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Signal Structure of the Starlink Ku-Band Downlink

Todd E. Humphreys, Peter A. Iannucci, Zacharias Komodromos, Andrew M. Graff

arXiv:2210.11578v3eess.SP

TL;DR

The paper addresses the challenge of blindly identifying operational Starlink OFDM signals and characterizing their structure for potential PNT use. It develops and applies a blind identification technique, reveals the downlink’s frequency- and time-domain structure, and identifies synchronization sequences that support pseudorange-based positioning, navigation, and timing.

  • Problem

    Blind identification of operational OFDM signals is more demanding than prior work and has not previously achieved exact determination of embedded synchronization sequences.

  • Method

    The authors develop and apply a blind signal identification technique using signal cyclostationarity, synchronization estimation, clustering, and frequency- and time-domain analysis.

  • Results

    The procedure uncovers Starlink’s Ku-band downlink structure and identifies four synchronization sequences that can be used for pseudorange-based PNT.

  • Takeaways & Limitations

    The characterization illuminates the path toward passively exploiting Starlink signals as a backup to traditional GNSS for PNT.

Abstract

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We develop a technique for blind signal identification of the Starlink downlink signal in the 10.7 to 12.7 GHz band and present a detailed picture of the signal's structure. Importantly, the signal characterization offered herein includes the exact values of synchronization sequences embedded in the signal that can be exploited to produce pseudorange measurements. Such an understanding of the signal is essential to emerging efforts that seek to dual-purpose Starlink signals for positioning, navigation, and timing, despite their being designed solely for broadband Internet provision.

I. INTRODUCTION

The paper addresses whether Starlink downlink signals can support opportunistic PNT by developing blind identification and characterizing their embedded synchronization structure. It uses a custom, GPS-disciplined capture system to analyze the Ku-band signal and identify features relevant to pseudorange-based positioning and timing.

  • Motivation: Starlink’s detailed broadcast-signal properties remain an open question for assessing opportunistic PNT beyond Doppler positioning.The relevant properties include modulation, timing, and spectral characteristics.
  • Contributions: The authors develop blind identification for operational Starlink OFDM signals in the 10.7 to 12.7 GHz band, including exact synchronization sequences.They describe this as an expansion beyond prior methods applied successfully only to simulated signals.
  • Contributions: The identification technique is intended to generalize to OFDM signals, except for steps estimating synchronization structures likely unique to Starlink.
  • Contributions: The signal characterization covers current Starlink versions 0.9, 1.0, and 1.5 and may extend to later versions because of backward compatibility.
  • Signal Capture: A custom system captures one satellite at a time using off-the-shelf hardware, custom software, and a highly stable GPS-disciplined oscillator.The setup uses a steerable 90-cm dish, public ephemerides, and a co-located terminal streaming high-definition video to guarantee downlink activity.
  • Signal Capture: The system combines narrowband and wideband capture modes because narrowband captures can analyze embedded structures but cannot provide synoptic signal analysis.Signal identification primarily uses narrowband data, except for primary synchronization-sequence estimation.

B. Received Signal Model

The received-signal model accounts for channel and receiver effects, including substantial Ku-band LEO Doppler. Because Doppler causes both frequency shift and time compression or dilation, the model must represent both effects.

  • Channel and Receiver Effects: The LEO-to-Earth channel and receiver introduce multipath fading, noise, Doppler, delay, filtering, and digitization into the transmitted signal.
  • Channel and Receiver Effects: For the directional high-elevation capture setup, delay spread is negligible, while Ku-band coherence bandwidth is primarily limited by atmospheric dispersion.
  • Doppler Model: Ku-band LEO Doppler is substantial enough that a frequency-shift-only model is inadequate for appreciable channel bandwidth.The model therefore includes frequency shift together with compression or dilation of the baseband signal.
  • Doppler Model: Doppler compression or dilation becomes negligible only when βFsTsync ≪1; otherwise, FFT misalignment produces inter-symbol interference.
  • Doppler Model: For β < 2.5 × 10^-5 and Tsync = 1 ms, enforcing βFsTsync < 0.1 limits Fs to 4 MHz, below the Starlink channel bandwidth.This numerical example motivates including both Doppler effects in the received-signal model.
  • Capture-Mode Scope: Equations (5) and (6) apply strictly to narrowband capture because wideband operation uses distinct mixing and sampling clocks.

IV. SIGNAL IDENTIFICATION PRELIMINARIES

The paper formulates blind OFDM signal identification around estimating structural parameters and synchronization sequences from received frame-length data. It exploits cyclostationarity, especially cyclic-prefix-induced autocorrelation, to estimate symbol and guard-interval structure without prior timing or frequency determination.

  • Terminology and Parameters: An OFDM channel contains N overlapping orthogonal subcarriers, and its frequency-domain coefficients become time-domain symbols through an IFFT and cyclic prefix.
  • Terminology and Parameters: Synchronization sequences are predictable OFDM symbols within frames that enable receiver time and frequency synchronization, while guard bands, frame guard intervals, and cyclic prefixes are distinct structures.
  • Problem Statement: The identification task estimates OFDM parameters from frame-length received data accurately enough to determine transmitted symbols and identify synchronization sequences.
  • Problem Statement: Prior blind-OFDM studies used simulated signals, simplified Doppler models, or limited waveform-discrimination goals rather than comprehensive identification of operational signals.
  • Exploiting Signal Cyclostationarity: With iid random symbols, cyclic autocorrelation is nonzero at τ ∈ {0, N, −N}; its periodicity in n is N + Ng because cyclic prefixes align with copied symbol portions.
  • Exploiting Signal Cyclostationarity: The cyclic autocorrelation function enables estimation of N and Ng without prior time and frequency determination.
  • Exploiting Signal Cyclostationarity: The successive estimators for N and Ng are computationally more efficient than a joint cyclic-correlation method without loss of accuracy.

V. SIGNAL IDENTIFICATION PROCEDURE

The procedure identifies OFDM parameters by combining design constraints with cyclic-autocorrelation estimation and validation against empirical Starlink behavior. It uses power-of-two structure, synchronization-based frequency estimation, and safeguards against misleading autocorrelation maxima.

  • The procedure is presented step by step to solve the Starlink signal-identification problem and facilitate replication.
  • A. Estimation of N: Increasing N improves throughput, but cyclic-prefix duration must exceed channel delay spread and narrower subcarrier spacing tightens CFO-estimation requirements.
  • A. Estimation of N: Known synchronization symbols expose a coherent carrier for estimating β, while the Cramér–Rao bound constrains allowable CFO error.
  • A. Estimation of N: N < 5316 ensures ϵ < 0.02 when Nsync = 210 and SNR = 10 dB.
  • A. Estimation of N: N must be a power of two for efficient transmitter and receiver IFFT and FFT operations.
  • A. Estimation of N: Because the receiver sampling rate may differ substantially from Fs, the method estimates N and Fs using power-of-two constraints and an approximate spectrum-derived Fs.
  • A. Estimation of N: Empirical Starlink data can produce a prominent central autocorrelation lobe, so candidate N values require a validation test that rejects insufficiently distinct maxima.
  • A. Estimation of N: For Starlink Ku-band signals, ν = 10 dB empirically excludes spurious maxima, with sufficiently large p needed to explore off-peak values.

B. Estimation of Fs

The method refines Fs after estimating N by mapping receiver-sampled candidates to the corresponding OFDM structure and exploiting likely integer-MHz channel bandwidths. Figure 3 shows the cyclic-frequency structure used to identify the fundamental period and its harmonics.

  • After obtaining N̂, the method estimates Fs more accurately using the relationship between N̂r/N̂ and Fr/Fs.
  • Because Fs is extremely likely to be an integer multiple of 1 MHz, the estimator uses this numerology to select Fs.
  • In the bottom panel, the fundamental cyclic frequency corresponding to Ng + N appears at normalized frequency α̃ = 1, with additional harmonic peaks.
  • The power-of-two constraint on N̂ is the key to the estimator’s accuracy.

C. Resampling

After estimating Fs, the received signal is resampled at F̂s so that subsequent OFDM-parameter estimation uses the inferred sampling rate. The resampling preserves the signal’s useful frequency content while adapting the sampling rate to the capture mode.

  • The received signal is resampled at F̂s to facilitate estimation of the remaining OFDM parameters.
  • Sinc-based resampling changes the sampling rate while leaving useful frequency content |f| < Fh unchanged.
  • For wideband captures, resampling follows lowpass filtering and conversion to a lower sampling rate, after which y(n) denotes the signal at F̂s.

D. Estimation of Ng

The method estimates Ng and the frame period from design constraints and cyclic autocorrelation after resampling at F̂s. Reliable Ng estimation requires enough samples to span a frame and sufficient SNR, while frame-period estimation uses synchronization-sequence alignment.

  • D. Estimation of Ng: Ng is bounded by the requirement that Tg exceed the channel delay spread, with Ku-band worst-case 95% RMS delay spread reported as Td = 108 ns.
  • D. Estimation of Ng: After resampling, Ng estimation uses cyclic autocorrelation Rαy(N̂) over a finite candidate set A(ξ) indexed by p.
  • D. Estimation of Ng: Np values above N/Ng provide no accuracy improvement, while Starlink narrowband estimation was reliable for Np as low as 1 when M ≥ TfFs and SNR > 3.5 dB.
  • D. Estimation of Tf: Synchronization-sequence alignment across nearby frames creates a peak in R0y(τ), which supports estimating the frame period Tf.
  • D. Estimation of Tf: Frame-period estimation uses samples spanning multiple adjacent frames and candidate periods constrained by observed active intervals and expected numerology.
  • D. Estimation of Tf: The estimators for N, Ng, and Tf remain robust to nonzero Doppler when βFcTss ≪ 1.

F. Symbol and Carrier Frequency Synchronization

The authors blindly estimate OFDM symbol timing and carrier-frequency offset by searching candidate values and scoring the resulting symbol constellations. The approach recovers information symbols for both 4QAM and 16QAM, while identifying a special first-frame interval as a repeating time-domain sequence rather than an OFDM symbol.

  • Blind synchronization is required because the sequences designed to enable OFDM symbol and carrier-frequency synchronization are initially unknown.
  • The estimator searches candidate sample indices and CFO values, using prior frame-boundary information and an uncertainty range around the CFO estimate.Candidate sample indices are generated from an approximate frame start and integer OFDM-symbol intervals; candidate CFO values use a prior estimate and search stride.
  • The synchronization score isolates a trial symbol, removes the trial CFO, applies an FFT, and evaluates automatically clustered constellation structure.For bs ≤ 2, the score is the empirical SNR based on cluster centroids and variances, and it is insensitive to constellation rotation.
  • The estimator worked for both 4QAM and 16QAM Starlink modulation, including signals whose SNR was too low for error-free cluster identification.
  • The first OFDM-symbol interval in each frame instead contains a repeating pseudorandom time-domain sequence, but its timing and CFO estimates were recovered from the next interval.The reported estimates are n̂_m00 = n̂_m10 − N̂ − N̂_g and β̂_m0 = β̂_m1.

G. Estimation of the Synchronization Sequences

The paper locates and estimates Starlink’s embedded synchronization sequences by comparing corresponding frame intervals and exploiting recovered OFDM timing. It identifies distinct primary, secondary, coda-minus-one, and coda synchronization structures with different repeatability and constellation properties.

  • Synchronization-sequence locations are found by isolating corresponding OFDM intervals across frames and testing whether their features repeat.The first frame symbol was identified as a synchronization sequence despite lacking discernible frequency-domain constellation structure.
  • The primary synchronization sequence is recovered by coherently stacking eight repeated subsequences, and its values are identical across frames and satellites.Wideband capture is required because the subsequence spans the full OFDM-channel bandwidth.
  • The secondary synchronization sequence occupies the second OFDM-symbol interval and is a standard 4QAM OFDM symbol.Narrowband data can reveal the in-band information symbols, initially up to a phase offset and differential ambiguity.
  • The coda synchronization sequence occupies the last nonzero OFDM symbol at i = 301 and is a standard 4QAM symbol with a constellation rotated 90 degrees relative to the SSS.Its clusters form a box aligned with the horizontal and vertical axes, whereas the SSS has a diamond configuration.
  • The coda-minus-one synchronization sequence occupies the penultimate nonzero symbol at i = 300 and contains only some information symbols that remain constant across frames.

H. Estimation of Nsf, Nsfd, and Tfg

Using estimated symbol timing, frame timing, and the known initial synchronization symbols, the authors estimate Starlink’s frame-structure parameters. They also describe procedures for estimating channel center frequency and modeling short-term frame timing.

  • The estimated OFDM symbol duration is T̂_sym = (N̂ + N̂_g)/F̂_s, and the number of whole symbol intervals in a frame is obtained by flooring T̂_f/T̂_sym.
  • Knowing that the first two intervals are synchronization sequences enables estimation of N_sf, N_sfd, and T_fg.
  • The final interval is vacant, so the estimated number of nonzero symbols excludes that interval.
  • Channel-center-frequency estimation separates carrier-frequency offset from center-frequency error by using the fact that only the former compresses or dilates the modulation.
  • For intervals up to one second, frame timing is accurately modeled as a second-order polynomial, with coefficients obtained by least-squares batch estimation.

VI. RESULTS

The identified Starlink Ku-band signal contains structured synchronization sequences, including a PSS with repeated subsequences, polarity inversions, and an explicitly specified phase sequence.

  • The PSS consists of eight repetitions of a length-N/8 subsequence preceded by a cyclic prefix.
  • The cyclic prefix and first repeated PSS subsequence have inverted polarity relative to the remaining repetitions.
  • The PSS subsequence uses symmetric DPSK to encode a length-127 maximal-length LFSR m-sequence.
  • The PSS phase sequence is specified by pk = exp(jπ[1/4 + qk/2]) for k in the stated subsequence range.
  • The SSS is represented by complex frequency-domain coefficients, while its detailed presentation is deferred to a later publication.

VII. DISCUSSION

Starlink’s downlink uses a relatively simple, structured frame with multiple predictable synchronization sequences that support channel estimation and passive PNT observables. The sequences enable sensitive correlation measurements, but their reuse across satellites creates an assignment ambiguity.

  • Signal and channel structure: Eight 240-MHz channels span the Ku-band downlink, with vacant central subcarriers and satellite-dependent leakage tones in gutters and guard bands.Adjacent channels are separated by 10-MHz guard bands; leakage-tone behavior varies across satellites and channel locations.
  • Frame structure: Each frame contains 302 4.4-µs intervals plus a guard interval, begins with PSS and SSS sequences, and ends with CM1SS, CSS, and the frame guard interval.A subsequent frame may be immediately present or absent depending on user demand.
  • Synchronization sequences: Known SSS and CSS symbols support channel estimation across all subcarriers, while predictable CM1SS elements may provide additional estimation support.These sequences enable interpolation of channel estimates within each frame.
  • Synchronization sequences: PSS correlation produces sharp peaks at frame beginnings, and phase coherence across frames permits coherent integration of synchronization sequences.The resulting pseudorange and Doppler observables can be extracted below -6 dB SNR, below communication decoding requirements.
  • PNT implications: Starlink synchronization sequences are not satellite-unique, so assigning measurements to satellites requires approximate location, ephemerides, Doppler, and frame-arrival time.This differs from GNSS spreading codes and creates a combinatorial assignment problem.
  • Synchronization sequences: The PSS repeats a length-N/8 subsequence eight times, with polarity inversion in the cyclic prefix and first repeated subsequence.The repeated structure can make initial Doppler and frame-start searches more efficient, while m-sequence and phase-shift choices provide autocorrelation and spectral benefits.

D. Gap to Capacity

The discussion examines how Starlink balances spectral and temporal efficiency against communications margin. Wide guard bands and frequent synchronization occupy resources, while the short cyclic prefix reflects the low-delay-spread space-to-Earth channel.

  • Channel occupancy: A 10-MHz guard band separates adjacent channels, reducing spectral occupancy and suggesting simultaneous channel activation with lower user-terminal sampling and filtering requirements.The unused bandwidth spans over 42 subcarrier intervals.
  • Cyclic-prefix margin: Starlink’s useful-to-full OFDM symbol interval ratio is 32/33, reflecting efficient design and exploiting the low delay spread of the space-to-Earth channel.The 130-ns guard interval exceeds the cited 108-ns worst-case 95% RMS Ku-band delay spread.
  • Synchronization overhead: Synchronization sequences occupy four intervals every 1.33 ms, an unusually high allocation relative to terrestrial OFDM waveforms such as LTE.Bookending frames with synchronization sequences supports their operational role but consumes frame resources.
  • PNT implications: The identified synchronization sequences can support pseudorange-based PNT and may provide a path toward using Starlink as a backup to traditional GNSS.The paper reports identifying four synchronization sequences and explicitly evaluating two.
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