Effect-LoRA: Doppler Mitigation in LoRa DtS

• Effect-LoRA is a methodology for estimating and compensating Doppler shifts in LoRa direct-to-satellite links, enhancing IoT communications.
• It employs four frameworks—point, linear, midamble-point, and midamble-linear estimation—to address varying Doppler shift regimes and maintain signal integrity.
• Deployment guidelines stress optimizing spreading factor, bandwidth, and error correction to achieve performance close to the AWGN baseline in dynamic LEO environments.

Effect-LoRA refers to the estimation and compensation of the Doppler effect in LoRa (Long Range) modulation used for direct-to-satellite (DtS) communications, with a particular focus on scenarios involving low Earth orbit (LEO) satellites servicing Internet of Things (IoT) devices. In these contexts, robust configuration and signal processing strategies are essential to counteract the adverse performance impact of time-varying Doppler shifts induced by the relative motion between the ground terminal and the LEO satellite. Four primary frameworks—point estimation, linear estimation, midamble-point estimation, and midamble-linear estimation—form the cornerstone methodologies for Doppler mitigation, each exhibiting distinct strengths across varying Doppler shift regimes (Farhat et al., 25 Jun 2025).

1. Doppler Shifts in LoRa DtS Links

A LoRa chirp, defined by its baseband envelope

$$s(t)=\exp\!\left\{j\left[2\pi f_0\,t+\pi\tfrac{B}{T}\,t^2\right]\right\}$$

for $0\le t\le T$, experiences frequency offset when transmitted over a moving LEO satellite. The satellite’s instantaneous line-of-sight velocity $v(t)$ imparts a Doppler shift

$f_D(t) = -\frac{v(t)}{c} f_c,$

with $f_c$ as the carrier frequency and $c$ as the speed of light. For practical DtS LoRa, $v(t)$ may be approximated as constant over a chirp, yielding a received waveform shifted in frequency by $f_D$. If $v(t)$ varies appreciably within a chirp, an additional quadratic baseband phase must be tracked by the receiver (Farhat et al., 25 Jun 2025).

2. Doppler Estimation and Compensation Frameworks

The standard LoRa frame (preamble up-chirps, sync down-chirps, payload) supports four distinct Doppler estimation and compensation strategies:

Method	Doppler Model	Compensation Update
Point estimation	Constant shift	Once (start of payload)
Linear estimation	Constant rate	Once (start of payload)
Midamble-point	Piecewise-constant	At each midamble
Midamble-linear	Piecewise-linear	At each midamble

1. Point Estimation (constant-shift model): Uses the final preamble down-chirp for a single Doppler offset estimate, applying a static compensation throughout the payload.
2. Linear Estimation (constant-rate model): Utilizes both first and last down-chirps to estimate a linear Doppler variation, compensating for both frequency shift and slope across the payload.
3. Midamble-Point Estimation: Integrates periodic up-chirp midambles into the payload for sequential Doppler re-estimation and segmental (piecewise constant) compensation.
4. Midamble-Linear Estimation: At every midamble, estimates both frequency offset and slope locally, yielding piecewise-linear compensation within payload segments (Farhat et al., 25 Jun 2025).

3. Performance Impact and Recovery

In representative scenarios (carrier $f_c=868$ MHz, $B=125$ kHz, coding rate CR=½), high static Doppler (e.g., 20 kHz, low satellite elevation) or high Doppler rate (e.g., $~300$ Hz/s, high elevation) can degrade the symbol error rate (SER) by orders of magnitude if uncompensated. Specifically, at spreading factor $\mathrm{SF}=12$ and $E_s/N_0=14$ dB, uncompensated Doppler yields $\mathrm{SER}>10^{-1}$, while the LoRa AWGN baseline is $\mathrm{SER}\approx10^{-4}$.

• Point estimation recovers most of the static shift in low-rate regimes but fails under high Doppler rates and high SF.
• Linear estimation aids in high-rate cases, especially for $\mathrm{SF}=12$, but introduces noise for predominantly static Doppler.
• Midamble-point estimation consistently achieves within 1–2 dB of the AWGN baseline, yielding $\mathrm{SER}\sim10^{-3}$–$10^{-4}$ at $E_s/N_0=14$ dB for both low and high Doppler cases.
• Midamble-linear estimation performs similarly to midamble-point, with marginal improvement if Doppler slope varies significantly within the payload (Farhat et al., 25 Jun 2025).

4. Trade-offs between Spreading Factor, Bandwidth, FEC, and Residual Error

The selection of spreading factor (SF), bandwidth (BW), and coding rate (CR) directly influences the Doppler effect’s impact:

• Time-on-air: $T_{\rm ToA}\propto 2^{\mathrm{SF}}/B$, with higher SF or lower BW increasing Doppler accumulation.
• Residual frequency error: After compensation, residual error scales as $$\varepsilon_f\approx\frac{\alpha\,T_{\rm seg}}{2B/M}$$ due to uncompensated Doppler slope or FFT quantization, with $T_{\rm seg}$ as the relevant segment duration.
• LDRO Mode: The Low Data Rate Optimization (LDRO) reduces FFT bins $M\to M/4$, increasing bin spacing to $4(B/M)$, thus quadrupling Doppler tolerance at the expense of a fourfold raw bit-rate reduction.
• Forward Error Correction (FEC): Lower code rate (higher redundancy) marginally extends $T_{\rm ToA}$ and thus Doppler exposure (Farhat et al., 25 Jun 2025).

5. Configuration and Design Guidelines

Optimal LoRa DtS operation under Doppler is governed by the following strategies:

1. No onboard compensation: Limit $T_{\rm ToA}$ by using $\mathrm{SF}\le10$ and/or $B\ge250$ kHz; enable LDRO for $\mathrm{SF}\ge11$ at $B=125$ kHz.
2. Moderate Doppler rates ($\le100$ Hz/s): Use point estimation for $\mathrm{SF}\le10$. For $\mathrm{SF}=12$, employ at least six down-chirps in the preamble for improved estimation.
3. High Doppler rates ($\ge200$ Hz/s): Insert midambles with the following recommended intervals to maintain residual Doppler within one FFT bin:
   • $\mathrm{SF}=12$: every symbol (interval = 1 chirp)
   • $\mathrm{SF}=10$: every 4 chirps
   • $\mathrm{SF}=7$: every 12 chirps
4. Method selection: Midamble-point estimation provides robust, low-complexity compensation with $\le1$ dB performance loss. Use midamble-linear only if non-linear Doppler slope changes exceed $\sim$100 Hz per segment.
5. Overhead: Ensure that preamble length ($n_{\rm up}=8$, $n_{\rm dw}\ge2$) and the midamble interval comply with regulatory and energy constraints (Farhat et al., 25 Jun 2025).

6. Practical Implications for LoRa DtS Deployments

Deployments adhering to these estimation and compensation frameworks can maintain performance close to the LoRa AWGN baseline, even with Doppler shifts in the tens of kHz and Doppler rates in the hundreds of Hz/s typical of LEO satellite passes. Effective integration of midamble-point or midamble-linear strategies allows LoRa systems to extend connectivity to remote and IoT sites via satellites without prohibitive degradation in link reliability. The specific choice of SF, BW, FEC, and Doppler estimation method should be driven by anticipated Doppler dynamics and system constraints (Farhat et al., 25 Jun 2025).