[Lf] PSK sidebands

[Bob Bruhns]

I suggest three possible solutions to the excessive sideband problem: GMSK, filtered MFSK, and filtered PSK.  I have experience with GMSK at 9600 BPS in a weak-signal application, using simple frequency-discriminator demodulators.  I have experience with BPSK and DSBSC, which is an analog speech mode that is technically similar in transmission to BPSK.  I have some experience with MFSK in high-speed paging.  (See the article about MFSK in the January 2001 issue of QST.)  I have no experience with outphasing or outphasing as applied to switching amplifiers, but I think this is a way to generate filtered BPSK.

Considering only the binary modulation modes, and neglecting possible SSB data modes:

When properly filtered, PSK requires about the minimum bandwidth of any data mode.  FSK will always require more bandwidth than corresponding PSK modulation because the frequency shift adds to the sideband bandwidth caused by the data transitions.  However, filtered PSK varies in amplitude.  These variations are reduced with Offset-QPSK, but they still exist.

High efficiency amplifiers tend to be non-linear, and this distorts the varying envelope, which defeats the filtering to a greater or lesser extent, and increases occupied bandwidth.  Power amplifiers designed to be amplitude-linear tend to be less efficient.  For this reason, certain binary FSK modes optimized for minimum bandwidth have become popular, because they have constant amplitude.  The best of these modes are MSK, GMSK and MFSK (if data filtering is applied).

MSK

In MSK, data is unfiltered (square), and the frequency shift is equal to half of the bit rate.  Carrier phase does not jolt at the data transitions, but begins to advance or retard slowly when frequency is shifted.  For 1200 BPS, the frequency shift would be 600 Hz.  With a frequency shift of 600 Hz, the carrier phase shifts 180 degrees during a bit time (1/1200 second) compared to relative phase of the previous carrier frequency.

MSK still has fairly broad sidebands, because the transitions are still somewhat jarring.  This sharpness can be softened by filtering the data waveform before applying it to the frequency modulator.  This is what is done in GMSK.

GMSK

If you low-pass filter a data waveform, you soften the transitions.  A little of the data energy is lost, so performance is somewhat reduced.  But you can soften the transitions considerably before the data becomes greatly degraded.  The advantage is that the occupied bandwidth of the resulting signal is considerably less than MSK, and the low-level sideband energy farther away from the center frequency is very much less than MSK.  Good compromise is possible between bandwidth reduction and performance degradation.

A data low-pass filter with a cutoff frequency close to the data rate is optimum.  With a single stage RC filter, a -3dB frequency as low as 0.5 times the data rate can be used for narrow bandwidth, with only a few dB of performance degradation.

The resulting GMSK can be applied to a frequency modulator.  Typical GMSK deviation is 0.5 times the data rate, like MK.  Since the frequency shift occurs gradually, the resulting phase shift during a bit time is not as great as with MSK.  Both MSK and GMSK can be demodulated with a frequency discriminator, although better results are possible with phase-synchronous detectors.

There are a few popular GMSK modems.  I know of the MX-Com MX589 and MX909.  Some good information on GMSK is available in various application notes at the MX-Com website at http://www.mxcom.com/products.htm 

With a data filter consisting of a second-order filter such as a Sallen-Key, with a cutoff frequency of about 0.8 times the data rate, the bandwidth vs. data-quality compromise is even better.  This may not technically qualify as GMSK, but the idea is about the same.

MFSK

MFSK is Multiple Frequency Shift Keying.  By using several center frequencies, multiple bits can be sent during a symbol time.  Data low-pass filtering can be applied with the same tradeoffs that apply to GMSK; there will be an optimal amount of data low-pass filtering that minimizes occupied bandwidth without greatly reducing performance.  MFSK can be received with frequency-discriminator or phase-synchronous detectors.

PSK

For minimum occupied bandwidth, the data fed to a PSK modulator should be filtered very much as GMSK data waveforms are filtered.  Again, this reduces data energy and reduces performance somewhat - but again, a very good balance can be achieved between bandwidth and performance.  A data low-pass filter cutoff frequency close to or slightly below the data rate is optimum.  However, in the case of PSK, this filtering produces signal level variations that must be considered.

It is possible to predistort the envelope of a PSK signal driving a non-linear modulator or amplifier, and produce a linearized output signal.  The precise characteristics of modulators and high-efficiency amplifiers can be unstable over voltage, temperature and loading conditions, but precompensation and negative feedback can still be effective if carefully applied.

BPSK is the same as double sideband without carrier, symmetrically modulated by a data waveform.  When rounded waveforms are sent, it is difficult to amplify this efficiently without serious distortion and resulting splatter.  There have been several approaches to this problem over the years.

For BPSK, I think the outphasing technique may be a way to go.  In this technique, two high efficiency amplifiers are driven by phase modulated signals.  The phase modulation is applied in equal amounts and opposite polarity in the two amplifiers, so modulation causes the amplifiers to vary in phase difference.  Then the output is derived by combining the outputs of the two amplifiers.  For example, the data waveform would vary from 0 to 1, and the corresponding phase difference would vary from -180 to +180 degrees.  By varying the phases of both amplifiers by equal and opposite amounts, the difference signal will vary smoothly from full output in the positive direction to full output in the negative direction.  All amplitude levels are produced at high efficiency, except for the very lowest levels, where the power loss is small.  However, the transfer characteristic has odd-order curvature, and this linearity issue should be handled carefully by precompensation and (probably) negative feedback.

In a switching amplifier, this is the equivalent of Pulse Width Modulation.  But by using two switches in series, it is not necessary for either switch to transition extremely quickly when output pulse widths need to be extremely narrow.  Each switch can be on for 180 degrees, and the phase variations between the switches cause the on times to be misaligned, resulting in wider and narrower output pulses.  This results in continuously variable amplitude, from zero to maximum output, without impossible switching times.

  Bob Bruhns, WA3WDR