LEO-based Carrier-Phase Positioning for 6G: Design Insights and Comparison with GNSS

1 LEO-based Carrier -Phase Positioning for 6G: Design Insights and Comparison with GNSS Harish K. Dureppagari, Harikumar Krishnamurthy , Chiranjib Saha, Xiaofeng W ang, Alberto Rico-Alv ari ˜ no, R. Michael Buehrer , Harpreet S. Dhillon Abstract —The integration of non-terrestrial networks (NTN) into 5G new radio (NR) enables a new class of positioning capabilities based on cellular signals transmitted by Low-Earth Orbit (LEO) satellites. In this paper , we investigate joint delay- and-carrier -phase positioning for LEO-based NR-NTN systems and pro vide a conv ergence-centric comparison with Global Navigation Satellite Systems (GNSS). W e show that the rapid orbital motion of LEO satellites induces strong temporal and geometric diversity across observation epochs, ther eby improv- ing the conditioning of multi-epoch carrier -phase models and enabling significantly faster integer-ambiguity conv ergence. T o enable rob ust carrier -phase tracking under intermittent po- sitioning refer ence signal (PRS) transmissions, we propose a dual-wav eform design that combines wideband PRS for delay estimation with a continuous narro wband carrier f or phase track- ing. Using a realistic simulation framework incorporating LEO orbit dynamics, we demonstrate that LEO-based joint delay- and-carrier -phase positioning achieves cm-level accuracy with con vergence times on the order of a few seconds, whereas GNSS remains limited to meter-le vel accuracy over comparable short observation windows. These r esults establish LEO-based cellular positioning as a strong complement and potential alternative to GNSS for high-accuracy positioning, navigation, and timing (PNT) services in future wireless networks. Index T erms —NTN positioning, LEO-based positioning, pre- cise positioning, carrier phase positioning, joint delay and carrier phase positioning, integer ambiguity , con vergence analysis. I . I N T R O DU C T I O N Positioning has been an inte gral capability of wireless networks, initially dri ven by regulatory requirements and later by the gro wing demand for location-a ware services. The introduction of NTN into 5G NR, starting from Release 17, enables cellular services via satellites in low-earth orbit (LEO), medium-earth orbit (MEO), and geostationary-earth orbit (GEO) [1], [2]. While this development has allo wed emerging LEO constellations, such as Starlink and OneW eb, to provide global enhanced mobile broadband (eMBB) and internet-of-things (IoT) services, it also creates an opportunity to enable satellite-based positioning using cellular signals. LEO satellites, typically orbiting at altitudes of around 600 km, offer substantially stronger link budgets and higher receiv ed signal po wer than GNSS satellites operating at around 20,200 km. This improved signal strength, combined with access to wider bandwidths, can significantly reduce time-to-first- fix (TTFF) relative to GNSS. Moreov er , LEO-based cellular H. K. Dureppagari, R. M. Buehrer , and H. S. Dhillon are with W ire- less@VT , Department of ECE, V irginia T ech, Blacksbur g, V A 24061, USA. Email: { harishkumard, rbuehrer , hdhillon } @vt.edu. H. Krishnamurthy , C. Saha, X. W ang, and A. Rico Alvari ˜ no are with the Qualcomm Standards and Industry Organization, Qualcomm T echnologies Inc., San Diego, CA 92121, USA. Email: { harkris, csaha, wangxiao, albertor } @qti.qualcomm.com. The support of the US NSF (Grant CNS-2107276) is gratefully ackno wledged. positioning has the potential to reduce reliance on dedicated GNSS radios in user equipment (UE), which, as of Release 19, are still required for NR-NTN connectivity , thereby reducing power consumption and hardware complexity . W ith GNSS remaining a cornerstone of PNT services, a fundamental question remains: can LEO constellations serve as a viable alternati ve or complement to GNSS for PNT using 6G cellular infrastructure? In our prior work [1], we presented our vision for NTN-based localization, outlining prospectiv e study cases for accurate positioning in 6G, highlighting the role of LEOs, and identifying key challenges in integrating such systems into 5G and beyond. Building on this vision, in our subsequent work [2], we in vestigated the feasibility of repurposing communication-centric LEO constellations for positioning, presented NR-NTN-compliant design guidelines, and demonstrated that sub-10m accuracy can be achiev ed using delay-based methods with 10 MHz bandwidth, yielding performance comparable to GNSS [3]. T raditional delay-based positioning methods cannot achiev e cm-le vel accuracy due to sev eral limitations, including atmospheric biases, multi- path, satellite clock errors, and UE clock errors. Moreover , positioning using delay-based methods is limited by band- width and receiver sampling rate. This motiv ates the need for more adv anced positioning techniques that exploit carrier- phase measurements, which offer orders-of-magnitude higher ranging precision and form the basis of high-accuracy satellite positioning systems. Prior Art. High-accuracy satellite positioning has tradition- ally relied on carrier-phase measurements [4], where cm-lev el accuracy is achiev ed through phase continuity and integer ambiguity resolution, typically aided by code-phase measure- ments. Integer ambiguity is an unknown inte ger number of full carrier cycles accumulated along the signal propagation path, which cannot be directly observ ed from instantaneous carrier- phase measurements. Joint processing of carrier-phase mea- surements across multiple observation epochs helps resolve this ambiguity , while code-phase measurements provide coarse range information that significantly accelerates ambiguity res- olution. W ith the integration of NTN into NR, this paradigm has recently attracted interest in the context of LEO-based positioning. Studies in [5], [6] hav e shown that carrier-phase tracking is feasible using communication-centric LEO signals- of-opportunity (SOP), such as Starlink, by coherently tracking beat carrier phase and reco vering phase-based measurements suitable for positioning from wav eforms not originally de- signed for PNT . Subsequent studies have further extended this line of work to study differential carrier-phase positioning and ambiguity resolution in LEO megaconstellations, as well 2 as theoretical formulations of ambiguity fixing under carrier- phase models that account for frequency variations caused by high Doppler dynamics [7]–[9]. Howe ver , existing studies primarily focus on SOP-based architectures, assume long observation windo ws (on the order of se veral minutes), do not discuss con ver gence behavior or systematic comparisons with GNSS, and, importantly , do not address NR-NTN constraints. Although carrier -phase posi- tioning has also been explored in terrestrial 5G-Advanced NR [10], these techniques cannot be directly extended to NR-NTN due to fundamentally dif ferent dynamics, including high Doppler and Doppler-rate effects and communication- centric constellation designs. Consequently , NR-NTN litera- ture has largely focused on delay-based positioning, which alone cannot achie ve carrier -phase-grade accuracy . T o this end, our work lays the foundation for using a joint delay-and- carrier-phase positioning framew ork tailored to LEO-based NR-NTN systems, demonstrating rapid con vergence and cm- lev el accuracy by explicitly lev eraging the fast satellite motion inherent to LEO constellations and positioning LEO-based PNT as a potential alternati ve to GNSS. Contributions. In this paper , we in vestigate the joint ex- ploitation of carrier-phase and delay-based measurements for high-precision positioning, aiming to achie ve cm-lev el accu- racy . W e begin by describing how the carrier phase is measured and tracked, and analyze the impact of satellite motion on carrier-phase ev olution and the accuracy of Doppler-based phase approximations in both LEO and GNSS systems. W e then study the temporal e volution of the phase transformation matrix obtained by jointly processing carrier-phase measure- ments ov er multiple epochs, with particular emphasis on its conditioning properties quantified by the condition number , and compare its con ver gence behavior for LEO and GNSS constellations. Next, we present a comprehensiv e compara- tiv e analysis of integer ambiguity resolution and positioning performance under delay-only positioning and joint delay- and-carrier-phase positioning framew orks for both LEO- and GNSS-based systems. Through our analysis, we demonstrate that the rapid satellite motion in LEOs significantly enhances geometric di versity across observation epochs, leading to faster ambiguity resolution and substantially reduced con ver gence time compared to GNSS. Subsequently , we show that LEO- based joint delay-and-carrier-phase positioning achie ves cm- lev el accuracy with con vergence times on the order of a few seconds, thereby deliv ering superior performance compared to GNSS within short observation windows. W e conclude our discussion by establishing that LEO-based positioning is a potential alternati ve to GNSS, serving as a standalone, high- accuracy PNT solution in future wireless networks. I I . C A R R I E R - P H A S E M E A S U R E M E N T S & T R AC K I N G Carrier-phase measurements enable range estimation with a precision on the order of the carrier wa velength, offering sev eral orders of magnitude improvement ov er delay-based measurements. Conceptually , the carrier phase represents the accumulated phase of the receiv ed sinusoidal carrier relati ve to the transmitted signal. As illustrated in Fig 1, the carrier phase Fig. 1: Intr oduction to Carrier Phase : Carrier phase measurements ov er time. is measured over multiple epochs as the satellite traverses in its orbit. At any giv en observation epoch, the measured carrier phase consists of two key components: a fractional phase that can be directly observed, and an unknown integer number of full carrier cycles that hav e elapsed along the signal propagation path. This unknown integer offset, commonly referred to as the integer ambiguity , is constant over time as long as phase continuity is preserved. At an initial observation epoch, only the fractional part of the carrier phase is measur- able, while the integer ambiguity remains unknown. As the satellite moves along its orbit and subsequent observations are made, the total carrier phase accumulates full carrier cycles ev olved and a new fractional phase at each epoch. By jointly processing carrier-phase measurements across multiple epochs, it becomes possible to resolve the integer ambiguity , i.e., achie ve highly accurate range estimation, which in turn enables cm-le vel positioning accuracy . In practice, delay- or code-phase measurements, even when relati vely coarse com- pared to carrier-phase measurements, play a critical role in accelerating integer ambiguity resolution. By providing an initial range estimate, delay-based measurements significantly reduce the feasible integer ambiguity search space, enabling much faster and more reliable ambiguity resolution than would be possible using carrier-phase measurements alone. W e discuss the complementary use of delay and carrier-phase measurements in detail in the next section. Howe ver , carrier-phase tracking poses sev eral fundamental challenges, particularly in LEO-NTN systems. First, maintain- ing phase continuity without c ycle slips is inherently dif ficult. Carrier-phase tracking is highly sensiti ve to impairments such as noise, oscillator instability , and multipath propagation. Sudden changes in the receiv ed signal or an insufficient signal- to-noise ratio (SNR) can cause the tracking loop to lose lock, leading to cycle slips that reset the integer ambiguity and in validate pre viously accumulated phase information. Once a cycle slip occurs, the carrier -phase history must be reinitial- ized, significantly degrading positioning performance. Second, 3 the accuracy of the frequency estimate is critical, especially for maintaining phase continuity without cycle slips. Any residual frequency error leads to rapid phase drift, which can cause the predicted carrier phase to deviate significantly from the true phase over short time intervals. In high-mobility LEO scenarios, even modest frequency estimation errors can result in large phase uncertainties within tens of ms, making it infeasible to bridge gaps between intermittent measurements without continuous tracking. For instance, if the PRS trans- mission periodicity is 40ms, the frequency error between any two consecutiv e PRS occasions, including Doppler variation, should not exceed 25 Hz in order not to lose an y cycles in carrier phase estimation. Third, resolving the inte ger ambiguity to achieve cm-lev el positioning accuracy requires consistent multi-epoch phase observations with reliable continuity . If the phase ev olution between observation epochs is not accurately known, the ambiguity search space grows rapidly , making integer ambiguity resolution unreliable or ev en infeasible. This issue is exacerbated in LEO-NTN systems, where rapid satellite motion induces large Doppler shifts and Doppler rates, causing the carrier phase to ev olve by thousands of cycles ov er short time intervals. These challenges become particularly se vere in NR-NTN, where PRS is typically transmitted intermittently with config- urable periodicity and muting patterns to limit ov erhead and enable multiplexing with communication services. Wideband PRS transmissions are typically le veraged to obtain high- resolution code-phase measurements. While wideband PRS is well-suited for estimating signal delay and pro viding absolute timing references, its intermittent nature prevents continuous observation of carrier-phase ev olution. As a result, the phase change between consecutive PRS occasions becomes unob- servable, leading to severe integer ambiguity growth and a high likelihood of cycle slips. T o address these limitations in LEO-based NR-NTN sys- tems, we propose a dual-wav eform design that combines wideband PRS with a continuous narrowband carrier wav e- form as illustrated in Fig. 2. While PRS transmissions are intermittent wideband b ursts, the narro wband carrier waveform is continuous and spans the entire interval between consecutiv e PRS occasions. The fundamental motiv ation behind this design is to decouple the roles of code-phase (delay) estimation and carrier-phase tracking, which hav e fundamentally different wa veform and transmission requirements. In this approach, while wideband PRS transmissions provide accurate delay estimates, a continuous narrowband carrier wa veform allows the receiver to continuously estimate and track the carrier phase and Doppler frequency , and, in high-dynamic LEO scenarios, the Doppler rate as well. At each PRS occasion, wideband PRS measurements pro- vide an absolute timing reference that is used to re-initialize the tracking states. Between PRS transmissions, the narro w- band carrier enables continuous phase and frequency tracking via phase-locked loop (PLL) and/or frequency-locked loop (FLL) or Kalman-filter-based architectures, enabling reliable phase propagation across PRS gaps. This continuous tracking is essential for maintaining phase continuity , prev enting cy- cle slips, and enabling multi-epoch carrier-phase positioning. Fig. 2: Dual wav eform. When the next PRS burst arrives, the predicted carrier phase can be v alidated and corrected using the ne wly acquired timing reference. This joint operation enables rob ust phase continuity across epochs and facilitates reliable integer ambiguity reso- lution. Importantly , the narrowband carrier wav eform does not require a lar ge bandwidth; as little as one physical resource block (PRB) is sufficient. For example, with a subcarrier spac- ing (SCS) of 15 kHz, one PRB occupies only 180 kHz. Despite its narrow bandwidth, such a wav eform provides an adequate SNR and processing gain through coherent integration ov er time, enabling accurate carrier-phase and Doppler estimation ev en under high LEO dynamics. From a practical NR-NTN perspectiv e, the narrowband carrier wav eform can be flexibly accommodated within the system bandwidth. In particular, it can be placed within av ailable guard bands or at the edge of an allocated carrier, resulting in negligible to no impact on communication throughput. This makes the proposed dual- wa veform design highly compatible with existing NR-NTN resource allocation and scheduling mechanisms, while incur- ring minimal overhead. In the context of a comparative analysis of GNSS- and LEO-based carrier-phase positioning, we first inv estigate how satellite motion impacts carrier-phase ev olution and assess the accuracy of Doppler -based phase approximation relativ e to the true carrier phase. A Doppler-based approximation typically models the carrier phase as a linear function of the estimated Doppler , whereas the true carrier phase e volution is generally nonlinear due to time-v arying Doppler, particularly for LEO satellites. For this analysis, we consider a representative LEO satellite orbiting at 600 km and a GNSS satellite at around 20,200 km, both initially positioned at nadir , corresponding to a 90 ◦ elev ation angle at the UE. LEO satellites orbit at velocities on the order of 7.5 km/s, while GNSS satellites orbit at approximately 3.9 km/s. The higher orbital velocity of LEO satellites results in significantly larger Doppler shifts and, more importantly , substantially higher Doppler rates as the satellite tra verses its orbit. In particular , at 90 ◦ elev ation angle, the Doppler v ariation reaches its maximum: the Doppler rate is approximately 600 Hz/s for the LEO satellite at a 2 GHz carrier frequency , whereas it is approximately 3.9 Hz/s for the GNSS satellite operating at 1575.42 MHz (GPS L1). Fig. 3a presents the temporal e volution of the true carrier phase and its Doppler-based approximation ov er the observa- tion windo w for both GNSS and LEO satellites. This analysis is conducted over a 30 ms observation windo w , with Doppler estimates updated ev ery 10 ms. As anticipated, the carrier phase ev olves much more rapidly in the LEO case due to the significantly higher orbital velocity than GNSS satellites. 4 (a) Phase evolution. (b) Phase error . Fig. 3: Carrier Phase evolution and err or: GNSS vs. LEO: a) True phase and Doppler approximation over time (G - GNSS, L - LEO, TP - True Phase, and D A - Doppler Approximation); b) error (dif ference between TP and D A) due to Doppler approximation ov er time. Although the ov erall phase e volution trend appears similar for both systems, the absolute phase deviation between the true carrier phase and the Doppler approximation is noticeably larger for LEO satellites. This indicates that the Doppler- based linear approximation is considerably more accurate for GNSS than for LEO, owing to slo wer Doppler variations in GNSS. T o further quantify this ef fect, Fig. 3b depicts the phase approximation error , defined as the difference between the true carrier phase and the Doppler-approximated phase, for both GNSS and LEO systems. The phase approximation error is substantially higher in the LEO case than in GNSS due to higher Doppler variations. Importantly , while this increased Doppler variation caused by faster satellite motion leads to larger phase approximation errors in LEOs, the same can be lev eraged to achie ve quicker con vergence, higher temporal div ersity in carrier phase acquisition, thereby achie ving higher positioning accuracy compared to GNSS, which we discuss in detail in Section III. Notably , ev en with linear models, the range of phase approximation errors decreases as the satellite mov es away from nadir and the Doppler variation decreases. Furthermore, the phase approximation errors in LEO systems can be reduced by employing more accurate nonlinear phase models that incorporate Doppler rate and higher -order motion terms. I I I . C O N V E R G E N C E A N A L Y S I S A N D P O S I T I O N I N G P E R F O R M A N C E In this section, we present a comprehensiv e con ver gence analysis and positioning performance comparison of GNSS and LEO satellite-based positioning. The con ver gence analysis is done in two stages to systematically highlight the funda- mental differences in con vergence behavior between the two systems. First, we examine the conditioning of the phase- ev olution transformation matrix for GNSS and LEO satellites when carrier -phase measurements are jointly processed across multiple epochs, thereby assessing satellite motion and geo- metric div ersity as satellites traverse different orbits. Second, we analyze the con ver gence behavior of integer ambiguity resolution when joint delay-and-carrier-phase measurements are employed, emphasizing the impact of satellite dynamics on ambiguity conv ergence. Follo wing the con ver gence anal- ysis, we ev aluate the resulting positioning performance un- der delay-only and joint delay-and-carrier -phase measurement framew orks, demonstrating the performance gains achiev ed by incorporating carrier-phase measurements alongside delay measurements. This final stage explicitly demonstrates how the conv ergence of integer ambiguity resolution results in improv ed positioning accuracy and faster con vergence in LEO satellites compared to GNSS. It is important to note that, for ev aluation purposes, we assume repurposing communication- focused LEO constellations for positioning, consistent with the NR-NTN context considered in this work. While there are sev eral challenges in adapting communication-centric LEO constellations for high-accuracy positioning, a detailed dis- cussion of these issues is beyond the scope of this paper . Interested readers are referred to [2] for a comprehensive discussion of these challenges. Carrier-phase positioning can be implemented using se veral well-established frameworks, including con ventional static po- sitioning, semi-kinematic positioning, and real-time kinematic (R TK) positioning [4]. In this work, we adopt the con ven- tional static positioning framework for ev aluation purposes. Under this framew ork, we assume a stationary reference receiv er with its location perfectly known and select one satellite as the reference satellite (typically the one with the strongest SNR), similar to delay-based time-dif ference-of- arriv al (TDO A) positioning. Carrier-phase measurements are then double-differenced across both satellites and receivers, where dif ferences are taken with respect to both the reference satellite and the reference receiver . Differencing with respect to the reference satellite suppresses UE clock drift, while differencing with respect to the reference receiver ef fectiv ely eliminates satellite clock drift and reduces atmospheric errors. The unknown parameter v ector to be estimated consists of the relativ e coordinates of the UE with respect to the reference receiv er , along with the corresponding carrier-phase integer ambiguities. Carrier -phase integer ambiguities typically do not hav e a time index and are constant throughout the observ ation window as long as phase continuity is maintained, and no cycle slips occur . A cycle slip causes an abrupt jump in the ambiguity by an integer multiple of the carrier wa velength and can be reliably detected using standard hypothesis-testing techniques [4], [11]. Upon detection, cycle slips can be han- dled either by adapting the ambiguity parameters to preserve temporal consistency or by discarding the carrier-phase mea- surements collected prior to the cycle slip and reinitializing the measurement process. Note that the double-differenced carrier- phase measurements ov er multiple epochs can be expressed as a linear function of the unknown parameter vector through a phase transformation matrix. By jointly processing the double- differenced measurements across multiple observ ation epochs, both the relati ve position and the integer ambiguities can be estimated. Finally , an estimate of the UE location can be obtained by combining the estimated relati ve coordinates with the known location of the reference recei ver [4]. It is worth noting that, while we adopt the static positioning framework for our ev aluation, the choice of framew ork does not affect 5 Fig. 4: Condition Number Analysis: GNSS vs. LEO : Conditioning of phase e volution transformation matrix ov er measurement time. the key insights and conclusions presented in this work. A. Conditioning of Phase Evolution T ransformation Matrix Before analyzing the conditioning of the phase-evolution transformation matrix, we first describe the ev aluation setup. For the LEO case, we consider a typical communication- focused constellation with orbits at 600 km altitude and an inclination of 70 ◦ , comprising 30 orbits with 28 satellites per orbital plane, for a total of 840 satellites. These parameters are chosen to reflect realistic LEO constellation designs that ensure global coverage and adequate satellite visibility [12]. For the GNSS case, satellite positions are generated using the MA TLAB built-in GNSS toolbox, which computes satellite positions and velocities for MEO constellations based on the orbital parameters specified in the IS-GPS-200M interface control document [13]. The GNSS satellites are modeled at an inclination of 55 ◦ . In both cases, the UE is assumed to be located at latitude 0 and longitude 0. A satellite is considered visible if the elev ation angle with respect to the UE exceeds 15 ◦ . Observation epoch is assumed to be 10ms. At each observation epoch, the set of visible satellites is identified, and the corresponding carrier-phase measurements at the UE are collected to construct the phase-ev olution transformation matrix for that epoch. Carrier-phase measurements are then accumulated over multiple epochs and jointly processed to form a unified phase transformation matrix that captures the temporal evolution of the carrier phase. The conditioning of the resulting phase transformation matrix is ev aluated as the number of observ ation epochs increases. Notably , the set of visible satellites ev olves across epochs, particularly in the LEO case, due to the significantly faster satellite motion and frequent changes in satellite geometry . Fig. 4 presents the conditioning behavior of the phase- ev olution transformation matrix for GNSS and LEO satellite constellations by plotting the condition number as a function of the measurement duration. The condition number of a matrix is the ratio of the largest singular value to the smallest singular value. The lower the condition number , the better the rank and conditioning. In the context of carrier-phase positioning, the condition number reflects the combined ef fect of UE-to-satellite geometry and the temporal e volution of the carrier phase induced by satellite motion. As shown in Fig. 4, LEO constellations e xhibit significantly lo wer condition num- bers compared to GNSS, indicating substantially improv ed conditioning. More importantly , the condition number for LEOs con verges much faster than that for GNSS. Specifically , con ver gence is achie ved within approximately 200 seconds for LEO satellites, whereas the condition number for GNSS does not con ver ge even after 500 seconds of observ ation. Furthermore, it can be observed that, beyond a certain point in the observation windo w (approximately 120–130 seconds), the condition number for the LEO case be gins to e xhibit mild rippling behavior . This behavior arises from changes in the set of visible LEO satellites due to their low orbital altitude and high orbital velocity . As satellites enter and e xit visibility , the UE begins acquiring carrier-phase measurements from newly visible satellites, thereby increasing the total number of integer ambiguities to be resolved. Howe ver , since the UE position has already con ver ged to a relati vely accurate estimate by this stage, the ne wly introduced ambiguities can be resolved rapidly , and the ov erall conditioning remains fav orable. In contrast, the set of visible GNSS satellites remains largely unchanged ov er sev eral minutes due to their much higher orbital altitude and slower orbital motion. Consequently , the number of integer ambiguities remains fix ed ov er the obser- vation window , and the conditioning impro ves only gradually , as temporal div ersity increases at a significantly slower rate than in the LEO case. It is worth noting that both the absolute values of the condition numbers and the associated con vergence times are relativ ely large in this analysis. This behavior arises because conditioning is ev aluated under a carrier-phase-only position- ing framework, in which integer ambiguity resolution relies solely on the temporal ev olution of carrier-phase measure- ments. In such cases, ambiguity resolution typically requires sev eral minutes of observation. As noted in Section II, in practical positioning systems, delay- or code-phase measure- ments are jointly exploited with carrier-phase measurements to provide coarse range information and significantly reduce the integer ambiguity search space. In the subsequent analysis, we demonstrate that by incorporating delay measurements alongside carrier -phase measurements and capitalizing on the faster satellite motion, LEO-based positioning systems can achiev e ambiguity resolution and high-accuracy positioning (sub-m) within a few seconds. B. Integ er Ambiguity Resolution Next, we ev aluate the performance of integer ambiguity resolution by comparing GNSS- and LEO-based satellite po- sitioning systems. T o enable rapid con ver gence, we consider delay measurements alongside carrier-phase measurements for this e valuation. The total measurement time is set to 3 seconds, with individual observ ation epochs spaced at 10 ms intervals. The primary objectiv e of this study is to demonstrate how faster satellite motion in LEOs enables quicker con ver gence in carrier-phase positioning, especially when coupled with coarse delay measurements, and to assess the ability of LEO- 6 Fig. 5: Inte ger Ambiguity Resolution: GNSS vs. LEO : Integer ambi- guity resolution over measurement time. based positioning to achiev e cm-level accuracy . Accordingly , a detailed in vestigation of algorithms for measuring and tracking carrier-phase and the corresponding implementation- specific intricacies is not the main focus of this paper . T o this end, we use an error-modeling-based simulation framew ork. Specifically , both delay and carrier-phase measurement errors are modeled using v ariances deriv ed from the Cram ´ er-Rao lower bound (CRLB). For the LEO case, Equiv alent Isotropic Radiated Po wer (EIRP) density is configured to 34 dBW/MHz. The system operates in S-band at a 2 GHz carrier frequency (n256), with a 1 MHz bandwidth and a 15 kHz subcarrier spacing (SCS), consistent with NR-NTN specifications and validation methodologies [14]. For the GNSS case, we con- sider an operating frequency of 1575.42 MHz, GPS L1 coarse acquisition (C/A) or ci vilian code transmitted at 1.023 Mbps, and link budget numbers as gi ven in [3]. Additionally , for our demonstration purposes, we assume a maximum of 4 visible satellites, specifically , those with the highest elev ation angles, for positioning. This is particularly relev ant for LEO constella- tions, which are primarily designed for communication rather than dedicated positioning. Fig. 5 depicts the inte ger ambiguity resolution performance as a function of measurement time for GNSS and LEO- based satellite positioning systems. Gi ven that four satellites are considered and carrier-phase measurements are double- differenced, a total of three integer ambiguities must be resolved in both scenarios. As shown in the figure, joint exploitation of delay and carrier-phase measurements enables significantly faster ambiguity resolution in LEO constellations than in GNSS. In particular, for the LEO case, all integer ambiguities are resolved within 500 ms to 1 second, whereas for GNSS, ambiguity resolution is not achiev ed ev en with an observation window of 3 seconds. This is a significant result, as it clearly shows that faster satellite motion in LEOs provides greater temporal di versity in carrier-phase measure- ment acquisition and enables quicker con vergence than GNSS. Additionally , the zoomed-in view in Fig. 5 further reveals that, for the LEO case, all integer ambiguity errors con ver ge to zero within a 3-second observation window , indicating successful and stable ambiguity resolution. In contrast, for GNSS, the ambiguity errors remain on the order of tens of (a) Delay-only positioning. (b) Joint delay-and-carrier-phase positioning. Fig. 6: P ositioning performance: Positioning performance comparison between LEO and GNSS considering delay-only and joint-delay-and- carrier-phase measurements. carrier cycles over the same observation interval. The differ - ences in ambiguity-conv ergence behavior between GNSS and LEO systems directly translate into differences in positioning accuracy and con ver gence time, which we discuss next. C. P ositioning P erformance: Joint Delay-and-Carrier-Phase Finally , we ev aluate the positioning performance of GNSS- and LEO-based positioning systems. For this assessment, we reuse the same ev aluation setup employed in the integer ambi- guity resolution analysis. T wo positioning scenarios are con- sidered: 1) positioning using delay-only measurements and 2) positioning using joint delay-and-carrier-phase measurements. In both scenarios, measurements collected across multiple observation epochs are jointly processed to estimate the UE location. Recursive weighted least squares (R WLS) [15] is adopted as the positioning engine to enable efficient joint processing of delay and carrier-phase measurements acquired ov er multiple time epochs. Fig. 6a presents the horizontal and vertical positioning errors obtained using delay-only measurements, while Fig. 6b illustrates the corresponding positioning performance achieved using joint delay-and-carrier-phase measurements for both LEO and GNSS constellations. As observed, GNSS performs 7 better than LEO in the delay-only case, primarily because of its fav orable satellite geometry , which is particularly op- timized for dedicated positioning services. Howe ver , neither system achiev es cm-level accuracy when relying solely on delay measurements. It is important to note that this analysis considers a single PRS transmission for delay estimation. In our prior work [2], we demonstrated that LEO-based positioning can achiev e sub-10m accuracy using multi-symbol PRS transmissions, with best-case performance approaching the meter-le vel using delay-only measurements. In contrast, Fig. 6b demonstrates that by jointly exploiting delay and carrier-phase measurements, LEO-based positioning systems can achieve cm-lev el accuracy within a 500-ms observation window . This rapid conv ergence is consistent with the integer ambiguity resolution beha vior shown in Fig. 5. Although GNSS positioning performance also improves when carrier- phase measurements are incorporated alongside delay mea- surements, ambiguity errors remain on the order of 10s of carrier cycles e ven after a 3-second observation windo w . These residual ambiguity errors result in range estimation errors on the order of meters, thereby limiting the achiev able positioning accuracy . In addition to con ver gence analysis, these results further v alidate that the faster satellite motion inherent to LEOs not only enables quicker conv ergence but also helps achiev e cm-lev el accuracy within a short observation window by providing higher temporal di versity in carrier -phase acquisition than GNSS. I V . R E S E A R C H L A N D S C A P E A N D O P E N P RO B L E M S While the results presented in this paper are encouraging, sev eral fundamental research challenges and system-level as- pects must be addressed before carrier-phase-enabled LEO positioning can be realized in practical NR-NTN deployments. Phase Coher ence and P ayload Constraints. A cen- tral assumption in carrier-phase positioning is sufficient phase stability and coherence of the transmitted wav eform. Communication-focused LEO constellations are not designed to meet GNSS-grade phase stability requirements, and oscil- lator impairments, payload switching, and beam hopping may introduce phase discontinuities. Future work must quantify the allow able phase noise and coherence requirements and in vestigate mitigation techniques. Cycle Slip Detection and Recovery . Although this work assumed reliable phase continuity within the observ ation win- dow , c ycle slips remain a critical challenge in high-Doppler LEO environments, particularly under low SNR or multipath conditions. Adv anced cycle-slip detection and ambiguity adap- tation strategies are essential for reliable ambiguity resolution. Inte ger Ambiguity Resolution. Although rapid satellite mo- tion in LEOs accelerates ambiguity conv ergence, reliable integer ambiguity resolution remains challenging due to in- termittent PRS transmissions and high Doppler rates. Future work should focus on robust ambiguity fixing and validation methods that exploit joint delay-and-carrier -phase information under realistic NR-NTN constraints. Extension to Kinematic and Network-Based P ositioning. This study focused on a con ventional static positioning frame- work to isolate con ver gence beha vior . Extending carrier -phase positioning to kinematic users, UE-assisted/network-based ar- chitectures, and multi-UE cooperative scenarios remains an open problem. Multi-LEO and Hybrid GNSS–LEO Carrier-Phase Fu- sion. While this work considered repurposed communication- focused constellations, future systems are likely to in volve multi-LEO cooperation and hybrid GNSS–LEO carrier-phase fusion, particularly in challenging en vironments with partial visibility . Designing ambiguity-consistent fusion frameworks across heterogeneous constellations and orbital regimes is a promising yet nontrivial research direction. Standar dization and NR-NTN Inte gration. From a stan- dards perspectiv e, enabling carrier-phase positioning raises important questions regarding PRS design, signaling support, wa veform multiplexing, and recei ver requirements in NR- NTN. Future releases of 3GPP will need to carefully balance positioning accuracy , overhead, and backward compatibility . The dual-wa veform concept introduced in this work provides a potential starting point, but its standardization implications require further inv estigation. R E F E R E N C E S [1] H. K. Dureppagari, C. Saha, H. S. Dhillon, and R. M. Buehrer , “NTN- Based 6G Localization: V ision, Role of LEOs, and Open Problems, ” IEEE W ir el. Commun. , vol. 30, no. 6, pp. 44–51, 2023. [2] H. K. Dureppagari, C. Saha, H. Krishnamurthy , X. W ang, A. Rico- Alvari ˜ no, R. M. Buehrer, and H. S. Dhillon, “LEO-Based Positioning: Foundations, Signal Design, and Receiver Enhancements for 6G NTN, ” IEEE Commun. Mag. , vol. 63, no. 11, pp. 130–137, 2025. [3] E. D. Kaplan and C. J. Hegarty , Understanding GPS Principles and Applications, Second Edition . Artech, 2005. [4] P . J. T eunissen, O. Montenbruck et al. , Springer Handbook of Global Navigation Satellite Systems . Springer , 2017, vol. 10. [5] J. Khalife, M. Neinav aie, and Z. M. Kassas, “The First Carrier Phase T racking and Positioning Results W ith Starlink LEO Satellite Signals, ” IEEE T rans. Aer osp. Electr on. Syst. , v ol. 58, no. 2, pp. 1487–1491, 2022. [6] S. K ozhaya, J. Saroufim, and Z. Z. M. Kassas, “Un veiling Starlink for PNT, ” J . Navig. , v ol. 72, no. 1, 2025. [7] J. Khalife, M. Neinav aie, and Z. M. Kassas, “Na vigation with dif ferential carrier phase measurements from megaconstellation leo satellites, ” in IEEE/ION PLANS , 2020, pp. 1393–1404. [8] S. Y ang, A. Khodabandeh, S. Zaminpardaz, and P . T eunissen, “ Ambiguity-resolved short-baseline positioning performance of leo frequency-v arying carrier phase signals: a feasibility study , ” J. Geod. , vol. 99, no. 2, p. 17, 2025. [9] A. Khodabandeh and P . T eunissen, “ Ambiguity-fixing in frequency- varying carrier phase measurements: Global navig ation satellite system and terrestrial examples, ” J. Navig. , vol. 70, no. 2, 2023. [10] A. F ouda, R. K eating, and H.-S. Cha, “T o ward cm-Level Accuracy: Carrier Phase Positioning for IIoT in 5G-Advanced NR Networks, ” in IEEE PIMRC , 2022, pp. 782–787. [11] P . T eunissen, “GPS double difference statistics: with and without using satellite geometry, ” J . Geod. , vol. 71, no. 3, pp. 137–148, 1997. [12] F . S. Prol et al. , “Position, Navigation, and Timing (PNT) Through Low Earth Orbit (LEO) Satellites: A Survey on Current Status, Challenges, and Opportunities, ” IEEE Access , vol. 10, pp. 83 971–84 002, 2022. [13] GPS Directorate, “Navstar GPS Space Segment/Na vigation User Inter - faces, ” IS-GPS-200M, U.S. Space Force, W ashington, DC, USA, May 2023. [14] “T echnical Specification Group Radio Access Network; Solutions for NR to support non-terrestrial netw orks (NTN) (Release 16), ” 3GPP TR 38.821, version 16.2.0 , 2023. [15] S. A. Zekav at and R. M. Buehrer, Handbook of P osition Location: Theory , Practice, and Advances , 2nd ed. IEEE Press and W iley , 2019.