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I believe I am familiar with simulating $E_s/N_0$ by adding noise to the output of the matched filter, but what would be the correct way to simulate $E_s/N_0$ starting with the analog signal at the receive antenna and corresponding to a transmitted signal of the following form: $$x(t)=\sum_k x_kp(t-kT)$$ where $x_k$ are the channel symbols and $p(t)$ is the pulse shaping waveform?

My understanding is that if I have AWGN with power spectral density $N_0$, the output of the matched filter is a Gaussian random variable with variance $N_0$. As for $E_s$, would this depend on the energy $E\{|x_k|^2\}$ of the channel symbols, the energy $\int |p(t)|^2 dt$ of the pulse shape, and path loss between the transmitter and the receiver?

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$E_s$ would be the energy of the channel symbols at the output of the matched filter as scaled by the path loss between transmitter and receiver as long as all timing and carrier offsets have been corrected for and channel equalization completed - consider how after matched filtering with carrier and timing offsets removed we use just one sample per symbol at the symbol decision.

If equalization for channel multipath is not yet corrected for and multipath distortion exists, this would not be the case since the symbol energy is still distributed across multiple samples within each symbol (and across symbols).

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