LoRa mesh and field networks

Why this matters

There is no mobile coverage in the mangroves, so the team must build its own network to bring sensor data and people’s positions back to the station. LoRa reaches far on little power but trades that for very low data rates, and a mesh lets each node relay data onwards. The drone knowledge base’s deep-dive units on LoRa/Mesh and on swarm coordination over LoRa mesh give an overview of real use; this module goes into the numbers used for design.

LoRa parameters

LoRa uses spread-spectrum modulation. The spreading factor (SF), 7 to 12, sets how long each symbol lasts: one step up doubles the symbol length, reaching farther and resisting noise better, but taking longer on air. The SX1276 datasheet, section 4.1.1.7, gives the time-on-air formula in the formula box, where $PL$ is the payload in bytes, $CR$ the coding rate (1 = 4/5), $IH$ = 1 without a header and $DE$ = 1 with low data rate optimisation on.

Thailand uses the AS923-1 channel plan in 920–925 MHz under the LoRa Alliance’s LoRaWAN Regional Parameters (RP002). For NBTC rules in this band, the Telecommunications Association of Thailand summarises that IoT devices may use up to 500 mW e.i.r.p. without a licence and that the band maximum is 4 W e.i.r.p. This comes from a secondary source and must be checked against the NBTC announcement in the Royal Gazette before real use. The 10% duty cycle in the example is Meshtastic’s setting for the TH region, not a requirement checked against the announcement.

import math

def time_on_air(pl, sf, bw=125e3, cr=1, n_pre=8, crc=1, ih=0):
    de = 1 if sf >= 11 else 0
    t_sym = 2 ** sf / bw
    n_pay = 8 + max(math.ceil((8 * pl - 4 * sf + 28 + 16 * crc - 20 * ih) / (4 * (sf - 2 * de))) * (cr + 4), 0)
    return (n_pre + 4.25) * t_sym + n_pay * t_sym

for sf in range(7, 13):
    t = time_on_air(20, sf)
    per_hour = {dc: int(dc * 3600 / t) for dc in (0.10, 0.01)}
    print(f"SF{sf:<2}: {t * 1000:7.1f} ms, max {per_hour[0.10]:>5} msgs/h at 10% duty, {per_hour[0.01]:>4} at 1%")

SF7 :    56.6 ms, max  6363 msgs/h at 10% duty,  636 at 1%
SF8 :   102.9 ms, max  3498 msgs/h at 10% duty,  349 at 1%
SF9 :   185.3 ms, max  1942 msgs/h at 10% duty,  194 at 1%
SF10:   370.7 ms, max   971 msgs/h at 10% duty,   97 at 1%
SF11:   741.4 ms, max   485 msgs/h at 10% duty,   48 at 1%
SF12:  1318.9 ms, max   272 msgs/h at 10% duty,   27 at 1%

Mesh networks

In a mesh, nodes pass messages along until they reach the gateway; each pass is one hop. Meshtastic sets a default hop limit of 3, with a maximum of 7. A drone can act as a temporary airborne relay, but every hop adds loss and delay and reuses the same channel.

Li et al. (2001) analysed chains of wireless nodes on one channel and found that in the ideal case a long chain carries only about 1/4 of a single link’s throughput, and about 1/7 in 802.11 simulations, because relaying nodes interfere with each other.

P_HOP, TOA_S = 0.90, 0.185                 # success chance per hop, SF9 time on air

for hops in (1, 2, 3, 5):
    row = []
    for retries in (0, 2):
        hop_ok = 1 - (1 - P_HOP) ** (retries + 1)
        tries = sum((1 - P_HOP) ** k for k in range(retries + 1))      # mean attempts per hop
        row.append(f"R={retries}: {hop_ok ** hops:6.1%}, airtime {hops * tries * TOA_S:.2f} s")
    print(f"{hops} hop(s): " + " | ".join(row))

1 hop(s): R=0:  90.0%, airtime 0.18 s | R=2:  99.9%, airtime 0.21 s
2 hop(s): R=0:  81.0%, airtime 0.37 s | R=2:  99.8%, airtime 0.41 s
3 hop(s): R=0:  72.9%, airtime 0.55 s | R=2:  99.7%, airtime 0.62 s
5 hop(s): R=0:  59.0%, airtime 0.93 s | R=2:  99.5%, airtime 1.03 s

Module lab

Common mistakes

Summary

• One SF step nearly doubles time on air, reaching farther but carrying fewer messages.
• Thailand uses AS923-1 in 920–925 MHz; check power and conditions against the NBTC announcement.
• Delivery probability falls exponentially with hop count; retries help a lot.
• A single-channel chain carries only a fraction of a single link’s throughput (about 1/4 ideally).

Check your understanding

1. What is the symbol time at SF10 and BW 125 kHz?
2. A message takes 0.5 s on air with a 1% duty cycle. How many messages per hour at most?
3. Each hop succeeds 80% of the time; three hops without retries succeed how often?
4. What is Meshtastic’s default hop limit?
5. Why does a single-channel chain of wireless nodes carry less than a single link?