Optimization of the pre-m filter using the interim error is biased in the presence of uncorrelated additive interference since the output of the FM discriminator will consist of the demodulated primary signal plus a distortion component correlated with both the primary and secondary signals. Consequently, minimization of the interim error variance will result in a biased filter solution that attempts to model both the undistorted primary signal component and the distortion components. The experimental results presented in the next section show that interim filter bias is non-problematic. The pre-m adaptive filter also must account for carrier frequency offset in the receiver tuning as well as frequency drift in both the transmitter and receiver. Carrier offset manifests itself in terms of a dc offset in the FM discriminator output.
Frequency drift shows up as a slow variation of that dc offset.
The frequency offset can be modeled by injecting a constant value into the adaptive filter output. This value can be adaptively determined by incorporating an additional weight in the adaptive filter with the weight input tied to a constant value. The LMS adaptation will then choose the weight value that results in a best match to the dc offset in the desired response. The time constant of the dc tracker is determined by the step size and the constant value tied to the weight input. Once the pre-m adaptive filter converges to its optimal value, the filter output signal should closely mimic the FM discriminator output component corresponding to the primary signal.