---
title: Experimental PN-PSD Characterization
url: https://www.emergentmind.com/topics/experimental-pn-psd-characterization
type: topic
---

# Experimental PN-PSD Characterization

Experimental PN-PSD characterization refers to the suite of measurement and analysis techniques aimed at determining power spectral density (PSD) or phase noise power spectral density (PN-PSD) using pseudorandom noise (PN) sequences or via experimental pulse-shape discrimination methodologies. PSD and PN-PSD characterization underpin a wide array of applications in signal integrity, photonic metrology, and particle discrimination, demanding rigorous calibration and artifact suppression for reliable quantitative interpretation.

## 1. Fundamentals of PN-PSD Characterization

PN-PSD characterization leverages the correlation properties of pseudorandom noise sequences and/or pulse-shape waveform analysis to extract spectral or temporal system information. In channel measurements, maximal-length linear PN sequences with near-ideal autocorrelation facilitate high-resolution impulse response estimation, enabling conversion to channel PSD via Fourier analysis [2407.01307]. In phase noise metrology, experimental PN-PSD denotes the direct measurement and digital correction of the phase noise spectrum, notably within optical self-heterodyne setups where interference fringes can severely bias the PSD estimate if unmitigated [2505.15500]. In particle detection, PSD characterizes the ability to distinguish neutron-like from gamma-like events by exploiting differences in temporal scintillation waveform features [2001.07518, 2410.20804].

## 2. Methodologies: Experimental PN-PSD Workflows

### 2.1 Correlative PN Sounding for Channel Characterization

- Maximal-length PN sequence of degree $m$ (e.g., $m=13$, $N=8191$ chips) is generated and transmitted at a chip rate sufficient to Nyquist-sample the bandwidth of interest (e.g., $5\,\mathrm{MHz}$ chip rate for $0$–$2.5\,\mathrm{MHz}$) [2407.01307].
- The receive path records the system output, and cross-correlation of the received signal with the known PN yields an impulse response estimate $\hat{h}[n]$.
- Windowing (e.g., Hann) and averaging over multiple ($\geq 30$) realizations reduce sidelobes and statistical variance.
- Discrete Fourier transform of $\hat{h}[n]$ produces the channel transfer function $H[f]$ and power spectral density $S_h(f) = |H(f)|^2$.

### 2.2 Experimental Phase Noise PSD Extraction

- Asymmetric Mach–Zehnder self-heterodyne configuration with delay $\tau$ and frequency offset $f_\text{AOFS}$ is employed [2505.15500].
- The phase-difference PSD $S_{\Delta\varphi}(f)$ is distorted by $|H(f)|^2 = 4\sin^2(\pi f\tau)$, inducing spectral notches (fringes).
- Naïve inversion diverges at fringe nulls; robust compensation uses a Wiener-type equalization filter incorporating $\mathrm{SNR}(f)$, constructed from regions with high SNR via kernel ridge regression (KRR) on log-transformed spectral data.
- Final artifact-free PN-PSD is synthesized via a combination of KRR-based spectral interpolation and Wiener filtering.

### 2.3 Experimental PSD in Particle Discrimination

- Digitized scintillation waveforms are acquired at $500\,\mathrm{MHz}$ or higher, often using dual-end photomultiplier tube (PMT) readout [2001.07518, 2410.20804].
- Integration gates on the waveform (Q₁: short/fast, Q₂: long/total) yield correlated charge pairs, with template-based or empirical fits defining gamma- and neutron-like ridges in $Q_1$–$Q_2$ space.
- Value-assigned PSD (VPSD) and position-corrected projections (PPSD) assign normalized continuous PSD scores to each pulse, correcting for longitudinal attenuation and maximizing separation as measured by the figure-of-merit (FoM).
- Performance is quantified via analytic or simulated evaluation of likelihood discrimination, with efficiency curves as a function of photoelectron count (NPE).

## 3. Experimental Setups and Key Parameters

| Method/Domain               | Signal/Source           | Instrumentation                                 |
|-----------------------------|------------------------|-------------------------------------------------|
| PN-based channel sounding   | PN sequence (m=13)     | Arbitrary waveform generator, oscilloscope, optocoupler isolation [2407.01307] |
| Short-delay self-heterodyne | CW laser, AOFS         | Mach–Zehnder, AOFS, fiber delay, balanced photodetector, ≥5 GS/s scope [2505.15500] |
| Particle PSD                | NE-213/Gd-LS + PMTs    | FADC ≥500 MHz, dual PMT, cubic spline interp. [2001.07518, 2410.20804] |

Parameterization is directly tied to system response characteristics:

- Sequence length ($m$) and zero-padding in PN sounding define delay spread and frequency resolution [2407.01307].
- Delay-line length $\tau$ in self-heterodyne systems sets fringe periodicity and must be chosen relative to spectral analysis window [2505.15500].
- Integration gate timings and charge extraction parameters are tuned to waveform shape and sampling interval; spline interpolation is favored for peak timing and charge resolution [2001.07518].

## 4. Data Analysis Strategies and Artifact Mitigation

Robust PN-PSD characterization necessitates meticulous treatment of windowing effects, statistical averaging, and systematic artifacts:

- In PN channel sounding, zero-padding avoids circular correlation artifacts; windowing the CIR suppresses spectral sidelobes, and optocoupler isolation cancels ground-loop-induced noise [2407.01307].
- In self-heterodyne PN-PSD, digital power spectrum equalization based on KRR-trained SNR models retains measurement fidelity across fringe nulls, mitigating divergence seen in naïve inversion [2505.15500].
- In scintillation PSD experiments, longitudinal light attenuation is analytically modeled and corrected via coordinate transformations; ridge fitting to $Q_1$–$Q_2$ data allows intrinsic separation of pulse species, and gate optimization ensures near-optimal FoM (<10% loss with $\pm10\,\mathrm{ns}$ gate variance) [2001.07518].

## 5. Quantitative Results and Performance Metrics

### 5.1 Channel Sounding and Intrabody Links

- For galvanic intrabody communication using chicken-breast tissue as phantom, the measured channel gain is approximately $-52.2\,\mathrm{dB}$ at $100\,\mathrm{kHz}$, rolling on at the $370\,\mathrm{kHz}$ cutoff and improving to $-43.2\,\mathrm{dB}$ by $2.5\,\mathrm{MHz}$ [2407.01307].
- The measured PSD after averaging over 40 acquisitions is noise-limited below $-80\,\mathrm{dB}/\mathrm{Hz}$; experimental curves are within $2$–$3\,\mathrm{dB}$ of FEM simulation.

### 5.2 Self-Heterodyne PN-PSD

- Simulation and experimental validation show that the KRR+PSE method yields residual bias $<\pm0.5\,\mathrm{dB}$ for SNR $>10\,\mathrm{dB}$; spectral spikes $>15$–$20\,\mathrm{dB}$ at fringe positions are fully suppressed [2505.15500].

### 5.3 Particle PSD

| Neutron Rejection ($\epsilon_n$) | Gamma Retention ($\epsilon_\gamma$) | Required NPE |
|-----------------------------------|-------------------------------------|--------------|
| 90%                               | 97.8%                               | 49           |
| 95%                               | 99.4%                               | 79           |
| 99%                               | 99.9%                               | 150          |

Separation sharpens with increasing NPE, and FoM scales roughly as $\sqrt{\mathrm{NPE}}$; logistic functional forms empirically capture the rapid rise in $\epsilon_n$ versus NPE [2410.20804]. In NE-213 bar systems with dual PMTs, FoM improves by up to 75% at bar ends (position-corrected VPSD versus geometric-mean method), with benefits extending to analog readout at modest gate timing offsets ($<10$% FoM loss) [2001.07518].

## 6. Practical Guidelines and Limitations

- For PN-based channel sounding, degree $m\geq13$ and chip rate $\geq2\times$ the max frequency of interest are recommended; at least $N$ zeros padding, optocoupler isolation, and averaging over $30$–$40$ runs suppress artifacts [2407.01307].
- In short-delay PN-PSD, select $\tau$ such that $2$–$5$ fringes span the SNR-rich region, use high-bandwidth balanced photodetectors and ≥5 GS/s digitization, and restrict KRR training set to high-SNR frequencies ($T_\mathrm{SNR}\sim2$–$3$ dB) [2505.15500].
- In PSD of scintillation signals, digitization at $500$ MHz with cubic splines and separate ridge fitting by particle type are favored; NPE thresholds should be matched to application-driven rejection/retention targets with a minimum of $49$ PE for $\epsilon_n=90\%$, $\epsilon_\gamma=97.8\%$ [2410.20804].
- The KRR interpolation assumes smooth lineshapes; sharp spectral spurs $<1$ kHz may be insufficiently captured. Computational cost in KRR scales as $O(N_{\text{train}}^3)$, limiting training sets to a few hundred points [2505.15500].

## 7. Extensions and Applications

Experimental PN-PSD characterization underpins quantitative modeling of communication channels (e.g., implantable intrabody links), laser phase noise metrology (yielding artifact-free spectral estimation over six or more decades of Fourier frequency), and advanced scintillator-based particle discrimination. Methodological advances in artifact rejection and position correction are directly generalizable to large detector arrays and emerging high-density readout applications [2407.01307, 2001.07518, 2410.20804, 2505.15500]. Further integration of machine learning for model-free spectral compensation, as demonstrated for PN-PSD equalization, is a promising direction for future work in this domain.

Source: https://www.emergentmind.com/topics/experimental-pn-psd-characterization