Gain Normalization

Gain normalization ensures that the instantaneous amplitude of an IQ stream is scaled to a consistent reference level before inference. Without this step, a classifier trained on high-power signals will fail on identical modulation schemes received at lower gain settings. The process typically involves computing the root mean square (RMS) power of a segment and dividing each complex sample by this value, resulting in a unit-power signal. This forces the neural network to rely on phase transitions, cyclostationary signatures, and constellation shape rather than raw magnitude.

Two dominant strategies exist for gain normalization in IQ preprocessing pipelines:

• Z-Score Normalization: Subtracts the mean and divides by the standard deviation of the complex samples. This centers the constellation and scales it to unit variance, preserving the relative dynamic range of the signal envelope.
• Min-Max Scaling: Linearly maps the IQ values to a fixed range, such as [-1, 1], based on the observed minimum and maximum. This is more sensitive to impulsive noise outliers but guarantees a bounded input tensor. The choice depends on the downstream classifier's activation functions and whether DC offset has been previously removed.

Gain normalization can be applied with different statistical scopes:

• Per-Segment Normalization: Computes the scaling factor independently for each IQ segment fed to the classifier. This is the standard approach for real-world deployment where receiver automatic gain control (AGC) varies between bursts.
• Global Normalization: Uses a fixed mean and variance derived from the entire training dataset. This is only viable in controlled laboratory settings and breaks catastrophically when the operational SNR or receiver gain drifts. Per-segment normalization is essential for open set recognition and cross-deployment robustness.

Physical receivers employ automatic gain control (AGC) circuits that dynamically adjust amplifier gain to keep the signal within the analog-to-digital converter's dynamic range. This introduces a time-varying scaling factor that is unknown to the classifier. Gain normalization in the digital domain effectively inverts this unknown gain, creating a gain-invariant representation. However, aggressive normalization can amplify noise in low-SNR segments, requiring careful noise floor estimation to avoid scaling silence or noise-only segments to full scale.

While gain normalization is necessary, it can inadvertently destroy discriminative information for certain modulation pairs. Amplitude-shift keying (ASK) and quadrature amplitude modulation (QAM) rely on multiple amplitude levels to encode information. Per-segment normalization collapses these levels to a unit circle, making high-order QAM constellations appear similar to phase-shift keying (PSK). To mitigate this, advanced pipelines preserve a complementary amplitude feature—such as the variance of the instantaneous amplitude or the signal kurtosis—as a separate input channel alongside the normalized IQ stream.

Standard normalization treats the I and Q components as independent real-valued streams, applying separate scaling or a single real-valued factor. Complex-valued normalization preserves the circular symmetry of the baseband signal by computing a single complex scaling factor. This is critical when using complex-valued neural networks (CVNNs) where the phase relationship between I and Q must be maintained. The complex RMS is computed as sqrt(E[|x|^2]), where x is the complex IQ sample, ensuring the normalized signal lies on the unit circle in the complex plane.