Why is the needed channel bandwidth for a matched filter higher than the normal bandwidth derived by the nyquist theorem (2B=R, assuming L=2)?
After some digging I found this source that states the following:
Overcome the practical difficulties encountered with the ideal
Nyquist channel by extending the bandwidth from the minimum value W =
R_b/2 to an adjustable value between W and 2W.
What are these practical difficulties and how does increasing the channel bandwidth overcome them? Why do these difficulties only occur when using a matched filter?
edit 1:
In response to "not specific to matched filter" comments, I realize that in practice 2.2 (or more) times the highest f is used instead of 2 to overcome imperfections. However, in my handbook B=R is used for matched filters (both in theory as in exercises) and 2B=R is used in every other context.
F.e. my handbook states the following for a matched filter:
$$
BER = Q(\sqrt{\frac{(A_1 – A_0)^2 T_s}{4N_0/2}}) = Q(\sqrt{\frac{(A_1 – A_0)^2}{2N_0 B}})$$
which implies R=B, does it not?
edit 2:
My question was inherently flawed. Unluckily, in my handbook it just happened to be so that both the relevant exercise and the theory section about matched filters used a (flawed) sampling method at the middle of the bit puls merely as an example. The usage of B=R stemmed from this coincidence, not from the fact that a matched filter was used.
Best Answer
One of these difficulties is,that you need a sampling rate that is higher than the double of the highst frequency in the signal. For that reason, signal paths for sampling include an low-pass filter to get rid of the higher spectrum of the signal that is not used. But the problem which come with the low-pass filter is, that they have an infinit spectrum and can not perfectly cut-off frequencies.
Example: If you would like to sample a signal and get a bandwith of 20kHz, you musst cut-off at 20kHz but you will still get signal components beyond 20kHz. Because of that, your sampling rate would not be > 40kHz, rather than 50kHz or more. It depends on the signal to noise ratio that your application needs.