980953.fig.009a
(a)
980953.fig.009b
(b)
Figure 9: In (a) the CRB and the Chernoff bound for 𝑅 is shown for varyious values of 𝜏 at 𝑅 0 = 50 m ( 𝜇 0 ≈ − 5 2 . 5  dB), 𝑁 = 1 0 0 and 𝜎 𝑛 = 4  dB. Observe that the performance degradation is exponential as ( 𝜏 − 𝜇 0 ) / 𝜎 𝑛 increases for different crossover probabilities. (b) shows the MSE, variance and ( b i a s ) 2 for 𝑅 with varying 𝜏 with 𝑅 0 = 5 0  m ( 𝜇 0 ≈ − 5 2 . 5  dB) 𝑁 = 1 0 0 and 𝜎 𝑛 = 4  dB. The MSE also has an exponential growth with respect to ( 𝜏 − 𝜇 0 ) / 𝜎 𝑛 ; however, we notice the peculiar behavior of multiple critical points due to the bias and variance effect of the MLE of 𝑅 .