How can I calculate rate /spectral efficiency (bit/s/Hz) for any given channel with any distribution?

Suppose I have a system model like given below, x is a complex input signal, y is the received signal and n is the complex channel noise with any distribution.

y=x+n

I like to calculate the rate (bit/s/Hz) for any distribution like gaussian, or Gaussian mixture or exponential distribution with different mean and variances. I dont want to calculate the optimal capacity. I can use ML detection. But for rate calcualtion from a system model and different channel how should I approach. I apologize if I could not make my qustion clear.

**** Note: I know how to calculate BER like transmit input signal, add noise, decode/ demodulate the signal. Calculate BER from numer of fliping bit/symbol.