Hi Himanshi,
I understand that you are interested in the variation in the Bit Error Rate (BER) of Alice-Eve link and its relationship with the signal-to-noise ratio (SNR).
Let's consider a model 
where, y is the received signal, x is the transmitted signal and 
are Rayleigh fading channel response and noise, both of which are circularly symmetric Gaussian noise with zero mean respectively.
are Rayleigh fading channel response and noise, both of which are circularly symmetric Gaussian noise with zero mean respectively.Please note that, we are considering Single-input-single-output system (SISO), which implies the dimension of the all the variable are one.
For this system, the BER can be expressed as:
(1)
(2)From equation (1), we observe that the BER depends on the channel \distribution of the channel h . In our case, equation (2) considers 
. Therefore, the variation in the BER indicates how different the channel is between Alice-Bob and Alice-Eve for the same transmitted signal.
. Therefore, the variation in the BER indicates how different the channel is between Alice-Bob and Alice-Eve for the same transmitted signal. If Eve's channel experiences more multipath fading, shadowing, or other impairments, the effective SNR for Eve's received signal might not improve as much as for Alice-Bob link, resulting in a higher BER.
Conversely, if Eve has a better channel condition or is much closer to Alice than Bob, the received SNR would be higher, leading to a lower BER.
I hope this resolves your query.
