An Open-Source LoRa Physical Layer Prototype on GNU Radio

I. INTRODUCTION

• The GNU Radio SDR includes receiver components for operation at very low SNRs, jointly corrects STO and CFO, and provides the first reported fully end-to-end experimental low-SNR receiver results.The implementation is publicly available for LoRa receiver research.Source: Contributions · p. 1

II. LORA PHY

• The paper describes a complete LoRa PHY transmitter and receiver chain, including whitening, channel coding, interleaving, Gray mapping, and packet structure.Source: §II · p. 1

A. LoRa Modulation and Demodulation

• LoRa symbols span the bandwidth and increase in frequency by B/N per chip, while demodulation dechirps the received signal and applies a DFT to estimate the symbol.At a sampling rate equal to B, real transmissions introduce aliasing distortion because the continuous-time chirp occupies slightly more than B.Source: A. LoRa Modulation and Demodulation · pp. 1–2

B. Complete LoRa Transceiver Chain

• The transmitter applies whitening, Hamming encoding, interleaving, and Gray mapping before chirp modulation; the receiver reverses these steps after demodulation.Source: B. Complete LoRa Transceiver Chain · p. 2

1) Whitening:

• Whitening XORs information bits with a pseudo-random sequence, and the implementation derives its whitening matrices from the CR = 4/8 base matrix with rate-specific changes.For CR = 4/5, the parity bit is computed from whitened data, so whitening precedes that coding step.Source: 1) Whitening · p. 2

2) Error-Correction Coding:

• LoRa supports rates 4/5, 4/6, 4/7, and 4/8; the three lowest rates use (4,n) Hamming codes, while 4/5 uses an even parity-check code.Source: 2) Error-Correction Coding · p. 2

3) Interleaving:

• The diagonal interleaver spreads up to SF bit errors from a symbol error across multiple ECC codewords, increasing the probability that codewords decode correctly.Most codewords will then contain only a single bit error.Source: 3) Interleaving · p. 2

4) Gray mapping:

• Reverse Gray mapping makes an adjacent-symbol demodulation error cause one bit error, which Hamming codes at CR = 4/7 and CR = 4/8 can correct.This property is useful when CFO or STO recovery leaves ±1 demodulation errors.Source: 4) Gray mapping · p. 2

1) Preamble:

• The packet structure is shown in Fig. 1, and its first component is a preamble consisting of a variable number of upchirps.The default preamble length is 8; valid lengths range from 6 to 65,535.Source: 1) Preamble · p. 2, C. LoRa Packet Structure · p. 2

2) Network identifiers:

• Two network identifier symbols follow the preamble; cited descriptions differ on whether they are {x, N − x} or {x, x}.The first description recommends a minimum distance of three between network identifiers to avoid problems from ±1 demodulation errors.Source: 2) Network identifiers · p. 2

3) Downchirps:

• Two and a quarter downchirps follow the network identifiers and help distinguish sampling time offset from carrier frequency offset.Source: 3) Downchirps · p. 2

4) Header (Optional):

• The optional header carries packet length, code rate, CRC presence, and a checksum; without it, receiver parameters must be configured manually.Source: 4) Header (Optional) · p. 2

5) Payload and CRC:

• The payload is the packet’s final part, may include a 16-bit CRC, and is limited to 255 bytes.Source: 5) Payload and CRC · p. 2

III. LORA FRAME SYNCHRONIZATION

• Ideal synchronization assumptions often fail in practice, so the receiver adds frame synchronization and STO/CFO correction for correct demodulation.The receiver addresses these offsets during frame synchronization, not only in the data portion of the frame.Source: §III · pp. 2–3

• Decision windows contain N samples and can straddle two preamble upchirps; τSTO measures the offset from the first chip of the window to the first chip of its second upchirp.Source: A. Frame Synchronization Signal Model · p. 3
• The carrier frequency offset is Δfc = fc1−fc2, the difference between transmitter up-conversion and receiver down-conversion frequencies.Source: A. Frame Synchronization Signal Model · p. 3
• The signal model represents the carrier offset through c[n], with h as channel gain, x[n] as the transmitted signal, and z[n] as AWGN.Source: A. Frame Synchronization Signal Model · p. 3
• STO and CFO each split into integer and fractional parts, and their combined effect makes joint estimation and correction challenging.Source: A. Frame Synchronization Signal Model · p. 3

1) Preamble detection:

• The receiver detects a preamble when Npr−1 consecutive symbols fall within {s−1, s, s+1}, allowing for ±1 errors caused by fractional STO–CFO offsets.Source: 1) Preamble detection · p. 3
• A majority rule over the in-range symbols sets the preamble synchronization value and discards N−ŝpr samples for coarse time synchronization.Source: 1) Preamble detection · p. 3
• Coarse synchronization leaves possible time misalignment because integer CFO and fractional-offset effects can shift the estimated preamble position.Source: 1) Preamble detection · p. 3
• The receiver separates integer STO and CFO using the 2.25 downchirps, re-synchronizes with integer STO, and removes integer CFO with a frequency shift.Avoiding integer-CFO-induced time misalignment is desirable because it results in inter-symbol interference.Source: 2) Estimation and Compensation of LSTO… · p. 3
• Fractional CFO is estimated before fractional STO using RCTSL-based spectral methods; the CFO estimate is corrected by multiplying the received signal by a complex exponential.For CFO estimation, the receiver dechirps the remaining Npr−2 preamble symbols and computes a length-2(Npr−2)N DFT.Source: 3) Estimation and Compensation of λSTO… · pp. 3–4
• After CFO correction, the receiver reuses the Npr−2 preamble symbols to estimate fractional STO from combined length-2N DFTs, then compensates it by time-domain interpolation.Source: 3) Estimation and Compensation of λSTO… · p. 4

• The open-source GNU Radio LoRa PHY implementation is publicly available for research and development of receiver algorithms.The paper also uses the implementation in a testbed to experimentally assess LoRa error-rate performance.Source: §IV · p. 4

A. GNU Radio LoRa PHY Implementation

• The receiver synchronizes packets, estimates and corrects STO and CFO, then demodulates and decodes the received data.Its chain includes Gray demapping, deinterleaving, Hamming decoding, dewhitening, and CRC checking.Source: A. GNU Radio LoRa PHY Implementation · p. 4
• The transmitter chain inserts headers and CRCs, whitens and encodes data, interleaves and Gray-maps it, then modulates it.Source: A. GNU Radio LoRa PHY Implementation · p. 4
• Users can configure transmission parameters including spreading factor, coding rate, bandwidth, header and CRC presence, and message.Source: A. GNU Radio LoRa PHY Implementation · p. 4

B. Testbed description

• The testbed uses NI 2920 USRPs at 915 MHz, with a shared reference clock available for zero-CFO validation and ground truth.A cable and attenuators replace antennas to avoid interference in the 915 MHz ISM band.Source: B. Testbed description · p. 4, Figure 2 · p. 4
• A commercial LoRa transceiver and receiver-side amplifier extend the testbed to transmissions between USRPs and commercial devices.The MiniCircuits amplifier provides approximately 19 dB gain at the USRP receiver.Source: B. Testbed description · p. 4

C. Testbed results

• Uncoded LoRa matches AWGN simulation closely with STO alone, while STO and CFO together leave less than 1 dB degradation.The figure compares testbed and simulation BER for uncoded and coded LoRa at SF = 7.Source: Figure 3 · p. 5, C. Testbed results · p. 5
• Coded LoRa stays within 1 dB of AWGN simulation with STO alone, and adding CFO causes almost negligible degradation.The authors attribute this to effective CFO correction and coded LoRa’s resistance to small residual CFO.Source: C. Testbed results · p. 5

V. CONCLUSION

• The GNU Radio SDR implementation’s measured error-rate performance is within 1 dB of MATLAB simulations, even with fully decoupled transmitters and receivers.Source: §V · p. 5
• The authors present an open-source LoRa PHY implementation and describe its synchronization and offset-correction algorithms.Source: §V · p. 5
• The implementation provides a testbed for stable experimental validation of proposed algorithms for improved LoRa transceivers.Source: §V · p. 5