Cyclic Domain Profile (CDP)

The CDP is generated by projecting the two-dimensional Spectral Correlation Function (SCF) magnitude onto the cyclic frequency (α) axis. This is typically achieved by integrating or taking the maximum value of the SCF across the spectral frequency (f) axis for each α. This collapses the complex bifrequency plane into a single, information-dense vector, drastically reducing computational complexity for downstream machine learning models while retaining the fundamental cyclostationary signatures.

A CDP exhibits distinct, theoretically predictable peaks at specific cyclic frequencies that act as a fingerprint for the modulation scheme:

• BPSK: A strong peak at α = 2fc (twice the carrier frequency) and a weaker feature at α = 2fc ± Rs (symbol rate).
• QPSK: A dominant peak at α = 2fc, with the symbol rate feature only appearing in higher-order cyclic cumulants.
• OFDM: A characteristic peak at α = Tu⁻¹ (the useful symbol duration) induced by the Cyclic Prefix.

A key advantage of the CDP is its inherent resilience to stationary Gaussian noise. Because noise is a stationary process, its spectral correlation is zero for all non-zero cyclic frequencies (α ≠ 0). By ignoring the α = 0 profile slice, the CDP effectively filters out the noise floor, allowing for signal detection and classification at very low Signal-to-Noise Ratios (SNRs) where conventional power spectral density methods fail.

In practice, the CDP is estimated efficiently using the FFT Accumulation Method (FAM). The FAM algorithm decimates the signal into narrowband frequency channels and computes the complex cross-correlation between channels separated by a specific α. The CDP is then formed by summing the magnitude of these correlations across all frequency channels for each candidate α, producing a high-resolution profile suitable for real-time applications.

The CDP is an ideal input feature vector for Automatic Modulation Classification (AMC) and Emitter Identification models. Instead of feeding raw IQ samples into a neural network, the pre-computed CDP provides a compact, physically meaningful representation. A 1D Convolutional Neural Network (CNN) or a simple multi-layer perceptron can then be trained on the CDP's peak locations and amplitudes to classify the signal type or identify a specific transmitter based on its unique hardware impairments.

For many digital modulation formats, the CDP provides a direct, blind method for Symbol Rate Estimation. The cyclic frequency corresponding to the symbol rate (α = Rs) manifests as a distinct peak in the profile. By scanning the CDP for this peak, an intercept receiver can determine the baud rate of an unknown emitter without any prior knowledge of the signal's parameters, a critical capability for spectrum monitoring and cognitive radio.

The two-dimensional transform from which the CDP is directly derived. The SCF measures the spectral correlation density between frequency-shifted versions of a signal, revealing hidden periodicities. The CDP is formed by taking the magnitude of the SCF and projecting it onto the cyclic frequency axis, collapsing the spectral frequency dimension to create a compact one-dimensional signature.

The independent variable of the CDP, representing the separation between correlated spectral components. Key cyclic frequencies correspond to physical signal parameters:

• Symbol Rate: Fundamental periodicity of digital modulation
• Carrier Frequency Offset: Twice the carrier offset for BPSK
• Frame/Pilot Rate: Induced by repetitive protocol structures Peaks in the CDP at these alpha values serve as robust identifiers for modulation recognition.

A normalized version of the SCF that provides a scale-invariant measure of cyclostationarity. When the CDP is extracted from the spectral coherence function rather than the raw SCF, it becomes insensitive to signal power variations, making it a more robust feature for machine learning classifiers operating in dynamic environments with fluctuating signal-to-noise ratios.

The FFT Accumulation Method is the most computationally efficient algorithm for estimating the SCF and, by extension, the CDP. It operates by:

• Channelizing the input signal into narrowband frequency bins via a short-time FFT
• Computing the complex demodulate for each channel
• Correlating channel pairs to populate the SCF matrix The CDP is then generated by integrating along the frequency axis.

The CDP is a specific type of cyclic feature vector—a structured, compact representation of a signal's cyclostationary signature. In machine learning pipelines, the CDP is sampled at discrete alpha values corresponding to known modulation-specific periodicities. This vector serves as the input to neural network classifiers for automatic modulation classification and emitter identification.

A spectrum sensing method that uses the CDP to detect the presence of primary users in cognitive radio. By testing for statistically significant peaks in the CDP at candidate cyclic frequencies, the detector can identify specific signal types even at low SNR. This method is robust to noise uncertainty, a critical advantage over energy detection in contested or dynamic spectrum environments.