter 7            Filters without Group Delay  

Chapter 8            Pulse Position Phase Shift Keying

Chapter 9            Modulation with Broad Pulses

Chapter 10          Detecting Ultra Narrow Band Modulation

Chapter 11          Sideband and Carrier Vectors

Chapter 12          Unnecessary Sidebands and Grass

Chapter 13          Signals plus Interference

Chapter 14          Measuring Bit Error Rate

Chapter 15          Shannon’s Channel Capacity and BER

Chapter 16          Doppler Effects and AFC

Chapter 17          Multipath Effects

Chapter 18        Amplitude Pulse Modulation Systems

Chapter 19        Quadrature Modulation Methods


1)    Universal Resonance Curve

2)    Fourier Analysis

3) Measured Effects of Abrupt Phase Change Modulation

4) Some Proven Applications

5) Filter Overload

6) Bessel Products.

7)    Abrupt Phase Change Modulation Analysis.

Index ( Still under preparation ).

Extensive changes have been made to Chapter 7. Chapters 18 and 19 have been added.

Download the book < Click here:

The Ultra Narrow Band principal appears to some engineers to violate some established rules, in that sidebands are shown to be unnecessary to meet FCC regulations, and that all necessary phase modulation data is available from the carrier alone, or from one sideband alone. Ultra Narrow Band Modulation does not actually violate any established rules, as is explained in great detail in the textbook and some of the following papers.

 Textbook and test confirmation is attached to the files.

There are several "prove it yourself files" below . Skeptics will claim this concept is impossible. We advise them to study the "Measured Results", "Theory Explained", "MCM" and "Experimenters" files, then try it before they comment further. The concept is only impossible if positive group delay filters are used.

The skeptics are proven wrong because these methods are being used and sold in working systems.  The mathematical and experimental proof is covered in the textbook above.

When there is a pure Fourier spectrum, the spectral components are separable when a negative or zero group delay filter is used.

VMSK ( Very Maximum Sideband Keying ) modulation in its original form was a Single Sideband Suppressed Carrier phase modulation method. The ultra narrow bandwidth characteristic was created in the baseband waveform. This was then applied to a balanced AM modulator to remove the carrier. Additional filtering was added to remove one sideband and the numerous Fourier products in the spectrum. Only one sideband was required ( separable from carrier and the opposite sideband ). The Fourier products are amplitude modulation products, which were shown to be useless in phase modulation, so they could be removed by filtering.

The name VMSK has been associated for the past 9 years almost totally with the baseband "aperture" code. It is only one form of Ultra Narrow Band modulation. The original SSB-SC method is referred to as "Very Maximum Sideband Keying". The newer Pegasus MSB methods are "Very Minimum Sideband Keying". The carrier is used without sidebands.

There are other Ultra Narrow Sideband modulation methods in use that did not originate at Pegasus.  See the "comments" and the list in the preface to the textbook. Much new work is being done in China supported by the Chinese National Science Foundation.

Although every effort is made to keep these files current, they always seem to be out of date and need revision. Some errors and oversights are unavoidable. The latest revision date is marked. 

Please accept our apologies for any prior incorrect analysis of the " VMSK or MSB Technology". We are still correcting the analysis of the various methods and updating these files.

Please send any comments or suggested corrections to: <pegasusdat@aol.com>

[1]Click here for the latest comments( Current 4/15/10 )

Technology advances rapidly.

[2] Latest Technical Discussion -

All about UNB methods used for pulse transmission -- including Data and Radar like systems. ( 4/15/10 )

[3] Latest Technical Discussion -

UNB methods used for pulse transmission -- including Data and Radar like systems do not require sidebands. ( 4/15/10 )

[4] A "Layman's" explanation of Ultra Narrow Band Technology (12/10)

This paper is for the person who wants to know about narrow band technology in general, but does not have an engineering background. Engineers might find it useful in discussing uses for UNBT. ( 4/15/10 )

[5] This is a thorough explanation as to how it works( 12/15/10 )

All, or most of,  the theoretical details for data transmission are here.

[5A] This is a thorough explanation as to how it works( 12/15/10)

More of the theoretical details are in this second explanation.

[5B] This is another thorough explanation as to how it works( 4/15/10)

Ultra Narrow Band Modulation is a form of Pulse Width Amplitude Modulation.  Analyzed as such it becomes clear how the single frequency is obtained with a low C/N for a given BER.

[6] This File is a more extensive explanation of MSB Modulation(  4/15/10 )

This file contains a complete explanation with scope shots and spectrum analyzer plots. It compares the various phase modulation methods with MSB.

[7] This File explains about Radar improvement(  6/23/10 )

This file contains a complete explanation of how Radar, IFF, DME and other pulse methods can have the receiver SNR improved by 30-40 dB. Prior work by others have used Wavelet filters. This file uses the UNB zero group delay filters,

[7A] Click here for a Tutorial on Negative and Zero group delay ( 12/10 )

The UNB methods require a filter with zero rise time, or group delay. This is a general description of Negative Group Delay filters.

[8] Click here for the latest Mathematical Analysis( 2/15/10 )

This Mathematical Analysis is a copy of Appendix A7 from the textbook.

[9] Sensitivity Required ( 4/15/10).

The receiver sensitivity required for a given 10-6 BER is shown for MSB, BPSK and 256 QAM.  MSB has a very large C/N advantage over other methods.

[10] A Successful Microwave System Trial Using UNB and the Hardware used.

[11] Click here for an engineering explanation of 3PRK and MCM, the origins( 4/15/10)

It was found that the old VeryMaxSidebandKeying method resulted in a waveform with a missing cycle.  This could be duplicated in the carrier without going through the SSB-SC-PM hassle. The old VeryMaxSideband and the new VeryMinSideband carrier method were seen to be closely related, both sub-classes of MSB.

[12] Critics say it is all in the sidebands( 4/15/10)

Sidebands are unnecessary in UNB, but they are partially correct. One sideband is transmitted for VMSK, but only the carrier is needed for MSB. See how biphase reality refutes their belief and criticism. See also 'Fourier Analysis' in the textbook and [7] above for an in depth discussion. UNB modulation is "Pulse Width End to End Modulation, an AM method.

[13] More about it is all in the sidebands( 4/15/10)

This file shows that neither grass nor sidebands are necessary or used and that removing the sidebands has little effect on the detected phase angle.

[14] Filter testing with 3PRK show almost no sidebands

The sidebands can be reduced -100dB average power below the carrier and still be detected. The phase angle transmitted has negligible loss.

[15] Click here for an engineering description of Microwave MSB.( Current 4/16/10 )

3PRK Modulation, one of the MSB methods, has been satisfactorily used on a microwave link and is now being used on Cable TV systems as well.

[16] Microwave and Satellite Modems have AFC.( Current 4/16/10)

70 MHz Modems presently being built for microwave and satellite use have AFC to track Doppler and offset in the links.

[17] Direct Microwave Modulation is good to 60 GHz.( Current 02/02/04)

Experiments at Marki Microwave have shown the method works to 60 GHz.

[18] Mixing - Up/Down Conversion ( 5/13/06 )

There are some tricks to up and down conversion.

[19] Click here for an engineering explanation of 3PSK( Current 8/25/04)

This is a file on 3PSK that shows the effects of changing the baseband duty cycle and phase, which can be from 1 RF cycle with 3PRK to 1/2 the bit period with WPSK.  PSK is used with NRZMSB for an improved GSM equivalent.

[20] Digital Audio and Video Broadcasting Using FM-SCA ( could be updated )

VeryMinSK is shown to be the very best method for DAB and DVB. A nationwide network is in the planning stage with FCC licenses being applied for.  See also [35]below.

[20] MSB Modulation can use the NRZ data raw for 90 degree phase changes.

(Current 01/15/07 )

The highest possible data rates are obtained using NRZ as the baseband code, with 90degree phase modulation.

[21] NRZ/MSB Modulation can tolerate some group delay. (02/07/04)

3PRK and 3PSK are intolerant of group delay in the network filters. Some group delay can be accepted with VMaxSK, RZ and NRZ inputs.

[22] Click here for Cable TV application of MSB ( Current)

3PRK and NRZ coding are now being used in a Cable TV demonstration to add one 12 Mb/s data Channel between each present analog channel. This adds 100 UNB channels to a 100 channel CATV system - without interference to the analog channels.

[23] Click here for Cable TV application of MSB ( 5/12/06)

This information on digital TV was provided by Silicon Valley Tech. for reference regarding their H264 chip set.  It show the use of the "Mobilygen" chips with UNB.

[24] Oscilloscope Photos of various codes are available( Current)

This is collection of scope photos showing various data rates and the phase detected signal after 30 dB of sideband reduction with a zero group delay filter.

[25] Click here to see the analysis "trap" most critics fall into.

( Current )

A large number of people claim VMSK and similar Ultra Narrow Band methods will not work. They cannot possibly work they say, because their flawed analysis proves it. Here we show them to be wrong in their analysis. Ultra Narrow Band methods do work and are in use, but you cannot analyze them at baseband and you must use the special zero group delay filters. Simulation programs do not include these filters.  Refer to the textbook.

[26] Click here to see the proper analysis method.

UNB has a Nyquist BW = the IF, a transmission BW = 1 Hz and a receiver noise BW of approximately 500 Hz.

[27] A summary of Ultra Narrow Band zero group delay filters (09/06/09)

 Ultra Narrow Band modulation requires the use of special filters with extremely low group delay. Ordinary filters, for example multi-pole crystal filters, cannot be used. Some of the known RF filters that do work are described here. The paper also explains why ordinary filters do not work. Contains Important recent update information. When the filter bandwidth is too wide, the filters and the limiter can be overloaded. A pre-narrow band filter is required ahead of the narrow band crystal filters.

[28] The LC-TRS Filter.

TRS filters can use LC resonators and still obtain very low group delays.  They are used as pre filters in Superhet. circuits to reduce the overall input noise and interference

[27] Click here to see how the filters are impulse tested ( Current )

Ordinary filters exhibit a rise time and group delay, which can destroy MSB modulation. Filters for MSB and other UNB methods must be as free of group delay as possible. This is possible using some proprietary circuits. The test results showing some filters to be almost free of group delay are given here.

[28] Click here for a discussion of the BER measurement method ( Current 1/15/06)

The effectiveness of a modulation method is dependent upon its BIT ERROR RATE    ( BER ) when operating at a specified Carrier to Noise Ratio. ( C/N or CNR ). The measured results for the old VMSK/2b and the newer UNB methods are better than for BPSK.

[29] The Theoretical BER can be calculated ( Current 9/05)

The measured BER and the theoretical value have been found to be very close to the same. They are directly related to the Q function.

[30] Click here to see the "Effects of Interference" ( Current )

As long as the Signal to Noise ratio exceeds 6 dB after narrow band filtering, the signal can be detected almost error free. The filter response used for BER measurements etc. is discussed.

[31] An explanation of the 'R' Effect ( Current 10/20/05 )

Ultra Narrow Band modulation using correlative detection is heavily dependent upon this little known, but widely used effect. When it is fully effective, UNB can  be better than for BPSK, or even OFSK, as shown in BER measurements above.

[32] "Notes on Shannon's Limit" ( Chapter15 from book )

Some critics claim that operation at 100 bits per second per Hz or higher must violate Shannon's Limit. This paper explains how 'Shannon's Limit' is not violated in any way, using textbook references and Shannon's original work to justify the analysis made. This is clearly shown in the "Illustrated" paper below as well.  Nor, is the Nyquist sampling theorem violated. Sampling is done at the data rate, or at a greater rate, namely the IF frequency, as required by both Shannon and Nyquist.

[33] Click here for "The UNB/MSB Spectrum" ( to be reviewed )

The MSB spectrum for 6 Mb/s is shown to fit a 30 kHz AMPS cellular channel. Even higher data rates are possible, since the UNB signal has no bandspread.  Five adjacent 6 Mb/s channels are currently being transmitted with 30 kHz channel separation.

[34] "MSB Audio"   09/06/09

Normally UNB has been used for digital data transmission. It is possible however to use it for single channel audio transmission in an analog mode without a CODEC and without usable sidebands.

[35] Archive file on Multipath

Measurements made on multipath simulators for VMSK/2b are equally valid for 3PSK and 3PRK. See Chapter 17 of Book.

[36] RMS Power in Sinx/x Spikes (From Archives ). The power level in the Fourier sinx/x spikes has been measured. 

The archive files covering the old VMaxSK method, which used Single Sideband Suppressed Carrier technology have been removed from this site.  This method has not been used since Jan 2001, but has some merit since filters with some group delay can be used.

The methods are adequately described in the textbook.

See also " Comments "

Most photos are in the JPEG format and require a JPEG reader unless they have been inserted in .DOC or .PDF files. All printouts from digital spectrum analyzers and scopes have been converted to  MS Word or .pdf format.


PEGASUS DATA SYSTEMS, is not owned by any other company. We are licensed independent consulting engineers providing services to others.

--Contact < pegasusdat@aol.com > for details.


Some help is now available from Universities, which will speed up error correction and omissions.

Check the dates on the files. Some may not have been updated.

Several pre-production products have been demonstrated using UNBT

See the Textbook Appendix.

In case of doubt, contact H.R. Walker at     pegasusdat@aol.com , or the author of the paper.