Low-Power Wide-Area Networks

01 / 10

Link budget is not a distance guarantee

A receiver advertises a better sensitivity. Does the installed fleet now reach the next valley?

Sensitivity belongs to a receiver, waveform and error criterion at a declared input plane. Distance belongs to an installed link through a distribution of channels. A metal enclosure, rotated antenna or obstructed valley can change that distribution enough to reverse the selection. “Low power” also needs an interval: a modest average supply current can hide a long, expensive transmission.

Think about itWhich missing condition could reverse a coverage claim before any airtime calculation?

Answer

The mounted antenna pattern and polarization across the actual installation/channel population. A conducted advantage cannot establish the lower tail of received power, unique delivery by deadline, or whether a gateway exists where it is needed.

$P_{\mathrm{R1,RX}} = P_{\mathrm{R1,TX}} - L_{\mathrm{TXfeed}} + G_{\mathrm{TX}} + G_{\mathrm{RX}} - L_{\mathrm{channel}} - L_{\mathrm{RXfeed}}$ A bookkeeping example in dBm/dB for one direction and installed antenna state. Gains refer to that direction; channel loss includes the declared propagation and polarization treatment once. No values or distance law are assigned here. Compare the resulting R1-RX distribution to a sensitivity measured for the same waveform and error criterion.

Follow the planes: D0 application payload → D1 framed/coded bits → R1-TX radio port → feed/match → R2-TX antenna feed → S0 spatial propagation → R2-RX antenna feed → receive feed → R1-RX radio input → R3 receiver decisions → D0. R1/R2 suffixes map to the portfolio planes. R3 is a decision boundary, never an antenna connector.

Bring the foundations

07.1 owns evidence reading; 07.2 owns topology and state accounting. Revisit 05.3 sensitivity and 06.5 channel distributions. This lesson owns the LPWAN traffic decision. Cellular state detail belongs to 07.5; deployment operations and national authorization remain later work.

Common misconceptionMore link budget is a kilometre guarantee.

A single budget does not specify mounted gain, channel percentile, interference, gateway availability or latency. Keep conducted power, EIRP, ERP and OTA evidence distinct. Decide which distribution must be measured before predicting distance.

02 / 10

Freeze the remote fleet’s traffic

Can private gateways and an operator network be compared if one is given less traffic?

Freeze P07-M04-REMOTE-FLEET-v1 before selecting a technology. The earlier 2.450 GHz QPSK waveform remains a generic baseline; the LE, Thread and Wi-Fi variants keep their own identities. This new case changes the report interval explicitly.

Common service basis · chosen requirements, no field measurements
Quantity / boundary	Frozen remote-fleet variant
Population and installation	N = 1000 fixed nodes. Metal-machine and open-pole strata; upright and rotated enclosure orientations. No mobility modeled.
Application traffic	L = 32 D0 bytes per generated report, T = 600 s per node; m = 1 preplanned transmission initially.
Uplink acceptance goal	At least 99% complete unique reports at application-server D0 within 60 s of node D0 generation, in each installation/orientation stratum. Late and lost reports fail.
Urgent command goal	One command for d = .01 of reports. At least 99% at node D0 within 30 s of server release, including arbitrary phases of the report cycle.
Channel / gateway basis	C = 3 equal independent resources, one collision domain; g = 1 receiving gateway. Actual channel plan, ownership, sites, power and backhaul unknown.
Markets / qualification	CH and EU/EEA are candidate markets. Exact band, region, equipment class, national applicability and qualification program remain unresolved.
Separate preliminary screen	Unique-report probability ≥ .90 in the traffic proxy is a shortlist screen. It does not satisfy or predict the 99% field goal.

Count every generated sequence ID in the uplink denominator and every released command in the downlink denominator. Count a duplicate once. Record latency from generation or release, including queueing, access, backhaul and endpoint processing. A success percentage among received packets silently drops the failures that matter.

Think about itA report arrives twice. Has the application delivered twice as much useful information?

Answer

No. Two successful copies consume resources but deliver one unique report. Keep generated reports, packet attempts, successful copies and unique D0 delivery as four different counters.

Decision: compare both architectures on this exact traffic and deadline basis. Gateway ownership is an unresolved dependency, not a free resource in the private option.

03 / 10

Explain the coverage mechanisms and their price

How can a low-rate waveform hear weaker signals, and who pays for that improvement?

Reducing noise-equivalent bandwidth reduces integrated thermal noise when temperature and receiver noise figure stay fixed. Coding and spreading change the error-performance tradeoff for the selected receiver. Repetition spends more transmissions on the same information. These mechanisms can improve a link, but they consume time, resources or energy.

$N = k T_{\mathrm{phys}} B_{n} F\qquad \Delta N_{\mathrm{dB}} = 10 \log _{10}(\frac{B_{\mathrm{n,2}}}{B_{\mathrm{n,1}}})$ N is input-equivalent noise power in watts; k is Boltzmann’s constant, T_phys absolute temperature in kelvin, B_n noise-equivalent bandwidth in hertz and F linear noise factor. Halving B_n gives −3.010299957 dB with the other terms fixed. Modulation bandwidth and noise-equivalent bandwidth are not automatically identical.

Coverage mechanism and resource consequence
Mechanism	Possible benefit	Price / evidence needed
Narrower receiver bandwidth	Less integrated noise	Lower information rate or different waveform; measured selectivity and error criterion.
Spreading / coding	Different required signal-to-noise ratio	Longer symbols or redundancy; exact modem mode and packet error evidence.
Repeated copies	Another reception opportunity	More offered airtime and TX/RX energy; independence is unproven in shared fading.
Antenna / placement	Better mounted distribution or spatial diversity	Site ownership, feed loss, pattern, orientation and propagation evidence.

Common misconceptionAdd processing gain to the datasheet sensitivity to get extra margin.

If that sensitivity already includes the spreading, coding and detection behavior of the stated mode, adding a generic processing gain counts the same benefit twice. Compare mode-specific input sensitivity at a common error criterion, then propagate installation losses once.

Go deeperWhy signal energy and battery energy are different

A receiver may benefit from more useful signal energy per information bit. The battery supplies wake, oscillator, processing, TX, listening and sleep states. DC energy is ∫V(t)I(t)dt at the supply; it is not conducted RF power times the whole reporting period. The ledger below estimates radio supply energy only.

Prediction for the next calculation: increasing spreading factor makes each symbol longer. Even if fewer coded symbols are needed, packet time can rise sharply.

04 / 10

Separate modulation, protocol, and region

Does selecting “LoRa” specify the frame, receive policy and permitted regional mode?

Pin three layers: the selected Semtech modem formula describes conventional LoRa modulation; TS001-1.0.4 describes the LoRaWAN link layer; RP002-1.0.5 supplies its regional companion. The Alliance catalogue lists these documents and errata. A catalogue proves identity, while the selected text supplies the actual framing and timing evidence. [LA-INDEX] [LA-L2] [LA-RP]

Original byte-accounting schematic from LA-L2 / LA-RP. MHDR is the MAC header; FHDR is the frame header; FPort identifies application traffic; MIC is the message integrity code. PL excludes physical overhead handled by the airtime equation.

PL accounting · TS001-1.0.4 application data uplink, no FOpts
Field	Bytes / scope
MHDR	1 MAC-header byte.
FHDR	7 = DevAddr 4 + FCtrl 1 + FCnt 2 + FOpts 0.
FPort	1 application-port byte in this variant.
FRMPayload	32 application bytes at D0, represented in the encrypted frame.
MIC	4 integrity bytes.
Total supplied as PL	1 + 7 + 1 + 32 + 4 = 45 bytes. Physical preamble, header and CRC are accounted for by the symbol formula separately.

Think about itWhy is airtime for 32 PHY bytes the wrong answer for this 32-byte report?

Answer

The application boundary excludes 13 bytes of this selected LoRaWAN framing. Use PL = L + 13. Additional FOpts, MAC commands or application overhead would require a named new variant; never silently inherit this overhead for every packet.

The exercise holds bandwidth at 125 kHz, explicit header, uplink payload CRC, coding ratio 4/5 and eight programmed preamble symbols. Device Class A/B/C controls receive behavior; SF describes modulation; a regional data-rate index maps to a context-specific mode. None substitutes for the others. [SEM-PACKET]

Common misconceptionUnlicensed means unrestricted.

Regional parameters do not settle national applicability, power/antenna limits, channel use, dwell or listen-before-talk policy. The selectable 51 D0 byte ceiling is a chosen teaching limit. Actual region/data-rate/repeater/dwell context remains unknown, as do final product qualification and permission.

Decision: retain a bounded mathematical mode and an explicit unknown-region state. There is no fabricated regional preset.

05 / 10

Calculate airtime before discussing efficiency

Will the packet occupy the channel for a few milliseconds, or for seconds?

The SX1276 Rev. 7 formula rounds coded payload blocks before calculating time. Use SF7–12 only. At this fixed bandwidth, low-data-rate optimization DE is 0 for SF7–10 and 1 for SF11–12; the latter have symbols longer than 16 ms. Do not generalize that mapping to other bandwidths or modems. [SEM-PACKET]

$T_{\mathrm{sym}} = \frac{2^{\mathrm{SF}}}{\mathrm{BW}}$ SF is the spreading-factor index; BW = 125000 Hz; T_sym is seconds per symbol. SF7 gives 1.024 ms; SF12 gives 32.768 ms, exactly 32 times longer.

$N_{\mathrm{payload}} = 8 + \max(\operatorname{ceil}(\frac{8\mathrm{PL} - 4\mathrm{SF} + 28 + 16\mathrm{CRC} - 20\mathrm{IH}}{4(\mathrm{SF} - 2\mathrm{DE})}) \times (\mathrm{CR} + 4), 0)$ PL is framed PHY payload bytes, excluding physical overhead handled here. CRC = 1; IH = 0 for explicit header; CR = 1 gives coding ratio 4/(4 + CR) = 4/5. DE is the selected low-data-rate flag. Round the quotient upward first, then multiply by CR + 4.

$T_{\mathrm{packet}} = (n_{\mathrm{pre}} + 4.25 + N_{\mathrm{payload}}) \times T_{\mathrm{sym}}$ n_pre = 8 programmed preamble symbols. The remaining physical overhead is already in this formula: do not add header or CRC bytes to PL again. Preserve integer and quarter-symbol counts until converting to seconds.

Independent anchor derivation · PL45, same packet choices
Mode	Rounded blocks → payload symbols	Total symbols × symbol time
SF7 · DE0	ceil(376/28) = 14 → 8 + 14×5 = 78	90.25 × 1.024 ms = 92.416 ms
SF12 · DE1	ceil(356/40) = 9 → 8 + 9×5 = 53	65.25 × 32.768 ms = 2138.112 ms

Think about itSF12 uses 53 payload symbols instead of 78. Is it faster?

Answer

No. Each symbol is 32 times longer. The full packet is 23.135734072 times longer. The same small report can now occupy more than two seconds before any receive windows.

Byte steps · fixed SF7, independently checked integer boundaries
D0 L (bytes)	PL (bytes)	Payload symbols	Packet (ms)
30	43	73	87.296
31	44	78	92.416
32	45	78	92.416
33	46	78	92.416
34	47	78	92.416
35	48	83	97.536

L = 31, 32 and 33 all produce 92.416 ms. The adjacent 30→31 and 34→35 transitions add one five-symbol block. A byte does not always add airtime, but dropping bytes across a rounding boundary can help. PL above 255 lies outside this selected PHY kernel; L above 51 violates the teaching profile even when the PHY math exists. No fragmentation is modeled.

Engineering experiment · Class 1

LPWAN Airtime, Energy & Capacity Ledger

Change one term, identify the constraint, and choose the next evidence. This bounded experiment uses one conventional uplink format; it does not simulate a deployed network.

JavaScript is off. The complete canonical results below, SF7/SF12 comparison, counterexamples and native model-answer disclosures remain available. Controls require JavaScript.

Predict airtime for 32 D0 bytes at SF7 / 125 kHz

Packet preset and documentary context

Restore a complete fixtureRestores all numeric inputs, profile and review metadata together.

Profile / region evidenceBand, region, device class and authorization unresolved in both choices. Unknown is not unlimited permission.

Teaching source-review stateChanging this field is a teaching scenario, not a real source attestation.

Pinned documents: Semtech Rev.7, TS001-1.0.4, RP002-1.0.5. BW 125000 Hz; CR index 1; n_pre 8; IH 0; CRC 1. DE 0 for SF7–10, DE 1 for SF11–12 only in this fixture. No real regional-mode preset.

Packet · fixed conventional uplink

Spreading factor (SF index)7–12; step 1; default 7 SF index.

Application payload L (D0 bytes)1–512; step 1; default 32 D0 bytes. No fragmentation; PHY ceiling 242 D0 bytes, chosen profile 51.

Traffic · one shared collision domain

Fleet population N (nodes)1–100000; step 1; default 1000 nodes.

Report period T (s)1–86400; step 0.001; default 600 s.

Preplanned copies m (attempts / report)1–5; step 1; default 1 attempts / report. Fixed copies; not ACK-driven retries.

Independent channels C (resources)1–8; step 1; default 3 resources.

Same-domain gateways g (receivers)1–8; step 1; default 1 receivers. No automatic divisor in G.

Exogenous noncollision PER (0–1 probability)0–1; step 0.01; default 0 0–1 probability. Independent of collisions by assumption.

Downlink · separate aggregate allocation

Reports needing one downlink d (0–1 fraction)0–1; step 0.001; default 0.01 0–1 fraction.

Synthetic downlink airtime (s / downlink)0.01–10; step 0.01; default 0.05 s / downlink.

Aggregate gateway TX allocation (0–1 time fraction)0.001–1; step 0.001; default 0.01 0–1 time fraction.

Committed result · Canonical SF7 · teaching 51-byte profileDownlink opportunity and infrastructure evidence bind the architecture decision.

L01 · unknown. Urgent downlink within 30 s is unproven. Class A depends on an uplink-triggered opportunity; average capacity cannot guarantee a deadline.
G01 · unknown. 1 same-domain gateway: G is unchanged. Spatial diversity/capture benefit and site/backhaul ownership are unknown.
R01 · unknown. Market, band/region, device class, channel permissions, antenna and national applicability remain unresolved. No preset grants authorization.
S01 · screen. Conditional telemetry experiment candidate under the chosen 90% proxy screen; 99% by deadline and the urgent-downlink architecture still need evidence.

Curve: P = exp(−2G), without p_ext. Dots show the current input only when G≤1.5; larger loads remain unmodified in the table. No capture, fading, interference cancellation or gateway-diversity benefit is predicted.

Current airtime, traffic and service ledger · full precision used for decisions
Quantity / boundary	Derived from current illustrative inputs
D0 / PHY payload	32 / 45 bytes
Mode / bandwidth / code	SF7 · 125000 Hz · 4/5 · DE=0
Ceiling input / rounded blocks	376/28 → 14
Payload / total symbols	78 / 90.25
Symbol / packet time	1.024 / 92.416 ms
Generated reports / packet attempts	1.666666667 generated reports/s; 1.666666667 packet attempts/s
Per-node TX duty	0.015402667 % of T
Fleet offered airtime	0.154026667 channel-seconds / second
G · per-channel offered load	0.051342222
P_no_collision / S	0.90241169 / 0.046331822
P_attempt / p_ext	0.90241169 / 0
Independent-copy unique probability	0.90241169
Successful copies / unique reports	1.504019483 copies/s / 1.504019483 unique reports/s
Useful D0 throughput · proxy	385.028987554 bit/s
Serial reservation / period	2.117416 / 600 s · fits
Charge / generated report	5.401365168 mC
Energy / generated report	16.204095504 mJ at 3 V
Average radio current over T	9.00227528 µA
Energy / unique delivery · independent copies	17.956433512 mJ
Downlink release rate / airtime demand	0.016666667 commands/s / 0.000833333 time fraction
Downlink allocation utilization	8.333333333% · within allocation
Generic scheduled demand / allocation	100 / 100 reports/min · 100% · at allocation · no reserve

Radio supply ledger · 3 V · one generated report period
State	Duration (s)	Current (mA)	Charge (mC)
Wake · once	0.005	5	0.025
TX · all copies	0.092416	40	3.69664
RX1 + RX2 · all copies	0.04	12	0.48
Sleep · includes window waits	599.862584	0.002	1.199725168

Energy per unique delivery divides expended radio energy by the separately stated independent-copy probability. It is not energy conditioned on a known ACK sequence.

Framing fixed: no FOpts/extra MAC commands; explicit physical header; CRC on; eight programmed preamble symbols. Empty-window policy: 5 ms wake once, TX 40 mA, 2×20 ms RX at 12 mA per copy, sleep 2 µA including waits. Gateway count is evidence only. All numeric values are illustrative/derived, never measured.

Region/band/class and national applicability: unknown. Profile: chosen 51 D0 byte ceiling. Source model: Semtech Rev.7 / TS001-1.0.4 / RP002-1.0.5; real selected-source access 2026-09-08; review due 2026-12-07. lpwan-airtime-energy-capacity-ledger/2.0 · p07-m04-traffic-v1. Printed values round to nine decimal places; decisions use full precision.

Choose the architecture hypothesis to investigate

Private: secure gateway ownership and a receive plan

Shortlist a telemetry experiment only if the mathematical screens hold. Site, power, backhaul, antenna distribution and network-server ownership remain unknown. Report-only Class A cannot establish the 30 s arbitrary-phase command requirement; investigate a separately specified receive architecture.

Current binding constraint: Downlink opportunity and infrastructure evidence bind the architecture decision.

Keep a complete reference beside the experiment

The following canonical comparison remains available on a first visit, without JavaScript and in print. It uses the same equations, empty-window policy and traffic basis as the initial interaction. An independent rational/decimal oracle checks the production kernel; the Semtech web interface returned no airtime after submission, so calculator agreement is not claimed. [SEM-CALC]

Complete canonical SF7 / SF12 ledger · same fleet, channels and empty windows
Quantity	SF7 · canonical	SF12 · only SF changed
D0 / PHY payload	32 / 45 bytes	32 / 45 bytes
Mode / bandwidth / code	SF7 · 125000 Hz · 4/5 · DE=0	SF12 · 125000 Hz · 4/5 · DE=1
Ceiling input / rounded blocks	376/28 → 14	356/40 → 9
Payload / total symbols	78 / 90.25	53 / 65.25
Symbol / packet time	1.024 / 92.416 ms	32.768 / 2138.112 ms
Generated reports / packet attempts	1.666666667 generated reports/s; 1.666666667 packet attempts/s	1.666666667 generated reports/s; 1.666666667 packet attempts/s
Per-node TX duty	0.015402667 % of T	0.356352 % of T
Fleet offered airtime	0.154026667 channel-seconds / second	3.56352 channel-seconds / second
G · per-channel offered load	0.051342222	1.18784
P_no_collision / S	0.90241169 / 0.046331822	0.092951261 / 0.110411226
P_attempt / p_ext	0.90241169 / 0	0.092951261 / 0
Independent-copy unique probability	0.90241169	0.092951261
Successful copies / unique reports	1.504019483 copies/s / 1.504019483 unique reports/s	0.154918768 copies/s / 0.154918768 unique reports/s
Useful D0 throughput · proxy	385.028987554 bit/s	39.659204633 bit/s
Serial reservation / period	2.117416 / 600 s · fits	4.163112 / 600 s · fits
Charge / generated report	5.401365168 mC	87.225113776 mC
Energy / generated report	16.204095504 mJ at 3 V	261.675341328 mJ at 3 V
Average radio current over T	9.00227528 µA	145.375189627 µA
Energy / unique delivery · independent copies	17.956433512 mJ	2815.188722696 mJ
Downlink release rate / airtime demand	0.016666667 commands/s / 0.000833333 time fraction	0.016666667 commands/s / 0.000833333 time fraction
Downlink allocation utilization	8.333333333% · within allocation	8.333333333% · within allocation
Generic scheduled demand / allocation	100 / 100 reports/min · 100% · at allocation · no reserve	100 / 100 reports/min · 100% · at allocation · no reserve

Go deeperWhat this kernel deliberately cannot calculate

FSK, LR-FHSS, SF6, implicit-header packets, arbitrary modem generations and downlinks with different CRC conventions need their own supported models. The downlink input later is explicitly synthetic airtime; it is not obtained by feeding a downlink into this uplink formula.

06 / 10

Shared spectrum carries shared load

Can a thousand mostly sleeping nodes still offer more airtime than the channels contain?

Yes. A node’s TX duty is its own transmitted time divided by its reporting period. The fleet offers the sum of all attempted packet times, including overlaps. Offered airtime is demand and may exceed one channel-second per second. A duty fraction, a legal time limit and a network service probability answer different questions.

$\lambda = \frac{N m}{T}\qquad D_{\mathrm{node}} = \frac{m T_{\mathrm{packet}}}{T}\qquad G = \frac{N m T_{\mathrm{packet}}}{T C}$ λ is fleet packet attempts/s; N nodes, m preplanned copies per generated report, T seconds per report, C independent uniformly selected resources. G is dimensionless offered packet-airtime per channel-time. The fleet total before dividing by C is N m T_packet/T. Gateway count is absent.

Imagine the tagged packet starts at time zero and lasts t = T_packet. Another equal-length packet starting anywhere from −t to +t overlaps it. Under independent Poisson starts on one unslotted collision domain, the expected number of these competing starts is 2G. The Poisson zero-arrival probability gives the following proxy. [ALOHA]

$P_{\mathrm{no\_collision}} = \exp (-2G)\qquad S = G \exp (-2G)$ P_no_collision is a per-attempt no-overlap probability; S is successful packet-airtime per channel-time. Equal packet lengths, uniform independent channels, no capture, cancellation, fading or gateway diversity are assumed. This is neither a guaranteed upper nor lower bound for real LoRaWAN service.

Same population and interval · no external loss, one copy
Quantity	SF7	SF12
Fleet offered airtime (channel-s/s)	.154026666667	3.56352
Per-channel G	.05134222222222222	1.18784
No-collision probability	.9024116895793257	.0929512608580765
Per-node TX duty (%)	.015402666667	.356352

Common misconceptionTiny payload means tiny network load.

Load includes framing, physical overhead, symbol duration, population and copies. The SF12 fleet offers 3.56352 channel-seconds every second across three resources. Clamping that demand to 100% would hide the overload.

Go deeperThe ALOHA peak is a model result

Differentiating S gives exp(−2G)(1−2G). Its maximum occurs at G = .5 and equals 1/(2e) ≈ .183939720586. That is the toy channel’s successful-airtime peak, not a hardware gateway capacity rating. Real mixed spreading factors, correlated traffic and capture need a different model and measurements.

Decision: blanket SF12 fails the chosen 90% preliminary traffic screen for this fleet. Even SF7’s 90.24% proxy does not establish the 99% by-deadline field goal.

07 / 10

Compare private and scheduled network resources

Does handing scheduling to an operator remove the need for a capacity and energy budget?

Scheduling changes resource ownership and access. It does not make resource demand disappear. A private architecture needs gateway sites, power, backhaul and a network-server owner. An operator-backed option needs a compatible modem, band, provisioning and actual service at the installed site.

Same 1000-node service case · architecture evidence, not carrier advice
Question	Private LoRaWAN hypothesis	Operator-backed LTE-M / NB-IoT hypothesis
Access resource	Chosen C=3 resources; random-access proxy	Actual scheduling/allocation unknown
Illustrative capacity screen	SF7 no-collision proxy .902411689579	Generic allocation 100 complete reports/min after all overhead and repetitions
Demand at 32 D0 bytes / 600 s	1000/600 = 1.666666667 generated reports/s	1000×60/600 = 100 reports/min; 100% utilization, no reserve
Infrastructure owner	Unknown: secure sites, power, backhaul, maintenance and server	Unknown: service/provisioning, coverage evidence and contractual responsibility
Supply energy / availability	Synthetic empty-window radio ledger only	Unknown until modem/network state timing and current are obtained

The 100 reports/min allocation is invented for comparison and already includes every declared protocol overhead and repetition. It is not a 3GPP requirement or a carrier offering. Do not apply the LoRa packet kernel or ALOHA equation to its scheduler.

3GPP’s historical November 2016 presentation places eMTC and NB-IoT in Release 13 and introduces power-saving context. The indexed primary excerpt supports that orientation only; the full PDF was unavailable. A current product decision still needs the exact release, TS, modem capabilities, network configuration and installed service evidence. [3GPP-IOT]

Think about itThe generic scheduled allocation equals demand. Is there operational reserve?

Answer

No. Equality is a capacity boundary. Bursts, outages or a changed reporting interval need additional allocation or queue/deadline evidence. Power, coverage and availability remain unknown; a neat average does not supply those missing measurements.

Handoff to 07.5: pin PSM/eDRX reachability, registration, connection and transfer state timing, repetitions, bands and service support before comparing battery energy.

08 / 10

Downlink and receive windows change the battery story

If the node sleeps for ten minutes, when can a command reach it?

In the selected Class A behavior, an uplink creates receive opportunities. Class B adds scheduled receive slots with synchronization; Class C listens much more continuously except while transmitting. These are receive-policy choices with different costs. An addressed valid reception in RX1 can suppress RX2; our empty-window ledger does not assume such a success. [LA-L2]

Freeze opening delays independently of RX-on duration. Actual preamble detection, clock error and successful reception can lengthen listening; this 20 ms assumption does not establish decodability at any SF. Table values carry the quantitative energy model.

One empty-window event · chosen 3 V supply policy
State / timing reference	Duration	Supply current
Wake once before first copy	.005 s	.005 A
TX per copy	T_packet	.040 A
RX1 opening / RX-on	1 s after TX end / .020 s on	.012 A while on
RX2 opening / RX-on	2 s after TX end / .020 s on	.012 A while on
Sleep including waits	Remaining period after wake, TX and RX-on	.000002 A

The regional companion supplies default delay orientation; actual delays can be configured. The 20 ms windows and all currents are synthetic implementation assumptions. Preamble detection, clock uncertainty and a received frame can require more RX time. This fixture proves no downlink is decodable at any selected SF. [LA-RP] [LA-L2]

$.005 + m(T_{\mathrm{packet}} + 2.020) \le T$ Each serialized copy reserves TX plus the full interval to the end of RX2. Wake occurs once. Waiting may use sleep current, but it still occupies the schedule. If the reservation exceeds T, period energy is unavailable; never create negative sleep to make it fit.

$Q = \sum I_{\mathrm{state}} t_{\mathrm{state}}\qquad E = 3Q\qquad I_{\mathrm{avg}} = \frac{Q}{T}$ Q is coulombs at the radio supply, E joules per generated report period, and I_avg amperes averaged over T. These are not RF output energy or whole-product battery-life predictions.

Canonical charge check · m=1, T=600 s
State / result	SF7	SF12
Wake (mC)	.025	.025
TX (mC)	3.69664	85.52448
RX1 + RX2 (mC)	.48	.48
Sleep (s)	599.862584	597.816888
Sleep (mC)	1.199725168	1.195633776
Total charge (mC)	5.401365168	87.225113776
Energy (mJ)	16.204095504	261.675341328
Average current (µA)	9.00227528	145.375189626667

Now isolate the downlink budget. Let d be the fraction of generated reports releasing one command, t_DL synthetic seconds per command and a_DL the chosen aggregate gateway TX-time allocation. For d = .01, the release rate λ_DL = Nd/T is 1/60 command/s.

$D_{\mathrm{DL}} = (\frac{N d}{T}) t_{\mathrm{DL}}\qquad \mathrm{utilization} = \frac{D_{\mathrm{DL}}}{a_{\mathrm{DL}}}$ D_DL is requested gateway TX-time per wall-time. a_DL = .01 is an exercise allocation, not a duty-cycle law. It is held aggregate and fixed when receiver count changes.

A low-duty node can coexist with an overloaded downlink service
Synthetic t_DL	Gateway demand fraction	Use of .01 allocation	Opportunity / deadline
.05 s	.000833333333333	8.333333333%	Unknown: low average demand creates no receive slot.
1 s	.016666666666667	166.666666667% · over allocation	Capacity fails in addition to the unresolved deadline.

Think about itNode TX duty is only .015402667%. Can the server guarantee a command within 30 s?

Answer

No. A command released just after the Class A windows can wait almost an entire 600 s reporting cycle for the next uplink-triggered opportunity. The .05 s downlink clears the average allocation screen but provides no any-phase deadline guarantee. At 1 s it also exceeds the chosen allocation.

For a separate chosen 1% per-node TX-time screen, canonical SF7 is below the ceiling while the 1 s downlink service exceeds its aggregate allocation. Both 1% numbers are exercise budgets, never legal limits. Subband, averaging period, dwell/LBT policy, class and RX1/RX2 scheduling, gateway half-duplex behavior and backhaul queues remain unresolved. An ACK also consumes downlink resources and can change subsequent retries and RX states; this model uses fixed copies and empty windows instead.

09 / 10

Scale nodes, modes, and gateway placement carefully

Which improves a crowded channel: another receiver, another channel, or another copy?

Same-domain counterexample · SF7, m=1, T=600 s
Controlled variant	Per-channel G	No-collision probability	What changed
N1000 / C3 / g1	.05134222222222222	.9024116895793257	Canonical fleet
N2000 / C3 / g1	.10268444444444444	.8143468574894134	Population doubled
N2000 / C3 / g2	.10268444444444444	.8143468574894134	Only receiver count doubled
N2000 / C6 / g2	.05134222222222222	.9024116895793257	Truly independent resources doubled

Common misconceptionA second gateway halves collisions.

Overlapping receivers hear the same offered traffic. Their spatial positions can change capture, fading and which packets are received, but that benefit is unknown here. Dividing G by g would invent isolation. Only a separately demonstrated spatial/frequency partition could justify splitting the population into independent collision domains.

$P_{\mathrm{attempt}} = (1 - p_{\mathrm{ext}}) \exp (-2G)\qquad P_{\mathrm{unique}} = 1 - (1 - P_{\mathrm{attempt}})^{m}$ p_ext is exogenous noncollision packet error probability, independent of collisions by assumption; default zero isolates the collision mechanism. The second equation additionally assumes independent outcomes across preplanned copies. Shared fading and repeated collisions can violate it. Do not count collision loss again inside p_ext.

Useful D0 throughput is (N/T)P_unique L×8 bits/s. Successful copies arrive at (Nm/T)P_attempt copies/s, which can count a report more than once. Energy per unique delivered report is expended energy per generated report divided by P_unique under that same delivery assumption. Zero modeled delivery makes this ratio unavailable, never a finite success estimate.

Common misconceptionRetries improve reliability without loading the network.

Increasing m also increases G, so per-attempt success falls while TX/RX charge rises. At high load even the independent-copy unique probability can worsen. These are preplanned copies with randomized starts; no ACK retry/load feedback loop is solved.

Go deeperNumerical zero is not a field observation

At extreme permitted loads, exp(−2G) can underflow floating-point range. The ledger explicitly reports that limitation and withholds a finite delivery-energy claim. With p_ext = 1, zero delivery instead follows directly from the chosen proxy. Neither is a measured fleet statistic.

Decision: investigate channel support and installed gateway diversity separately. Adding receivers cannot rescue the SF12 traffic arithmetic by itself.

10 / 10

Choose an architecture and a field experiment

Which architecture deserves the next experiment, and what result would reverse that decision?

Reject the attractive blanket SF12 mode under this traffic basis: long airtime drives the no-collision proxy to 9.295126%. Conditionally retain SF7 for a telemetry experiment under the preliminary 90% screen. Both remain unqualified for the 99% field goal, and report-only Class A cannot establish the arbitrary-phase urgent-command requirement.

Architecture A · private gateways / conventional LoRaWAN
Decision field	Common remote-fleet basis
Mode decision	Reject blanket SF12. Conditionally shortlist SF7 / 125 kHz / 4/5, exact framing retained, for telemetry evidence gathering.
Uplink / energy evidence	SF7: 92.416 ms, G=.05134222222222222, proxy=.9024116895793257, 16.204095504 mJ per generated report at the radio supply. Derived, not measured.
Downlink decision	Report-only Class A does not establish 30 s any-phase delivery. Investigate a separately specified receive architecture and its energy cost before retaining the full service hypothesis.
Gateway ownership decision	Unknown; do not assume a site or purchase decision. Infrastructure owner must secure power, backhaul, installation access, maintenance and server responsibility.
Applicability / next evidence	Pin band, region/data rate, device class and configuration; qualify and assess national applicability separately. RF/lab and firmware owners execute LPWAN-FIELD-01.

Architecture B · operator-backed LTE-M / NB-IoT hypothesis
Decision field	Same 1000 nodes, 32 D0 bytes / 600 s and deadlines
Capacity decision	Generic 100 reports/min allocation equals demand with no reserve. This is a synthetic screen, not an actual network offering.
Energy / coverage decision	Unknown: do not transfer the LoRa current ledger, sensitivity or collision model.
Receive and service evidence	Obtain exact modem/release/band, provisioning, scheduled allocation, PSM/eDRX behavior and measured command reachability; verify site availability and backhaul/service responsibility.
Ownership / next decision	Product and infrastructure owners obtain actual service evidence. Module 07.5 resolves cellular state/capability questions; then compare installed delivery and supply energy on the common basis.

LPWAN-FIELD-01 · proposed experiment, no completed measurement
Test element	Predeclared conditions / reversal evidence
Installation and orientation	RF/lab owner records enclosure, board/firmware, antenna/feed, mount height, metal-machine and open-pole strata, upright/rotated orientations, coordinates and actual environmental conditions. Calibrate conducted and supply planes separately.
Traffic and channel population	N=1000 fixed nodes; L=32 D0 bytes / 600 s, m=1 initially. Record exact permitted centres, bandwidths, SF distribution, all participating nodes, observed other users and channel-selection policy. C=3 is tested only if the real configuration supports it.
Gateway experiment	Compare one gateway with a second at documented overlapping and spatially separated positions; retain matched traffic and channels. Record per-gateway packet IDs and joint reception, capture clues, site/backhaul outages and ownership. Do not infer N/g isolation.
Observation duration / denominator	Seven continuous days per controlled configuration: 1008 scheduled reports/node, hence 1008000 generated reports if all 1000 nodes operate throughout. Log actual generated IDs and all omissions. Report each installation/orientation stratum and time interval; lost/late IDs remain failures. This count alone does not establish statistical confidence under correlation.
Uplink / downlink roles and deadlines	Synchronized node/server logs measure complete unique uplink D0 delivery by 60 s; release one downlink for 1% of reports, stratifying release phase across the full 600 s cycle. Measure complete node D0 delivery by 30 s, including lost commands. Log gateway queues and actual receive windows.
Radio supply evidence	Firmware/lab owners align TX and RX-enable traces with current at the 3 V supply, including wake, real decoding, retransmissions and sleep; report uncertainty and temperature. Separate radio-only energy from sensors, host and battery losses.
What reverses the shortlist?	Reject the service configuration if any predeclared stratum misses 99% by deadline; investigate failures and confidence before a deployment claim. Unexpected correlated losses, longer receive states, channel occupancy or unavailable sites can reverse SF7’s shortlist. Retain an urgent-downlink architecture only after measured any-phase evidence; use an independently checked uncertainty method for acceptance.

This complete local evidence card preserves earlier fixture IDs and makes unknowns visible without saved progress or another page visit.

Technology evidence card · p07-technology-evidence-card-v1
Field	P07-M04-REMOTE-FLEET-v1 · complete static snapshot
Identity / owner	p07-technology-evidence-card-v1 · P07-M04-REMOTE-FLEET-v1 · RF systems owner
Inherited IDs	P07-M01-LE-EXT-v1 · P07-M02-LE-CONN-v1 · P07-M02-THREAD-SED-v1 · P07-M03-HE-BACKHAUL-v1 · p06-evidence-map-v1 · M01-A · M01-B-LOSS · M01-INSTALL-UNKNOWN
Scenario	Illustrative remote fleet: 1000 fixed condition-monitoring nodes, metal-machine and open-pole installation strata, upright and rotated enclosure orientations. No mobility modeled. Earlier 2.450 GHz QPSK, LE, Thread and HE cases remain distinct.
Requirements	32 D0 bytes per node every 600 s. Field goal: ≥99% complete unique reports by 60 s from generation in each site/orientation stratum. One urgent command for 1% of reports: ≥99% delivered to node D0 within 30 s of server release, any phase of the reporting cycle. Preliminary traffic-only proxy screen: ≥90%, not a service acceptance criterion.
Family	Private conventional LoRa/LoRaWAN Class A telemetry hypothesis versus operator-backed LTE-M/NB-IoT hypothesis under exactly the same offered traffic.
Standard / release / profile / mode	LoRaWAN TS001-1.0.4 data uplink; no FOpts/extra MAC commands; application FPort present. SX1276-style LoRa at 125 kHz, SF7–12, coding 4/5, explicit header and uplink CRC. RP002-1.0.5 is the documentary companion. Cellular exact TS/release/profile/module remains unknown; Release 13 is historical orientation only.
Band / region / device class	CH and EU/EEA are candidate markets; actual band, regional data-rate mapping, equipment class, dwell/repeater and national applicability unknown. The selectable 51-byte profile is illustrative. No real region preset or approval is claimed.
D0 payload / latency definition	256 bits every 600 s. Uplink: complete node D0 generation to application-server D0 delivery. Downlink: server D0 command release to node D0 delivery. Unique sequence IDs count once; lost and late reports fail. Denominators include every generated report or released command, not received packets only.
PHY / MAC resources	13 framing bytes gives PL 45. Three equal independent channel resources, one collision domain, uniformly chosen channels and independent Poisson starts. Fixed m=1 copy/report initially; g=1 receiver. p_ext=0 is a chosen isolated noncollision-loss assumption, not a measurement. Generic scheduled allocation 100 reports/min after overhead and repetitions.
Radio state assumptions	Wake once/report: 0.005 s at 0.005 A · TX per copy, SF7 canonical: 0.092416 s at 0.04 A · Two empty RX windows per copy: 0.04 s at 0.012 A · Sleep remainder, including waits: 599.862584 s at 0.000002 A
Antenna / RF interfaces	D0 → framing at D1 → radio R1-TX → feed/match loss once → R2-TX → antenna/polarization/channel at S0 → R2-RX → receive-feed loss once → R1-RX → receiver/R3 decisions → D0. R1/R2 suffixes map to portfolio planes; R3 is never an antenna input. No numerical RF budget, EIRP, ERP or distance guarantee. Energy is at the 3 V radio supply, not RF output.
Infrastructure dependencies	Gateway ownership unknown. Private option needs surveyed sites, power, gateway/channel support, backhaul, network server, provisioning and maintenance owner. Operator option needs module/band support, provisioning, contracted service and measured site availability; operator scheduling is not assumed from a label.
Qualification questions	Standards/quality owner must determine applicable LoRaWAN certification or cellular GCF/PTCRB/operator program and actual product/firmware record. Program evidence is separate from national permission.
Regulatory questions	Compliance owner must resolve market, subband, averaging interval, channel use, power/antenna, dwell/LBT and installed device class. Neither the 1% downlink allocation nor the 51-byte ceiling is law.
Claim-level evidence	C-FRAME → LA-L2, LA-RP: Selected documentary framing; local no-FOpts variant \| C-AIRTIME → SEM-PACKET, SEM-CALC: Derived; separate oracle verified, web calculator returned no result \| C-ACCESS → ALOHA: Illustrative Poisson collision proxy; not a bound on actual service \| C-WINDOW → LA-L2, LA-RP: Class orientation sourced; 20 ms RX and current values illustrative \| C-CELLULAR → 3GPP-IOT: Historical informative excerpt; present deployed capability unknown \| C-ENERGY → illustrative fixture only: Synthetic radio-only state integration; no measured trace or battery lifetime \| C-DELIVERY → illustrative fixture only: Unknown field delivery and latency statistics \| C-MARKET → LA-RP: National applicability unknown; regional document is not permission
Uncertainty / evidence status	Mounted gain/channel percentiles, actual sensitivity/PER, other users, capture, correlated copies, gateway diversity, receive timing, clocks, current traces, queues, backhaul and downlink reachability remain unknown. Evaluation frozen at 2026-09-08 UTC.
Decision	Reject blanket SF12 for this single-domain traffic: 2.138112 s/copy and 9.295126% no-collision proxy. Conditionally shortlist SF7 for a telemetry experiment (90.241169% preliminary proxy), while rejecting report-only Class A as evidence for an any-phase 30 s urgent command. Investigate a separately specified receive architecture or operator service. Gateway purchase/ownership decision remains on hold pending a named site owner.
Next evidence / owner	LPWAN-FIELD-01: RF/lab and firmware owners log generated/delivered IDs and radio states across installed strata, density and gateway placement. Infrastructure owner secures sites/backhaul or operator evidence; standards/compliance owners pin mode and market applicability.
Review / trigger	2026-12-07 · 2026-12-07 or document/errata, firmware, traffic, channel, gateway placement/ownership, antenna, installation or market change, whichever comes first.

Ungraded review

Check your understanding

Answer each question in your own words, then reveal the model answer.

01Why does a 32-byte report become 45 PHY payload bytes?
Model answer
This data-uplink variant has MHDR 1 + FHDR 7 (DevAddr 4 + FCtrl 1 + FCnt 2, no FOpts) + FPort 1 + D0 payload 32 + MIC 4 = 45 bytes. The LoRa preamble, physical header and physical CRC are handled by the airtime formula, not added again as PL bytes. Extra application security or MAC commands would create another variant.
02How can SF12 use fewer payload symbols and take longer?
Model answer
SF7: ceil(376/28)=14 blocks, 78 payload symbols, 90.25 total ×1.024 ms =92.416 ms. SF12: ceil(356/40)=9 blocks, 53 payload symbols, 65.25 total ×32.768 ms =2138.112 ms. Packet time rises by 23.135734072, despite fewer symbols.
03Double N, then double g on the same channels. Which term changes?
Model answer
G=N m T_packet/(T C). At SF7 N=2000 gives G=.10268444444444444 and exp(−2G)≈.81434685749. Doubling overlapping receivers g from 1 to 2 leaves both unchanged. Increasing genuinely independent channels from 3 to 6 would halve G; unproven spatial diversity cannot be substituted for that division.
04Reproduce canonical radio energy and distinguish RX waits from RX-on time.
Model answer
Wake charge .025 mC; TX 3.69664 mC; two RX windows .48 mC; sleep 599.862584 s ×.002 mA =1.199725168 mC. Total 5.401365168 mC at 3 V =16.204095504 mJ, average 9.00227528 µA over 600 s. Windows open 1 and 2 s after TX ends, but together consume only 40 ms RX-on in this empty-window assumption.
05Does low node duty prove urgent downlink service?
Model answer
No. Canonical node TX duty is .0154026667%. One downlink for 1% of 1000 reports/600 s gives 1/60 command/s. At 1 s airtime it needs .0166666667 of aggregate gateway time, exceeding the chosen .01 allocation. Even .05 s airtime uses only8.333333% of that allocation but does not create a Class A opportunity within 30 s of an arbitrary release. Capacity, opportunity, reachability and deadline are separate.
06A 52-byte payload fits the PHY. Can you declare it admissible?
Model answer
PL65 is within the selected 255-byte PHY kernel, but 52 exceeds the chosen 51-byte profile; that combination is rejected. With an unknown regional limit, the same arithmetic may be shown as an unqualified calculation only. Pin region/data rate/repeater/dwell context and current source text, then obtain national applicability separately. Overdue review triggers rechecking rather than changing the formula or assuming failure.

Carry the same endpoints, generated-report denominator and urgent-command requirement into 07.5. The next decision needs cellular ecosystem and state evidence, not another unsupported coverage radius.

References and further study

Actual source access 2026-09-08 UTC; review due 2026-12-07, earlier on document/errata, mode, firmware, traffic, channel, antenna, installation, infrastructure or market change. Frozen evaluation: 2026-09-08 UTC. lpwan-airtime-energy-capacity-ledger/2.0 · p07-m04-traffic-v1 · p07-m04-architecture-rules/1.0. Chosen numbers are illustrative; formula outputs are derived. No measured or certified product result is presented. A source-review exercise cannot alter a real access record.

LA-INDEX · LoRa Alliance
Technical Specifications and 1.0.4 package · Live catalogue snapshot · Status checked 2026-09-08; page publication unknown.
Consulted: L2, regional-parameter and errata listings. Document identity/status only.
Lists TS001-1.0.4, RP002-1.0.5 and D2D errata. Does not establish every deployed network’s version or product certification.
LA-L2 · LoRa Alliance
LoRaWAN L2 Specification · TS001-1.0.4 · ©2020 document; library entry 2023-09-28.
Consulted: §2.1 pp9–10; §§3.3–3.3.6 pp12–13; §§4–4.1 p15; §§4.3–4.3.1 p17. Selected normative text read in the linked 90-page PDF; original paraphrases.
Frame fields, receive opportunities, Class A/B/C orientation and timing conditions. No implementation, complete conformance or national determination. D2D errata are listed; this conventional node-to-network example excludes D2D and multicast.
LA-RP · LoRa Alliance
LoRaWAN Regional Parameters · RP002-1.0.5 · October 2025, Final; library publication 2025-10-08.
Consulted: §2 p11; §3.3 p29; §3.4.2 p33; §§5.1.1–5.1.2 pp103–104, Tables 111–113. Selected normative/informative text in linked 116-page PDF.
Separate regional companion, physical frame and default timing orientation. No national legal limits or real regional payload preset are implemented. Three independent resources and 51 D0 bytes are chosen teaching assumptions, not a reproduced regional table.
SEM-PACKET · Semtech
SX1276/77/78/79 datasheet · Rev. 7 · May 2020.
Consulted: §§4.1.1.6–4.1.1.7, pp29–31. Manufacturer-authored PDF read via SparkFun mirror; informative modem model.
Conventional packet airtime, symbol rounding, explicit-header/CRC choices, PL 1–255 and low-data-rate optimization. Official product page lists the 2020-05-26 datasheet; direct Semtech retrieval was unavailable. This pinned revision is not asserted to be the newest modem documentation. No FSK, LR-FHSS, SF6, implicit mode, or new modem generation.
SEM-CALC · Semtech
LoRa Calculator · Web interface; no revision exposed · Accessed 2026-09-08.
Consulted: Device, header, CRC, SF/BW/CR, preamble, payload and LDRO controls; submitted SF7 and SF12. Calculator settings inspected; numeric result unavailable.
sx127X, explicit, CRC on, 125 kHz, 4/5 short interleaver, preamble8, PL45; SF7/LDRO off and SF12/on attempted. ToA stayed blank after submission. No manufacturer-calculator agreement is claimed; separate rational/integer oracle supplies the independent check.
ALOHA · Norman Abramson / University of Hawaiʻi
The ALOHA System—Another Alternative for Computer Communications · AFIPS Fall Joint Computer Conference · 1970, pp281–285.
Consulted: Printed pp283–284, random-access assumptions and equations (1)–(2). Original primary paper; selected full text read.
Unslotted starts, the two-packet vulnerable interval and exponential no-overlap approximation. Our m is fixed preplanned copies. The paper’s retransmission feedback is not implemented; real LoRaWAN capture, fading and multi-gateway service are excluded.
3GPP-IOT · 3GPP
3GPP Standards for the Internet-of-Things · Smart Summit Singapore presentation · November 2016.
Consulted: Slide5, Introduction & timeline; indexed primary-source text. Informative historical presentation excerpt read; direct PDF retrieval returned 403.
Release13 orientation for eMTC, NB-IoT and EC-GSM-IoT; PSM context. No TS body, current operator deployment, exact state power, scheduler capacity or modem capability inferred. Obtain pinned TS/release and network evidence in 07.5.

Precision: SI internally; displayed results normally round to nine decimal places. Independent checks use absolute 1e−9 s airtime, 1e−10 load/probability, 1e−8 mC/mJ energy and relative 1e−9 positive ratios. Rules use unrounded values. Overdue review requires rechecking; it does not automatically invalidate a selected legacy mode.

Low-PowerWide-Area Networks

Link budget is not a distance guarantee

Freeze the remote fleet’s traffic

Explain the coverage mechanisms and their price

Separate modulation, protocol, and region

Calculate airtime before discussing efficiency

LPWAN Airtime, Energy & Capacity Ledger

Keep a complete reference beside the experiment

Shared spectrum carries shared load

Compare private and scheduled network resources

Downlink and receive windows change the battery story

Scale nodes, modes, and gateway placement carefully

Choose an architecture and a field experiment

Check your understanding

References and further study

Low-Power
Wide-Area Networks