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Does the matched filter actually improve SNR or does it maximize it (making sure that it is not less than what it should be) ? improving SNR would not make sense to me as suppose a receiver has a certain NF that defines an SNR for a signal at a certain power level and a certain BW, improving SNR would mean reducing NF, and that wouldn't make sense, would it?

Assuming a pulse shaped BPSK signal with a symbol or bit rate =1/BW (a roll off almost equal to zero), the SNR at the matched filter output =Eb/No, multiplying the denominator and the numerator by BW we get: signal power/ noise power and noise power would of course be a function of NF, so in that case where is the improvement? or do you want to say that already assuming that signal BW=1/rate because of pulse shaping is the condition that did the job?

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There is no contradiction. Matched filters are often used because they are an implementation of a sliding correlator, which is the optimum detector (in the maximum-likelihood sense) for linear modulation in the AWGN channel. That is, the SNR at the output of the matched filter will be maximized when the filter lines up with the point of reception of the signal that the filter matches.

This doesn't contradict the known properties of your receiver (i.e. its noise figure). The point to notice is that the SNR can be different at the input of the matched filter than it is at the filter output. The SNR at the matched filter input (i.e. your front end's output) is determined by the signal power at the receiver input and the noise figure of the front end. But by applying signal processing techniques, like matched filtering, you can improve that SNR to achieve more accurate detection.

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improving SNR would mean reducing NF

Not so. Through the magic of filtering (not necessarily matched filtering), it is possible to enhance the relative strength of the signal components as compared to the noise components, thereby effectively increasing the SNR. Matched filtering is just the ultimate of what can be achieved by this method: you cannot get an SNR that is larger than what the matched filter is giving you. For more than what you probably want to know about matched filters (in additive white Gaussian noise channels), see this answer of mine elsewhere on this forum.

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  • $\begingroup$ So if a signal BW =symbol rate, and the SNR at the output of the matched filter=energy per bit/noise spectral density =E/No $\endgroup$ – Hatem Tawfik Jul 18 '18 at 6:15
  • $\begingroup$ @HatemTawfik For me, matched filter is the necessary condition to apply Eb/No to discrete-time samples (output of de-pulse-shaping and sampling in classic receiver). $\endgroup$ – AlexTP Jul 18 '18 at 8:24
  • $\begingroup$ accept Assuming a pulse shaped BPSK signal with a symbol or bit rate =1/BW (a roll off almost equal to zero), the SNR at the matched filter output =Eb/No, multiplying the denominator and the numerator by BW we get: signal power/ noise power and noise power would of course be a function of NF, so in that case where is the improvement? or do you want to say that already assuming that signal BW=1/rate because of pulse shaping is the condition that did the job? $\endgroup$ – Hatem Tawfik Jul 24 '18 at 23:46
  • $\begingroup$ @HatemTawfik Whatever you choose to believe about what matched filtering is doing (or failing to do) with regard to improving SNR is fine by me. I have nothing further to add to what I have said above. $\endgroup$ – Dilip Sarwate Jul 25 '18 at 3:39

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