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I'm in the process of designing the analog front end for a RF receiver. The system will use BPSK modulation. I was wondering what effect non-linear phase filters (such as Chebyshev and Butterworth) would have on my system, and front ends in general.

I know that having a variable group delay in the band of interest will distort signals due to a nonlinear phase shift across frequencies (nonlinear in the sense that phase shift is not proportional to frequency). That being said, I also know that filters, such as Chebyshev filters, are commonly used in communication systems. Thus my question is how ordinary communications systems are able to communicate at all with so much variation in group delay? Do receivers perform group delay correction digitally? Note that I'm strictly speaking about analog filters here, not digital FIR filters (which I know can have linear phase).

As an example, I might design a receiver that has a narrow Chebyshev bandpass filter to select our band of interest. But within this band, the phase of the filter undergoes some change that does not linearly follow frequency, thus introducing non-flat group delay. Why doesn't this (or does it?) cause problems in standard communication systems?

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All analog filters used in RF receiver frontends are in the class of Analog Infinite Impulse Response filters and, therefore, they can’t have stability and linear-phase properties at the same time. In your application, the signal has a constant envelope and all the data is stored in the phase of the signal. This signal is affected by so many parameters in the path that it is almost impossible to have a successful BPSK transmission in the first place! A part of these problems (including AM to PM distortion caused be nonlinear-phase filters and nonlinear amplifier/mixers) is solved using a Training Sequence. These are pre-known data streams that are initiated with the purpose of tuning the equalizers and vector analyzers. For example, imagine a pre-known stream of 10101010 is sent before the actual data transmission. The processor tunes the equalizer coefficients and the vector analyzer so that the constellation of the received signal looks like the intended pattern. After this calibration, actual data transmission can begin. To the best of my knowledge, this process is done 30 times a second in the GSM mobile technology.

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    \$\begingroup\$ Could you please rephrase the first part: "all analog filters ... are IIR filters". It's confusing. :-) \$\endgroup\$ – a concerned citizen Mar 8 at 17:48
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    \$\begingroup\$ Simply, all analog filters are IIR filters. \$\endgroup\$ – Ben FM Mar 8 at 17:51
  • \$\begingroup\$ Thanks for the answer! Things are making a lot more sense. This is definitely beyond the scope of the question/answer, but I'm curious how a receiver would detect the training sequence in the first place. My understanding is that the receiver uses something like a cross-correlation between the known sequence and what it receives to determine where the sequence starts. But if there is so much distortion of the received signal, how could a cross-correlation ever possibly work? \$\endgroup\$ – LetterSized Mar 8 at 17:56
  • \$\begingroup\$ @BenFM I know what you mean, but since the term IIR is attributed to digital filters, the expression that you used can be confusing for people coming in contact with this information for the first time. Imagine a followup question: "I need help choosing the values for LC in this IIR filter". Imagine it posted on dsp.ee. I wonder how many downvotes would that gather? :-) Maybe "all filters are nonlinear phase", or similar? \$\endgroup\$ – a concerned citizen Mar 8 at 18:02
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    \$\begingroup\$ I am still learning this stuff myself, so I am going to mention what I have seen and learned myself. Every receiver may have its own dedicated structure to achieve a specific purpose, but commercial receivers are designed to globally work and therefore, have certain properties. They transmit constantly and the receivers wait for some certain time to be able to extract the clock frequency and bit patterns through eye diagrams. To be more clear: They look for a known pattern amongst a flood of data (meaningless bits used just for calibration). After they found the pattern, calibration can start. \$\endgroup\$ – Ben FM Mar 8 at 18:10
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Phase shifts cause AM_PM conversion, and vice versa. Is that a problem for the data eye?

Think about the data recovery needs, the ISI tolerance, and only then define the acceptable phase nonlinearity.

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The best detector for bits are "matched filters"; if you have unknown phase behaviors, the ideal bit recovery system also becomes unknown.

Phase linear systems remove some of the uncertainty.

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  • \$\begingroup\$ Could you please elaborate on your answer? I'm not even considering ISI at this point, but merely how a receiver could demodulate, or even detect, something like BPSK in the presence of non-flat group delay. \$\endgroup\$ – LetterSized Mar 8 at 17:59

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