Phase Error

In a quadrature modulated (QM) system, phase error (shown as θ in the equation below) occurs when the measured phase of the received symbols deviates from the ideal phase values. If the symbol sequence is {d₀, d₁, d₂, ..., d_N-1}, then the sequence of phase errors is {θ₀, θ₁, θ₂, ..., θ_N-1}. The peak phase error over the N symbols is express as

θ_peak = max(θ_i)        i = 0, 1, 2, ..., N-1

and the RMS phase error over N symbols is