With the same channel S/N, the normalized mean square error differs

I am working on a research work on transmitting ECG signals over wireless body area network. The signal is affected by noise and small scale fading. The normalized mean square error(NMSE) is used to estimate the quality of the reconstructed signal at the receiver. When I run the same m file in matlab several times, I obtain different values for the NMSE, although the same channel signal to noise ratio is used.

• I think this is reasonable, do you agree?
• If so, how can I obtain a single value to represent the quality of the reconstructed signal at the receiver?
• I want to plot a curve with the S/N at the $x$-axis and NMSE at the $y$-axis, how can I plot this curve if the value of NMSE differ with different runs of the same m file with the same value of S/N?

1 Answer

The problem you describe is likely due to the randomness of your noise: Even though the S/N ratio remains the same for each run, the actual realization of the noise is different in each run. Hence, the NMSE is different for each run.

The standard procedure here is to run the algorithm several times for a single S/N ratio, measuring all the obtained NMSEs. Then, you calculate the mean of the measurements to find the overall NMSE for a given S/N ratio. Additionally, you can draw errorbars (MATLAB errorbar) around each points, which indicate the standard deviation of each measurement.

• How many times shall I run the algorithm for a single S/N ratio? 10, 20, ...100?
– Noha
Nov 13 '16 at 6:02