Determine the probability of error for the detector

Question

Response to the following problem:

Determine the probability of error for the detector with input metrics given by Equation for BPSK modulation and a Rayleigh fading channel.

Assume that the components of h_j are iid, zero-mean, complex-valued Gaussian random variables.

Equation:

μ_j = h_j^H yj

   = √(ε_s/N_T) s_j ||h_j||²_F + h^H_jη_j,          j = 1, 2, ....,N_T