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Ultra-wideband (UWB, ultra wideband, ultra-wide band and ultraband) is a radio technology that can use a very low energy level for short-range, high-bandwidth communications over a large portion of the radio spectrum.[1] UWB has traditional applications in non-cooperative radar imaging. Most recent applications target sensor data collection, precise locating,[2] and tracking.[3][4] UWB support started to appear in high-end smartphones in 2019. For a detailed list of Ultra-wideband supported mobile devices, see List of UWB-enabled mobile devices.

Characteristics

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Ultra-wideband is a technology for transmitting information across a wide bandwidth (>500 MHz). This allows for the transmission of a large amount of signal energy without interfering with conventional narrowband and carrier wave transmission in the same frequency band. Regulatory limits in many countries allow for this efficient use of radio bandwidth, and enable high-data-rate personal area network (PAN) wireless connectivity, longer-range low-data-rate applications, and the transparent co-existence of radar and imaging systems with existing communications systems.

Ultra-wideband was formerly known as pulse radio, but the FCC and the International Telecommunication Union Radiocommunication Sector (ITU-R) currently define UWB as an antenna transmission for which emitted signal bandwidth exceeds the lesser of 500 MHz or 20% of the arithmetic center frequency.[5] Thus, pulse-based systems—where each transmitted pulse occupies the UWB bandwidth (or an aggregate of at least 500 MHz of a narrow-band carrier; for example, orthogonal frequency-division multiplexing (OFDM))—can access the UWB spectrum under the rules.

Theory

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A significant difference between conventional radio transmissions and UWB is that conventional systems transmit information by varying the power level, frequency, or phase (or a combination of these) of a sinusoidal wave. UWB transmissions transmit information by generating radio energy at specific time intervals and occupying a large bandwidth, thus enabling pulse-position or time modulation. The information can also be modulated on UWB signals (pulses) by encoding the polarity of the pulse, its amplitude and/or by using orthogonal pulses. UWB pulses can be sent sporadically at relatively low pulse rates to support time or position modulation, but can also be sent at rates up to the inverse of the UWB pulse bandwidth. Pulse-UWB systems have been demonstrated at channel pulse rates in excess of 1.3 billion pulses per second using a continuous stream of UWB pulses (Continuous Pulse UWB or C-UWB), while supporting forward error-correction encoded data rates in excess of 675 Mbit/s.[6]

A UWB radio system can be used to determine the "time of flight" of the transmission at various frequencies. This helps overcome multipath propagation, since some of the frequencies have a line-of-sight trajectory, while other indirect paths have longer delays. With a cooperative symmetric two-way metering technique, distances can be measured to high resolution and accuracy.[7]

Applications

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Real-time location

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Ultra-wideband (UWB) technology is utilised for real-time locationing due to its precision and reliability. It plays a role in various industries such as logistics, healthcare, manufacturing, and transportation. UWB's centimeter-level accuracy is valuable in applications in which using traditional methods may be unsuitable, such as in indoor environments, where GPS precision may be hindered. Its low power consumption ensures minimal interference and allows for coexistence with existing infrastructure. UWB performs well in challenging environments with its immunity to multipath interference, providing consistent and accurate positioning. In logistics, UWB increases inventory tracking efficiency, reducing losses and optimizing operations. Healthcare makes use of UWB in asset tracking, patient flow optimization, and in improving care coordination. In manufacturing, UWB is used for streamlining inventory management and enhancing production efficiency through accurate tracking of materials and tools. UWB supports route planning, fleet management, and vehicle security in transportation systems.[8]

UWB uses multiple techniques for location detection:[9]

  • Time of flight (ToF)
  • Time difference of arrival (TDoA)
  • Two-way ranging (TWR)

Mobile devices with UWB capability

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Apple launched the first three phones with ultra-wideband capabilities in September 2019, namely, the iPhone 11, iPhone 11 Pro, and iPhone 11 Pro Max.[10][11][12] Apple also launched Series 6 of Apple Watch in September 2020, which features UWB,[13] and their AirTags featuring this technology were revealed at a press event on April 20, 2021.[14][4] The Samsung Galaxy Note 20 Ultra, Galaxy S21+, and Galaxy S21 Ultra also began supporting UWB,[15] along with the Samsung Galaxy SmartTag+.[16] The Xiaomi MIX 4 released in August 2021 supports UWB, and offers the capability of connecting to select AIoT devices.[17]

The FiRa Consortium was founded in August 2019 to develop interoperable UWB ecosystems including mobile phones. Samsung, Xiaomi, and Oppo are currently members of the FiRa Consortium.[18] In November 2020, Android Open Source Project received first patches related to an upcoming UWB API; "feature-complete" UWB support (exclusively for the sole use case of ranging between supported devices) was released in version 13 of Android.[19]

Industrial applications

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  • Automation and robotics: Its high data rate and low latency enable real-time communication and control between machines and systems. UWB-based communication protocols ensure reliable and secure data transmission, enabling precise coordination and synchronization of automated processes. This enhances manufacturing efficiency, reduces errors, and improves overall productivity. UWB can also be integrated into robotic systems to enable precise localization, object detection, and collision avoidance, further enhancing the safety and efficiency of industrial automation.[20]
  • Worker safety and proximity sensing: Worker safety is a concern in industrial settings. UWB technology provides effective proximity sensing and worker safety solutions. By equipping workers with UWB-enabled devices or badges, companies can monitor their location and movement in real-time. UWB-based systems can detect potential collisions between workers and machinery, issuing timely warnings to prevent accidents. Moreover, UWB technology allows for the creation of safety zones and controlled access areas, ensuring the safe interaction of workers with hazardous equipment or restricted zones. This helps enhance workplace safety, reduce accidents, and protect employees from potential hazards.[21]
  • Asset tracking and management: Efficient asset tracking and management are crucial for industrial operations. UWB enables precise and real-time tracking of assets within industrial facilities. By attaching UWB tags to equipment, tools, and inventory, companies can monitor their location, movement, and utilization. This enhances inventory management, reduces asset loss, minimizes downtime, and streamlines maintenance processes. UWB-based asset tracking systems provide accurate and reliable data, empowering businesses to optimize their resource allocation and improve overall operational efficiency.[22]

Radar

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Ultra-wideband gained widespread attention for its implementation in synthetic aperture radar (SAR) technology. Due to its high resolution capacities using lower frequencies, UWB SAR was heavily researched for its object-penetration ability.[23][24][25] Starting in the early 1990s, the U.S. Army Research Laboratory (ARL) developed various stationary and mobile ground-, foliage-, and wall-penetrating radar platforms that served to detect and identify buried IEDs and hidden adversaries at a safe distance. Examples include the railSAR, the boomSAR, the SIRE radar, and the SAFIRE radar.[26][27] ARL has also investigated the feasibility of whether UWB radar technology can incorporate Doppler processing to estimate the velocity of a moving target when the platform is stationary.[28] While a 2013 report highlighted the issue with the use of UWB waveforms due to target range migration during the integration interval, more recent studies have suggested that UWB waveforms can demonstrate better performance compared to conventional Doppler processing as long as a correct matched filter is used.[29]

Ultra-wideband pulse Doppler radars have also been used to monitor vital signs of the human body, such as heart rate and respiration signals as well as human gait analysis and fall detection. It serves as a potential alternative to continuous-wave radar systems since it involves less power consumption and a high-resolution range profile. However, its low signal-to-noise ratio has made it vulnerable to errors.[30][31]

Ultra-wideband is also used in "see-through-the-wall" precision radar-imaging technology,[32][33][34] precision locating and tracking (using distance measurements between radios), and precision time-of-arrival-based localization approaches.[35] UWB radar has been proposed as the active sensor component in an Automatic Target Recognition application, designed to detect humans or objects that have fallen onto subway tracks.[36]

Data transfer

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Ultra-wideband characteristics are well-suited to short-range applications, such as PC peripherals, wireless monitors, camcorders, wireless printing, and file transfers to portable media players.[37] UWB was proposed for use in personal area networks, and appeared in the IEEE 802.15.3a draft PAN standard. However, after several years of deadlock, the IEEE 802.15.3a task group[38] was dissolved[39] in 2006. The work was completed by the WiMedia Alliance and the USB Implementer Forum. Slow progress in UWB standards development, the cost of initial implementation, and performance significantly lower than initially expected are several reasons for the limited use of UWB in consumer products (which caused several UWB vendors to cease operations in 2008 and 2009).[40]

Autonomous vehicles

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UWB's precise positioning and ranging capabilities enable collision avoidance and centimeter-level localization accuracy, surpassing traditional GPS systems. Moreover, its high data rate and low latency facilitate seamless vehicle-to-vehicle communication, promoting real-time information exchange and coordinated actions. UWB also enables effective vehicle-to-infrastructure communication, integrating with infrastructure elements for optimized behavior based on precise timing and synchronized data. Additionally, UWB's versatility supports innovative applications such as high-resolution radar imaging for advanced driver assistance systems, secure key less entry via biometrics or device pairing, and occupant monitoring systems, potentially enhancing convenience, security, and passenger safety.[41]

UWB products/chips

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Supplier Product name Standard Band Announced Commercial products
Microchip Technology ATA8350 LRP 6.2–7.8 GHz Feb 2021
Microchip Technology ATA8352 LRP 6.2–8.3 GHz Feb 2021
NXP NCJ29D5 HRP [42] 6–8.5 GHz[43] Nov 12, 2019
NXP SR100T HRP 6–9 GHz[44] Sept 17, 2019 Samsung Galaxy Note20 Ultra[45]
Apple Inc. U1 HRP[46] 6–8.5 GHz[47] Sept 11, 2019 iPhone 11, iPhone 12, iPhone 13, and iPhone 14,[48] Apple Watch Series 6, Apple Watch Series 7, Apple Watch Series 8, and Apple Watch Ultra, HomePod Mini and HomePod (2nd generation), AirTag, and AirPods Pro (2nd generation)
Apple Inc. U2 HRP 6–8.5 GHz Sept 12, 2023 iPhone 15, and iPhone 16, Apple Watch Series 9, Apple Watch Ultra 2, and Apple Watch Series 10
Qorvo DW1000 HRP 3.5–6.5 GHz[49] Nov 7, 2013
Qorvo DW3000 HRP 6–8.5 GHz[50] Jan 2019[51]
3dB Access 3DB6830 LRP 6–8 GHz[52]
Ceva RivieraWaves UWB HRP 3.1–10.6 GHz depending on radio Jun 24, 2021[53]
SPARK Microsystems SR1010/SR1020 N/A[54] 3.1–6 GHz, 6-9.25 GHz[55] Mar 18, 2020[56]
Samsung Electronics Exynos Connect U100 Unknown 6489.6 MHz/ 8987.2 MHz Mar 21, 2023[57]

Regulation

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In the U.S., ultra-wideband refers to radio technology with a bandwidth exceeding the lesser of 500 MHz or 20% of the arithmetic center frequency, according to the U.S. Federal Communications Commission (FCC). A February 14, 2002 FCC Report and Order[58] authorized the unlicensed use of UWB in the frequency range from 3.1 to 10.6 GHz. The FCC power spectral density (PSD) emission limit for UWB transmitters is −41.3 dBm/MHz. This limit also applies to unintentional emitters in the UWB band (the "Part 15" limit). However, the emission limit for UWB emitters may be significantly lower (as low as −75 dBm/MHz) in other segments of the spectrum.

Deliberations in the International Telecommunication Union Radiocommunication Sector (ITU-R) resulted in a Report and Recommendation on UWB[citation needed] in November 2005. UK regulator Ofcom announced a similar decision[59] on 9 August 2007.

There has been concern over interference between narrowband and UWB signals that share the same spectrum. Earlier, the only radio technology that used pulses was spark-gap transmitters, which international treaties banned because they interfere with medium-wave receivers. However, UWB uses much lower levels of power. The subject was extensively covered in the proceedings that led to the adoption of the FCC rules in the US, and in the meetings of the ITU-R leading to its Report and Recommendations on UWB technology. Commonly-used electrical appliances emit impulsive noise (for example, hair dryers), and proponents successfully argued that the noise floor would not be raised excessively by wider deployment of low power wideband transmitters.[60]

Coexistence with other standards

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In February 2002, the Federal Communications Commission (FCC) released an amendment (Part 15) that specifies the rules of UWB transmission and reception. According to this release, any signal with fractional bandwidth greater than 20% or having a bandwidth greater than 500 MHz is considered as an UWB signal. The FCC ruling also defines access to 7.5 GHz of unlicensed spectrum between 3.1 and 10.6 GHz that is made available for communication and measurement systems.[61]

Narrowband signals that exist in the UWB range, such as IEEE 802.11a transmissions, may exhibit high PSD levels compared to UWB signals as seen by a UWB receiver. As a result, one would expect a degradation of UWB bit error rate performance.[62]

Technology groups

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See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Ultra-wideband

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Ultra-wideband (UWB) is a radio technology that enables short-range, high-bandwidth communications and precise ranging by transmitting signals using very short-duration pulses across an extremely wide frequency spectrum, typically defined as a bandwidth exceeding 500 MHz or more than 20% of the center frequency. This approach results in low-power, low-complexity operation while providing robustness against multipath interference and the ability to penetrate obstacles such as walls. UWB systems are regulated to operate in unlicensed bands with stringent emission limits to minimize interference with narrowband services. In the United States, the (FCC) authorizes UWB devices in frequency bands including 3.1–10.6 GHz for communications, with power limits not exceeding -41.3 dBm/MHz indoors to ensure coexistence with other wireless systems. Globally, similar regulations apply, often aligning with FCC guidelines, enabling applications in diverse environments. UWB's defining advantages include centimeter-level accuracy in positioning, data rates up to several hundred Mbps over distances of 10–20 meters, and versatility for both communication and sensing tasks. Notable applications encompass indoor localization and tracking for and UAVs, through-wall imaging, in industrial settings, and secure keyless entry in automotive systems. Since the early 2000s, UWB has evolved from and uses to widespread consumer integration, with growing adoption in from major manufacturers; projections indicate that approximately 27% of global shipments will include UWB in 2025 for features like precise device finding and enhancements. Ongoing advancements focus on multi-user scalability, integration with / networks, and expanded applications for vital sign monitoring and .

Fundamentals

Definition and Overview

Ultra-wideband (UWB) is a short-range communication technology that transmits data using very low energy levels over a wide of frequencies, characterized by a bandwidth exceeding 500 MHz or a fractional bandwidth greater than 0.20, where fractional bandwidth is defined as BWfc>0.2\frac{BW}{f_c} > 0.2 with BWBW as the bandwidth and fcf_c as frequency. The U.S. (FCC) defines UWB signals as those with an effective isotropic radiated power (EIRP) limited to -41.3 dBm/MHz in the 3.1–10.6 GHz band to minimize interference with other services. This wide bandwidth enables UWB to operate like , allowing coexistence with systems without significant disruption. The core principles of UWB revolve around several primary transmission methods: impulse radio (IR-UWB), which uses short time-domain pulses for direct sequence spreading; multiband (MB-OFDM), which divides the into frequency-domain sub-bands and applies OFDM within each; and (DS-SS), which spreads the signal using pseudo-noise codes for enhanced robustness. These techniques leverage the ultra-wide to achieve high , supporting applications like precise tracking with centimeter-level accuracy. UWB offers operational advantages including data rates up to 1 Gbps, low power consumption suitable for battery-operated devices, and strong resistance to multipath interference due to its short durations that resolve signal reflections effectively. In contrast to technologies like , which provide ranges of 10–100 m but only meter-level positioning precision, UWB delivers sub-meter accuracy over shorter distances of 10–50 m, making it ideal for high-fidelity short-range scenarios.

Historical Development

The origins of ultra-wideband (UWB) technology trace back to the , when researchers began exploring short-pulse electromagnetics for applications. Gerald F. Ross demonstrated the feasibility of using UWB waveforms for and communications through his work on time-domain techniques at Sperry Research Center, publishing key findings on radiating elements in 1968. This laid foundational principles for impulse-based systems, enabling high-resolution imaging without traditional carrier frequencies. During the 1970s and 1980s, UWB saw significant military adoption, particularly in (GPR) for detecting buried objects and . Innovations like Rexford Morey's 1974 UWB GPR design at Geophysical Survey Systems Inc. marked early commercial viability in defense contexts, with systems achieving penetration depths of several meters in soil while maintaining sub-centimeter resolution. Commercial interest in UWB for communications emerged in the 1990s, driven by patents on impulse radio concepts. Time Domain Corporation secured a pivotal U.S. patent in 1994 (issued from a 1993 filing) for a time-domain transmission system using short pulses for low-power, high-precision wireless links, positioning impulse radio as a carrier-free alternative to narrowband technologies. Concurrently, the U.S. Department of Defense and DARPA's 1990 Ultra-Wideband Radar Review Panel assessed UWB's potential, investing approximately $25 million in research that extended its scope to secure communications by the late 1990s, emphasizing low-probability-of-intercept signals for military networks. Key contributors like Pulse~LINK, founded in 2000, advanced continuous-wave UWB architectures for high-data-rate applications, amassing over 300 patents and proposing interoperability modes like Common Signaling Mode in 2003 to bridge wired and wireless UWB systems. Regulatory advancements in the early unlocked civilian UWB deployment. The U.S. (FCC) issued its First Report and Order in 2002 (FCC 02-48), authorizing unlicensed UWB operations in the 3.1–10.6 GHz band under Part 15 rules, with power limits to minimize interference to existing services like GPS and ; this enabled indoor and hand-held devices while mandating detect-and-avoid mechanisms for some applications. In Europe, the European Telecommunications Standards Institute (ETSI) followed with harmonized standards in 2005, including EN 302 065, which defined emission masks and coexistence requirements for UWB devices across the 4.2–4.8 GHz and 6–9.3 GHz bands, facilitating market entry in the EU. The IEEE 802.15.4a task group ratified its standard in 2007, specifying low-rate UWB physical layers for wireless personal area networks (WPANs) with data rates up to 1 Mb/s and ranging accuracy better than 1 meter, boosting adoption in sensor networks. UWB's integration into consumer and industrial ecosystems accelerated in the late . Apple's introduction of the U1 chip in the series in 2019 marked a milestone, embedding FiRa-compliant UWB for precise spatial awareness features like Ultra Wideband-based and later Precision Finding for AirTags. The Consortium, formed in 2019, drove widespread rollout in the 2020s by standardizing ranging protocols for automotive secure access (e.g., digital keys) and IoT ecosystems, with over 150 members including automakers like and deploying UWB for relay-attack-resistant vehicle entry by 2022. Companies like Decawave, a leader in UWB ICs for location services, were acquired by in 2020 for approximately $400 million, enhancing supply chains for mobile and automotive chips with sub-10 cm accuracy. Subsequent advancements included the IEEE 802.15.4z standard in 2020, improving secure ranging for consumer applications, and rapid adoption in Android devices starting with the 6 and series in 2021; by the end of 2023, over 1.5 billion UWB-enabled devices had shipped, with UWB integrated in a growing share of premium smartphones by 2025.

Technical Characteristics

Theoretical Foundations

Ultra-wideband (UWB) systems operate by transmitting signals with extremely large bandwidths relative to their , typically achieved through the use of very short-duration on the order of nanoseconds. These can be , where the signal extends from near-zero up to several gigahertz, or carrier-based, modulating a with the short to shift the . In the , the signal consists of these impulsive waveforms, which inherently possess a wide content due to the inverse relationship between time duration and spread. The provides the frequency-domain representation, revealing how the energy of a short is distributed across a broad , enabling high-resolution processing in both domains. A fundamental relation in UWB signal theory is the approximate bandwidth B≈1τB \approx \frac{1}{\tau}, where τ\tau is the pulse duration, illustrating that shorter pulses yield wider bandwidths essential for UWB operation. This wide bandwidth directly translates to fine time-domain resolution, given by δt≈1B\delta t \approx \frac{1}{B}, which allows for precise measurements such as centimeter-level estimation using time-of-flight (ToF) techniques, where the propagation delay is resolved with high accuracy. In propagation environments, UWB signals exhibit low probability of intercept (LPI) characteristics owing to their spread-spectrum nature, where the transmitted power is distributed over a vast bandwidth, making detection by receivers difficult. Additionally, the power spectral density (PSD) of UWB signals is designed to operate below the ambient , minimizing interference to coexisting systems while still achieving reliable communication through advanced processing. Compared to systems, which concentrate power in a narrow leading to higher PSD and potential interference, UWB maintains low PSD levels across its wide band, thus preserving high effective throughput without exceeding regulatory power limits. UWB propagation in multipath-rich environments benefits from the short pulse duration, which resolves individual path arrivals separated by more than δt\delta t. To mitigate multipath and capture signal energy, rake receivers are employed, which consist of multiple fingers tuned to align and combine the delayed replicas of the signal paths, typically using maximal ratio combining to maximize the (SNR). This approach exploits the dense multipath structure in UWB channels, where numerous resolvable paths contribute constructively rather than destructively interfering as in systems. From an perspective, the Shannon capacity for UWB channels is given by C=Blog⁡2(1+SNR)C = B \log_2(1 + \mathrm{SNR}), highlighting how the enormous bandwidth BB dominates capacity even at low SNR, allowing robust performance in noisy environments by trading power for bandwidth rather than relying on high transmit power.

Spectrum and Modulation

Ultra-wideband (UWB) systems operate across designated spectrum allocations that vary by region to ensure coexistence with other wireless services. In the United States, the (FCC) permits indoor UWB operations in the 3.1–10.6 GHz band. Handheld UWB devices, which may operate indoors or outdoors without fixed infrastructure, use the same 3.1–10.6 GHz band with EIRP limits of -41.3 dBm/MHz in that range. In Europe, the European Telecommunications Standards Institute (ETSI) and CEPT allocate the 3.1–10.6 GHz band for indoor UWB communications, with harmonized standards emphasizing indoor use and specific emission controls. Globally, variations exist, such as Japan's allocation of bands including 7.25–10.25 GHz for indoor UWB applications under the Ministry of Internal Affairs and Communications (MIC) regulations. UWB signals are generated using distinct modulation techniques tailored to the technology's wide bandwidth. Impulse radio UWB (IR-UWB) employs short-duration pulses, often shaped as Gaussian monocycles or higher-order Hermite pulses, to achieve the required fractional bandwidth exceeding 20% or 500 MHz. Modern UWB implementations primarily follow the standards family, using IR-UWB with burst position modulation (BPM) and on-off keying (OOK) or (PSK) for low-power precise ranging and data rates up to 27 Mbps; the 802.15.4z amendment (2020) enhances security for applications like keyless entry, while 802.15.4ab (2025) supports extended ranges up to 100 m for sensing. In contrast, multiband (MB-OFDM) divides the UWB spectrum into multiple 528 MHz sub-bands, utilizing frequency hopping across these bands to mitigate interference and support scalable data rates, though it is now legacy following the WiMedia Alliance's dissolution. Encoding methods in UWB further adapt these modulations for efficient data transmission and multiple access. Common schemes include on-off keying (OOK), which transmits s for a '1' and omits them for a '0'; (PPM), which varies the timing within a symbol period; and binary (BPSK), which inverts the pulse polarity to represent bits. Direct-sequence UWB (DS-UWB) extends these by spreading the signal with pseudo-noise codes, enabling (CDMA) for concurrent users in shared spectrum. Power control is essential in UWB to adhere to regulatory emission masks and prevent interference. Devices operate in indoor or outdoor modes with effective isotropic radiated power (EIRP) limits, such as -41.3 dBm/MHz for indoor use in the FCC's primary band, alongside stricter peak power constraints for outdoor scenarios. Shaping filters, often root-raised cosine or Gaussian derivatives, are applied to waveforms to spectral shape the emissions, ensuring compliance with these masks while preserving . Implementation trade-offs between IR-UWB and MB-OFDM balance performance and complexity. IR-UWB offers simplicity and low cost through direct analog pulse generation, suiting low-power, short-range applications, whereas MB-OFDM achieves higher data rates—up to 480 Mbps as specified in the ECMA-368 standard—via digital OFDM processing, albeit at increased hardware demands.

Applications

Precise Location Tracking

Ultra-wideband (UWB) enables precise location tracking through time-based ranging techniques that exploit its wide bandwidth for high-resolution time-of-flight (ToF) measurements. The primary methods include two-way ranging (TWR), where a tag and anchor exchange signals to compute round-trip ToF and derive distance without requiring synchronized clocks; time-difference-of-arrival (TDoA), which uses synchronized anchors to measure signal arrival time differences at multiple points for hyperbolic positioning; and angle-of-arrival (AoA), employing antenna arrays to determine signal direction via phase differences across elements. These techniques achieve sub-10 cm accuracy in line-of-sight (LOS) conditions, as demonstrated in industrial evaluations showing mean errors of 10-11 cm. The theoretical ranging error follows the Cramér-Rao lower bound, approximated as σ=c2B2π\sigma = \frac{c}{2B \sqrt{2\pi}}
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