Dear LF group,
ON7YD's comment that BPSK "gives away" 3dB is only true for the
limiting case of phase-keying data input consisting of alternating 1s
and 0s, and therefore a phase transition for every bit. For real
data, I reckon there is on average around 1 transition for every 2
bits, so the "loss" in mean TX power is more like 1.3dB. I suppose
the real question is if this "missing" power were present, would it
do anything useful at the RX end? This would depend on the type
of modulation and demodulation used.
As far as continuously varying phase modulation goes, my
undergraduate text book makes the point that phase modulation is
essentially equivalent to frequency modulation. Saying that the
phase of a signal is varying relative to some reference phase is
the same thing as saying the instantaneous frequency is different
from the carrier frequency, since instantaneous frequency is the
time derrivative of phase. What Rik is proposing is a kind of FSK -
varying the phase linearly with time is the same as shifting the
frequency. In the limiting case, with a 101010... bit sequence at
10bits per second being a 5Hz square wave, for the phase to
change by +/-180degrees (pi radians) within a 1/10 second
period, the frequency shift would need to be at least +/-10pi
radians/sec, or +/-5Hz. I have not tried to analyse this in the
frequency domain, but it must have a spectrum with sidebands at
5Hz intervals with a sinx/x component, not unlike that of the original
un-shaped BPSK, but probably smaller.
With Andy's proposed scheme, in the 101010.. limiting case, and
with the raised-cosine phase modulating slope, this would be
equivalent to phase modulating with a 5Hz sine wave to a deviation
of +/-pi/2 radians, mf = pi/2. Inspecting the functions of FM and PM
modulated waves, this would be equivalent to FM with a modulating
frequency of 5Hz (and without the DC offset), and deviation of
7.8Hz. Looking at the Bessel function tables for mf = 1.5, this
means the sidebands at +/- 5Hz would be up 0.7dB on the carrier,
those at +/- 10Hz -6.9, at +/- 15Hz -18.5dB and so on.
For the 10101010... limiting case, and ideal sine - envelope
shaping, the BPSK signal is equivalent to a double sideband,
supressed carrier signal modulated with a 5Hz sine wave, with two
sidebands at +/- 5Hz only (see the article on PSK31 in the LF
handbook). I checked this when I was building my modulator, and it
was pretty close to what I actually got.
I realise that these are rather crude analyses of the 3 types of
modulation, and because the modulation is not in reality a uniform
101010.. string of data, other spectrum components will also be
present, and the spectrum will be continuous rather than discrete
sidebands. Also , the relative phase of the spectrum components
is not considered. However, the other 2 methods seem to be a)
different from the "ideal" BPSK, and b)apparently have more
sidebands. Perhaps someone could provide a more accurate
analysis, that would show whether either of these methods would
be as effective for communications, would produce a satisfactory
spectrum, or would require a different approach to demodulation.
Cheers, Jim Moritz
73 de M0BMU
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