[RAKE Demodulator for Two-Path Channel] Perform a Monte Carlo simulation to estimate and plot the error probability of a binary antipodal signaling communication system in which the channel is characterized by two resolvable Rayleigh fading signal paths. Thus, the received signal in the interval 0 ≤ t ≤ Tis, for a slowly fading channel,

where C₁ and C₂ are uncorrelated, complex-valued Gaussian random variables with zero mean and unit variance, and n(t) is a complex-valued AWGN process. The received signal is passed through a RAKE demodulator that crosscorrelates r ( t) with s ( t) and s ( t - 1 / W). Consequently, the output of the correlators may be expressed as

Therefore, the Monte Carlo simulation may be performed by generating the decision variable R at the input to the detector, with α₁ and α₂ being two statistically independent and identically distributed Rayleigh random variables and n being a real valued zero-mean Gaussian random variable with unit variance. Note that the {cd are independently selected in each symbol transmitted. Compare the estimated error probability from the Monte Carlo simulation with the theoretical (large SNR) results given by (9.3.19). Perform the simulation for N = 100, 000 sample.