DPD Teaching Lab — Instructions, Mathematics and Measurement Notes
This lab is a sampled complex-I/Q behavioral simulation intended for learning digital predistortion, nonlinear PA behavior, memory effects, spectrum regrowth and modulation-quality measurements. RF frequency labels are a display mapping; the simulation itself operates on a coherent complex-envelope representation.
1. Quick operating procedure
- Choose the QAM order, number of reference carriers and active OFDM subcarriers per carrier.
- For two carriers, choose the center-to-center separation as 1×, 2×, 5× or 10× the nominal channel spacing. 1× means adjacent component carriers.
- Set TX drive and PA memory/nonlinearity. Use Run model to inspect the untrained/bypass path.
- Choose DPD nonlinearity order K, memory order Q, optional GMP cross-terms, adaptation gain μ and iteration count.
- Use Train / adapt DPD for a repeatable experiment beginning at the identity predistorter. Use Continue adaptation only when you intentionally want a warm start.
- Click any block or stage-table row to inspect that observation point. Compare the spectrum, carrier-specific metrics and coefficient table.
- Use New OFDM seed to repeat the experiment with a different random QAM realization, and Export selected CSV for numerical inspection.
2. Display and metrics
Integrated-bandwidth ACPR/ACLR view. In two-carrier mode each carrier has its own exterior-side leakage measurements; IMD3 and IMD5 are measured and marked independently from ADJ/ALT windows.
The current waveform geometry is calculated from the active OFDM allocation.
Click any system block or row in the stage table to inspect its sampled waveform and spectrum.
The time-domain display shows I, Q and envelope magnitude for the selected observation point. The spectrum display uses the RF-equivalent 1 GHz teaching axis and overlays the selected stage with the DSP reference when enabled. Shaded MAIN, ADJ, ALT1 and ALT2 windows show exactly the FFT bins used by the integrated channel-power calculations. In two-carrier mode, IMD3 and IMD5 markers are placed from the actual coherently realized carrier centers, not from the requested nominal spacing.
The selected-stage metric panel reports composite RMS, composite peak, PAPR and full-waveform NMSE. The carrier metric table reports one row per wanted carrier: filtered wanted-carrier RMS, peak and PAPR; ACPR/ADJ, ALT1 and ALT2 leakage; IMD3 and IMD5 where applicable; and carrier-specific EVM in dB and percent. With two carriers, leakage is measured on the exterior side of each carrier so the other wanted carrier is never counted as adjacent-channel distortion.
3. Sampled waveform and frequency scaling
The FFT-bin spacing is fixed at exactly 15 Hz internally and displayed at ×1000, corresponding to 15 kHz OFDM subcarrier spacing. The capture length and sample rate expand automatically (power-of-two FFT sizes up to 65536 samples) when larger two-carrier spacing is selected, ensuring the displayed IMD5 integration bands remain inside Nyquist. The RF display is centered at 1.000 GHz.
Each component carrier uses the selected number of active subcarriers. The occupied bandwidth is
and this teaching profile defines nominal channel spacing from a 90% occupied-to-nominal ratio:
Thus 600 active subcarriers give 9 MHz occupied bandwidth and a 10 MHz nominal channel; 300 active subcarriers give 4.5 MHz occupied bandwidth and a 5 MHz nominal channel. All channel-power windows are recalculated from the selected allocation.
4. One- and two-carrier references
One-carrier mode places one OFDM carrier at the display center. Two-carrier mode creates two statistically similar carriers with identical modulation and occupied bandwidth. The selected separation multiplier m gives the requested center spacing
The exact center frequencies are rounded to coherent FFT bins. The GUI reports the actual realized separation. Each component is power-normalized before summation, and the final composite waveform is normalized to the same requested RMS drive as one-carrier mode. Therefore two-carrier mode gives approximately −3.0103 dB mean power per component carrier while preserving total composite mean power.
5. Channel power, ACPR/ACLR, ALT1 and ALT2
Channel power is computed by summing linear FFT-bin power inside the integration bandwidth; ratios are converted to dBc only after integration. This follows the integrated-bandwidth principle used in professional spectrum-analyzer ACLR measurements.
The integration bandwidth equals the active occupied OFDM bandwidth. ADJ, ALT1 and ALT2 are centered one, two and three nominal channel spacings from the wanted-carrier center. They are not moved to the other carrier when the two-carrier separation changes.
For one carrier, lower and upper leakage channels are measured independently and the worse value is shown. For two carriers, the carrier table reports the exterior-side leakage set for each wanted carrier: lower-side measurements for the lower-frequency carrier and upper-side measurements for the upper-frequency carrier. This avoids counting another wanted carrier or an internal allocation gap as adjacent-channel leakage. The internal gap remains visible in the spectrum.
6. IMD3 and IMD5 for two component carriers
With carrier centers f1 and f2, the classical odd-order intermodulation product centers are
Because the carriers are modulated, these products are spectral regions rather than single tones. The lab therefore marks the theoretical centers and integrates an occupied-bandwidth window around each corresponding product. IMD3/IMD5 values in the per-carrier table are relative to that carrier's wanted-channel power. When separation is 1×, the IMD3/IMD5 centers lie close to the exterior ADJ/ALT1 centers; at larger separations they move outward according to the equations above while ADJ/ALT1/ALT2 remain tied to nominal channel spacing.
7. RMS level, peak level and PAPR
Composite values use the complete sampled waveform. PAPR is calculated directly as 10 log10(Ppeak/Pmean), which is equivalent to 20 log10(Vpeak/VRMS) for the complex envelope. A predistorter normally increases the PA-input crest factor to counter AM/AM compression. With an ideal, fully converged inverse and sufficient PA headroom, the linearized PA-output PAPR approaches the DSP-reference PAPR; with finite adaptation, residual compression or clipping, the PA-output PAPR can remain lower even when RMS EVM is already small because the largest OFDM peaks are rare. Carrier-row values are obtained by isolating the wanted-carrier integration band in the frequency domain, inverse transforming it, and then calculating RMS, peak and PAPR on that filtered component.
8. EVM and NMSE
EVM is calculated on each carrier's active OFDM subcarriers. A best-fit common complex gain/phase term is removed independently for each carrier before the error vector is formed:
The aggregate EVM in the system calculations uses all wanted active subcarriers. NMSE uses the complete sampled waveform after one best-fit complex gain/phase alignment, so NMSE also includes out-of-band distortion.
9. PA behavioral model
The PA is a complex memory-polynomial teaching model with odd nonlinear orders through ninth order and delayed terms that create frequency-dependent memory:
Complex coefficients create both AM/AM and AM/PM behavior. The sliders scale memory and nonlinear coefficient strength; this is a behavioral model rather than a device-specific transistor/circuit model.
10. DPD basis and indirect learning
The base predistorter is a memory polynomial:
With GMP cross-terms enabled, additional terms use a delayed/advanced envelope relative to the complex sample:
The indirect-learning architecture fits a postdistorter from gain-normalized PA feedback to the actual PA input. With basis matrix U and target vector z, ridge-regularized complex least squares is
The fitted coefficients are transferred to the predistorter using the adaptation gain μ:
Train / adapt DPD always starts from the identity predistorter, making iteration-count comparisons meaningful. Continue adaptation retains the current coefficients and performs additional iterations.
11. Converter and IQ blocks
The DAC and ADC are uniform complex I/Q quantizers with selectable bit depth and normalized full scale. The IQ modulator can add gain and phase mismatch. The default observation demodulator is ideal so it does not introduce a hidden EVM/ACLR floor; ADC quantization remains explicitly visible at the feedback stage.
12. Interpreting results
- The DSP reference is constructed exactly on coherent FFT bins, so ideal out-of-channel power falls below the numerical display floor rather than appearing as windowing leakage.
- Increasing PA drive/nonlinearity generally increases spectral regrowth and EVM.
- Insufficient DPD K or Q leaves uncancelled nonlinear or memory distortion; excessive model size can become more sensitive to conditioning and regularization.
- Cross-terms can improve correction when envelope memory is not represented well by the diagonal memory-polynomial basis.
- For separated carriers, IMD products move with carrier separation while standard adjacent/alternate channel windows stay at fixed multiples of the nominal channel spacing.
- All values are deterministic for a given seed and configuration, allowing controlled teaching comparisons.
13. Measurement scope and limitations
This is a coherent sampled-data teaching simulator. It does not model RF phase noise, thermal noise, reconstruction filters, analog anti-alias filters, mixer LO leakage, real spectrum-analyzer RBW/VBW detector dynamics, or a specific PA device unless those effects are explicitly added. The reported quantities are therefore model measurements, not calibrated hardware measurements.
The ACLR presentation follows the integrated-channel-power concepts documented by Rohde & Schwarz: channel power is integrated over configured bandwidths, adjacent/alternate channels use configured spacings, and multi-carrier results are referenced to the applicable transmit carrier. The lab intentionally exposes the actual measurement windows on the plot so the numerical result can be checked visually.