I want to simulate a QPSK transmission through a multipath channel. I
see that some people use 1 sample per symbol while others use 8 or 16.
Could someone give me some hints about the advantages and
disadvantages of each option?
I'm thinking about...
- whether the 1 sample per symbol option is valid if we assume ideal
filtering, whether a doppler effect could be added in the future.
As well, could someone give an expression to calculate the noise
variance for a given Eb/No?
To finish with - is Eb/No what some people call SNRper_information_bit?
simulating QPSK modulation
Typically the QPSK transmission (I and Q samples) should be passed through a Root Raised Cosine filter for bandwidth limiting (pulse shaping) and mitigating the effects of Inter Symbol Interference (for which a complementary Root Raised Cosine filter is implemented in the receiver to form a Matched filter). The effect of pulse shaping RRC filtering is to provide a roundness in the QPSK constellation diagram.
The I and Q pulses are oversampled in order to provide continuous transition points, otherwise, just sampling at the symbol instants would give the constellation points only. These oversampled I and Q points can be used at the receiver for symbol timing recovery.
Another advantage of oversampling the I and Q samples will be that at the receiver we can employ a low-order Lowpass antialias filter (as opposed to an ideal filter which will require sharp cutoff if we have 1 sample per I and Q) since we can use a higher sampling rate (at the oversampled frequency). But it is important that after sampling, the output should be down-sampled at the symbol-rate in order to ease processing in a Digital Signal Processor in the next stage.
One way in which the noise-variance could be computed is by computing the variance in the I^2 and Q^2 samples over a period of time and moving-averaging it.The greater the period of time for estimation of variance (that is, the more the number of I and Q samples) the better would the estimate of noise be.
Hope this information helps.
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