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Phase rotation after matched filtering

Started by mkm10 7 years ago3 replieslatest reply 7 years ago323 views

Hi,

In some of the communications systems like MSK, Phase rotation or Bit rotation is performed after matched filtering operation. I am unable to understand why the operation is required or necessary. please enlighten me.

Thanks in advance..

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Reply by Rick LyonsMay 25, 2016

Hi mkm10,

  You'll have a better chance of receiving a meaningful answer to your question if you can give us more details of the signal processing you have in mind. Can you provide more explanation, and possibly a block diagram? Perhaps you could provide an Internet web page that shows the signal processing you're contemplating.

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Reply by Tim WescottMay 25, 2016

So, first, what Rick said -- if you're looking at a specific system then tell us, and we'll do a better job.  Otherwise we have to guess.

Second, here's my guess:

I'm assuming that you're talking about a system that's sending some form of coherent pulses that are modulated onto a carrier wave.  "Coherent pulses" meaning that phase, and not just amplitude, are important.

A typical, modern, DSP-ish way to demodulate such a signal is to first convert the narrowband signal from whatever frequency range it's in to baseband, then to demodulate at baseband.  This conversion is often done using inphase/quadrature mixing, giving a pair of channels (I & Q).

As part of the whole generate -> modulate -> upconvert -> transmit -> receive -> downconvert -> demodulate process, the exact timing of the transmitted signal is lost (sometimes the frequency, too -- that's a question for another post).  Assuming that your carrier frequencies are matched, this loss of timing shows up at the receiver as a phase rotation that's proportional to the phase difference between the transmit carrier phase, plus any transmission delay, minus your receive carrier phase.

If the timing information were never lost, your matched filters would generate pulses that are +/-1, +/-i, +/-1, etc. (treating the quadrature as complex numbers).  But because of the phase rotation, you see pulses that are +/-A, +/-Ai, +/-A, etc., where A is a complex number (which will be of constant magnitude if you have good AGC).

So in order to make sense of the received pulse train, the receiver has to deduce A, and multiply the signal by 1/A to reverse its effect.  Or, depending on what decisions the system designer has made, the information may be encoded in the phase difference between pulses, in which case one just compares the phase of the current pulse with the previous pulse to extract the data (this is also meat for another post).

For an alternate way of doing this, if you happen to fall into a wormhole and end up somewhere in a developed Earthen country in the late 1980's with a low budget, here's a link to my Master's thesis, which shows you how to do it either with CD4000-series analog switches and op-amps, or how to do it using 98% of the available processing power of a Motorola 68HC11, with Really Crappy* assembly code: http://wescottdesign.com/articles/MSK/mskTop.html.  You'll note that there's no phase rotation going on -- just adjustments to the timing of the carrier to get the phase aligned.

* Any assembly code that has an ISR that intentionally interrupts itself is crappy.  I didn't know better then -- I certainly do now.  For that matter, any embedded software that uses 98% of the available clock ticks to do vital tasks is crappy, or at least is the consequence of crappy system design.

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Reply by napiermMay 25, 2016

There are so many ways to skin the cat. In any digital receiver it has to AGC, frequency/phase match (rotator), filter and then sync timing.  Fred Harris had (has?) a good overview class in synchronization with digital modems.  His comment on timing, "If momma ain't happy, nobody's happy."  For a short answer, with no bit sync the constellation will be tilted.  If fact, it will probably be spinning.  Like Tim said, I would think that the adjustment after the matched filter would be a variable sample rate converter to center up in the "eyes".  The error loop that drives that converter would also be used to fine tune the rotator so that it would track phase/frequency offset.  That block is before the matched filter.  However, there are many ways to skin the cat....