Rebuttal to Karn's VMSK Misinterpretation

The analysis made by Karn's on his Web site <>


Fact: VMSK modulation is a form of modified BPSK modulation.

Fact: No one other than Karn attempts to analyze BPSK as Phase Modulation.

Fact: All modulation information is in the side bands.

Fact: One sideband is transmitted.

The reference used will be "Taub and Schilling" Principles of Communications Systems - to keep all references in one book.

Page 250. " BPSK can be thought of as an AM signal"

If Karn wishes to pursue the PM aspect, then he should at least use the correct his input data. ( Garbage in, Garbage out).

The modulation index is not 11.25 degrees for a 7,8,9 code, but plus or minus 90 degrees, or approximately 1.5 radians. This is wide band PM, or FM after integration. The SNR is better than that for AM.

This creates three main BESSEL products of approximately .8 for the J0 and .5 for each of the two J 1 sidebands. ( This is approximately the same sideband enery as that for AM).

The signal in BPSK and in VMSK is not dependent upon the deviation levels, but upon when the signal makes it's zero crossings. With BPSK, these occur at 'n' bit intervals. With VMSK, at approximately one bit period plus or minus a small time variation. Karn insists on keeping the J0 , holding it to be useless, and referring to the J 1 sidebands as grass. This is false. VMSK throws away the Jo and keeps only one J 1 sideband. ( assuming PM is retained as the modulation method.) This is a single sideband - with 1/2 of the modulation energy, - not a carrier. It alternates in polarity with each period change. As transmitted there is no carrier. Single sideband FM or PM exists, so the concept is not outrageous, but keep the J 1 sideband ONLY if you are going to simulate VMSK.

THROW OUT ALL OF KARN'S DISCUSSION OF NARROW BAND PM. His input data is incorrect. ( Garbage in, Garbage out).

Whether AM or PM, that sideband has all of the transmitted energy. The spectrum of that sideband is a single frequency line as anyone who cares to simulate it with MathCad or a similar program will easily determine. For those who do not wish to simulate, the schematics for building the encoding hardware are available from : Down load "Wirecom.pdf". See last pages.


On page three he shows the encoding form for the beginning stage of VMSK/2, which is VMSK/1. This is correct. On page 4 he shows the pulse width changes as carrying all of the energy. This is false. These pulse width changes only create the grass. The energy is in the total period of each positive and negative swing, as shown in the clock at the top, not in the changes. These larger pulse widths contain 16 times as much energy as the grass pulses. ( more later on this).

This total positive negative period results in sinx/x pulses which have the duration shown in T&S on page 306 under "partial response signaling". The differences in time Tb cause the peaks to shift in time so that to detect the signal, a peak detector must be used, or the coherent carrier inserted can be shifted in phase to result in the time differences appearing at the zero crossings. The same as in FM, PM, or BPSK AM. See plot below.

T&S pp 307 "The peaks of the responses are separated by times Tb"

"The total response is the sum of the individual responses."

In this case Tb varies slightly with the encoding. The individual responses alternate in polarity.

In VMSK the alternate sinx/x pulses, which carry the full energy of the bit period Tb plus or minus a small amount, are alternating in phase and are detected as positive or negative voltage swings. The modulation is still at the peaks, but the sum of the voltage levels becomes a (sinx/x) squared, or a triangular signal. The peaks are easily distinguishable. His figure at the center of page 9 is correct. The peaks are as shown and remain that way except that alternate peaks invert. T&S pp 306.

Page 4:

The changes are correctly shown. These do not carry the useful energy. They are the grass. An encoding chip has been constructed that will transmit only these changes and remove the main portion of the energy. There is a possibility that a coherent carrier, - note coherent carrier- could be used with these pulses to restore the signal, but this would be rediculous. The bandwidth is too broad. The detector used is not a coherent carrier reinserting type. It uses a reference locked to the sideband, which is 1/2 bit rate away from the actual carrier - now removed. The detected result using these ultra narrow pulses alone is a total disaster. As anyone who has worked with single sideband knows, inserting a beat frequency off carrier results in a screaming mess, or at least a howl.

The same result can be obtained by using a crystal to notch out the sideband main lobe, leaving only the grass. The higher the grass level, the worse the interference.

The grass is not coherent to the reference. See detector outputs below.

In no way does the grass contribute a useful signal component. The detected results ( printouts) using grass alone and with the grass removed by filtering are appended.


Karn has been given the filter response curve for one stage of filtering. This shows the grass is being reduced by about 25 dB per stage. The filters are cascaded for higher levels of rejection.

The detected output does not drop as the grass is removed.

The grass must be removed to obtain a clean detected signal and to pass FCC regs. ( Mask).

So much for Karn's claims regarding the grass. Look at the detected outputs.


His analysis on page 10 is false. The sinx/x pulses do not completely overlap as he shows. They would, if the filters had a high group delay. We use this high group delay concept to obtain a reference without modulation in the detector. The filters used for the signal path have been developed over the past 10 years to have a very low group delay, being at a level near or less than the bit period.

A filter reducing the group delay compared to that of the so called "ideal" filter by a factor of 5 to 1 was described in a paper by Walker in 1996. Later developments have reduced this by an additional amount. True, there is no zero group delay filter, but there are low group delay filters that can be used at RF when only a single frequency or very narrow bandwidth must be passed. We have patents on 4 or 5 of them issued or pending.


His analysis does not calculate a C/N for a given BER. He merely implies that it would be absolutely useless. For general information, the measured value is about 9 dB for 10-6 BER. This is being demonstrated at several locations at the present time.


Karn claims that I am deluding myself and others. If he would carefully read the latest version of the paper "Wirecom.pdf", he would see there is no delusion.

Isn't it amazing that I have about 200 fellow deluded scientists who have performed due diligence studies of VMSK ( using hardware) for their employers and arrived at the "horrible or inconceivable" idea that VMSK works. They haven't discovered any "Snake Oil".

It is amazing also that the baby Bells, that are allocating us test frequencies for over the air field tests, seem to accept the idea ( after their own lab. tests).

Development kits are being sent to prospective users. Karn won't get one. The circuits are available and he can build his own. Of course, it stands to reason, the kits would not be going out if they did not verify the claims made for VMSK.

Karn of course has never seen the hardware. He just makes incorrect assumptions.


In personal E-Mail, Karn has claimed I know nothing about modulation. Interesting!. I have been teaching it for years at Lucent, HP, National Semiconductor and other locations. In Dec. I have been invited to teach at several NASA locations. Next spring I expect to be a guest lecturer at U. Cal and four European Universities. I have about 15 patents on various modulation concepts, with about 6 more in the works. ( plus international filings).

I admit I am not the biggest brain in the business, but I do have a few accomplishments behind me.

Despite Karn's disclaimer, could there be a financial reason that Qualcomm would like to discredit VMSK ?.










(Sinx/x)2 pulses with outputs depending on reinserted carrier phase. The modulation information can be obtained from the peaks or from the zero crossings.

The early / late peaks correspond to the encoding time changes when locked to the clock.