Analytical Modeling of Latency and Energy Trade-offs in FiRa-Like BLE-UWB Ranging and Localization Systems

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Analytical Modeling of Latency and Energy Trade-offs in FiRa-Like BLE-UWB Ranging and Localization Systems

arXiv:2610.33423v1 [cs.NI] 24 Oct 2026

Adelina Giurea, Jorg Wieme, Ben Van Herbruggen, Jeroen Hoebeke, Eli De Poorter

Abstract—Accurate position and distance information provided by Ultra-Wideband (UWB) can enhance a wide range of applications. However, its receive-mode power consumption makes continuous channel monitoring impractical for energyconstrained devices. Consequently, UWB systems often rely on Bluetooth Low Energy (BLE) to discover peers and establish sessions before ranging begins. Although both technologies have been studied in isolation, an framework capturing the latency and energy consumption of the complete workflow is still lacking. To address this gap, we develop a unified analytical model for BLE-assisted UWB systems, from device-to-device ranging to infrastructure-based localization. The model includes closedform expressions for discovery, parameter exchange, and ranging, and evaluates the resulting latency and energy consumption. Evaluation of three representative BLE configurations shows that the scanner consumes 28-57× more energy per discovery than the advertiser. In addition, the 99th-percentile discovery latency is 2-3.4× higher than the mean and reaches up to 110 s in the lowest-power configuration. The one-time BLE setup overhead is amortized after 24-562 ranging rounds, depending on the discovery configuration. Overall, the analysis demonstrates that the BLE discovery phase can dominate both the latency and the energy budget during short UWB interactions, making discovery configuration as important as the ranging scheme. Index Terms—BLE, Energy Consumption, FiRa, Latency, Localization, Ranging, UWB.

I. I NTRODUCTION PATIAL awareness capabilities are integrated in the majority of mobile consumer devices such as smartphones, smartwatches, and smart door locks. At the same time, automotive manufacturers are equipping their vehicles and keys with wireless ranging to mitigate relay attacks. In large industrial environments, thousands of items are simultaneously tracked wirelessly. All these applications share the same key principles: (secure) high accuracy ranging, optimized radio usage to scale to systems with a large number of tags and low power consumption to enable long lifetime on a single battery. Although these ranging capabilities are integrated into wellestablished standards, including Bluetooth Channel Sounding [1], Wi-Fi fine timing measurement [2], and 5G [3], their localization accuracy remains below that achievable with UltraWideband (UWB) impulse radio, which continues to be the preferred technology for high-accuracy positioning. Its large bandwidth (typically 500 MHz or more) enables resolving frame arrival times with picosecond-level precision, supporting

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The authors are with IDLab Research Group, Department of Information Technology, Ghent University–imec, 9052 Ghent, Belgium (e-mail: adelina.giurea@ugent.be).

centimeter-level ranging even in multipath environments [4]. Recent studies have further demonstrated millimeter-level accuracy by exploiting phase information [5], [6]. Besides high ranging accuracy, the IEEE 802.15.4z [7] amendment also introduced secure ranging through the addition of the Scrambled Timestamp Sequence (STS) to the UWB packet structure. While UWB excels at accurate ranging and sensing, it is less suited for continuous channel monitoring and low-power device discovery [8], as detecting sporadic transmissions requires a receiver to continuously sample a wide bandwidth and process high-rate signals. This incurs a significant energy cost, making always-on UWB channel monitoring and contentionbased UWB medium access impractical. To address this limitation, commercial battery-constrained UWB systems typically use Bluetooth Low Energy (BLE) as a companion radio to provide low-power device discovery. A BLE connection can then be used for authentication and the exchange of UWB session parameters before ranging starts. Similar principles are applied in smartphone operating systems (Android [9] and iOS [10]) and standardization efforts such as the FiRa specification [11]. In this work, we refer to systems following this approach as FiRa-like systems. The hybrid BLE-UWB architecture introduces a trade-off between session setup and ranging. Establishing a session requires a one-time energy and latency cost for BLE discovery and commissioning, while subsequent ranging rounds add an incremental cost. As a result, the setup overhead can dominate short interactions (e.g. access control or point-and-control) particularly because BLE discovery is stochastic and strongly parameter-dependent. In infrastructure-based localization, the UWB cost can increase further as a single positioning update may involve multiple anchors and ranging exchanges. Prior work has treated BLE neighbor discovery and UWB ranging as separate components, leaving the end-to-end tradeoffs of a complete BLE-assisted UWB session unexplored. In particular, it remains unclear when BLE setup dominates latency and energy consumption, how many ranging rounds are needed to amortize this overhead, and which phase has the greatest impact on short interactions. Moreover, existing analyses on latency or energy primarily focus on device-todevice ranging, while infrastructure-based localization involving multiple anchors remains largely unexplored.

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The main contributions of this work are as follows: • We present, to the best of our knowledge, the first end-toend analytical model of latency and energy consumption of BLE-assisted UWB sessions, covering BLE discovery, BLE parameter negotiation, UWB startup, and ranging within a single framework. • We extend the model beyond device-to-device ranging to infrastructure-based localization. The framework covers multi-anchor Two-Way Ranging (TWR), Uplink-Time Difference of Arrival (UL-TDoA), and Downlink-Time Difference of Arrival (DL-TDoA), capturing the additional communication and ranging phases introduced by each localization scheme. • Using the model, we quantify how BLE discovery and setup contribute to the overall latency and energy consumption of ranging and localization sessions. We analyze the resulting asymmetry between devices, the growth of latency with the number of anchors or ranging rounds, and the number of ranging rounds required to amortize the BLE setup overhead. • We provide a public release of our code, enabling researchers and practitioners to estimate the latency and energy consumption for their own parameter configurations.1 The remainder of this paper is organized as follows. Section II reviews related work. Section III describes the analytical model, while Section IV discusses the model and its results. Section V extends the model to localization, Section VI outlines the limitations of the model and future work, and Section VII concludes the paper. II. R ELATED W ORK As this is the first paper to analyze BLE-assisted UWB systems, the related work is divided into the following parts: i) BLE neighbor discovery, ii) UWB ranging and localization and iii) hybrid multi-radio systems. In the fourth part of this section, current standardization efforts are discussed to position this work. A. BLE Neighbor Discovery: Latency and Energy BLE literature primarily studies neighbor discovery, focusing on the latency and energy consumption associated with advertising and scanning. Energy-efficient discovery between unsynchronized, duty-cycled devices is a classical problem in mobile computing. In BLE, discovery is governed by a periodic-interval (PI) scheme defined by the advertising interval, scan interval, and scan window. In [12] the authors, developed a comprehensive model for BLE-like protocols, proving that discovery latency is deterministic and bounded for almost all valid parameter configurations. However, their model evaluates discovery only up to the first successful packet reception. Existing BLE research models the discovery process on the three primary advertising channels, the pseudorandom advertising delay, and the packet exchange following a received advertisement. Their main differences are in how they 1 Code will be made available upon acceptance.

account for the unknown phase offset between the advertiser and scanner and whether the scanner operates continuously or in a duty-cycled way. The study presented in [13] partitions the three-channel advertising cycle according to where the advertising event starts and averages over the resulting cases. They assume continuous scanning, resulting in higher energy consumption than duty-cycled operation. In addition, the scan window is assumed to be at least as long as the advertising interval, ensuring that every advertising event can be observed within a single scan cycle. While these assumptions simplify the analysis, they do not capture the latency-energy trade-offs introduced by shorter scan windows. The authors in [14] instead derive a per-channel success probability that accounts for the scanner’s arrival offset through the residual scan window time, and sum these probabilities over repeated advertising attempts to obtain a closed-form expected latency. The scanner is allowed to duty-cycle, with continuous scanning as the special case. The authors of [12] extended their model to BLE in [15] where they numerically integrate over the advertiser-scanner offset and approximate the cumulative random advertising delay, supporting both duty-cycled and continuous scanning. They also extend the model to the energy consumption of discovery and subsequent BLE connection states. The work reported in [16] introduced a discrete timing model that captures 3-channel rotation and identifies latency bounds and synchronizing locks when advertising and scanning intervals align. Two aspects remain open. First, the interval reserved from the scan window for the packet exchange is defined differently in each work: only the time to receive the ADV_IND packet [13], only the response handshake [14], or the whole exchange [16]. More importantly, only [15] extends the analysis beyond discovery to the BLE connection state. However, it does not retain the outcome of the discovery process, such as the advertising round and channel on which discovery succeeds or the resulting energy cost for each device role. Existing models also do not distinguish between scan-response and connection-based discovery in the context of a subsequent UWB session. In particular, none carry the discovery and connection outcomes into the establishment and ranging phases. In this work, we build upon the 3-channel timing formulation of [16], but refine the effective scan window by reserving only the duration until the preamble and access address are received. Furthermore, we extract the exact successful round and channel to map discovery outcomes directly into statelevel energy models and subsequent session establishment. B. UWB Ranging and Localization: Latency and Energy Most UWB literature focuses on ranging and localization accuracy [5], [17], [18], with there is little attention paid to latency and energy consumption. In [19], the authors characterize the energy consumption of different transceiver states and show that reception consumes more energy than transmission since reception requires continuous correlation to search for the signal, while transmission only consumes power during the burst. In addition, they show that higher data rates reduce the overall energy by shortening packet duration,

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despite higher current consumption. The power consumption of a complete Double-Sided Two-Way Ranging (DS-TWR) exchange is measured in [4]. From these measurements it is concluded that receiver-active intervals between message transmissions dominate energy consumption, with channel, data rate, preamble length, and Pulse Repetition Frequency (PRF) as the main drivers of peak power. The work presented in [20] models the scalability, realtime performance, and energy efficiency of TWR and Time Difference of Arrival (TDoA), while the authors of [21] study UWB localization at high user densities. These works show that the number of messages a device transmits and receives, and hence the time it remains active, is a key factor in localization energy consumption. However, these studies assume that the devices are already configured for UWB ranging, including the required Physical Layer (PHY) parameters and, where applicable, schedules and keys. In secure ranging, the STS is derived from a session key that must be established before ranging begins [22]. The time and energy required to obtain this configuration are outside the scope of these works. Our model addresses this missing setup phase by linking BLE discovery and negotiation to the subsequent UWB ranging or localization exchange. C. Hybrid UWB and Out-of-Band (OOB) Systems Using a low-power radio to trigger a more power-hungry one is a well-established approach, ranging from wake-up receivers in WLAN [23] to sub-GHz companion radios in UWB [24]. In Wi-PoS [24], the sub-GHz link handles the communication and reporting, while UWB is used for ranging, reducing the reported power consumption by 14.3% at the tag and 20.5% at the anchor node. An alternative is to perform discovery directly over UWB, avoiding a companion radio altogether. In UWB-ND [8], advertisers periodically perform a short channel activity detection, while the scanner transmits a long wake-up call. Compared to PI discovery, UWB-ND reduces tag energy by up to 50% when discovery requests are rare (long idle windows of ≥ 70 s), but increases it by up to 64% when requests are frequent. Moreover, all nodes must share the sniffing interval, timing parameters and wakeup key in advance. Such approaches therefore target networks with mains-powered anchors and preconfigured nodes, rather than discovery between previously unknown devices. D. Standardization and Ecosystem Trends To improve interoperability and secure operation of UWB systems, different (industry-driven) standardization bodies are developing their own specifications for certification. These specifications often use a low-power radio for discovery, might use rough distance estimation based on RSSI values, and session setup before the actual UWB ranging phase. The IEEE 802.15.4z [7], introduced in 2020, defines secure ranging, while leaving discovery and session setup for upper layers. The authors in [25] note that PHY-level compatibility between UWB ecosystems is largely a configuration issue, whereas discovery and upper-layer interoperability remain open. FiRa typically addresses this through an OOB channel for discovery

TABLE I BLE D ISCOVERY PARAMETERS Symbol

Description

Range/Value

TAI

Advertising interval (step size: 0.625 ms) Pseudo-random advertising delay Mean/max pseudo-random delay Advertising event, TAI + µ Mean advertising event, TAI + µ̄ Time between two consecutive ADV_INDs Scan interval Scan window Inter-frame space

20 ms–10485.76 s

µ µ̄, µmax T adv T̄ adv τwa TSI TSW TIFS

[0, 10] ms 5 ms,10 ms ≤ 10 ms [2.5 ms, 40.96 s] [2.5 ms, TSI ] 150 µs

and session establishment using BLE [26]. Besides TWR, FiRa supports DL-TDoA-based indoor tracking [27], and since FiRa Core 4.0, UL-TDoA asset tracking [28]. Other ecosystems follow a similar approach: CCC Digital Key [29] authenticates phone and vehicle over BLE before a secure UWB ranging session is established, and Aliro 1.0 [30] specifies BLE in combination with UWB for hands-free building access. Android [9] and Apple [10] require ranging parameters to be exchanged over an OOB transport, typically BLE. Vendor implementations likewise use BLE for discovery and to trigger UWB on demand [31], [32]. The capability request, capability response, and configuration messages defined by Android [9] provide the basis for the negotiation phase in our model. The diversity of ranging parameters and deployment scenarios makes the negotiation of operational parameters an important component of modern UWB systems. III. A NALYTICAL M ODEL The goal of the model is to derive the expected end-toend delay and energy consumption of FiRa-like systems by combining (i) BLE neighbor discovery latency/energy, (ii) BLE negotiation overhead, and (iii) UWB startup, and ranging overhead. The three phases of the model are illustrated in Fig. 1. A. BLE Neighbor Discovery BLE is designed for devices with small batteries that must remain on a low duty cycle. It operates in the 2402–2480 MHz band, divided into 40 channels of 2 MHz. Three of these, channels 37, 38, and 39, are reserved for advertising and carry the Neighbor Discovery Process (NDP) (illustrated in Fig. 2) through which two devices discover each other before any data can be exchanged. The discovery parameters strongly influence discovery latency and power consumption and are listed in Table I, as defined in [33]. The advertiser periodically advertises ADV_IND packets to announce its presence and capabilities. A transmission across all three channels forms an advertising event Tadv , with τwa denoting the time between consecutive ADV_IND packets. Advertising events repeat every Tadv = TAI + µ, where TAI is the advertising interval and µ is a pseudo-random delay that

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Fig. 1. End-to-end model of a BLE-assisted UWB system. BLE discovery (Section III-A) followed by parameters exchange (Section III-B). Both converge at UWB ranging (Section III-C) where it splits into ranging or localization before the session ends.

window happens to overlap an ADV_IND packet. This timing overlap, adapted from [16], is formalized in the model below and determines the discovery latency. 1) Timing: To derive the latency and energy consumption of the BLE procedures, the on-air time of each exchanged packet is computed as SPDU = SHDR + STYPE + SMIC ,

(1)

8 × (SPRE + SAA + SCRC + SPDU ) , (2) RPHY where SMIC = 4 B on encrypted data packets and 0 otherwise. STYPE is the payload size of packet type TYPE ∈ {ADV, REQ, RSP, CONN} in bytes and RPHY is the PHY data rate. All parameter values are listed in Table II. 2) Discovery Latency: With the on-air time defined, we can now describe the discovery timing itself. Let t = 0 be the start of a scan interval on channel 37, and let ϕ denote the offset between that instant and the first ADV_IND packet transmitted on channel 37. Since the advertiser and scanner are unsynchronized, ϕ lies in the interval [0, 3TSI ). To simplify the model, [16] replaced the pseudo-random delay µ by its mean TTYPE =

Fig. 2. BLE NDP: the advertiser transmits one ADV_IND packet per primary channel (37, 38, 39) within each advertising event. Consecutive advertising events are separated by the fixed interval TAI plus a pseudo-random delay µ (replaced by µ̄ in the model). The hatched area indicates the interval during which the transmitter sleeps. The scanner listens on one channel per scan interval TSI for a scan window TSW . Discovery occurs when the scanner’s active window overlaps with an advertising event on the same channel.

TABLE II BLE PACKET F ORMAT IN LE 1M PHY Symbol

Description

Value

RPHY SPRE SAA SHDR SCRC SMIC SADV SREQ SRSP SCONN

PHY data rate Preamble field size Access address field size Protocol Data Unit (PDU) header size CRC field size Message Integrity Check field size ADV_IND payload size SCAN_REQ payload size SCAN_RSP payload size CONNECT_IND payload size

1 Mb/s 1B 4B 2B 3B 0/4 B 6–37 B 12 B 6–37 B 34 B

reduces repeated packet collisions by preventing advertisers from remaining in sync. The scanner operates independently. It turns its receiver on for a fixed scan window TSW once every scan interval TSI , then moves to the next advertising channel and listens again. Because the advertiser and scanner run on separate, unsynchronized clocks, discovery succeeds only when a scan

T̄adv = TAI + µ̄,

µ̄ = 12 µmax = 5 ms,

(3)

where µ ∼ U [0, µmax ] and µmax = 10 ms. Indexing the advertising channels as c1 = 37, c2 = 38, c3 = 39, the transmission start of the ADV_IND packet sent on channel ck during advertising round r is then tk,r = ϕ + (k − 1) τwa + r T̄adv , k ∈ {1, 2, 3}, r ∈ N0 .

(4)

The scanner visits channels c1 , c2 , c3 cyclically with period 3TSI , scanning channel ck during [(k − 1)TSI , (k − 1)TSI + TSW ) of every cycle. Reception succeeds only if the receiver synchronizes to the packet, i.e. receives its preamble and access address, before it is switched off. Once synchronized, the receiver is assumed to complete the reception even if it extends beyond the scan window. The transmission must therefore start at least Tsync = 8 × (SPRE + SAA )/RPHY before the end of the window as in (5). eff TSW = TSW − Tsync ,

(5)

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which is non-empty provided Tsync < TSW ≤ TSI . Packet (k, r) is therefore received if   eff tk,r mod 3TSI ∈ (k − 1)TSI , (k − 1)TSI + TSW , (6) k ∈ {1, 2, 3}, with tk,r as in (4). The instants tk,r are strictly increasing under the lexicographic order (r, k), so the packets are enumerated unambiguously in time. Let S(ϕ) denote the set of index pairs satisfying (6) for a given offset ϕ. The first successful reception is then
R(ϕ), K(ϕ) = lex min (r, k), (7) (r,k) ∈ S(ϕ)

where R(ϕ) is the advertising round in which overlap first occurs (R(ϕ) = 0 denoting the first event with offset ϕ) and K(ϕ) the channel index of that packet (K(ϕ) = 1 denoting channel 37). The advertiser discovery latency, measured from the first transmission of the ADV_IND packet until reception by the scanner is Ladv (ϕ) = (K(ϕ) − 1)τwa + R(ϕ) T̄adv + TADV .

(8)

Measured from the start of scanning, the scanner discovery latency is Lscan (ϕ) = ϕ + Ladv (ϕ). (9) Since ϕ is unknown, the expected discovery latencies are obtained by integrating over all its possible values, Z 3TSI 1 Lx (ϕ) dϕ, x ∈ {adv, scan}, (10) E[Lx ] = 3TSI 0 where we assume that T̄adv ̸= nTSI . We extend the model in [16] by making a distinction between two discovery modes. Once a scanner has received an ADV_IND packet, the response depends on the required UWB session type, which determines which of two discovery modes applies and, correspondingly, whether the scanner remains a scanner or becomes an initiator: • Scannable discovery: the scanner sends a SCAN_REQ and the advertiser replies with a SCAN_RSP that carries basic UWB configuration (e.g. channel, anchor group identifier). The advertiser continues advertising on all three channels regardless of whether a SCAN_REQ was received, and no BLE connection is formed. This mode is sufficient when the device only needs to identify which UWB infrastructure to join, e.g. when entering a public TDoA localization zone where no negotiation or further device authentication is required. • Connectable discovery: the scanner acts as an initiator and sends a CONNECT_IND in response to an ADV_IND on the overlapping channel. The advertiser then closes the advertising event and both devices transition to the Connection state. The resulting BLE connection carries the parameter exchange described in Section III-B. This mode is required when security material (session keys, two-way security certificates, configurations, addresses, etc.) must be negotiated before UWB ranging begins.

Both modes complete the discovery with a short deterministic exchange that follows the received ADV_IND, separated by the mandatory inter-frame space TIFS = 150 µs [33]. In scannable discovery the scanner sends a SCAN_REQ and the advertiser answers with a SCAN_RSP, in connectable discovery the initiator sends a single CONNECT_IND: ∆sc = 2TIFS + TREQ + TRSP , ∆conn = TIFS + TCONN .

(11)

Since ∆m , m ∈ {sc, conn}, is independent of ϕ, we calculate the on-air time using (2), this then adds a constant to (8)–(9) and factors out of (10), E[Lm x ] = E[Lx ] + ∆m ,

x ∈ {adv, scan}.

(12)

3) Energy Consumption: We adopt the state-level decomposition of an advertising event from [34] and [35], and extend it to cover the scannable and connectable discovery modes, distinguishing advertiser- from scanner-side energy consumption. The parameters and corresponding energy consumption used in the discovery phase are summarized in Table III. To calculate the energy consumption for the advertiser, we distinguish between an unsuccessful and a successful event. For each advertising channel, the advertiser transmits an ADV_IND, waits for TIFS switches to RX and opens a receive window, the duration of this is: ( TIFS + TREQ , m = sc, m Trx = (13) TIFS + TCONN , m = conn. which is opened whether or not a packet arrives. The energy per channel is ch Eadv = Ptx TADV + Etx-rx + Prx Trx ,

(14)

and the per advertising event overhead is Eevt =Ewake + Extal + Estnd + Estart + Epost .

(15)

The idle period after all advertisements are sent is calculated as in (16). Eidle,adv = Pidle T̄adv − 3(TADV + Trx )).

(16)

An event in which no SCAN_REQ or CONNECT_IND is received costs ch Eadv,no = Eevt + 3Eadv + 2Ech + Eidle,adv .

(17)

Let K(ϕ) be the channel index on which discovery occurs. The two modes differ in how the event terminates: in scannable discovery the advertiser replies with a SCAN_RSP and completes the event on all three channels, whereas in connectable discovery it closes the event immediately after the CONNECT_IND and enters the Connection state. With (
3, m = sc, (m) N K = (18) K, m = conn, and exchange cost ( (m) Eex,adv =

Erx-tx + Ptx TRSP , 0,

m = sc, m = conn,

(19)

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the successful event costs (m) ch Eadv,succ (K) = Eevt + N (m) (K) Eadv

(m) + N (m) (K) − 1 Ech + Eex,adv

(20)

Since R(ϕ) denotes the index of the successful round (R = 0 for the first event), exactly R(ϕ) events fail beforehand:
(m) (m) Eadv (ϕ) = R(ϕ) Eadv,no + Eadv,succ K(ϕ) . (21) The scanner is decomposed in the same way. Its perinterval overhead is the same Eevt , and an interval in which no ADV_IND is received consists of listening for the full scan window and staying idle in a low-power mode for the remainder of the scan interval,
Eidle,scan = Pidle TSI − TSW , (22) so that

TABLE III BLE POWER AND ENERGY PARAMETERS FOR THE N RF54L15 AT 1 M BPS , 0 D B M , AND 3 V [36]. Symbol

Description

Power

Time

Energy

Prx

Receive power consumption Transmit power consumption Idle power consumption

10.2 mW

-

-

14.4 mW

-

-

8.7 µW

-

-

Waking up the device from sleep Crystal ramp up Time to standby Starting the radio Switching from RX to TX Switching from TX to RX Post-processing time Channel switching

12.9 mW

123 µs

1.59 µJ

1.5 mW 0.6 mW 7.2 mW 3.6 mW

500 µs 1148 µs 103 µs 143 µs

0.75 µJ 0.69 µJ 0.74 µJ 0.51 µJ

3.6 mW

143 µs

0.51 µJ

8.4 mW 9.9 mW

115 µs 62 µs

0.97 µJ 0.61 µJ

Ptx Pidle Ewake Extal Estnd Estart Erx-tx Etx-rx

Escan,no = Eevt + Prx TSW + Eidle,scan .

(23)

In the interval in which discovery occurs the scanner listens only until the ADV_IND has been received, after which it performs the mode-dependent exchange and leaves the discovery phase. The elapsed listening time in that window is

δ(ϕ) = Lscan (ϕ) mod 3TSI − K(ϕ) − 1 TSI , (24) TADV < δ(ϕ) ≤ TSW , and the exchange costs   m = sc, Erx-tx + Ptx TREQ (m) Eex,scan = + Etx-rx + Prx TRSP ,   Erx-tx + Ptx TCONN , m = conn.

(25)

The successful scan interval is therefore (m) (m) Escan,succ (ϕ) = Eevt + Prx δ(ϕ) + Eex,scan .

(26)

the scanner has completed Nscan (ϕ) = Before that interval  Lscan (ϕ)/TSI unsuccessful ones, so that, analogously to (21), (m) (m) Escan (ϕ) = Nscan (ϕ) Escan,no + Escan,succ (ϕ).

(27)

As with the latency, the discovery energy depends on the unknown offset ϕ. The expected discovery energy is therefore obtained by averaging over ϕ, Z 3TSI h i 1 Ex(m) (ϕ) dϕ, x ∈ {adv, scan}, E Ex(m) = 3TSI 0 (28) in the same way as the latency in (10). B. BLE Negotiation and Security Exchange The previous phase ends when the advertiser receives the CONNECT_IND packet. Both devices then enter the Connection state, the advertiser becoming the peripheral and the initiator the central. The connection is established when a packet is received [33]. Because the connection was created with CONNECT_IND on the primary advertising physical channel, the LE 1M PHY is used in both directions. We do not consider the PHY update procedure.

Epost Ech

CONNECT_IND carries transmitWindowDelay D, transmitWindowOffset O and transmitWindowSize W , which bound the interval in which the central sends its first data packet. This window allows the central to schedule connection events across concurrent connections. The first transmission from the central defines the anchor point, after which connection events recur every connInterval C. 1) Per-Message Payload Sizes: Typical UWB initialization requires the device address, session ID, STS session key, ranging role and configuration profile. A complete configuration would require many PHY- and MAC-layer parameters (preamble length, data rate, timing settings, and ranging method (e.g. Single-Sided (SS)- or Double-Sided (DS)-TWR)). Predefined profiles reduce this to a profile identifier plus a small set of session-specific fields. Android [9] follows a similar approach through the use of a UWB configuration type together with a sessionKeyInfo of 64 bits for static STS and 128 or 256 bits for provisioned STS. Our model therefore assumes only the profile identifier and session-specific parameters are exchanged. 2) Message Flow: Following Android [9], three messages precede ranging: the central first requests the parameter values the peripheral supports, the peripheral replies with its supported set, and the central concludes by selecting one value per parameter. The parameter values used throughout this subsection and their corresponding descriptions are listed in Table IV. Let Si denote the payload of message i ∈ {1, 2, 3} and let Sopcode = 1 B be the message-type field present in all three. a) M1 : Ranging Capability Request (C → P): Carries only the message type and a bitmap of the ranging technologies for which capabilities are requested S1 = Sopcode + Stech = 2 B.

(29)

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b) M2 : Ranging Capability Response (P → C): Reports the supported UWB parameter sets. ∗ ∗ S2 = Sopcode + Sch + Spre + Sslot + Sint + Sprof + Srole

= 11 B. (30) c) M3 : Ranging Configuration (C → P): Carries the selected value of each parameter together with the session ID (Ssid ) and STS (Skey ): S3 = Sopcode + Saa + Ssid + Skey + Srole + Sprof .

(31)

This is the dominant message, and the only one whose size depends on the selected STS mode, giving S3 ∈ [19, 43] B. In the worst case maxi Si = S3 = 43 B ≪ Spayload,max = 250 B, so each message fits in a single packet and the exchange consists of exactly three BLE packets. Ranging starts directly after the last packet, so no reply for the peripheral needed. 3) Packet Airtime: The airtime of message i is given by (2) with STYPE = Si and SM IC = 4 B, since the link isP assumed encrypted. The total exchange therefore occupies i TSi + 2TIFS ∈ [0.89, 1.08] ms over the considered payload range, which is well below the minimum connection interval. 4) Negotiation Latency: Measured from the end of the CONNECT_IND packet to the end of M3 , i.e. the instant at which the peripheral starts ranging, the latency is identical for both roles: Lneg = Tconn +

3 X

TSi + 2TIFS + Tpost ,

(32)

TABLE IV BLE N EGOTIATION / C OMMISSIONING PARAMETERS Symbol

Description

Value/Size

D O W

Transmit window delay Transmit window offset Transmit window size

C

Connection interval

1.25 ms [0, C] ms [1.25, min(10, C − 1.25)] ms [7.5 ms, 4 s]

Sopcode Stech Sch Spre Sslot Sint ∗ Sprof

Message type field Supported technologies Supported channel bitmap Supported preamble indices 9-32 Minimum slot duration Minimum supported ranging interval Supported profiles

1B 1B 1B 4B 1B 2B 1B

∗ Srole Saa Ssid Skey Srole Sprof

Supported role sets UWB device address Session ID size STS key size Chosen UWB role Chosen UWB profile identifier

1B 4B 4B {8, 16, 32} B 1B 1B

TABLE V UWB ENERGY PARAMETERS FOR THE DW3000 ON CH5, 3 V [37]. Symbol

Description

Value

POSC PIDLE PLL

4.8 mW 54 mW

UWB Ptx UWB Prx Pdeep sleep

Oscillator start-up power consumption Idle state with PLL enabled (124.8 MHz clock) power consumption Transmit power consumption Receive power consumption Deep sleep power consumption

TOSC TIDLE PLL Tdeep sleep

Oscillator start-up interval Idle state with PLL enabled Idle time between ranging rounds

1000 µs 20 µs variable

i=1

where the connection establishment delay follows from Tconn = D + O + W 2 + Twake ,

(33)

assuming the central transmits uniformly within the window. 5) Energy Consumption: The parameters used throughout this section are summarized in Table IV. The central transmits M1 and M3 and receives M2 , while the peripheral does the opposite. In addition, the central stays idle in a low-power mode for the whole interval D + O + W/2 and then transmits, whereas the peripheral must open its receive window at D + O and listen for W/2 on average before the anchor point is detected. Hence
cen + Ewake + Eneg = Pidle D + O + W
2 (34) Ptx TS1 + TS3 + Prx TS2 + 2Pidle TIFS + Epost ,
per Eneg = Pidle D + O + Ewake + Prx W 2
+ Prx TS1 + TS3 + Ptx TS2

(35)

+ 2Pidle TIFS + Epost . The message asymmetry compounds the role asymmetry: the peripheral not only pays the window-listening penalty Prx W/2, it also receives the largest packet while transmitting only the middle one. The commissioning energy is therefore structurally unequal between the two roles even though the latency is not.

42 mW 48 mW 0.78 µW

C. UWB Ranging Following the BLE negotiation phase, both devices activate and configure their UWB subsystems using the exchanged session parameters. The parameters used throughout this section are summarized in Table V. 1) Startup: Before any frame can be transmitted or received, the transceiver must first wake up and prepare its clock and RF synthesizer. This wake-up phase consists of the oscillator start-up interval TOSC and an idle interval TIDLE PLL , during which the RF synthesizer locks and the transceiver becomes ready to transmit or receive. The time needed is UWB Tstart = TOSC + TIDLE PLL ,

(36)

and the consumed energy is UWB Estart = POSC TOSC + PIDLE PLL TIDLE PLL .

(37)

8

TABLE VI DW3000 S YMBOL D URATION [37] PRF (MHz)

Data Rate (Mbps)

τSHR (ns)

τDATA (ns)

16 16 64 64

0.85 6.81 0.85 6.81

993.59 993.59 1017.63 1017.63

1025.64 128.21 1025.64 128.21

2) Packet Airtime: In order to analyze the latency and power consumption of UWB ranging, we consider the structure of the UWB PHY Protocol Data Unit (PPDU) (Fig. 3), the symbol duration of Table VI, and the STS packet configurations introduced by the IEEE802.15.4z amendment [25]. Each PPDU consists of a synchronisation header (SHR), containing the preamble and start frame delimiter (SFD), followed by a Data Portion (DP). As shown in Fig. 3, SP0 is the legacy configuration without an STS, while SP1 and SP2 add the STS before and after the payload, respectively. SP3 contains only the SHR and STS, enabling timestamping without a PHY header (PHR) or payload. This version is used whenever a frame only needs to be timestamped, e.g. for the POLL and RESPONSE frames of a ranging exchange, while any additional information, such as the measured timestamps, is instead reported using one of the other frame formats. Timing durations in IEEE 802.15.4/z are expressed as an integer number of symbols. Symbol durations depend on the data rate (0.85 or 6.81 Mbps for the DW3000) and the Pulse Repetition Frequency (PRF) (16 or 64 MHz). Table VI lists the resulting SHR symbol duration τSHR and DP symbol duration τDATA . The duration of each field is then TSHR = τSHR (Npre + NSFD + NSTS ) ,    8L , TDATA = τDATA NPHR + 8L + 48 330

(38) (39)

where Npre is the number of preamble symbols, NSFD ∈ {8, 16}, NSTS is the configured STS length (a power of two between 32 and 2048 symbols, or 0 if the packet configuration carries no STS), NPHR = 21 symbols (or 0 in SP3), L is 8L the payload length in bytes (L = 0 for SP3), and 48 330 accounts for the Reed-Solomon parity bits appended to every 330 (or fewer) data bits. Combining (38) and (39), the airtime of a packet is simply Tpacket = TSHR + TDATA .

(40)

3) Ranging Latency and Energy Consumption: The latency of a range round depends on the ranging mode, both modes are illustrated in Fig. 4. Single-Sided Two-Way Ranging (SSTWR) uses one request-reply exchange between two unsynchronized devices to measure the distance. DS-TWR adds a second exchange in the opposite direction, combining both round-trip measurements to cancel out most of the clock-drift error. For these two most common ranging modes, ( 2, if ranging method SS-TWR (Fig. 4 left), nf = (41) 3, else DS-TWR (Fig. 4 right).

Fig. 3. Packet Formats of IEEE802.15.4z [25].

Fig. 4. Timing diagram of TWR, SS-TWR (left) and DS-TWR (right).

The airtime of every exchanged packet Tpkt,i depends on the packet format, the payload and the reply time Treply between reception and transmission. Trng =

nf X

Tpkt,i + (nf − 1)Treply .

(42)

i=1

The energy consumed per ranging attempt depends on the airtime, ranging mode and role (transmit or receive) of every frame, which differs slightly depending on whether the device is the controller (X = ctrl) or the controlee (X = cle). X UWB Erng = Ptx

X

UWB Tpkt,i + Prx

X

Tpkt,i

X i∈Frx

X i∈Ftx

(43)

+ (nf − 1) Treply PIDLE PLL , ctrl ctrl where Ftx = {1, 3, 5, . . . } and Frx = {2, 4, 6, . . . } denote the sets of frames transmitted and received by the ctrl controller, respectively, such that |Ftx | = ⌈nf /2⌉ and ctrl UWB |Frx | = ⌊nf /2⌋ (reversed for the controlee), and Ptx , UWB Prx , and PIDLE PLL are the transmit, receive, and idle power levels. The parameters are listed in Table V. The total latency of the UWB phase over Nr ranging rounds is
UWB LUWB = Nr Tstart + Trng + (Nr − 1) Tdeep sleep , (44)

and the corresponding energy consumption is X UWB X EUWB = Nr Estart + Erng

+ (Nr − 1) (Pdeep sleep Tdeep sleep ) .

(45)

9

D. End-to-End Latency and Energy The session-level metrics compose the three phases: BLE discovery, BLE negotiation/commissioning, and UWB ranging. Because the connection-oriented exchange of Section III-B is only required when security material must be negotiated, the commissioning phase is present in connectable discovery (m = conn) and absent in scannable discovery (m = sc), where the configuration is delivered in the SCAN_RSP. We capture this with the indicator 1{m=conn} equal to 1 when its condition holds (i.e. m = conn) and 0 otherwise. 1) End-to-end Latency: The session latency is measured from the instant the initiator starts scanning until the last ranging round completes. The discovery contribution is the scanner latency (12) and the post-discovery phases are common to both devices and independent of the phase offset ϕ: h i (m) E Le2e = E[Lm (46) scan ] + 1{m=conn} Lneg + LUWB . 2) End-to-end Energy: Energy is accounted per device, as the two roles transmit and receive a different number of frames in every phase. We let the initiator/scanner act as BLE central / UWB controller and the advertiser as BLE peripheral / UWB controlee. Using the discovery energy (28), the commissioning energy (34), and the ranging energy (45): h i h i cen,(m) (m) cen E Ee2e = E Escan + 1{m=conn} Eneg ctrl + EUWB ,

i h i h per,(m) (m) per E Ee2e = E Eadv + 1{m=conn} Eneg cle + EUWB ,

TABLE VII PARAMETER VALUES USED IN THE DISCUSSION SECTION . Parameter

Selected value

BLE discovery configurations: TAI /TSI /TSW Low-latency 100/100/100 ms Balanced 250/500/200 ms Low-power 1000/5000/500 ms Common BLE settings Discovery mode Connectable Advertising packet spacing τwa 1.5 ms ADV payload SADV 37 B Connection interval C 7.5 ms Transmit window offset O 0 ms Transmit window size W 6.25 ms Session key size Skey 16 B Common UWB settings Ranging method DS-TWR PRF 64 MHz Data rate 6.81 Mb/s Preamble length Npre 64 symbols SFD length NSFD 8 symbols STS length NSTS 64 symbols POLL/RESPONSE packet format SP3 FINAL packet format SP1 FINAL payload length L 12 B Inter-frame reply time Treply 400 µs Inter-round sleep time Tdeep sleep 100 ms

(47)

(48)

IV. D ISCUSSION AND M ODEL S COPE In this section, we use the analytical model to examine how BLE discovery and UWB ranging influence the latency and energy consumption. Three discovery configurations are considered: low-latency, balanced, and low-power. The advertising intervals are inspired by Android settings, while the scan intervals and windows are selected to represent different duty cycles (100%, 40%, 10%). These configurations and the remaining evaluation parameters are summarized in Table VII. We consider connectable BLE discovery followed by parameter negotiation and DS-TWR ranging. The scanner subsequently acts as the BLE central and UWB controller, while the advertiser becomes the BLE peripheral and UWB controlee. A. Energy Costs of the Scanner and the Advertiser Roles Figure 5 shows the expected energy required to complete a discovery event for both the advertiser and scanner roles. Across the three parameter configurations, the scanner consumes more energy than the advertiser, requiring approximately 28×, 54×, and 57× more energy. This difference arises because the scanner spends significantly longer with the receiver active, whereas advertising consists of short transmission bursts. While Fig. 5a quantifies the energy required to

complete a discovery event, Fig 5b shows the average power consumed while waiting for a discovery opportunity. The latter is obtained as Eadv,no Escan,no Padv,wait = , Pscan,wait = . (49) TSI T̄adv As shown in Fig. 5b, the average power consumed while waiting decreases as the duty cycle is reduced. For the scanner, the average waiting power drops from approximately 10.2 mW in the low-latency configuration to 1.03 mW in the lowpower configuration, reflecting the reduced time spent actively listening. Although the low-power configuration consumes less power over time, it also increases the expected discovery latency because the scanner listens less frequently. The longer waiting time before a discovery occurs outweighs the reduction in instantaneous power consumption, leading to a higher total energy cost per discovery. For example, the scanner discovery energy increases from approximately 1.6 mJ in the low-latency configuration to 38.2 mJ in the low-power configuration. These results highlight the fundamental duty-cycling trade-off. Reducing the duty cycle lowers the average power consumption while waiting for a discovery event, but increases the expected discovery latency. B. Discovery Latency Analysis The expected discovery latency in (12) describes only the average behavior. For interactive applications such as digital keys, interactive museum displays, collision warnings, and access control, however, higher-percentile latencies are often

10

28×

advertiser scanner

10

average power while waiting [mW]

energy per discovery [mJ]

100

54× 57×

1 0.1 0.01

low-latency 100/100/100 ms

balanced 250/500/200 ms

low-power 1000/5000/500 ms

(a)

100

advertiser scanner

10 1 0.1 0.01

low-latency 100/100/100 ms

balanced 250/500/200 ms

low-power 1000/5000/500 ms

(b)

Fig. 5. Energy consumption of advertiser and scanner discovery for the low-latency, balanced, and low-power configurations (TAI /TSI /TSW ): (a) average energy per discovery event and (b) average power consumed while waiting for a discovery opportunity. Lower duty cycles reduce waiting power but increase energy cost of a successful discovery due to longer discovery latencies.

1.0 0.8

probability

missioning, and a ranging-dependent cost due to UWB startup and DS-TWR exchanges. The crossover point Nr⋆ is defined as the number of ranging rounds at which the cumulative UWB ranging energy equals the one-time energy associated with session establishment.

low-latency (100 / 100 / 100 ms) balanced (250 / 500 / 200 ms) low-power (1000 / 5000 / 500 ms)

0.6 0.4 0.2 0.0

100

101

102

103

104

scanner discovery latency Lscan( ) [ms]

105

Fig. 6. Cumulative distribution of scanner discovery latency over the phase offset ϕ for three BLE configurations (TAI /TSI /TSW ).

more relevant than the mean. Fig. 6 shows the cumulative distribution of the scanner discovery latency for the same three BLE configurations. All distributions exhibit a right tail, with p99 latencies ranging from 2× to 3.4× the mean latency. The low-latency configuration achieves a mean latency of 153 ms and a p99 latency of 302 ms. For the balanced configuration, these values increase to 1.19 s and 4.01 s, respectively, while the low-power configuration yields a mean of 35.8 s and a p99 of 110 s. These results demonstrate that the mean latency alone does not fully capture discovery performance. As the duty cycle decreases, the tail of the latency distribution grows significantly, making percentile metrics such as p95 and p99 essential for assessing the responsiveness experienced by users. These large latencies may be acceptable for infrequent asset-tracking applications, but are unsuitable for interactive use cases such as digital keys, access control, or point-andcontrol interactions. C. Discovery Energy versus Ranging Energy The total energy of a ranging session can be decomposed into a fixed setup cost, comprising BLE discovery and com-

  h (m) i X E Ex + 1{m=conn} Eneg + Pdeep sleep Tdeep sleep  Nr⋆ =    UWB + E X + P Estart deep sleep Tdeep sleep   rng (50) Figure 7 illustrates this crossover point for TAI = 100 ms, TSI = 100 ms, TSW = 100 ms. The figure shows the energy consumption of the scanning device, which subsequently assumes the BLE central role and the UWB controller role. For this configuration, the crossover occurs at Nr⋆ = 24. Therefore, after 24 complete DS-TWR ranging rounds, the cumulative energy consumed by UWB operation exceeds the one-time energy required to establish the session through BLE discovery and commissioning. For shorter sessions, the BLE initialization phase contributes a significant fraction of the total energy consumption. As the number of ranging rounds increases, however, the impact of the BLE overhead becomes less important and the total energy is increasingly determined by UWB operation. Although Fig. 7 includes the negotiation energy associated with connectable operation, its contribution is negligible compared to the discovery energy. For the considered configuration, the negotiation phase consumes approximately 11.2 µJ, whereas BLE discovery requires approximately 1.6 mJ. Consequently, the negotiation contribution is effectively invisible at the scale of the figure. A purely scannable implementation without BLE connection establishment would therefore exhibit nearly identical crossover behavior in the ranging case. The value of Nr⋆ depends directly on the energy consumed during the BLE discovery phase. Configurations with lower discovery energy require fewer ranging rounds before UWB becomes the dominant contributor to the total energy budget. For the low-latency configuration shown in Fig. 7, the

controller device energy [mJ]

11

8 7 6 5 4 3 2 1 0

resulting connection enables secure transfer and configuration at the cost of additional discovery latency and higher BLE energy consumption. In this section, we investigate how discovery behaves against a group of advertisers rather than a single one, and how one UWB round changes when ranging is replaced by localization. Because the anchors are typically mains-powered, the energy model considers only the tag.

BLE discovery BLE negotiation UWB startup UWB ranging

Nr = 24

A. Discovery of an Anchor Group

20

40

60

number of ranging rounds Nr

80

100

Fig. 7. Energy breakdown of the controller device as a function of the number of DS-TWR ranging rounds for TAI = TSI = TSW = 100 ms. BLE discovery and commissioning contribute a fixed one-time energy overhead, whereas UWB startup and ranging energy increase with the number of ranging rounds. The crossover point Nr⋆ denotes the number of ranging rounds at which the cumulative UWB energy equals the BLE session-establishment energy.

crossover occurs after only 24 ranging rounds. In comparison, the balanced configuration and the low-power configuration yield crossover points of approximately 80 and 562 rounds, respectively. These results demonstrate that the relative importance of BLE discovery and UWB ranging is highly dependent on the selected discovery parameters. The crossover analysis highlights the complementary roles of BLE and UWB in FiRa-like systems. BLE introduces a one-time discovery overhead that enables devices to exchange the information required to initiate a ranging session, while UWB provides the actual ranging functionality. For shortlived sessions involving only a limited number of ranging exchanges, BLE discovery can account for a substantial portion of the total energy consumption. For longer sessions, the initialization overhead becomes amortized over a large number of ranging rounds and the total energy budget is dominated by UWB operation. V. F ROM R ANGING TO L OCALIZATION The model so far assumed a device-to-device session ending in a TWR exchange. In an infrastructure deployment the tag is instead localized by a group of anchors, using one of three UWB localization approaches: TWR with each anchor in turn; UL-TDoA, in which the UWB tag transmits and the synchronized anchors report their received timestamps to a server; or DL-TDoA, in which theUWB anchors transmit and the tag solves for its own position. These architectures can be expanded to estimate the Angle of Arrival (AoA) in multiantenna systems. Since the BLE parameters a tag needs to join a zone are identical for every tag in that zone, our model delivers them in the SCAN_RSP. This approach minimizes complexity and is sufficient whenever neither authentication nor parameter negotiation is required. Some deployments, however, require device authentication, credential exchange, or dynamic negotiation of parameters. In such cases, connectable advertisements are used to establish a BLE connection. The

Anchors of the same group advertise the same infrastructure identity, so the tag does not discover each anchor individually: discovery ends as soon as any anchor of the group is discovered. Let NA be the number of anchors in the group and NAvis ≤ NA the number of anchors within range of the tag. Eqs. (6)–(9) hold per anchor j with its own offset ϕj ∼ U[0, 3TSI ), and the anchors are mutually unsynchronized, so the different ϕj are independent and identically distributed. The group discovery latency is then Lloc scan (ϕ) = min Lscan (ϕj ), vis j≤NA

ϕ = (ϕ1 , . . . , ϕNAvis ).

(51) R∞ Using the identity E[X] = 0 Pr(X > t) dt for a nonnegative random variable X, with t ranging over all candidate discovery times, the single integral of (10) is replaced by a product of complementary distribution functions, Z ∞   vis E Lloc = F̄ (t) NA dt, scan 0 (52) {ϕ : Lscan (ϕ) > t} , F̄ (t) = 3TSI which is strictly decreasing in NAvis where a dense deployment is discovered faster than a single peer at the same advertising interval (see Section V-C). B. UWB Phase A single distance is no longer enough to calculate the position of a tag; at least three anchors are needed in 2D and four in 3D [20]. We assume a coordinated infrastructure in which discovery of any anchor provides the group configuration, or a reference to a predefined profile, including the information needed to identify the participating anchors and their scheduled exchanges. We further assume that the anchors visible over BLE are also within UWB range, and that the anchors are synchronized for both TDoA modes. The establishment of the schedule and the synchronization are outside the scope of the model. The three localization schemes differ in the number and direction of their frame exchanges. In TWR, the tag ranges with NAuse ≤ NAvis anchors and repeats (42) once per anchor. Since every additional anchor costs a full exchange, the tag ranges with only as many anchors as required, i.e. at least three in 2D and four in 3D. In UL-TDoA, the tag transmits a single uplink frame, which every visible anchor receives and timestamps, so all NAvis anchors contribute at no extra cost to the tag. DL-TDoA reverses this: the anchors transmit a block

12

In DL-TDoA, the tag does the reverse and receives all NAvis anchor frames, which, for frames of identical airtime Tpkt , gives
DL UWB Erng = NAvis Tpkt Prx + NAvis − 1 Tslot PIDLE PLL . (60)

TABLE VIII PARAMETERS FOR L OCALIZATION S CHEMES (TAG S IDE ) Scheme

nf

ntx

nrx

Treply

Nex

SS-TWR DS-TWR UL-TDoA DL-TDoA

2 3 1 vis NA

1 2 1 0

1 1 0 vis NA

Treply Treply – Tslot

use NA use NA 1 1

C. Discussion

of NAvis frames in assigned slots, and the tag receives all of them. We capture all schemes Y ∈ {SS, DS, UL, DL} by letting Y the frame count nYf , the time between frames Treply , and Y the number of exchanges per position fix Nex depend on the scheme: nY

Y Trng =

f X

Y Tpkt,i + nYf − 1 Treply ,

(53)

i=1

Y Y Y Y Tfix = Nex Trng + Nex − 1 TIDLE PLL .

(54)

Equation (53) gives the duration of one exchange, and (54) Y times, separated by an idle time TIDLE PLL , repeats it Nex to obtain one position estimate. Table VIII summarizes the parameters of each scheme. Generalizing (44), the total UWB phase latency for localization is
UWB Y LYUWB = Nr Tstart + Tfix + (Nr − 1) Tdeep sleep (55) + 1{Y =UL} Tinfra , where Tinfra covers the anchor-to-server reporting, the multilateration, and, if the tag needs to know its own position, the downlink delivery of the result. It is only added for Y = UL, since only in UL-TDoA is the position computed by the infrastructure. In TWR and DL-TDoA, the tag computes its own position. The per-exchange energy of (43) generalizes to X X Y UWB UWB Erng = Ptx Tpkt,i + Prx Tpkt,i Y Y i∈Frx i∈Ftx (56)
Y Y + nf − 1 Treply PIDLE PLL , Y Y where Ftx and Frx denote the sets of frames transmitted and Y Y received by the tag, with |Ftx | = nYtx and |Frx | = nYrx as listed in Table VIII. The energy per position fix is
Y Y Y Y Efix = Nex Erng + Nex − 1 PIDLE PLL TIDLE PLL , (57)

and the total UWB phase energy over Nr rounds is
Y UWB Y EUWB = Nr Estart + Efix + (Nr − 1) Pdeep sleep Tdeep sleep .

(58)

The two TDoA modes differ markedly in tag energy. In ULTDoA, the tag only transmits a single frame, so its energy is independent of the number of anchors: UL UWB Erng = Tpkt Ptx .

(59)

Fig 8 provides an analysis of the latency of the BLE anchor discovery phase and the UWB localization phase. Fig. 8a shows that the expected group discovery latency decreases with NAvis for all three BLE configurations, since discovery completes at the earliest of NAvis independent advertisers. The largest gains occur for the first few anchors: three visible anchors already halve the latency compared to a single one, from 154 ms to 77 ms for the low-latency configuration and from 35.8 s to 11.3 s for the low-power configuration. With twenty visible anchors, the latency is reduced by a factor of 10 to 13 across all configurations, down to 16 ms, 88 ms, and 2.8 s, respectively. A dense deployment therefore allows longer advertising intervals, and thus lower anchor duty cycles, for the same discovery latency. Since anchors are often mains powered, potentially even lower advertisement intervals can be used to further reduce the discovery latency. Fig. 8b shows the UWB latency per position estimate on the tag side, i.e. excluding Tinfra . For DS-TWR, the latency grows linearly with NAuse by 1.26 ms per anchor, from 4.8 ms for three anchors to 26.1 ms for twenty, since every additional anchor adds a full three-frame exchange and an idle gap. Thus, TWR provides high ranging accuracy, requires no network synchronization, and relies on mature, wellunderstood protocols, making it well suited for secure access control and point-to-point positioning. However, if secure localization is required, BLE discovery and negotiation must be performed with each participating anchor, and scalability is limited because every tag must actively exchange messages with every anchor it uses. DL-TDoA also grows linearly, but by only 0.56 ms per anchor, since the tag must remain awake until it has received the frames of all participating anchors, each requiring a single frame and slot instead of a full exchange. Thus, DLTDoA offers strong privacy, as the tag computes its position locally without reporting measurements to the infrastructure. It is therefore particularly attractive for smartphone navigation and user-centric localization services. However, the tag must receive frames from all visible anchors and maintain its clock reference between receptions, which prevents the use of (deep) sleep modes during the block and makes its energy grow with NAvis . The latency of UL-TDoA is constant at 1.2 ms, since the tag transmits a single frame regardless of the number of anchors. In UL-TDoA, therefore, a larger number of anchors improves the position estimate at no cost in tag latency. Thus, UL-TDoA minimizes the tag’s communication overhead and energy consumption, and since the tag’s airtime is independent of the number of anchors, it scales well to many tags and anchors. This makes it attractive for low-power, large-scale industrial Real-Time Location System (RTLS) applications such as asset and worker tracking. Its main drawback is that

100000

low-latency balanced low-power

10000 1000 100 10

1

3

5

7

9

11

13 visible anchors NAvis

15

17

19

(a)

UWB latency per position estimate [ms]

mean group discovery latency [ms]

13

DS-TWR UL-TDoA DL-TDoA

25 20 15 10 5 0

3

5

7

9

11

13

used anchors NAuse

15

17

19

(b)

vis for three BLE configurations. (b) Fig. 8. (a) Expected latency (logarithmic scale) to discover any one anchor versus the number of visible anchors NA use for DS-TWR, UL-TDoA, and DL-TDoA. UWB latency per position estimate on the tag side versus the number of used anchors NA

the position estimate resides within the infrastructure rather than on the device itself. The choice of architecture is primarily driven by scalability, privacy requirements, and whether the position estimate is required on the device or within the infrastructure. BLE serves as a common admission mechanism across all approaches, enabling infrastructure discovery, parameter distribution, and optional authentication while leveraging the BLE and UWB radios already integrated in many smartphones and IoT devices. VI. L IMITATIONS AND F UTURE W ORK Several extensions could further increase the accuracy of the proposed model. First, the current analysis considers a single advertiser-scanner pair and, for localization, a single tag interacting with independent anchors on an otherwise idle medium. Future work could investigate the impact of network density, contention, collisions, and anchor scheduling on both discovery performance and energy consumption. Second, the BLE discovery model assumes that the radio can enter a sleep state between consecutive scan and advertising windows. In practice, the achievable power state depends on the ratio between the configured interval and window durations, and short gaps may require the radio to remain in an idle or standby state. Incorporating adaptive power-state selection would improve the accuracy of the energy model. Finally, following [16], the discovery analysis employs the mean-delay approximation of the BLE advertising delay. While this approximation is accurate for the non-resonant parameter configurations considered in this work, future models could explicitly incorporate the random advertising delay to study resonant operating points and their impact on discovery latency. VII. C ONCLUSION This paper presented an analytical model of the end-to-end latency and energy consumption of BLE-assisted UWB ranging and localization systems. By combining BLE discovery,

BLE negotiation, UWB startup and ranging in a single framework, the model quantifies the cost of an entire session and attributes it to individual phases and device roles. The analysis leads to three main observations. First, BLE discovery is highly asymmetric: depending on the discovery configuration, the scanner consumes between 28× and 57× more energy than the advertiser because it must keep its receiver active while the advertiser transmits only short packets. Second, reducing the BLE duty cycle lowers the average power while waiting for discovery, but increases both the energy required per successful discovery and the tail of the latency distribution. Across the evaluated configurations, the 99th-percentile discovery latency ranges from 2× to 3.4× the mean, reaching up to 110 s. Third, the energy required to establish the BLE connection and negotiate session parameters is negligible compared to the discovery phase, and the associated setup overhead is amortized only after 24-562 ranging rounds. For localization, the model highlights the different scaling behavior of the considered architectures. UL-TDoA keeps the tag-side energy consumption independent of the number of anchors, whereas DL-TDoA and TWR require additional tag activity as anchor count increases. The results also show that group discovery becomes more efficient as more anchors are available, reducing the expected time until a suitable anchor is detected. Overall, the results indicate that BLE discovery should not be treated as a negligible bootstrap step. In many practical deployments, particularly those involving short interactions, discovery dominates the latency and energy budget of the complete UWB session. Consequently, the choice of discovery mode, parameter configuration, and device role should be considered an integral part of the design of BLE-assisted UWB ranging and localization systems. ACKNOWLEDGMENTS This research was funded by the imec ICON project NGUWB (Agentschap Innoveren en Ondernemen project nr. HBC.2024.0882) and the DistriMuSe project (HORIZONKDT-JU-2023-2-RIA HORIZON JU Research and Innovation Actions) under Grant 101139769.

14

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