DBPSK (Sigfox)
How Sigfox Encodes Bits in Phase Transitions
Sigfox is an ultra-narrowband LPWAN technology that trades data rate for range and battery life. Its uplink occupies the sub-GHz ISM bands, 868 MHz in Europe and 902 MHz in North America, and squeezes the entire transmission into a channel only 100 Hz wide. Within that channel, each bit is mapped to a 180-degree phase transition of the carrier: a binary one inverts the phase relative to the previous symbol while a binary zero leaves it unchanged (or the reverse, depending on the differential convention). Because the information lives in the phase difference, the receiver never needs to know the absolute phase, only how it moved from one symbol to the next.
That distinction is what separates DBPSK from ordinary coherent BPSK. A coherent BPSK receiver must lock to the transmitter's carrier phase with a recovery loop and hold that lock for the whole packet. At 100 Hz and the very low signal-to-noise ratios Sigfox operates in, with received power often near minus 142 dBm, building and holding such a lock against low-cost crystal drift and Doppler is impractical. Differential detection sidesteps the problem entirely by comparing adjacent symbols, accepting a small sensitivity penalty of roughly 0.5 to 1 dB in exchange for robustness and a far simpler, cheaper device transmitter.
Reliability is reinforced outside the modulation itself. Each Sigfox message is transmitted three times on three pseudo-random frequencies and time slots, providing frequency and time diversity against narrowband interference and fading. The base station listens across the full uplink band with a software-defined radio and FFT detection, locating each device wherever it happens to land in the spectrum. The downlink, by contrast, abandons phase modulation and uses GFSK at 600 bps, since downlink timing is anchored to a preceding uplink and a constant-envelope frequency scheme eases the device receiver.
Differential Encoding and Detection
The transmitter forms each output symbol phase from the previous transmitted phase plus the current bit's phase shift, so the differential encoder has memory of exactly one symbol. The receiver inverts this by multiplying the current complex sample by the conjugate of the previous one and slicing the real part. The penalty relative to coherent BPSK arises because noise on two consecutive symbols influences a single bit decision, doubling the effective noise contribution at the decision point.
Governing Relationships
Pb = ½ × e−Eb/N0
Coherent BPSK (for comparison):
Pb = Q(√(2×Eb/N0))
Ultra-narrowband link budget:
PRX = PTX + GTX + GRX − PL, with in-band noise power N = −174 dBm/Hz + 10·log10(B) = −154 dBm at B = 100 Hz
Where Eb/N0 is energy per bit over noise density, B ≈ 100 Hz is the channel bandwidth, PTX ≈ 14 dBm, and PL is path loss. Example: B = 100 Hz gives a thermal floor near −154 dBm, leaving usable SNR even at PRX ≈ −142 dBm. The DBPSK curve sits roughly 0.5 to 1 dB right of coherent BPSK at a 10−3 BER.
Sigfox Modulation Comparison
| Parameter | DBPSK uplink (EU) | DBPSK uplink (US) | GFSK downlink | Coherent BPSK |
|---|---|---|---|---|
| Bit rate | 100 bps | 600 bps | 600 bps | Scheme dependent |
| Channel bandwidth | 100 Hz | 600 Hz | 1.5 kHz | = symbol rate |
| Band | 868 MHz ISM | 902 MHz ISM | 869.5 MHz | Any |
| Carrier recovery | None (differential) | None (differential) | None (FSK) | PLL required |
| BER penalty vs BPSK | ~0.5 to 1 dB | ~0.5 to 1 dB | ~3 to 4 dB | Reference |
| Max payload | 12 bytes | 12 bytes | 8 bytes | n/a |
Frequently Asked Questions
Why does Sigfox use differential BPSK instead of coherent BPSK?
In a 100 Hz channel at very low SNR, recovering and tracking an absolute carrier phase with a PLL is impractical against low-cost crystal drift and Doppler. DBPSK carries each bit in the phase change between consecutive symbols, so the demodulator only compares one symbol to the previous one. This noncoherent scheme needs no carrier recovery loop, costing roughly 0.5 to 1 dB of sensitivity versus ideal coherent BPSK because noise on two adjacent symbols affects each decision.
What is the symbol rate and channel bandwidth of the Sigfox DBPSK uplink?
The European uplink is 100 bps in a 100 Hz channel near 868 MHz; the North American profile is 600 bps in a 600 Hz channel near 902 MHz. Since DBPSK carries one bit per symbol, the symbol rate equals the bit rate. Concentrating a 14 dBm (25 mW) transmission into such a narrow band raises the power spectral density and link budget enough to reach base stations tens of kilometers away.
How does the receiver demodulate Sigfox DBPSK at very low SNR?
The base station scans the whole uplink band with a wide-band SDR and FFT detection, since each device picks a random center frequency. On finding a signal it multiplies each symbol by the conjugate of the previous symbol and takes the sign of the real part to recover the bit. The 100 Hz noise window is so narrow that even near minus 142 dBm the SNR supports a BER below 10−3, helped by each message being repeated three times on different frequencies and times.