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Assuming the transmitted signal to have propagated through an additive white Gaussian noise channel with a power spectral density of , a model of the received discrete‐time signal r[m] after radio frequency (RF) front‐end processing: down‐mixing, a quadrature approach to bandpass sampling [52], and quantization can be expressed as

(38.5)

where t_s(t_m) ≜ δt_TOF + Δ(t_k − δt_TOF) is the PN code phase of the BTS, t_m = mT_s is the sample time expressed in receiver time, T_s is the sampling period, δt_TOF is the time of flight (TOF) from the BTS to the receiver, θ is the beat carrier phase of the received signal, and n[m] = n_I[m] + jn_Q[m] with n_I and n_Q being independent and identically distributed Gaussian random sequences with zero mean and variance . The receiver presented in Section 38.5.2 will operate on the samples of r[m] in Eq. (38.5).