Rethinking Battery-free Sensing Communication via Wake-up Radios

1

Rethinking Battery-free Sensing Communication via Wake-up Radios Gaosheng Liu

Abstract—Battery-free sensors expose short, stochastic communication windows and may lose timing state whenever their main energy domain browns out. MagPie combines a microampere wake-up radio (WuR) with a separately backed low-power real-time clock (LP-RTC): the WuR widens the first-contact window, while the LP-RTC preserves the acquired phase for later exchanges. Energy gates, epoch-versioned schedules, and idempotent slot allocation extend this mechanism to static, singlehop All-to-One collection without a powered control anchor. The analysis accounts for role selection and duty-cycled listening, and bounds scheduled-retry tails only under explicit conditional quantile coverage. Evaluation separates three scopes. In independent, administratively censored simulation trials, MagPie completes 100/100 first rendezvous events in each of five traceparameterized harvesting scenarios; Find completes 36–100/100. A single-collision-domain slotted-Aloha study shows that adaptive K is necessary at high contender density and reports mean, P95, and confidence intervals through 120 components. Finally, controlled STM32WL33 experiments validate alignment, clock persistence, and six-device slot execution, including an 11.05hour functional run. The study does not claim measured endto-end energy, ambient-harvesting performance, or multi-hop scalability; highly variable harvesting still limits collection because coordination cannot create missing energy. Index Terms—Battery-free networks, energy harvesting, intermittent computing, wake-up radio, clock synchronization, Internet of Things, wireless sensor networks.

B

I. I NTRODUCTION

ATTERY-FREE sensors harvest ambient radio-frequency, solar, or kinetic energy instead of carrying a battery. They can reduce maintenance and electronic waste in pervasive sensing deployments [1], [2], and are an important part of the emerging Ambient IoT vision [3]. Their communication problem, however, differs fundamentally from conventional duty cycling. A small capacitor powers the device only briefly; after voltage falls below a shutdown threshold, the processor and main radio lose power until the harvester replenishes the buffer. Figure 1 illustrates the resulting temporal asymmetry. Active windows can be only a few milliseconds, whereas charging intervals are two to five orders of magnitude longer [4], [5]. Intermittent-computing systems preserve local progress through checkpointing or idempotent tasks [6]– [10], but a checkpoint cannot make two independently powered radios awake at the same time. Communication therefore remains a system-level bottleneck. Gaosheng Liu is with the Department of Information Engineering and Computer Science, University of Trento ( e - mail: lgselite@ 1 6 3 . com) .

short active window

D1

D2 Von

stochastic charging interval Voff

Time Fig. 1. Intermittent operation. A millisecond-scale active window is separated from the next by a much longer, stochastic charging interval. Main-radio communication requires two active windows to overlap.

Office

Washer

Stairs 104

103 102 102 0

400

800

Charge-cycle index

0

400

800

Charge-cycle index

0

400

800

Charge-cycle index

Fig. 2. Charging-time traces from the Bonito dataset [11]. The vertical axis is logarithmic; the orange band is a 60-cycle rolling mean ± one standard deviation. Variability differs markedly across source and location.

The difficulty is not merely a long mean charging time. Figure 2 shows that charging varies across cycles and devices even within one harvesting setting. Find and Bonito predict or learn future charging behavior [4], [5]; a prediction error can invalidate the intended rendezvous. Flync exploits mainsfrequency light flicker, but only where that shared periodic signal exists [4]. A second family instead imposes a slotted schedule from a powered beacon or coordinator [12]– [14]. This can be fast, but reintroduces powered infrastructure and a distinguished point of availability. These approaches expose two requirements. First, an infrastructure-free pair must discover one another despite stochastic, non-overlapping active windows and then retain the acquired timing state. Second, a network must turn pairwise contacts into a recoverable collection schedule without assuming that every device is powered in every round. Key idea. Instead of predicting a narrow main-radio window, MagPie uses a WuR to widen it. Let X > 0 be a receiver’s charging interval, w its main-radio active width, δ its WuR listening duty factor, and K the identifier-hashed role modulus. Conditional on X , assume the peer’s beacon phase is uniform over that interval. Exactly one endpoint of a pair transmits

2

listening duty cycle; the second gives a miss-tail bound under explicit conditional quantile coverage without temporal independence.

TABLE I C OORDINATION MECHANISMS AND BROWNOUT SEMANTICS . “E XTERNAL ” MEANS THAT AN ALWAYS - ON ANCHOR RECREATES TIMING ; IT IS NOT LOCAL PERSISTENCE .

We extend pairwise schedules to single-hop All-to-One collection through versioned discovery, idempotent range assignment, and recovery after clock or link-state loss, and evaluate its slotted-Aloha contention envelope. • We separate evidence from an STM32WL33 mechanism prototype, independently censored trace-parameterized simulations, and a collision-domain MAC study. Results include seed-block confidence intervals and explicitly bounded claims. •

Protocol

Rendezvous basis

Powered After node anchor brownout

Find [4] Flync [4] Bonito [5] CATO [15] Swift [12] Pulsar [13] FreeBeacon [14]

random prediction flicker lock learned prediction addressed WuR slotted beacon slotted beacon slotted beacon

No No No No Yes Yes Yes

re-learn re-lock re-learn rediscover external external external

MagPie (ours)

WuR + LP-RTC

No

local restore collection

Scope pair pair pair ND/MAC network collection collection

with probability prole = 2 K _ _ 1 ( 1 _ K _ _ 1 ) , giving

II. R ELATED W ORK A. Intermittent Computing

≈ prole δ ( Tlisten + w ) E [ X _ _ 1 ] , where the second line applies only when (T listen +w)/X < 1 with high probability. The expectation is over the interval distribution; replacing it with 1/E[X] is generally incorrect. Equation (1) is not distribution free: correlated or nearly periodic charging can violate the uniform-phase premise and create a beat frequency with the LP-RTC tick. The role hash breaks sender symmetry but not such phase locking; repeated misses must therefore trigger phase re-estimation (and, in a deployed implementation, an identifier-derived tick dither). Listening is sustainable only while the harvester covers WuR and leakage current; otherwise δ < 1 trades reception probability for charge progress. MagPie builds on this observation. A WuR handshake establishes relative phase, and an LP-RTC in a separately backed domain preserves it while the MCU and main radio are off. Subsequent energy misses do not erase timing state. Multi-threshold voltage gates prevent a radio phase from starting below its configured budget, and a sender-owned epoch reconciles cycle updates after missed notifications. At network scale, component representatives contend to construct a versioned merge tree; a two-pass range allocation then assigns collision-free collection slots without a battery-powered control anchor. The novelty is not the WuR primitive by itself, nor a new general-purpose routing metric. It is the hardware–protocol co-design that (i) listens during charging, (ii) separates timing persistence from the main energy domain, (iii) admits work only when a characterized voltage interval can fund it, and (iv) turns one probabilistic contact into a recoverable schedule. We deliberately scope the network layer to stationary, singlehop All-to-One collection. Multi-hop routing and mobility are not evaluated and are stated as limitations rather than implied capabilities. Our contributions are as follows: We design a WuR–LP-RTC communication stack for intermittently powered devices, including energy gating, phase acquisition, persistent scheduled exchange, and explicit fallback re-alignment. • We separate first-contact opportunity from scheduled energy availability. The first analysis includes role probability and •

Checkpointing systems save volatile state before power loss and restore it after reboot [6], [8], [16]– [18]; task-based runtimes instead divide a program into safely repeatable units [7], [9], [19]. Later work handles peripheral state [20], verification [21], and complete applications [22], [23]. These systems preserve computation on one node. MagPie addresses the complementary problem of acquiring and retaining timing state shared by multiple intermittently powered nodes. Energy-harvesting wireless sensor networks traditionally use rechargeable batteries or large buffers and schedule sleep over much longer intervals. Duty-cycling [24]– [26] and energyaware routing [2 7] – [2 9] generally assume that a sleeping node retains state and can wake at a predetermined time. MagPie instead targets main-domain brownouts and short active windows. B. Wake-Up Radios Wake-up radios offload idle listening to a receiver drawing microwatts rather than milliwatts [30]– [33]. Greentooth combines WuR and TDMA around a powered base station [34]. CATO is the closest batteryless WuR design: its BEWAREMAC supports addressed exchange and WEND builds broadcast neighbor discovery [15]. MagPie addresses a different state boundary—retaining relative time when the MCU and main radio repeatedly lose power—and adds energy-gated scheduled collection. CATO is therefore discussed as complementary rather than dismissed or treated as a numerically interchangeable baseline. A direct comparison would require porting both stacks to the same WuR, capacitor, and harvester; the present clock-loss stress test isolates only the persistence mechanism and is not a CATO reimplementation. C. Battery-Free Rendezvous and Networking Classical asynchronous neighbor-discovery protocols illuminate the duty-cycle tradeoff. Disco uses co-prime wake schedules, U-Connect combines symmetric and asymmetric schedules, and Searchlight systematically probes slots [35]– [3 7]. They provide deterministic or bounded rendezvous under retained clocks and conventional sleep, assumptions that fail when the timing domain itself browns out. MagPie borrows their lesson that schedule density must be priced against discovery

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delay, but first acquires and then protects a cross-brownout phase. It does not supersede their mobility or heterogeneousduty-cycle results. Find uses optimized random delays to discover a peer without infrastructure, and Flync accelerates it when both endpoints observe mains-frequency light flicker [4]. Bonito learns charging-time distributions online and schedules later exchanges from the learned model [5]. These methods avoid a powered coordinator, but their rendezvous quality depends on a charging model or an environmental timing signal. Coordinator-based systems take the opposite approach. Swift broadcasts synchronization signals from a powered coordinator [12]; FreeBeacon uses coprime cycles to reduce repeated misses after failures [14]; and Pulsar demonstrates scheduled aggregation [13]. Camaroptera and Kingdom likewise use powered infrastructure [38], [39], whereas RICS assumes comparatively stable energy when routing through an intermittent network [40]. Hybrid light/backscatter and other backscatter networks move cost to the physical layer or reader infrastructure [41], [42]; they remain relevant alternatives rather than drop-in protocol baselines. A powered schedule can outperform MagPie, as the Stairs result shows. The distinction is architectural rather than universal performance: MagPie retains a schedule without an always-on control anchor. Its network contribution is versioned single-hop collection, not general topology control or multi-hop routing. III. M AG P IE S YSTEM D ESIGN We first state the device model and the hardware primitives the design rests on (§III-A) and the multi-threshold energy mechanism governing every operation (§III-B), then detail pairwise communication (§III-C–§III-D) and the networking protocol (§III-E). §III-F quantifies the resulting overhead. A.

Preliminaries: Device Model and Hardware Primitives 1) Device and Energy Model: A battery-free device comprises an energy harvester, a storage capacitor C, a microcontroller (MCU), a main radio, a wake-up radio, nonvolatile memory, and a low-power real-time clock. Let V (t) be the capacitor voltage: the main domain is active while V (t) exceeds the shutdown threshold V off and charging otherwise. Write X i,k for device i’s charging time in cycle k, from V off to the boot threshold. We make no parametric assumption about its distribution. The analysis in §III-D2 states the weaker conditional coverage property it needs; when that property stops holding, the protocol detects repeated misses and reestimates its cycle. Devices are stationary, uniquely identified, and within single-hop range.

2) Primitive 1: Capacitor Voltage Thresholding: The energy state machine of §III-B needs the MCU to detect when V (t) crosses each of five thresholds. The STM32WL33 provides an analog comparator, a 6-bit DAC, an ADC, and a programmable voltage detector [43]. The proposed power path senses the storage node through a switchable divider, references the comparator from the DAC, and arms only the next expected crossing; an interrupt then selects the following level in Eq. (6). This path is a design specification, not an end-to-end integrated

measurement on the present prototype. Divider, comparator, regulator, and reference currents are consequently parameters in the sizing rule below rather than measured MagPie savings. 3) Primitive 2: Non-Volatile State: Protocol state that must outlive a main-domain failure comprises the LP-RTC snapshot, peer offsets, synchronization cycle and epoch, aggregation slot, membership version, and neighbor table N i. Timing-critical state fits in the AM1805’s 256-byte backup RAM, which shares the separately backed clock domain [44]; stable identifiers and topology versions are mirrored to MCU flash only when they change, not once per charge cycle. A topology update is committed after the state transition and before the V radio-off – V off reserve is consumed. If the RTC backup domain itself fails, its oscillator-failure flag invalidates the backup-RAM record, so stale offsets are never trusted. We do not checkpoint application state, and we do not claim measured NVM-write energy; MagPie composes with existing intermittent-computing runtimes [7], [9], [10]. 4) Primitive 3: The Persistent LP-RTC: Clock persistence is the load-bearing hardware assumption of MagPie. An oscillator sharing the radio’s storage capacitor would stop when that capacitor drains and invalidate every cached offset. We therefore place the LP-RTC in a separate always-on power domain: an AM1805 crystal oscillator and counter drawing approximately I rtc = 55 nA in crystal mode, isolated from the main storage node and backed through its dedicated VBAT input [44]. The main domain may brown out while the clock continues, provided the backup reservoir has charge. How long the clock survives. Let Crtc be the reservoir capacitance and ∆V rtc the voltage headroom between Voff and the oscillator’s own brown-out level. Ignoring the harvester, the clock domain survives an outage of duration

where I leak includes reservoir, isolation, and board leakage. The backup reservoir is therefore sized independently of the main capacitor. Ignoring leakage, 10 mF and 1.5 V of usable headroom yield 75.8 hours (3.2 days) at 55 nA. That value is an ideal upper bound, not a prototype measurement. Leakage of 0.1, 0.5, 1, and 5 µA reduces the same example to 26.9, 7.5, 4.0, and 0.82 hours, respectively. Temperature, component tolerance, and dielectric leakage can therefore reverse the apparent benefit of a large reservoir. An outage exceeding Thold invalidates cached offsets; MagPie detects that condition (§III-C3) and performs a fresh alignment. Section IV-D4 quantifies only the protocol consequence of loss, not a measured failure distribution. How fast the clock drifts. Even while running, two crystals disagree. If each oscillator has fractional frequency error bounded by ρ, their relative offset after an interval T since the last alignment is at most 2ρT. A scheduled overlap therefore remains valid only while

which fixes the staleness threshold at which cached offsets must be discarded. For ρ = 20ppm and T guard = 10ms, Eq. (3)

4

gives τ stale = 250 s. Here ρ must be the worst-case error over the deployment’s temperature range, not a room-temperature typical value. Wake-response jitter and timestamp quantization consume part of Tguard at T = 0; only the remaining margin covers drift. Increasing the guard extends that interval but raises receiver energy in every exchange; §III-F quantifies the tradeoff. 5) Sizing the Storage Capacitor: Each protocol phase ϕ starts only when its assigned voltage interval [Vl,ϕ , Vh,ϕ] can fund the load, conversion loss, state commit, and quiescent draw: E req,ϕ = E load,ϕ /η ϕ + E commit,ϕ + V̄ϕ I q,ϕT ϕ + E m,ϕ , 2Ereq, ϕ (4) . C ≥ max ϕ V2h ,ϕ − Vl2,ϕ

TABLE II V OLTAGE THRESHOLDS DEFINING THE ENERGY STATE MACHINE . E ACH THRESHOLD GATES A CLASS OF OPERATIONS , ENSURING SUFFICIENT ENERGY BEFORE COMMITMENT ; THE SAME FIVE LEVELS ARE DRAWN IN FIGURE3.

Here η ϕ is conversion efficiency, Iq,ϕ aggregates static current over duration Tϕ , and V̄ϕ is the corresponding average rail voltage. This phase-wise rule is stricter and more useful than assigning an entire handshake to one window, but it becomes predictive only after every term is measured on the target board. The prototype uses 1000 µF; the simulator’s 47 µF value normalizes Bonito charging times and is not evidence that the prototype can execute its full exchange from that capacitor. Capacitance is not a free performance improvement. Under an ideal constant charging current, both stored energy and the charge time over a fixed voltage interval scale linearly with C ; the prototype’s 1000 µF buffer therefore takes 21.3 × as long to traverse that interval as 4 7 µ F . Larger electric- double - layer capacitors also introduce leakage, aging, and coldstart delay. We consequently use equal 47 µF normalization in every simulated protocol comparison and treat the 1000 µF testbed only as mechanism validation, not as evidence of an energy or latency advantage over small-buffer baselines. The WuR listens while the main store is charging. If Iharv > I WuR + I leak , it reduces net charging current and stretches a charge interval approximately by (1 − I WuR / (I harv − I leak )) —1 . At or below that break-even current, continuous listening would stall charging, so the implementation duty-cycles the WuR. Thus widening Tlisten is inexpensive only when the local power budget supports it. Equation (1) also gives an implementable tuning rule. Let q ( L ) = E [ min{ 1 , ( L + w ) / X } ] , estimated from the recent charge history, and let E0 be fixed energy per opportunity. Under the renewal approximation, expected listening-side energy per successful first contact is proportional to

vastly different energy requirements. To reserve the characterized energy for each committed operation, we partition the capacitor voltage range into five ordered thresholds (Table II):

A device can search its allowed (L,δ) values and choose the smallest J subject to a latency constraint; K = 2 maximizes pairwise role separation, while dense component discovery instead uses K ≈ m for m contenders. This is a first-order controller because the present prototype has no end-to-end current trace from which to calibrate E0. B. Multi-Threshold Energy Decision Mechanism MagPie spans two radio subsystems—the WuR for lowpower coordination and the main radio for data exchange—with

Threshold Description V WuR-2x V WuR-1x V radio-on Vradio-off Voff

Boot threshold; device initiates WuR TX or enters WuR-RX WuR lower bound; proceed to main radio, continue WuR, or recharge Main radio activation threshold Radio communication termination threshold; NVM commit point Critical shutdown; device powers off, LP-RTC domain continues

V W u R - 2 x > V W u R - 1 x > V r a d i o - o n > V r ad i o- of f > V of f

(6)

This provides staged decision-making and an energy reserve: a radio phase starts only after the voltage interval assigned by Eq. (4) is available. The margin absorbs characterized converter and load variation; it is not a guarantee outside the measured operating range. The energy budget between adjacent thresholds is dimensioned as follows. The region [V WuR- 1x , V WuR- 2x ] reserves energy for one WuR operation (either Radio WuR-tx or WuR rx ). The region [V radio-on , V WuR- 1x ] reserves a second WuR operation, providing a two-step coordination budget before mainradio engagement. The region [V radio-off , V radio-on ] sustains one complete main-radio transaction (a TX followed by an RX, or the reverse). Below Vradio-off the device commits state to NVM and sleeps until V off . This creates an asymmetry favoring rapid recovery: a device whose WuR handshake fails to reach a main-radio link falls only to V radio-on and recovers two regions, whereas a completed exchange falls to V radio-off and recovers three. Failed coordination is therefore cheaper than successful communication, producing a listen–charge–listen pattern that maximizes the fraction of time a device can hear a WuR beacon. C. Pairwise Synchronization We now describe how two battery-free devices discover each other and align their clocks. The protocol proceeds in three stages: role selection, clock alignment via WuR handshake, and persistence of the resulting alignment across power failures. 1) Role Selection Under Identical Conditions: A rendezvous requires exactly one transmitter and at least one listener. A naive rule—transmit whenever the LP-RTC counter reaches a multiple of K—fails when co-deployed devices advance in lockstep and repeatedly transmit together. MagPie instead derives the decision from identity. At each clock edge, device i with counter ci transmits a WuR beacon if and only if H (IDi ∥ ci) ≡ 0

(mod K),

(7)

where H is a lightweight hash, and otherwise listens in WuR-RX. Each eligible device therefore transmits on a pseudorandom 1/K fraction of edges. Unique identifiers decorrelate

5

WuR beacon wake after T

resp

VWuR− ! 2x VWuR− ! 1x

reply at next Rr

1 2

scheduled ioedo erlap

3

Vradio− ! on

4

Vradio − ! off Voff RTC D1 RTC D2 Δ 12

sender D2

receiver D1

Time

Fig. 3. Clock alignment. (1) D 2 sends a WuR beacon; (2) D 1 wakes after T resp and measures phase; (3) D 1 replies at its next LP-RTC edge; and (4) both devices later open the main radio in the guarded overlap. Dashed lines are the five thresholds in Table II.

roles even with identical energy histories, and re-evaluation prevents one collision from becoming permanent. It does not by itself randomize a periodic wake phase, which is why repeated misses invalidate the alignment premise rather than proving peer absence. Collision behavior. With m eligible contenders in one collision domain, the probability of exactly one transmission in an opportunity is

maximized near K = m. The choice of K therefore trades idle opportunities against collisions. A failed attempt receives no handshake reply and is retried after a fresh identifier–counter hash; no persistent backoff state is needed. Pairwise simulation uses K = 2, and the six-device firmware conservatively uses K = 32. For network formation, each component nominates one representative from its current roster and sets K from the advertised component count; a new epoch re-elects representatives. Section IV-D 1 evaluates this slotted-Aloha rule separately from the energy simulator, including fixed K, false wakes, and N = 120. That model assumes one collision domain and no capture; hidden terminals remain a multi-hop issue. 2) Clock Alignment via WuR Handshake: The purpose of alignment is to estimate the relative LP-RTC phase ∆ ij = ϕ i _ ϕ j

(mod Tclk)

(9)

between two devices, so that each can compute the other’s clock edges thereafter. Figure 3 illustrates the procedure. Suppose Eq. (7) selects D 2 as sender while D1 listens in WuR-RX: a) D 2 transmits a WuR beacon (Radio WuR-tx ) carrying its current LP-RTC counter value c2 , and records its own local transmit instant ttx 2 . b) D1 detects the beacon and its MCU becomes ready after the nominal wake-up response time Tresp , dominated by oscillator stabilization. Let tr1x be D1’s local time at that moment and let T sleep be the residual interval until D 1 ’s next clock edge. Using the calibrated mean response, D1 recovers the phase difference as

and equivalently obtains Tsleep = T clk _ ∆ 12 as the wait to its own next edge. The arithmetic is modulo Tclk , so Tresp may span more than one tick; its measured jitter, rather than its mean, contributes to Tguard . c) D 1 replies with a WuR beacon at its next clock edge, carrying c 1 and the measured ∆ 12. This lets D2 compute the reverse offset ∆ 21 = _ ∆ 12 mod T clk and confirms to D1 that the link is bidirectional. After this exchange both devices hold each other’s phase and can compute the other’s clock edges without further measurement. The residual error in Eq. (10) is bounded by the LP-RTC resolution plus Tresp jitter—the quantity Tguard must cover at T = 0, growing thereafter at 2ρ per unit time. 3) Shutdown, Recovery, and Staleness Detection: When V(t) falls below Vradio-off , the device commits the state enumerated in §III-A to NVM and sleeps; below V off it powers down entirely, leaving only the LP-RTC domain alive. On recharging to V WuR- 2x it reloads that state and resumes from the last committed point. Because the LP-RTC has continued counting, the stored offsets are still meaningful: the device reads the current counter and computes the next scheduled rendezvous directly from ∆ij . A single successful alignment therefore persists across an arbitrary number of power failures, provided two conditions hold. The first condition is that the clock domain survived, i.e. the outage was shorter than Thold of Eq. (2). At boot, firmware checks the AM1805 oscillator-failure flag, which is asserted after initial power-up or oscillator failure [44]. A set flag invalidates all cached offsets; firmware clears it only after a successful alignment. The second condition is that accumulated drift has not exceeded the guard interval. The device compares the current counter against the stored snapshot; if the elapsed time exceeds τ stale from Eq. (3), it invalidates its cached offsets and re-enters alignment. Both conditions are checked at every boot, cost a handful of instructions, and fail safe: a device that wrongly believes its offsets are valid loses at most Rmax cycles before the fallback of § III- D 4 triggers a full re- alignment. D . Sustained Connection Once aligned, a pair exchanges data through scheduled radio overlap rather than repeated handshakes. 1) Sizing the Synchronization Cycle: Both devices must agree on how long to wait between communication opportunities. Let X1 , X2 denote their charging times, and let q̂ i (α) be device i’s empirical α-quantile over its last W cycles (W = 32). During alignment each device transmits q̂ i (α), and both adopt l Tcyc = 「max{ q̂ 1 (α), q̂ 2 (α) } /Tclk · Tclk . (11) The estimate is a quantile, not a maximum: it deliberately accepts nominal miss probability 1 _ α instead of pretending that the next sample is bounded by the past. We use α = 0.9. More generally, the distribution-free attempt bound below suggests choosing

6

k=0

k=1

k=2

k=3

sender D2

charge WTX

charge W TX

charge WTX

charge WTX

receiver D1

charge WRX

charge W RX

charge Wgate charge WRX

<

Tcyc charging

insufficient energy

>

WuR notify

guard

main radio

Fig. 4. Sustained pairwise connection. A sender notification (W) precedes each guarded main-radio overlap. At k = 2 the receiver’s energy gate blocks its radio; the persistent schedule is retained and the pair retries at k = 3.

subject to the application’s required miss tail. This prices a longer cycle against fewer expected attempts. The current firmware fixes α rather than running this controller. Its rolling empirical quantile also does not guarantee conditional coverage under arbitrary drift; an online calibration test must treat a sustained excess miss rate as a regime change and advance the schedule epoch. 2) Rendezvous Analysis: We can now bound what MagPie guarantees. Equation (1) concerns whether a beacon can be heard; the remaining uncertainty is whether both endpoints hold enough energy at the scheduled boundary. Fix Tcyc and let Fk— 1 contain the charging history before cycle k. The estimator is conditionally calibrated at level α when, for each endpoint i and cycle k, Pr[Xi, k ≤ Tcyc | Fk— 1 ] ≥ α .

(13)

This explicitly rules out an unobserved regime shift that makes the selected cycle systematically too short. Under Eq. (13), the conditional probability that both endpoints are ready is bounded by the Fréchet–Hoeffding inequality: pk ≥ p 0 ≜ max(0, 2α _ 1).

(14)

If the two charging processes are conditionally independent, the stronger bound pk ≥ α 2 applies. Proposition 1 (Rendezvous tail bound). Under Eqs. (13)–(14), the number of cycles M until the first successful exchange satisfies Pr[M > m] ≤ (1 _ p 0 ) m ,

E

(15)

For independent, identically distributed cycles with constant joint success probability p, these inequalities reduce to the familiar geometric equalities. At α = 0.9, p 0 = 0.8, so the expected number of attempts is at most 1.25 and five consecutive misses have probability at most 3.2 × 10 — 4 . The result is a bound, not determinism. When the conditional coverage premise fails, no tail guarantee follows. Operationally, however, a miss does not erase phase: the next opportunity remains computable from the surviving clock, whereas a prediction-based discovery may have to search for the peer again.

Cycle updates. Equation (13) can fail after an environmental change. The sender therefore owns a monotonically increasing schedule epoch and carries (epoch, Tcyc , tnext) in each WuR notification. It recomputes Eq. (11) from its rolling window and the peer’s last advertised estimate; the receiver adopts only newer epochs. After Rmax receiver-observed misses, that receiver initiates the full-handshake fallback of §III-D4, during which the sender transfers a fresh estimate and schedule. This explicit versioning avoids assuming that an unpowered receiver and a one-way sender observe the same miss sequence. 3) Acknowledgment-Free Scheduled Activation: A full alignment uses a return WuR beacon to measure both directions. Once phase is known, scheduled activation omits that WuR acknowledgment (Figure 4). The sender emits a notification at the cycle boundary and schedules its main-radio packet to coincide with the receiver’s wake-up, computed from ∆ ij and T resp . The receiver opens its radio T guard early to absorb residual error. Both endpoints verify V (t) > V radio-on before main-radio activation; an energy-starved endpoint simply remains absent. This optimization must not be confused with end-to-end reliable delivery. In a one-way collection slot, the sender receives no data acknowledgment and therefore cannot infer that the sink accepted its packet. The simulator reports receiverside receptions, and the testbed reports packets logged at the sink. An application requiring confirmation must add a later cumulative bitmap or a short main-radio ACK and include its energy in Eq. (4); neither mechanism is implemented or evaluated here. “Acknowledgment-free” in this paper consequently describes scheduled activation, not a reliability guarantee. 4) Failure Recovery: A receiver that was energy-qualified and heard a notification but observed no scheduled payload can count a miss; possible causes include sender energy, payload loss, drift, or a stale cycle. A one-way sender cannot make the symmetric observation. An isolated receiver-side miss leaves the schedule intact. Equation (3) prevents known drift from exceeding Tguard , while the epoch mechanism communicates cycle changes whenever the receiver is reachable. After R max observable consecutive misses (R max = 3), the observing endpoint initiates a full bidirectional WuR handshake and remeasures phase and cycle. In All-to-One collection this endpoint is normally the sink; if it is itself unpowered, recovery cannot start until it returns. A smaller threshold performs more needless alignments; a larger one can leave the pair disconnected for Rmax Tcyc . The evaluation fixes this parameter and models observable misses; it does not claim end-to-end acknowledgment semantics or an experimentally optimal value. E. Networking Protocol We now extend pairwise communication to N reporting battery-free devices and one logically distinguished sink in a static, single-hop radio domain. Each reporter transmits in a distinct slot of a shared distribution cycle Cdis . The sink does not allocate indices and need not be externally powered; however, a collection round can begin only when it has enough energy to receive that round. The simulator idealizes this gate as always true, an explicit limitation in §IV-A. Construction has

7

TABLE III L OGICAL MESSAGES AND TRANSPORT . “P ERSISTENT EFFECT ” IS

root owns [1,5]

COMMITTED BEFORE THE RESERVED SHUTDO WN MARGIN IS CONSUMED .

WuR WuR main radio main radio main radio

Persistent effect

ID, counter epoch, next tick comp. ID, epoch, bitmap epoch, interval, slot epoch, source, payload

peer phase cycle update membership slot assignment sink reception

collection cycle Cdis

D

2

3

5

Align Notify Roster Range Data

Core fields

D

Object Transport

Round 1 D1

Round 2 D2

D4

Round 3

n

Fig 6 Slot distribution for five reporters Root D1 owns [ 1, 5], retains slot 1, and partitions the remaining interval into disjoint subtree ranges A reporter stores (epoch , range , slot) before acknowledging; the final cycle is therefore unique despite message replay.

D3

D5

ubt ree ra ges re d j oi ． ．

Discovery tree

bership, and slot assignment survive main-domain brownouts, discovery is not repeated per packet. A device re-enters it only when an offset becomes stale, the RTC failure flag is set, or a membership epoch changes. 2) Phase 2: Slot Distribution: We set Cdis = NTclk . The smallest identifier roots the merge tree. An upward pass first reports each subtree’s size; a downward pass gives the root [1, N ] and recursively partitions it into contiguous child ranges in identifier order. Each node takes the first index of its range and divides the remainder according to the reported subtree sizes. Figure 6 shows the five-reporter case.

Fig. 5. Logical component merges for five reporters. Only inter-component contacts are retained, producing a tree with N — 1 timing edges. In one collision domain, at most one solo WuR transmission succeeds per contention opportunity.

two phases: component discovery, which creates a versioned timing tree, and slot distribution, which allocates a unique index to every reporter. Table III separates the logical control objects and their placement. The 15-byte bitmap at N = 120 is a main-radio roster payload after WuR alignment, not a WuR wake address. The evaluation fixes a 32-byte main-radio packet, so that bitmap leaves 17 bytes for the component identifier, epoch, and linklayer header in the modeled frame. Exact WuR serialization and link-layer overhead are platform specific and are not included in the simulator’s primitive-energy table. 1) Phase 1: Component Discovery: Figure 5 illustrates one five-reporter execution. Each component carries an exact membership bitmap and epoch, and nominates one identifierhashed representative per contention epoch. Representatives apply Eq. (7) with K matched to the estimated number of components. A solo beacon can align with a listening representative from another component; two or more concurrent beacons collide in the single-domain model. A successful intercomponent contact unions the rosters, advances the epoch, and becomes a merge-tree edge stored at both endpoints. Intracomponent contacts are ignored. Discovery completes when the merged bitmap contains the provisioned identifier universe of size N. This rule yields exactly N _ 1 accepted edges, but it does not discover an unknown population; dynamic join and leave require a separate membership service. Discovery is amortized. Because Ni , phase offsets, mem-

Why replay cannot create duplicate slots. Every assignment carries the component epoch and a closed integer range. A child writes (epoch , range , slot) to persistent state before acknowledging. Repeating a message after either endpoint browns out is therefore idempotent: an equal epoch and range reproduce the same decision, while an older epoch is discarded. Because sibling ranges are disjoint by construction, concurrent branches cannot issue the same index. A missing acknowledgement leaves a gap until the identical assignment is replayed; it does not release the range for reassignment within that epoch. After all confirmations, the root propagates (epoch, Cdis , t 0 ) and the sink adopts the same epoch and origin through its pairwise schedule with the root. 3) Maintenance Under Clock or Link-State Loss: Each tree edge is valid, suspect, or expired. R m a x observable misses make it suspect and trigger the full handshake of §III-D4; a successful handshake refreshes its offset and returns it to valid. If only the clock domain is lost while the topology epoch survives in flash, the node invalidates all adjacent offsets and re-aligns those edges before using its slot; it does not silently reuse their timestamps. After L max = 3 complete handshake timeouts, the endpoints expire the edge, increment the component epoch, and the detached subtree re-enters discovery. A parent outage can therefore pause its subtree but does not change siblings’ epochs until the edge expires. The static, error-free evaluation does not validate these timers under mobility or fading. Control and storage complexity. A completed merge tree has N _ 1 accepted alignments. The two slot passes use at most 2(N _1) successful parent–child transfers, and each collection round contains N reporter transmissions. Per-node persistent

8

TABLE IV M ODEL - BASED PRIMITIVE COSTS USED BY THE PROTOCOL .

DS Logic Analyzer View Powercast Transmitter 915MHz (Energy Source) Radio Harvesting Antenna (6.8 dBi Directional)

Phase

Cost Latency Frequency

WuR beacon TX 38.4 µJ 12 µW WuR listening Data packet TX 40.8 µJ 165 µJ Main-radio RX

1.12 ms per notification Tlisten while enabled 1.02 ms per exchange 11.0 ms payload + guard

storage is O (di) for di tree neighbors and total topology storage is O (N). Candidate selection can inspect O(N2 ) pairs in the worst case. Slotted contention adds a random number of idle and collided opportunities quantified in §IV-D 1; the separate energy simulator’s matching must not be used to infer that cost. 4) Cycle Reconciliation: A device must honor both its pairwise cycle Csync and the distribution cycle C dis . Rather than take an arbitrarily large least common multiple, it rounds Csync up to the next multiple of C dis :

expressed in T clk ticks and committed with the current epoch. This gives C sync ≤ C op < C sync + C dis ≤ 2max(C sync , C dis ). The added wait is less than one distribution cycle, not one clock tick. F. Overhead Analysis A coordination scheme that consumes the budget it protects is of no use. Table IV therefore exposes the primitive costs used by the energy gate and simulator. Values are computed as measured duration times configured active power; they are not end-to-end shunt measurements and exclude regulator loss and NVM commits. Excluding WuR listening, conversion loss, and state commits, the modeled active cost of one acknowledgment-free scheduled data transfer is 79.2 µJ at the sender (one notification plus data TX) and 165 µJ at the receiver. Initial alignment adds two WuR beacon transmissions, 76.8 µJ across the pair. Listening itself is not free: 12 µ W for the maximum 30 s window is 360 µJ drawn from the harvester and appears as a longer charge interval through the relation in §III-A5. A false wake additionally invokes platform-dependent MCU start-up and is not represented by these four primitives. The receiver is the expensive scheduled role: at the configured 15 mW, a 10 ms guard costs 150 µJ before payload reception. Equation (3) is therefore a genuine tradeoff. A wider guard extends offset lifetime but is paid every cycle; periodic re-alignment is preferable once its amortized cost is lower. Because the omitted terms can be comparable to the WuR load, the table supports a first-order design study only. End-toend shunt measurements of regulator input energy, threshold circuitry, false-wake handling, NVM commits, and backupdomain leakage are required before Eq. (4) can size production hardware or support an energy-efficiency claim. IV. E VALUATION We answer six questions: (1) How quickly does MagPie establish a pairwise schedule under right censoring? (2) What is

Powercast Eval Board (Energy storage and management)

Device3

Powercast

Device5 Device2

Harvester Device4

STM32WL33CC1 (WuR and Radio)

Device1

AM1 8 0 5 LP- RTC Breadboard

Device6

(a) Prototype

Logic analyzer

(b) Six devices

(c) Logic analyzer

Fig. 7. Experimental testbed: (a) prototype, (b) six-device All-to-One deployment, and (c) logic-analyzer setup. Device 6 is the sink. TABLE V P ROTOTYPE AND SIMULATOR PARAMETERS . Parameter

Prototype Simulator

4 µA WuR listening current WuR response T resp 133 ms LP-RTC tick T clk 100 ms Listening window T listen up to 30 s 32 Role modulus K 1000 µF Main storage Cycle quantile α 0.9 Retry threshold R max 3 Post-event state — Main-radio TX/RX 40/15 mW 32 B Data packet

12 µW at 3 V 113 ms 30 ms 30 s 2 ( pairwise) ; K ≈ m ( MAC study) 47 µF normalization 0.9 3 0.9/0.8/0.3 40/15 mW 32 B

the sustained exchange interval after alignment? (3) How does single-domain WuR contention scale? (4) How do collection and clock loss scale with N? ( 5 ) How sensitive are the results to cycle error, drift, and retry policy? (6) Which mechanisms execute on intermittently powered hardware? A. Experimental Setup 1) Prototype: The prototype uses the STM32WL33CC1, which integrates a Cortex-M0+ MCU, sub-GHz transceiver, and low-power wake-up receiver [43]. The WuR draws approximately 4 µ A while listening. An AM1 8 0 5 in the isolated domain of § III- A 4 provides the persistent 3 2 . 7 6 8 kHz time base [44]. A Powercast TX91502/P2110 link supplies controlled 915 MHz energy to a 1000 µF main buffer. Harvesting and communication are time-multiplexed because they share a band. Here “infrastructure-free” refers to control and scheduling, not to this laboratory energy source; the prototype is not an ambientharvesting deployment. Table V separates prototype settings from simulator settings. The pairwise simulator uses a finer tick and K = 2; the sixdevice firmware uses K = 32. The separate contention study adapts K to component density. Results from these artifacts are therefore not numerically interchangeable. 2) Simulation Framework: The Python discrete-event simulator represents charging intervals, five energy regions, WuR discovery, scheduled exchange, component construction, and slotted collection. It uses five harvesting settings published with Bonito [11]: Office and Stairs (indoor and outdoor light), Washer (machine vibration), Jogging (human motion), and Cars (vehicle vibration). Checked-in experiments use seeded synthetic traces parameterized from those settings, not direct HDF5 replay. Exponential, normal, or two-component Gaussian mixtures reproduce scenario-level mean, variance, drift, and device variation. Charging intervals are scaled from the Bonito artifact’s 17 µF reference to 47 µF by 47/17. The normalized storage state is 1 at WuR-ready; a receive timeout, unanswered WuR transmission, and completed main-radio operation leave

9

TABLE VI E VIDENCE MAP . E ACH ARTIFACT SUPPORTS ONLY THE CLAIM IN ITS ROW . Artifact

Supports

Does not support

2-node logic traces

alignment execution and rate

6-device run Pairwise simulator Network energy model Contention model

formation/slot execution censored relative latency slot/energy bookkeeping single-domain collisions

ambient energy or packet delivery a delivery ratio or large scale hardware energy RF contention or sink outage capture, hidden terminals, energy

0.9, 0.8, and 0.3. These are disclosed model parameters, not measured voltages. Pairwise synchronization uses 100 independent firstrendezvous trials per setting, arranged as ten trials in each of ten seed blocks. Each trial is administratively censored at τ = 5000 s. MagPie starts from the modeled post-exchange storage state 0.3, avoiding the zero-charge first event created by an initially full capacitor. We report completion count and restricted mean synchronization time RMST(τ) = E[min(T,τ)]; 95% intervals are Student-t intervals over the ten seed-block RMSTs. Completed-event CDFs are normalized by all 100 trials, so a curve ending below one exposes censoring. Baselines are Find and, only in Office, Flync [4]; the other sources provide no mains-frequency optical reference. An optimistic powered-coordinator reference captures the scheduled-cycle mechanism shared by FreeBeacon and Pulsar [13], [14]. Its cycle is selected per scenario from 17 candidates between 2 and 5003 ms using the lowest RMST on that scenario. This same-data oracle favors powered infrastructure and is not a feature-complete reimplementation. It also lacks a WuR and therefore is not a causal coordinator ablation: the full { WuR/no WuR}×{ backed clock/no clock }×

{coordinator/no coordinator} hardware matrix remains unmeasured. Sustained connection is compared with a seeded Bonito implementation using five warm-up samples and λ̂ = 1/X [5]. The network energy model runs ten seeds and 50 collection rounds per point. It assumes an error-free single-hop channel and an always-ready sink, and abstracts discovery as a random nonoverlapping matching. Its formation time is therefore discarded from the scalability claim; only energy gating, assigned-slot execution, and recovery bookkeeping are reported. A second, MAC-only experiment replaces that matching with one collision domain and slotted Aloha. Each component representative transmits with probability 1/K; exactly one transmitter plus a listener merges two components, whereas multiple transmitters collide without capture. Five hundred independent trials report mean, P95, and confidence intervals through N = 120. A false wake makes a representative unavailable for one opportunity. This model still excludes hidden terminals, fading, and energy readiness. B. Pairwise Synchronization Figure 8 and Table VII no longer discard timed-out trials. MagPie completes 100/100 in every scenario; Find completes all trials in Office, Stairs, and Washer, 93 in Jogging, and 36 in Cars. Its RMST is 82.7–755.8 × that of MagPie across the five parameterized scenarios. Office Flync completes all trials

with a 3 8 . 2 × RMST ratio. These ratios describe the disclosed simulator, not a universal hardware speedup. The powered reference exposes the architectural tradeoff. It is 1.3 × faster than MagPie in stable Stairs; MagPie has lower RMST in the other four settings. Because the reference is tuned on each scenario and changes both the coordinator and WuR factors, the result is a system comparison rather than an attribution of gain to one component. C. Sustained Pairwise Connection After discovery, both protocols complete 100 exchanges in the first four scenarios, while Bonito does not discover a peer in Cars before the horizon. MagPie reduces the mean sustained interval by 1.8–3.6 × . The gap is smaller than in first contact because both designs benefit once a shared interval exists. MagPie’s distinction is that the interval is retained by the backed clock and a miss triggers a bounded retry rather than immediate rediscovery. D . Network Evaluation 1) Collision-Domain Formation: Figure 10(a) replaces the nonoverlapping-matching assumption for the MAC question. At N = 1 2 0 , adaptive K = m needs a mean 3 1 8 . 0 opportunities (95% CI 316.1–320.0) and P95 359.0 (bootstrap CI 353.1– 362.1). If every 30 ms tick were energy eligible, those values would be 9.54 and 10.77 s; because energy readiness is omitted, they are lower bounds on wall-clock formation. Fixed K = 3 2 raises P9 5 to 7 2 5 opportunities. Panel ( b ) confirms Eq. (8): K/m = 1 is best among the tested ratios, whereas K / m = 0 . 5 and 2 increase mean opportunities from 3 1 8 . 8 to 441.3 and 385.0. In panel (c), making 40% of representatives unavailable per opportunity raises P9 5 from 3 5 5 to 4 1 2 . These results quantify collision and false-wake sensitivity only; capture, hidden terminals, and spurious-wake energy require measurements and a topology-aware PHY model. 2 ) Fixed Size: Table IX reports N = 2 0 reporters over ten seeds and 5 0 rounds. With Tclk = 3 0 ms, Cdis = 6 0 0 ms. Stable Stairs and Office reach 99.7–99.8% receiver-side delivery; Washer reaches 89.0%. Jogging and Cars fall to approximately 70% because reporters often lack radio-grade energy at their assigned instant. The error-free channel makes these losses energy-related by construction. 3) Scalability: Figure 11 scales assigned-slot execution from 6 to 120 reporters. Collection time grows with Cdis = NTclk : at N = 120 it is 3.57 s in Office, Stairs, and Washer, 4.32 s in Jogging, and 11.46 s in Cars. Mean receiver-side delivery is 99.8%, 99.7%, 88.3%, 70.4%, and 70.2%, respectively. The nearly flat delivery trend shows only that this energy model does not exhaust its assigned slots as N increases. It says nothing about collisions (Figure 10), interference, or an intermittent sink. 4) LP-RTC Failure Stress Test: We next force the backed clock to lose state independently with probability p per cycle. This is a protocol stress test, not a measured AM1805 distribution. At p = 0, delivery is 99.8% with no re-alignments. At p = 0.2, delivery is 80.6%, 79.2%, 80.2%, and 79.5% for N = 5, 10, 20, 40; mean re-alignments are 52.5, 111.8, 215.4,

10

Office

1.0

0.5

0.0

Stairs

1.0

0.5

0.5

0.0 10−1

100

101

102

103

0.0 10−1

First-rendezvous time (s)

101

102

103

10−1

100

MagPie Find

0.5

10−1

100

101

102

First-rendezvous time (s)

0.0

103

101

102

First-rendezvous time (s)

103

Cars

1.0

0.5

0.0

100

First-rendezvous time (s)

Jogging

1.0

W ash er

1.0

10−1

100

101

102

First-rendezvous time (s)

— …

F l yn c Powered coord.

103

Fig. 8. Empirical completion curves for independent first-rendezvous trials (logarithmic time). Each jump is divided by all 100 trials, so an endpoint below one shows administrative censoring at 5000 s. Flync is physically available only in Office. TABLE VII F IRST - RENDEZVOUS RMST IN SECONDS TO τ = 5000 S . B RACKETS ARE 95% INTERVALS OVER TEN SEED - BLOCK MEANS ; THE SECOND LINE IS COMPLETIONS /100 . “ N / A ” DENOTES AN UNAVAILABLE ENVIRONMENTAL TIMING SIGNAL .

MagPie Find Flync Powered coord.

Office

Stairs

Washer

Jogging

Cars

0.71 [0.65, 0.78] 100/100 288.57 [215.80, 361.34] 100/100 27.13 [21.63, 32.64] 100/100 1.05 [1.01, 1.08] 100/100

0.33 [0.31, 0.34] 100/100 27.30 [18.62, 35.99] 100/100

0.56 [0.52, 0.60] 100/100 156.02 [130.98, 181.07] 100/100

2.04 [1.73, 2.35] 100/100 1541.78 [1180.50, 1903.06] 93/100

5.86 [4.78, 6.94] 100/100 3892.44 [3513.67, 4271.21] 36/100

n/a

n/a

n/a

n/a

0.25 [0.24, 0.25] 100/100

0.79 [0.68, 0.89] 100/100

3.65 [3.15, 4.14] 100/100

11.41 [8.60, 14.21] 100/100

TABLE VIII S USTAINED CONNECTION AFTER DISCOVERY . E ACH SUCCESSFUL SETTING CONTAINS 100 EXCHANGES ; INTERVAL IS THE MEAN BETWEEN EXCHANGES .

Scenario MagPie (ms) Bonito (ms)

Ratio

3,258 780 2,174 5,484 —

3.43 × 3.64 × 3.34 × 1.80 ×

Office Stairs Washer Jogging Cars

951 215 652 3,052 9,479

—

TABLE IX N ETWORK ENERGY - MODEL RESULTS FOR N = 20 (10 SEEDS , 50 ROUNDS ) . B RACKETS ARE 95% SEED - LEVEL CONFIDENCE INTERVALS . Scenario Mean collection (s)

Delivery

0.57 [0.57, 0.57] 0.61 [0.60, 0.63] 0.58 [0.57, 0.58] 2.21 [2.02, 2.40] 6.90 [6.30, 7.50]

99.74 [99.55, 99.93]% 99.81 [99.71, 99.91]% 88.99 [88.26, 89.72]% 69.63 [69.10, 70.16]% 69.97 [69.40, 70.54]%

Stairs Office Washer Jogging Cars

and 448.9. The approximately linear recovery work explains why Eq. (2) should be sized conservatively. IID failures do not model a common temperature excursion or shared reservoir fault, which could invalidate many edges together.

E. Sensitivity and Assumption Checks Cycle estimation. For each seeded scenario we compute Eq. (11) from the previous W = 32 samples and test the next pair of charging times. With no artificial error, observed joint readiness is 84.7–94.1%, above the distribution-free 80% lower bound for a conditionally calibrated α = 0.9. A 25% underestimate reduces readiness to 25.4–74.5%; a 25% overestimate raises it to 9 1 . 4 – 9 9 . 9 % but lengthens every scheduled cycle by approximately 25%. Thus overestimation spends latency, whereas systematic underestimation can invalidate the operating point and trigger epoch updates. This sweep uses the same seeded synthetic generators as the main evaluation and is not a substitute for ambient-trace replay. Drift and retries. Figure 13(b) makes the guard tradeoff explicit. At ρ = 20ppm, 5, 10, and 20 ms guards remain valid for 125, 250, and 500 s; at 100 ppm those ages fall to 25, 50, and 100 s. Table X prices Rmax without assuming independent cycles: Eq. (15) bounds a needless fallback by (1 _ p 0 ) Rmax , while a true disconnection is recognized after at most R max T cyc . The selected R max = 3 caps that bound at 0 . 8 % and the detection delay at three cycles. Capacitance and role density. At fixed current and thresholds, ideal charge time scales with C: 100, 220, and 1000 µF take 2.13, 4.68, and 21.3 times the 47 µF reference interval. Below Eq. (4), an operation is infeasible; above it, storage trades fewer gate failures for a longer cold start. Role density is

11

Office

1.0

Stairs

1.0

0.5

0.5

0.5

0.0

0.0 2 × 100

100

2 × 10−1

3 × 100

Interval (s)

Jogging

1.0

Washer

1.0

3 × 10−1 4 × 10−1

0.0

6 × 10−1

Interval (s)

6 × 10−1

Interval (s)

C ars

1.0

0.5

0.5

0.0

2 × 100

100

MagPie- Conn

- - Bonito

0.0

2 × 100

3 × 100 4 × 100

6 × 100

Interval (s)

6 × 100

7 × 100 8 × 1009 × 100 101

Interval (s)

Fig. 9. CDF of sustained inter-exchange intervals on logarithmic horizontal axes after initial discovery. Bonito does not establish a Cars connection within 10,000 s. (b) Role density, N = 120

(a) Collision-domain scale 500

adaptive K = m fixed K = 32

600

(c) False wakes, N = 120 420

Mean P95

450

400

380

400

200

Mean P95

400

360 340

350

320

0 25

50

75

Initial components N

100

125

0.5

1.0

1.5

Role modulus ratio K/m

2.0

0

10

20

30

40

Busy representatives (%)

Fig. 10. MAC-only component formation over 500 trials. Solid lines are means; dashed lines are P95. Shading gives bootstrap 95% intervals for P95. (a) Adaptive K = m versus the prototype’s fixed K = 32; (b) role-density sweep; (c) a false wake makes one representative busy for one opportunity. All representatives are otherwise ready, and the model has one collision domain with no capture. Office Stairs

Washer Jogging

(a) Collection time

N=5

Cars 100

300

90

80

5

70

85

200

80

100

75

0

0 40

80

Number of reporters N

120

N = 40

(b) Recovery overhead 400

95

90

N = 20

(a) Delivery

(b) Receiver-side delivery

100 10

N = 10

0.00 40

80

Number of reporters N

120

Fig. 11. Network energy-model scalability over ten seeds of 50 rounds. Lines are seed means; shading is the 95% confidence interval. Discovery uses matching and is excluded.

0.00

0.08

0.16

0.08

0.16

Clock-loss probability p

Clock-loss probability p

Fig. 12. Effect of per-cycle LP-RTC failure probability p in Office (ten seeds). At p = 0.2, delivery is 79–81%, while re-alignments grow approximately linearly with N.

F. Testbed Validation

separate: Figure 10(b) empirically places the best tested point near K = m, consistent with Eq. (8). The fixed K = 32 firmware setting should therefore not be extrapolated to 120 contenders.

Pairwise synchronization. With controlled charging times between 500 and 5000 ms, the logic traces contain 459 complete MagPie latency pulses in 3459 s and 40 Find pulses in 3315 s. Normalized rates are 478 and 43 completed alignments per hour, an 11.0 × increase. Mean synchronization latency is 3678

12

(a) Cycle-estimation error

1.0

(b) Drift budget

100

Tguard = 5 ms Tguard = 10 ms

103

80

Tguard = 20 ms

60

0.5

40 102

20

Office Stairs Washer

0 −50

−25

0

Joggin g Cars

25

0.0

50

50

Estimate error (%)

Clock error ρ (ppm)

TABLE X R ETRY SENSITIVITY AT α = 0.9 (p 0 = 0.8) . 1

2

3

4% 0.8% Fallback bound 20% Detection delay Tcyc 2T c y c 3T c y c

4

10−2

10−1

100

101

Synchronization latency (s)

102

100

Fig. 13. Parameter sensitivity. (a) A multiplier perturbs the rolling 0.9-quantile cycle estimate; each point uses 4968 next-cycle decisions per scenario. (b) Safe schedule age τ stale = T guard /(2ρ) for three guard intervals.

R max

MagPie (n = 459) Find (n = 40)

5

0.16% 0.032% 4T c y c 5T c y c

versus 24,012 ms (6.5 × lower), and maxima are 34,405 versus 222,942 ms. Counts include only closed high pulses; rising and falling transitions are not treated as separate events. The smaller hardware gain relative to simulation is expected because the RF-powered testbed has a narrower energy range and includes real radio and firmware overhead.

Fig. 14. Synchronization latency from logic-analyzer high- pulse widths: 459 completed MagPie events over 3459 s and 40 Find events over 3315 s.

Energy accounting bounds the claim. The 1000 µF testbed buffer provides implementation margin but takes 21.3 × the ideal charge time of the simulator’s 47 µF reference over the same voltage interval. Equal simulated capacitance prevents that buffer from favoring MagPie, but it does not supply the missing shunt measurements. Converter efficiency, threshold circuitry, backup leakage, false wakes, and NVM commits can shift both thresholds and rankings. The present results therefore establish timing behavior and modeled primitive costs, not measured end-to-end energy efficiency. The powered reference is a system comparison. The perscenario coordinator oracle is faster in Stairs and slower in the other four parameterized settings. It simultaneously changes control infrastructure and removes the WuR, so it cannot attribute causality to either factor. A powered coordinator remains attractive where deployment and maintenance are acceptable. Completing the full WuR–clock–coordinator ablation grid on iso-storage hardware is necessary before claiming which primitive supplies each gain.

Network operation. Five reporting boards and one sink run for 11.05 hours. Formation completes in 945 s, after which the sink logs 2998 received data packets with 13.2 s mean source-to-sink latency. The firmware log does not contain the denominator of scheduled transmission opportunities, so these records cannot yield a packet-delivery ratio. The controlled Collection is limited by energy, not only slots. Fixed slots RF source and 1000 µF buffer validate execution of alignment, arrive while a reporter may lack radio-grade energy, yielding persistence, and slotting on real silicon; they do not validate approximately 70% receiver-side delivery in the two most ambient harvesting, large scale, or end-to-end energy. variable settings even under an error-free channel. An energyaware scheduler could order nodes by recent readiness, let the V. D ISCUSSION AND L IMITATIONS sink advertise unused slots, or reclaim a missed range in a later Three parameters govern different risks. The listening epoch. Such changes consume control energy and can break variables (Tlisten ,δ) determine whether a beacon is observable, idempotence if a brownout hides a reassignment; they must K controls role collisions, and α trades scheduled delay against therefore be versioned and evaluated rather than assumed to energy readiness. Equations (5), (8), and (12) expose these as recover the missing 3 0 % . One- way senders also lack delivery separate controls rather than one tuning knob. Their guarantees confirmation unless a cumulative ACK is added. remain conditional: a persistent beat frequency can defeat the uniform-phase approximation, and a regime shift can invalidate Evidence has deliberate boundaries. Controlled logic traces quantile coverage. The current firmware fixes the parameters; and the 1 1 . 0 5 -hour six- device run validate execution, but the online joint adaptation is a design direction, not an evaluated latter lacks an opportunity denominator and hence a delivery result. ratio. The Powercast source is energy infrastructure, not a Persistence is finite. A backed LP-RTC changes the cost of a scheduling anchor. Synthetic traces reproduce selected Bonito miss only while its domain survives and its drift stays within statistics but are not direct HDF5 replay. The network energy the guard. The leakage examples following Eq. (2) reduce a model assumes an available sink and error-free assigned slots; nominal 3.2-day ideal to hours, and the 100-ppm sensitivity the separate contention study adds collisions and false busy shortens a 10-ms guard to 50 s. The forced-failure experiment periods, but assumes continuously eligible representatives, one shows the protocol consequence, but IID loss is not a physical collision domain, and no capture. None of these artifacts alone failure model. Temperature-correlated drift or a shared reservoir demonstrates field-scale RF operation. fault could invalidate multiple edges at once and produce a Multi-hop is not a mechanical extension. In multiple collision domains, hidden terminals make one global K insufficient, more severe recovery burst. and capture or fading changes the solo-transmission model.

13

Each route would need persistent per-hop offsets and versioned forwarding epochs; delivery probability and guard energy would compound along the path. A parent clock loss can stall an entire subtree, while simultaneous low-energy parents can create cascading brownouts near the sink. The existing membership epoch and merge tree provide a recovery namespace, but not channel allocation, energy-aware parent selection, or loopfree repair under concurrent failures. Mobility further changes neighbors, link quality, and energy statistics together. These problems require a topology-aware MAC and a physical multihop deployment and are outside the claims of this paper. VI. C ONCLUSION MagPie demonstrates a specific co-design point: use a WuR to enlarge the first-contact opportunity and preserve the resulting phase in an independently backed clock. Its guarantees are conditional, notwhile deterministic; a stale energy prediction-based rendezvous, the powered reference quantile, confirms that excessive infrastructure drift, orcan lossbeoffaster the backup in somedomain regimes. forces The collision-domain study further showstrials that favor network formation re-alignment. Independent censored MagPie over depends on adapting K to contender density. Controlled hardware validates protocol execution, but the present evidence does not establish end-to-end energy efficiency, field-scale RF behavior, or multi-hop operation. Those claims require shunt-based power measurements, direct ambient-trace replay, a complete reliability denominator, and larger deployments with interference and intermittent sinks. R EFERENCES [1] G. Liu and L. Wang, “Self-sustainable cyber-physical systems with collaborative intermittent computing, ” in e- Energy ’ 21: The Twelfth ACM International Conference on Future Energy Systems, Virtual Event, Torino, Italy, 28 June - 2 July, 2021, H. de Meer and M. Meo, Eds. ACM, 2021, pp. 316–321. [2] S. Ahmed et al., “The internet of batteryless things,” Commun. ACM, vol. 67, no. 3, pp. 64–73, 2024. [3] Y. Kim et al., “Challenges and advances in ambient iot within 3gpp,” IEEE Commun. Mag., vol. 64, no. 1, pp. 182–188, 2026. [4] K. Geissdoerfer and M. Zimmerling, “ Bootstrapping battery- free wireless networks: Efficient neighbor discovery and synchronization in the face of intermittency,” in 18th USENIX Symposium on Networked Systems Design and Implementation, NSDI 2021, April 12-14, 2021, J. Mickens and R. Teixeira, Eds. USENIX Association, 2021, pp. 439–455. [5] K. Geissdoerfer and M. Zimmerling, “Learning to communicate effectively between battery-free devices,” in 19th USENIX Symposium on Networked Systems Design and Implementation, NSDI 2022, Renton, WA, USA, April 4 - 6 , 2 0 2 2 , A . Phanishayee and V. Sekar, Eds. USENIX Association, 2022, pp. 419–435. [6] B. Lucia and B. Ransford, “A simpler, safer programming and execution model for intermittent systems,” in Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation, Portland, OR, USA, June 1 5 - 1 7 , 2 0 1 5 , D . Grove and S. M. Blackburn, Eds. ACM, 2015, pp. 575–585. [7] A. Colin and B. Lucia, “Chain: tasks and channels for reliable intermittent programs,” in Proceedings of the 2016 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications, OOPSLA 2016, part of SPLASH 2016, Amsterdam, The Netherlands, October 3 0 - November 4 , 2 0 1 6 , E . Visser and Y. Smaragdakis, Eds. ACM, 2016, pp. 514–530. [8] K. Maeng and B. Lucia, “Adaptive dynamic checkpointing for safe efficient intermittent computing,” in 13th USENIX Symposium on Operating Systems Design and Implementation, OSDI 2018, Carlsbad, CA, USA, October 8-10, 2018, A. C. Arpaci-Dusseau and G. Voelker, Eds. USENIX Association, 2018, pp. 129–144.

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