четверг, 4 июня 2009 г.

FSK, GFSK, MSK, GMSK and some other modes.

Author: SergUA6

The reason of creation of this article is the interesting discussion on our forum, the second reason is that I’v got e-mail with same subject to discuss, after all I saw same problem discussed on the one of Internet’s forums.To ignore these coincidences would be a bad form, that’s why we will try to look into the existing problem of modulations.

This article is only own attempt of researchment and analysis of the modulation’s problem. I will stick to bases and general principles from the theory, I won’t go deep into details, but the common approaches and principles will be considered.

FSK

Let's consider FSK modulation. Standardly, in a general view, the modulator circuit looks like this (pic.1):

pic.1
The rectangular bit stream as 01001..11010, which is transformed to levels + / - 1 goes on the modulator (the Voltage Control Oscillator), where one frequency corresponds to level +1, and another one to level -1.In this case we have the classical FSK modulation on output. As we can see the frequency spacing (shift) is specified in the modulator and it can has any value, but no less than Br (BaudRate – manipulation speed). We won’t consider the reasons why it shouldn’t be less then BR, because it is well-described in theory, but I will note that it is impossible to demodulate the signal, where the frequency spacing is lesser then BR.

It is important to mark now, that the generator in the modulator and the bit stream, as a whole, are not directly linked and are not synchronized. The spectrum of such signal contains many harmonics, due to squareness of the impulses of modulation and due to sharp switching of the generator in the modulator in unsuitable moments of the time. The main energy is concentrated around the frequencies of manipulation in area, which is equal to Br. That gives minimum possible spectrum of such signal = 2*Br, with the spacing = Br, or Shift (spacing of frequencies of manipulation) + Br in the more common case. Harmonics, which are outside of this spectrum can be effectively suppressed without damage to successful demodulation, as becomes on practice.

pic.2



Please pay attention, that the spectrum around the frequency manipulation, with spacing equal to Br, is exactly fit into the space between frequencies without overlapping. If to put the frequencies together further, then there will be an overlap of spectra of "anothers" impulses and mutual strong interferences. This is evident graphics image of limitation of the minimum spacing at classical FSK (pic.2). The mathematical substantiation is well described in the theory. The main idea of reduction of the frequency spacing at the same speed of manipulation, (and as consequence rising of FSK efficiency ) is well-visible from the graphical representation(pic.2).

It is enough to reduce/restrict
an area of primary energy of laterals around the frequencies of manipulation, this way allows to decrease/reduce the spacing. This idea is realized through the pre-filtering of bit stream, before it’s feeding on the modulator.

Guassa filters are widespread in FSK, they provide:


  • effective enough narrowing of the band/strip by smoothing abrupt/sharp transitions of the voltage manipulation
  • good controllability of parameters.
In principle, any filter, which is smoothing abrupt/sharp transitions is good for this purpose, but the Gaussian filters have better performance and characteristics.

GFSK

The Classical FSK with preliminary filtering by Gaussian filter has received the name GFSK. The common circuit of the modulator is the same, but the bit stream passes through Gaussian filter(pic.3).

pic.3

This allows to evade from restriction of the minimum shift of the classical FSK, Shift> = Br towards reduction. The parameters of the Gaussian filter have an influence on how much the basic spectrum of laterals will be narrowed, and how much it is possible to shift the frequencies of manipulation. Let’s name this “how much” value as X. In practice (actually in the theory too) the size of X value is always more than Br/2, because the reduction of the laterals is reached by the strong declivity/sloping of fronts of manipulation voltage/power, that leads to incursion of one impulse on another impulse, and as consequence to impossibility of demodulation.

Typical reduction of the spacing for GFSK is about 30-40 % from the classical Shift = Br, that is Shift = (0.7-0.6) *Br. It is very difficult, in the general case, to say that it is GFSK is used at analysis, because the same or similar effect can be achieved with other filters.

pic.4


MSK


Further development of FSK manipulation technique led to the appearance of MSK manipulation, the manipulation with the minimal frequency shift.It has been theoretically well-founded under what conditions manipulation with the frequency spacing=Br/2 is possible. I will notice, that in this case there was a refusal from the Voltage Controlled Oscilator, and for creation of MSK manipulation quadrature modulators are used.

The Circuit of MSK modulator is essentially more difficult and looks approximately like this(pic.5).I will notice that there are a lot of circuits, but for us the general principle is important.

pic.5

It can seem that the modulator in MSK is also independent and not synchronized with a bit stream, however it not so, conditions of MSK manipulation demand, so as the change of bits would occur at extremums of oscillations of the generator in the manipulator, or is easier in absolute peaks of a sinusoid and-or in zeros. At performance of all conditions the frequency spacing of manipulation= Br/2 is automatically installed, and the common width of the spectrum is becoming approximately 1.5*Br.

It is not difficult to understand, that the manipulation is represented as one frequency, which is having different phase on the different impulses, and the phase is never stops, thus it gives two frequencies with the minimal spacing. All that is well represented in the theory.

pic.6


GMSK


Insertion(adding) Gaussian filter in MSK modulator’s circuit allows more reduce the common spectrum of the signal, but the payment for that will be reducing of the protectability from interferences(noise immunity further). Such manipulation has received GMSK name. Standardly, GMSK manipulation can has spectrum, which is bigger than BR only on 12-15 %, smaller values are perilous with strong losses of the noise immunity.

pic.7


pic.8

Certainly MSK manipulation has the most noise immunity at the coherent demodulator. However as it is not difficult to notice, that the essence of all tricks is the narrowing of a bar/stripe at FSK manipulation, that allows to demodulate MSK, GMSK modes by usual frequency detectors, but, ofcourse it is more likely forced way, and basically it is not so correct way. It is also not difficult to notice that MSK and GMSK, in the first, manipulate the phase of carrier oscillation, and in the second, demand the coherent demodulators for complete realization of their potential possibilities.


Thus we have following characteristics of these modulations:

  • FSK – the simplicity of implementation and relatively wide spectrum;
  • GFSK – the simplicity of implementation, and smaller spectrum, but also slightly worse noise immunity in relation to FSK
  • MSK – the very high noise immunity at relatively small spectrum, but the difficult circuit of the modulator-demodulator.
  • GMSK - the spectrum width is almost close to theoretical limit of Br, slightly worse noise immunity in comparison with MSK, and the complexity of the modulator-demodulator same as for MSK.

HALF-MODES

The "two-faced" signals, such as MSK and GMSK I name half-modes, ofcourse, it is not the standard name. It simply was required to allocate somehow this class of signals from the general PSK family, because such signals possessing both PSK signs and FSK signs.

The second harmonic of these half-modes, has two bright spectral lines, the spacing between these lines is equal to Br, that is one of the signs of these modes.This is the necessary condition of their
definition at the analysis, but not the sufficient. Two lines in the second degree/power can be also given by both SDPSK and OQPSK modes.

SDPSK, generally, does not demand synchronism of transitions in extremums of the carrier, and because of this, it has the bigger width of the spectrum than MSK. This width of the spectrum can be reduced by filtering of the bit-stream before feeding on the modulator, this procedure is usually realizing through RRC filters.

SDPSK (PSK-2 with phase rotation) in essence, has same resulting signal as MSK, only with wider spectrum. It can also be demodulated by FSK demodulator, becos of getting under definition of half-modes.

Modern methods of creation of the various signals do often erase the distinction between various modes, for the reason, that developers are almost always (it strongly simplifies development) aspire to select a multiple relation between the clock frequency of manipulation and the frequency of the carrier.

In this case developer declares and forms, for example,that the modulation is SDPSK, but the resulting signal, in essence, is MSK. Thus, casually or deliberately some confusion is brought into diversity of the various modes and their definitions.

Very often GFSK modulation is specified,in descriptions of the signals, while in actual fact it is typical SDPSK according to all signs. The example is the signal of the Finnish radiosonde.

When we are looking at the circuit of formation of GFSK modulation, it is easy to understand that if the clock frequency and the generator will be synchronized, and the frequency spacing will be choosen as BR/2, then such “GFSK” will easily turn into one of our half-modes, at defined parameters of Gaussian filter and high stability of generator’s parameters. Seems like developers just don’t think about it or just do not know.

By the way, in one’s time, by this reason, GFSK was mistakenly classified to these half-modes on one of sites the modulation ACARS VHF has been declared as GFSK.

In analysis it is very desirable to define what type of modulation is used, at least approximately. It is also necessary to be oriented on the width of the spectrum, which is occupied by the signal and on
its form.

At pure MSK modulation, width of the spectrum is about 1.5*Br, at GMSK spectrum is lesser than this value, and in it’s limit is very close to theoretical Br, at the same time the spectrum of MSK, GMSK is obviously expressed as bell-looking-like shape/form, at SDPSK the spectrum is more then 1.5*Br. The basic sign of half-modes is two lines in the second degree/power, the basic but not sufficient, it demands certain accuracy and attention. The spectrums form does also require certain accuracy, because often receivers distort it to unrecognizability, especially if the signal is taking off from AF’s output or from discriminator, in this sense it is much more preferable the I/Q record or IF.


MSM team