Power Spectral Density (PSD)

PSD quantifies how a signal's average power is distributed across frequency, measured in dBm/Hz. Unlike a simple spectrum analyzer trace, PSD normalizes power to a 1 Hz bandwidth, providing a resolution-independent metric. This normalization is essential for comparing measurements taken with different resolution bandwidth settings. For a digitally modulated signal, the PSD reveals the occupied bandwidth, spectral sidelobes, and any regrowth shoulders caused by power amplifier nonlinearity.

The primary diagnostic value of PSD analysis in DPD optimization is the direct visualization of spectral regrowth. When a signal passes through a nonlinear power amplifier, intermodulation distortion generates new frequency components outside the original channel. On a PSD plot, this appears as elevated spectral shoulders adjacent to the main channel. The difference between the in-channel power and the regrowth level defines the Adjacent Channel Leakage Ratio (ACLR). Effective DPD suppresses these shoulders, restoring the PSD to its original, pre-amplifier shape.

Regulatory bodies like the FCC and ETSI define spectral emission masks—frequency-dependent PSD limits that a transmitter must not exceed. PSD analysis is the direct method for validating compliance. The measured PSD of the amplified signal is overlaid on the mask. Any portion of the PSD trace crossing above the mask line constitutes a spurious emission violation. DPD algorithms are often tuned specifically to ensure the corrected signal's PSD remains below these regulatory thresholds across all operating conditions.

While PSD is a density function, integrating it over a specific frequency range yields the total power within that band. This is used to calculate:

• Occupied Bandwidth (OBW): The bandwidth containing 99% of the total signal power.
• Adjacent Channel Power (ACP): The total power leaking into an adjacent channel, used to compute ACLR.
• In-Band Power: The total power within the assigned channel. This integration capability makes PSD the foundational measurement for all power-based spectral metrics.

Nonlinear AM-PM distortion in power amplifiers causes phase shifts that vary with the instantaneous signal envelope. This mechanism often produces asymmetric spectral regrowth, where the lower and upper adjacent channel PSD levels are unequal. PSD analysis is uniquely capable of revealing this asymmetry, which cannot be detected by scalar power measurements alone. The presence of significant asymmetry indicates that a DPD model must include memory effects and phase correction terms, not just amplitude linearization.

The noise floor visible on a PSD plot represents the broadband thermal noise and transmitter chain noise in the absence of a signal. The distance between the peak in-channel PSD and the noise floor defines the measurement's Spurious-Free Dynamic Range (SFDR). A low noise floor is critical for observing deep DPD correction. If the corrected spectral regrowth falls below the noise floor, the true ACLR improvement cannot be verified. High-performance PSD analysis requires instrumentation with sufficient dynamic range to capture the full extent of DPD linearization.

The primary regulatory compliance metric for spectral regrowth. ACLR quantifies the ratio of transmitted power within an assigned channel to the power leaking into adjacent frequency channels. 3GPP specifications mandate minimum ACLR values (typically 45 dB for base stations) to prevent interference. PSD measurements directly visualize the spectral leakage that degrades ACLR performance.

Nonlinear signal products generated at sum and difference frequencies when multiple signals pass through a nonlinear device. Third-order intermodulation products (IMD3) fall closest to the carrier and are the primary contributors to spectral regrowth visible on a PSD plot. The Third-Order Intercept Point (IP3) is a theoretical figure of merit extrapolated from low-power measurements to characterize this nonlinearity.

A signal conditioning technique that reduces the Peak-to-Average Power Ratio (PAPR) of a transmitted waveform before amplification. High PAPR signals like OFDM force power amplifiers to operate with significant back-off to avoid clipping-induced spectral regrowth. CFR techniques include:

• Peak Windowing: Applies smooth time-domain windows to peaks
• Clipping and Filtering: Iteratively clips peaks and removes out-of-band distortion
• Tone Reservation: Reserves OFDM subcarriers for peak-canceling signals

Two fundamental nonlinear mechanisms visible in PSD analysis. AM-AM distortion is amplitude-to-amplitude conversion where output amplitude deviates from linearity, causing gain compression. AM-PM distortion is amplitude-to-phase conversion where phase shift varies with instantaneous envelope, creating spectral asymmetry in regrowth. Both are characterized by the 1dB Compression Point (P1dB), defining the onset of significant nonlinear behavior.

A phenomenon where the current output depends on past input states due to thermal dynamics, electrical biasing, or charge trapping in semiconductor materials. Memory effects cause frequency-dependent nonlinear behavior that complicates spectral regrowth cancellation. On a PSD plot, memory effects manifest as asymmetric spectral regrowth that cannot be corrected by memoryless predistortion alone.

A regulatory or standards-defined PSD envelope that limits maximum allowable out-of-band emissions. 3GPP, FCC, and ETSI define emission masks specifying dBm/Hz limits across frequency offsets. PSD measurements are the fundamental validation tool for mask compliance. Key mask parameters include:

• Occupied Bandwidth (OBW): Frequency range containing 99% of integrated power
• Guard Band: Unused spectrum between channels for filter roll-off
• Stopband Attenuation: Minimum suppression in adjacent channels