---
title: 'LoRa-FHSS: Frequency Hopping for IoT Networks'
url: https://www.emergentmind.com/topics/lora-frequency-hopping-spread-spectrum-lr-fhss
type: topic
---

# LoRa-FHSS: Frequency Hopping for IoT Networks

LoRa-frequency Hopping Spread Spectrum (LR-FHSS) is an uplink-only physical-layer option in LoRaWAN that replaces a single wide-band chirp transmission with a packet split into narrow 488 Hz blocks that hop pseudo-randomly across a wider operating channel width, while relying on header repetition, convolutional coding, and fragment recovery to improve scalability and robustness in dense terrestrial and direct-to-satellite IoT networks [2010.00491]. Across analytical, implementation, and measurement studies, LR-FHSS is associated with higher network capacity than classical LoRa, the same radio link budget as LoRa in some operating points, and a design space centered on fragment collisions, header detectability, Doppler tolerance, and multi-gateway or satellite reception [2505.01689].

## 1. Position within LoRaWAN and intended operating regime

Semtech introduced LR-FHSS in November 2020 as a new PHY mode in the LoRa family, and the protocol literature consistently treats it as a LoRaWAN extension for extremely long-range and large-scale communication scenarios such as satellite IoT [2312.13981]. The baseline mode is fast pure ALOHA uplink only; downlink remains LoRa-CSS. This asymmetry is operationally important, because ACKs, receive windows, and control procedures still inherit LoRaWAN Class A behavior even when the uplink PHY is LR-FHSS [2010.00491].

Comparative analyses report the same 155 dB link margin as LoRa SF12 for the 162 bps, CR \(1/3\) operating point, while emphasizing that LR-FHSS trades a single 125–500 kHz chirp channel for many narrow 488 Hz slices and statistical multiplexing in time and frequency [2010.00491]. It should not be reduced to LoRa-CSS with hopping: the transceiver literature defines a distinct narrowband PHY with GMSK-modulated hopping blocks, repeated headers, and fragment-wise coding and recovery [2305.13779].

## 2. Packetization, hopping mechanics, and regional parametrization

An LR-FHSS uplink packet comprises a PHY-header block, a sequence of \(N_H\) header replicas, and a sequence of \(N_F\) payload fragments. Header blocks last \(T_H=233.472\) ms, payload fragments last \(T_F=102.4\) ms, and the header carries the hopping-sequence seed, data rate, payload length, and code rate so that the receiver can reconstruct the fragment schedule [2305.13779]. In one protocol overview, the packet structure is summarized as SyncWord plus \(R\) header replicas plus \(L\) payload fragments; the payload is convolutionally encoded at rate \(\mu\), partitioned into \(L\) fragments, and successfully recovered if at least \(\lceil \mu L\rceil\) fragments are received [2505.01689].

Regional instantiations differ materially. In the FCC band, one analytical study uses an Operating Channel Width of 1.523 MHz, an Occupied Bandwidth of 488 Hz, and a hopping organization of \(52\) grids \(\times\) \(60\) OBWs with 25.4 kHz spacing; each payload fragment hops pseudo-randomly within one grid [2505.01689]. In the EU 868 MHz band, the reference overview reports \(B_{\rm OCW}=137\) kHz for DR8/9, \(B_{\rm OBW}=488\) Hz, minimum hop spacing \(\Delta f_{\min}=3.9\) kHz, and about \(280\) usable subcarriers per OCW [2010.00491].

One published hop model writes the \(n\)th fragment frequency as
$$
f_n = f_{\rm OCW,\,offset} + \Bigl[\{H(R+n\cdot2^{16})\}\bmod M\Bigr]\Delta f_{\min},
$$
where \(H(\cdot)\) is a 32-bit hash, \(R\) is a 9-bit seed from the header, and \(M\) is the number of usable subcarriers per device [2010.00491]. Header repetition and payload coding are DR-dependent: in the FCC analysis DR5 uses \(R=3\) and \(\mu=1/3\) at 162 bps, whereas DR6 uses \(R=2\) and \(\mu=2/3\) at 325 bps [2505.01689]; the EU overview uses DR8 and DR9 labels for 162 bps and 325 bps modes [2010.00491]. This suggests that LR-FHSS data-rate nomenclature is regional-parameter dependent rather than globally uniform.

## 3. Reception architectures, decoding constraints, and fragment recovery

Baseline LoRaWAN reception assumes that one gateway receives at least one header replica and a sufficient fraction of payload fragments. In the reference overview, the gateway listens to the entire OCW and reassembles a packet if it decodes at least one header and at least \(1/CR\) of the fragments [2010.00491]. Direct-to-satellite receiver designs implement this by wideband channelization, header detection, CFO estimation, buffering per-channel time series, payload extraction at predicted hop times, and Viterbi/CRC decoding; one design reports that GMSK outperforms QPSK under Doppler up to 400 Hz and reaches \(P_{md}<10^{-3}\) at SNR \(\approx -6\) dB for a 48-symbol search window [2305.13779]. Jung et al. extend this architecture with FFT-based channelization up to 3120 carriers, Doppler-rate tracking, and bidirectional SOVA; laboratory tests consider Doppler rates up to 400 Hz/s and co-channel interference up to 40% overlapping hops among devices [2403.14154].

Several studies identify header acquisition as the dominant bottleneck under high offered load. In a slotted, no-capture analytical model, the header reception probability is
$$
p_{\rm hdr}=1-[coll(233)]^R,
$$
and the authors explicitly show that in dense traffic \(p_{\rm hdr}\) falls much faster than the payload-reception term, motivating recovery of frames whose payload fragments are observable but whose headers are lost [2306.08360]. Their linear-programming formulation and sliding-window heuristic exploit the known set of 512 pseudo-random sequences; in simulation both approaches achieve TP\(=100\%\) for all tested loads, and in fast mode with 2000 frames legacy extraction is about \(1\%\) versus about \(30\%\) for headerless extraction [2306.08360].

Fragment-level macro-diversity removes a different bottleneck: the requirement that packet reconstruction occur at a single gateway. In the multi-gateway scheme, any gateway that decodes one header replica forwards it to a controller, the controller reconstructs the hopping sequence, instructs all gateways to monitor the packet, and then de-duplicates forwarded fragments by \((\text{device ID},\text{fragment index})\) until \(|\text{collected fragments}|\ge\lceil \mu L\rceil\) [2505.01689]. Numerical evaluation shows that, relative to nearest-gateway reception, macro-diversity extends the reliable load region by about \(4\)–\(5\times\); the reported reliable-load gains are from about \(1.7\) to \(7.9\) Mbps for DR5 and from about \(0.63\) to \(4.2\) Mbps for DR6 [2505.01689].

## 4. Analytical models of reliability, throughput, and optimization

A substantial part of the LR-FHSS literature models collisions at fragment granularity. For fragment-level macro-diversity, gateways are represented by a homogeneous Poisson point process \(\mathcal P_g\) of density \(\lambda_g\), devices by an independent Poisson point process \(\mathcal P_d\) of density \(\lambda_d\), and the effective interferer density is thinned by both time and frequency as
$$
\hat{\lambda}_d=\frac{2\eta_d(R t_H + L t_P)}{n_{ocw}n_{obw}}.
$$
With single-fragment success \(S_f^P\), the number of correctly received fragments obeys \(X\sim \mathrm{Binomial}(L,S_f^P)\), the payload succeeds when \(X\ge \lceil \mu L\rceil\), and overall packet success is \(S=S^H\cdot S^P\) [2505.01689].

At network level, the reference performance analysis casts LR-FHSS as multi-channel ALOHA. With offered load \(G=N\Lambda_{\max}T_{\rm ToA}\), ideal LoRa pure ALOHA yields \(S=Ge^{-2G}\) per channel, whereas LR-FHSS is approximated by
$$
S_{\rm FHSS}\approx mGe^{-2G/m}
$$
when \(m\) parallel subcarriers are available [2010.00491]. This model captures why LR-FHSS can maintain useful goodput under loads for which single-channel ALOHA collapses.

Optimization problems built on the collision model go beyond fixed standardized data rates. In a device-level probabilistic allocation strategy, the network server distributes a probability vector \(\Delta=\{\delta_k\}\) over setups \(S_k=(h_k,CR_k)\), yielding packet success
$$
P_s(\Delta)=\sum_{k=1}^K \delta_k P_{h,k}P_{\mu,k},
$$
goodput \(\mathcal G(\Delta)=P_s(\Delta)M\lambda l\), and energy efficiency \(\mathcal E(\Delta)=\mathcal G(\Delta)/W(\Delta)\); exhaustive-search results show that the optimal distribution rarely includes DR9, while DR8 contributes significantly to goodput and energy-efficiency optimizations [2410.03392]. A different reliability model studies message replication without ACKs and derives \(\mathrm{MDP}_{\mathrm{frame}} = 1-(1-\mathcal S)^r\) for frame replication and \(\mathrm{MDP}_{\mathrm{frag}}=\mathcal S_H\tilde{\mathcal S}_P\) for fragment replication, concluding that DR8 with frame replication is preferable at low traffic whereas DR9 with fragment replication becomes preferable at moderate to heavy traffic [2501.11984].

## 5. Reported performance in simulation, traces, and measurements

Packet-level simulation in EU 868 MHz reports up to \(36\times\) capacity gain over standard LoRa for LR-FHSS DR8 and \(15\times\) for DR9 on a one-channel basis, with simulated maximum goodput of \(3{,}500{,}000\) pkt/h for DR8 and \(1{,}480{,}000\) pkt/h for DR9 [2010.00491]. The same study reports PER values of \(5\%\), \(20\%\), and \(90\%\) for LR-FHSS DR8 at 100, 1\,000, and 10\,000 devices, versus \(80\%\), \(99\%\), and about \(100\%\) for LoRa DR0 in the same scenarios [2010.00491].

Measurement-driven studies also report tangible gains in urban operation. In an urban Halifax campaign in the US915 band, LR-FHSS achieved up to a \(20\%\) improvement in Packet Reception Rate over traditional LoRa in dense urban areas; at \(d\approx1.5\) km the study reports PRR\(_0\)(DR0)\(=75\%\), PRR\(_5\)(DR5)\(=85\%\), and a bootstrap 95% confidence interval for PRR\(_5\)-PRR\(_0\) of \([0.1663,0.2167]\) [2510.23152]. The same campaign reports minimum RSSI values of about \(-138\) dBm for DR5, about \(-137\) dBm for DR6, and about \(-120\) dBm for DR0, but also notes that part of the apparent sensitivity advantage stems from how the gateway computes RSSI for hopping versus continuous chirp signals [2510.23152].

Software-receiver processing of packet traces from an actual SX1261 transmitter gives a complementary view of LR-FHSS under practical impairments. Using real traces with frequency error, one study reports one-to-one SNR thresholds for PRR \(\ge 0.9\) of about \(-20\) dB for DR8 and about \(-17\) dB for DR9, together with trace-driven network capacities of about \(3.5\) kbps for DR8 and about \(2.7\) kbps for DR9 in both AWGN and NTN settings [2312.13981]. Its customized receiver raises DR8 AWGN capacity at 3.5 kbps load from \(2.8\) to \(3.2\) kbps with collision-aware erasure decoding and to \(3.5\) kbps with additional packet-level successive interference cancellation [2312.13981].

Energy evaluations show that LR-FHSS trades airtime for collision resilience and coverage. Measurements on real hardware in a fully operational LR-FHSS network indicate that, with optimal configuration, LR-FHSS end-device battery lifetime can reach 2.5 years for a 50 min notification period, and up to 16 years with a one-day notification interval using a coin-cell battery [2408.04908]. Experiment-based ToA and current-consumption models based on 460+ transmissions per DR report relative ToA error below 0.3%, observe that DR9 reduces ToA by about 50% relative to DR8, and state that battery life can reach about 3.8 years on 2400 mAh for a 10-byte packet at \(+14\) dBm every 15 min [2408.09954].

## 6. Extensions, caveats, and active research directions

Sequence design and receiver resource allocation remain active lines of work. One study compares Semtech’s default driver family with Li–Fan wide-gap frequency-hopping sequences and reports average cross-correlation \(0.48\) versus \(0.94\); when combined with Early-Decode and Early-Drop demodulator allocation, the reported packet success rate improves from \(20\%\) to \(40\%\) at \(N=5000\), and decoded payload throughput can double for \(P=100\), CR1, and \(N\approx2000\) [2407.03490].

Other extensions move beyond a single grant-free uplink. D2D-aided LR-FHSS with network coding derives closed-form outage expressions under a shadowed-Rice satellite channel and reports capacity increases of \(249.9\%\) for DR6 and \(150.1\%\) for DR5 at outage \(10^{-2}\), at the cost of a minimum of one and a maximum of two additional transmissions per end device in each time-slot [2212.04331]. The open-source LR-FHSS-Sim models fragments as SimPy events, reproduces the requirement of at least one collision-free header and a sufficient fraction of payload fragments, and is explicitly intended to host extensions such as SIC, alternative traffic models, Doppler, multi-gateway topologies, and custom hopping schemes [2404.09539].

Several recurrent comparisons require qualification. First, LR-FHSS is not a downlink PHY in the baseline system; downlinks, including ACKs, remain LoRa-CSS. Second, the literature continues to treat optimal or adaptive hopping sequences, dynamic hop sets, coexistence with legacy LoRa, spectrum planning, channel partitioning, and ADR extensions as open issues [2010.00491]. Third, spectral-efficiency figures are reported differently across bands: the EU overview gives \(\eta=162/137000\approx1.18\) bps/Hz for DR8, whereas the US915 measurement paper gives \(\eta_5=162\) bit/s \(/\) 1.523 MHz \(\approx0.106\) bit/s/Hz for DR5 and explicitly states that LR-FHSS strength lies in link budget and interference resilience, not pure throughput [2510.23152]. This suggests that cross-paper efficiency comparisons should be read in the context of the specific OCW and regional parameter set. Finally, because current deployments may require packet reconstruction at a single gateway, fragment-level macro-diversity suggests that gateway architecture—not only the hopping PHY—can limit realized scalability [2505.01689].

Source: https://www.emergentmind.com/topics/lora-frequency-hopping-spread-spectrum-lr-fhss