Suppose I transmit digital data(BPSK/QPSK/QAM) with symbol period T.Then minimum band width needed is 1/(2*T).If I use a transmit Root Raised Cosine Filter with roll off =1(100% excess band width)
In the receiver I use similar filter as matched filter.I use over sampling factor of 2 in the transmitter.
In the receiver after matched filtering I down sample by 2 and take symbol decisions.The channel is
AWWGN channel.Because of down sampling will all the signals in the output of matched filter from
1/(2T) to 1/T will alias back is it not?
This aliasing is different from NO ISI as at zero crossing of combined rc pulse only one symbol
When you do transmit filter, you must have already upsampled by 2 as you mentioned. When you downsample at receiver, there won't be aliasing hence.
In the transmitter I sample 2*symbol rate.Due to 100% excess band width signal
frequency upto symbol rate are passed through matched filter receiver.When I do
symbol rate sampling the signal from 1/2 *symbol rate to symbol rate will alias.
I know that due RRC in transmitter and receiver the combined filters have Zero crossing at symbol rate and hence there will be NO ISI.But the effect of aliasing in frequency domain I am unable to corelate with it.
I suggest that the Rx filter must cut off sharp at f = half symbol rate then decimate to Fs = symbol rate.
The question why use 100% roll off at Tx?
edit: I also believe that aliasing in the case of matched filter doesn't harm since your target is symbol recovery in one phase out of two.
as shown below:
x = randsrc(1,1024,[+1,-1]);
tx = upfirdn(x,h,2,1);
rx = upfirdn(tx,h,1,2);