Power Normalization

The most common normalization technique transforms the IQ sample sequence to have zero mean and unit variance. This is achieved by subtracting the empirical mean and dividing by the standard deviation of the signal magnitude. For complex baseband signals, this ensures the average symbol energy is normalized to 1, preventing saturation in subsequent neural network activation functions like sigmoid or tanh. This method is particularly effective for constant-envelope modulations like QPSK and GMSK.

Normalization must account for the PAPR of the incoming waveform. High-PAPR signals like OFDM require careful scaling to avoid clipping the high-amplitude peaks while maintaining sufficient resolution for low-amplitude samples. A common strategy is to normalize by the root mean square (RMS) value of the entire burst, but this can leave peaks unconstrained. Advanced techniques apply a soft limiter or μ-law companding before linear scaling to compress the dynamic range.

The choice of normalization window directly impacts classifier latency and accuracy:

• Per-Burst Normalization: Calculates statistics over an entire captured transmission burst. This is optimal for offline processing but introduces latency equal to the burst duration.
• Sliding Window Normalization: Uses a causal moving average and variance estimator to normalize samples in real-time. This is essential for streaming classification but can cause transient distortion at the start of a burst before the window fills.
• Exponential Moving Average (EMA): Applies a decay factor to give more weight to recent samples, allowing the normalizer to track slow power variations due to fading.

Standard mean and variance estimators are highly sensitive to impulsive noise and narrowband interference spikes. Robust normalization replaces these with median and median absolute deviation (MAD). The median is computed on the signal envelope, and the MAD provides a robust estimate of dispersion. This prevents a single high-amplitude noise burst from compressing the entire signal into a near-zero range, preserving the constellation structure for the classifier.

Power normalization in software often complements or replaces hardware Automatic Gain Control (AGC). While analog AGC adjusts the receiver's front-end gain to fit the ADC's dynamic range, residual power variations remain due to AGC settling time and gain step quantization. Digital normalization removes these residual fluctuations, providing a perfectly consistent input to the neural network. In simulation-only pipelines, normalization fully substitutes for AGC modeling.

For systems that output log-likelihood ratios (LLRs) or soft bit decisions, the scaling of the input directly affects the reliability information. If the signal is under-normalized, the LLR magnitudes will be compressed, making the decoder overconfident in near-zero decisions. Over-normalization saturates LLRs, erasing the distinction between moderately and highly reliable bits. Optimal normalization preserves the signal-to-noise ratio (SNR) proportionality in the soft outputs.

A closed-loop feedback circuit that dynamically adjusts receiver amplifier gain to maintain a constant signal envelope at the ADC input. AGC operates in the analog domain before digitization, preventing saturation and quantization noise.

• Typical attack time: < 1 µs for burst-mode signals
• Prevents clipping on signals with 60-80 dB dynamic range
• Complements digital power normalization by handling gross power fluctuations

Blind or data-aided algorithms that compute the ratio of signal power to noise power from received samples. Accurate SNR knowledge allows power normalization to distinguish between signal energy and noise floor.

• M2M4 estimator uses second and fourth moments for blind estimation
• Critical for setting decision thresholds in likelihood-based classifiers
• Enables adaptive scaling that avoids amplifying noise in deep fades

The process of isolating and measuring the variance of the additive white Gaussian noise component. Eigenvalue decomposition of the received covariance matrix separates signal subspace from noise subspace.

• Often performed during silent periods or guard intervals
• Minimum description length (MDL) criterion estimates noise dimensionality
• Prevents normalization from inflating noise to signal-level amplitudes

Digital correction of amplitude and phase mismatches between the I and Q branches of a direct-conversion receiver. IQ imbalance creates elliptical constellation distortion that power normalization alone cannot fix.

• Gain mismatch > 0.5 dB degrades classification accuracy
• Phase error > 3 degrees causes rotational skew
• Must be applied before power normalization for correct reference scaling

The known channel properties describing how a signal propagates from transmitter to receiver, encompassing scattering, fading, and power decay effects. CSI provides the ground truth against which normalization targets are calibrated.

• Includes large-scale fading (path loss, shadowing) and small-scale fading (multipath)
• Enables per-subcarrier power normalization in OFDM systems
• Used to compute the MMSE scaling factor for optimal soft-decision inputs

A statistical estimation framework that computes an optimal linear filter by minimizing the mean squared error between estimated and actual transmitted symbols. MMSE inherently incorporates noise power into its scaling, providing a form of soft power normalization.

• Requires knowledge of second-order statistics (signal and noise variance)
• Avoids the noise enhancement problem of zero-forcing equalizers
• Produces normalized soft outputs suitable for direct classifier input