Fig. 7.

Simulation of the effect of averaging $N$ signals with relative strength $I/2{\sigma }^2=10$ in (a) and $I/2{\sigma }^2=0.1$ in (b). Shown are the averaged signal-to-noise ratios calculated from $N$ simulated phasors ($\bullet$) alongside the corresponding theoretical plots (−). The SNRs without and with noise bias correction are plotted in the left and right panels, respectively. Without noise bias correction, the SNR_CPX shows a better performance for the strong signal in (a), whereas SNR_MAG dominates for $N=1$ to 100 both for theoretical calculation and simulation. With noise bias correction (rightmost column), complex averaging similarly provides an N-fold improvement of the respective SNR^′ = I/2σ² whereas an $\sqrt{N}$-fold improvement can be observed for magnitude averaging.