On Sat, Apr 16, 2016 at 6:36 PM, Laur Joost <darem...@gmail.com> wrote:
> The phase modulation is according to the equation > > S(t) = A*cos(2*pi*f*t + s(t)*pi/2), > s(t) = RRC(2*b(t) - 1) > > where > S - modulated carrier > A - Amplitude of the modulated carrier > f - carrier frequency > s - modulating signal (shaped pulses) > b - bit value at time t > I'm more at home with FSK, but, yeah, putting the RRC filter there doesn't seem to be the norm for PSK. (For FSK modulations, the pulse filter is applied to the pulses that make up the phase term.) > But I guess that's moot, given the next: > > If the transmitter used RRC, the matched filter in the receiver must be the >> corresponding RRC filter. If it is not Nyquist, you'll get ISI; if it is >> Nyquist, you >> won't get ISI. You'll have to accept and work with the ISI you get. >> Also, the receiver should be performing the matched filtering in a >> demodulation >> stage that corresponds to where the filter pulses were in the transmitter. > > > I guess the problem becomes one of matching the stages. How do I get a > continuous (non-mod(2pi)) phase in GnuRadio? > Since integral(d(phi)/dt) = phi, maybe something like this: -> quad_demod -> iir_filter( b=[1], a=[1 -1], oldstyletaps=False) -> But you see the problem with that integrator, right. Just like infinite phase unwinding, that integrator can blow up. > I hacked something together, but it has problems when noise causes a > more-than-pi/2 error, in which case it's suddenly > amplified to a -3pi/2 error. Though I guess a low-pass filter should limit > that happening. > The RRC filter is a low-pass filter; maybe it will be enough. > Is there a better way to do this? > My comments: a. I haven't though about the costas loop position and function. b. The rotator block does a z-plane rotation (aka, discrete freq spectrum translation with aliases/wrap-around), and not an I/Q plane phase rotation. Is a frequency translation by Fs/2 really what you want? If you want a phase rotation, just use a multiply const block with a complex exponential (cmath.exp(1j*phi), IIRC). c. Your RRC taps would go in the decimating FIR filter. d. The complex to arg block will be outputting your symbols as +/- pi/2, if all goes well. The M&M block wants peaks nominally at +/- 1.0. Scale your RRC filter gain accordingly. e. Replace the blocks after the M&M block with a binary_slicer block, to convert your soft bits to hard bits. The M&M block can output a 0, in which case the divide block will have problems. f. In the M&M block, Omega is the nominal samples per symbol and it need not be integral. Omega relative limit is the maximum variation in omega that you allow when recovering timing; in this case 0.005 is 0.5%, which is pretty tight given an omega of 3.0 samples/symbol. g. Nothing in this hier block deal with coarse frequency correction or the phase ambiguity of the initial phase rotation, AFAICT. Hopefully you're handling that somewhere else. > > > > I don't think that follows. Real pulses being input to real functions, >> yields real >> outputs. >> Complex filters are usually only needed when you need filter that is not >> symmetrical about DC (your channel center, aka your baseband). If you >> really >> are at baseband (which you should be if performing clock recovery), >> your pulse filter should not be complex, it will be real. Thus its >> conjugate will be >> real. > > > Thank you! That helped me understand something in another flowgraph. > > You're welcome. Regards, Andy > Laur > > > > > > 2016-04-16 23:18 GMT+03:00 Andy Walls <a...@silverblocksystems.net>: > >> Forgot to add the list >> >> >> ---------- Forwarded message ---------- >> From: Andy Walls >> Date: Sat, Apr 16, 2016 at 4:16 PM >> Subject: Re: [Discuss-gnuradio] matched filter for BPSK produced by phase >> shifting >> To: darem...@gmail.com >> >> >> *From*: Laur Joost *Subject*: [Discuss-gnuradio] matched filter for BPSK >> produced by phase shifting *Date*: Sat, 16 Apr 2016 19:30:29 +0300 >> ------------------------------ >> >Hi all! >> >> Hi. >> >> >I need a clue where to start. >> > >> >I have a signal that is BPSK that is modulated not by applying the >> filtered >> > baseband to the in-phase component, but instead doing literal analog >> phase >> > shifting. >> >> Please provide a mathematical expression for the above. The description >> is too >> ambiguous. Something like: >> >> m_filt(t) = RRC_filter(m(t)) >> s(t) = sin(w_c *t + pi*m_filt(t)) >> >> >> > The result is that the signal transitions between the -1 and 1 symbols >> not >> > through zero, but instead along the unit circle. >> >> Constant modulus, continuous phase - that's nice to work with. >> A PLL or a Costas loop should lock and track well. >> AGC can be simple. >> >> > The transmitted baseband is RRC-filtered. >> >> Again, a picture, or sequence of mathematical statements describing the >> modulation would be helpful. >> >> >> > My questions: >> > 1. Is Raised Cosine even a valid Nyquist filter for such a signal? >> After all, the >> > actual In-phase transition occurs not according to the RRC response, >> but >> > according to the sine OF the RRC. >> >> Well, the Nyquist filter criteria can't be rigorously evaluated without >> an expression >> to work with. But it really doesn't matter. >> >> If the transmitter used RRC, the matched filter in the receiver must be >> the >> corresponding RRC filter. If it is not Nyquist, you'll get ISI; if it is >> Nyquist, you >> won't get ISI. You'll have to accept and work with the ISI you get. >> >> Also, the receiver should be performing the matched filtering in a >> demodulation >> stage that corresponds to where the filter pulses were in the transmitter. >> >> >> > 2. The response of such a modulator to a unit impulse is necessarily >> complex. >> >> I don't think that follows. Real pulses being input to real functions, >> yields real >> outputs. >> >> >> > From what I gather, the matched filter is then, also complex (time >> reversed and >> > conjugated). >> >> Complex filters are usually only needed when you need filter that is not >> symmetrical about DC (your channel center, aka your baseband). If you >> really >> are at baseband (which you should be if performing clock recovery), >> your pulse filter should not be complex, it will be real. Thus its >> conjugate will be >> real. >> >> >How should I go about this in GnuRadio, given that the PFB Clock >> > sync only takes real taps? >> >> Do a separate matched filter with an FFT or FIR filter block, and follow >> that with >> an M&M clock sync block. >> >> With a separate matched filter block, you unfortunately cannot use the >> PFB clock sync block. It works with a peaked matched pulse filter and >> that filter's derivative, so passing in a trivial filter like >> [1,1,1,1,1,1,...,1] will cause the PFB clock sync block to crash. >> >> >> > 3. Or can I just take the real part of the matched filter and feed that >> to PFB >> > Clock sync? The constellation will have a weird spread (see picture). >> Will >> > that affect either Costas or PFB? >> >> Again, I don't think a complex baseband pulse filter makes sense. >> >> BTW, on a slightly related note, taking only the real part of a _signal_ >> before >> obtaining proper phase offset and bit timing is not a good idea. >> You will degrade your SNR. >> >> >> >> Depending on the the mathematical expression the modulator is >> actually implementing, you may have to do something a little >> different than the textbook GNURadio BPSK demodulation steps. >> >> > PS: The positioning of the constellation plots was not planned. >> > >> > All the best, >> > Laur >> >> Regards, >> Andy >> >> >
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