What is the relationship between spreading factor, range, and data rate in LoRa?

Increasing SF from 7 to 12 adds approximately 2.5 dB of processing gain per step, extending range by roughly 30% per SF increment. However, each SF step doubles the symbol duration (since the chip rate stays fixed at B chips/second and each symbol contains 2^SF chips), halving the data rate. At SF7 with 125 kHz bandwidth, LoRa achieves 5.5 kbps at -7.5 dB SNR sensitivity. At SF12, data rate drops to 0.3 kbps but sensitivity improves to -20 dB SNR, enabling reliable links at 15+ km in rural areas. Gateway receivers can simultaneously demodulate all SFs because each SF is orthogonal to the others.

Modulation & LPWAN

Chirp Spread Spectrum

Q: How does CSS encode data in frequency chirps?

In CSS, the channel bandwidth B is divided into 2^SF frequency bins, where SF is the spreading factor (7 to 12 in LoRa). Each symbol encodes SF bits by starting the up-chirp at one of the 2^SF possible frequencies. The chirp sweeps linearly from its starting frequency to the upper band edge, then wraps around to the lower edge and continues to the starting frequency. At the receiver, multiplying by a conjugate down-chirp (de-chirping) converts each symbol into a single-tone sinusoid whose frequency directly indicates the transmitted symbol value. An FFT of size 2^SF identifies the peak frequency bin, completing the demodulation. This process provides intrinsic resilience to multipath and Doppler.

Q: How does CSS compare to direct-sequence spread spectrum?

Both CSS and DSSS spread the signal across a wider bandwidth for processing gain, but their mechanisms differ. DSSS multiplies data by a high-rate pseudo-random chip sequence, requiring tight synchronization to within one chip period. CSS uses frequency chirps that are inherently Doppler-tolerant and easier to synchronize because the de-chirping process converts signals to tones detectable by FFT without precise timing. CSS also handles multipath better: reflections produce additional FFT peaks at different bins rather than degrading the correlation peak. However, DSSS supports more simultaneous users through code orthogonality (CDMA), while CSS relies on SF orthogonality with only 6 separable channels (SF7 through SF12).

/cherp spred spek-truhm/ (CSS)

A spread-spectrum modulation technique that encodes data symbols as cyclic time-shifted linear frequency chirps spanning the full channel bandwidth. Each symbol encodes SF bits (spreading factor, 7 to 12 in LoRa) by starting the chirp at one of 2^SF possible frequencies. CSS provides processing gain of 10 to 20 dB, enabling reliable demodulation at SNR as low as -20 dB. The LoRa implementation on sub-GHz ISM bands (868/915 MHz) achieves ranges of 5 to 15 km in rural environments at data rates of 0.3 to 50 kbps, making it the dominant physical layer for LPWAN IoT networks.

Category: Modulation & LPWAN

SF Range: 7 to 12

SNR Floor: -20 dB (SF12)

Understanding Chirp Spread Spectrum

CSS was originally developed for radar applications, where the linear chirp's time-bandwidth product provides processing gain for target detection. Semtech adapted this principle for communications in the LoRa modulation scheme, patented in 2014. Instead of encoding information in amplitude or phase of a carrier, CSS encodes it in the starting frequency of a linear up-chirp that sweeps across the entire channel bandwidth B (typically 125, 250, or 500 kHz). With spreading factor SF, each symbol carries SF bits of information and consists of 2^SF chips (frequency steps), with the symbol duration T_s = 2^SF/B.

Demodulation is elegantly simple: the receiver multiplies the received signal by a conjugate base down-chirp, converting the frequency-varying chirp into a single-frequency tone. The tone frequency directly indicates which of the 2^SF possible starting frequencies was transmitted, and thus which SF-bit symbol was sent. An FFT of size 2^SF identifies the peak bin. This de-chirping process provides processing gain proportional to the time-bandwidth product, enabling operation at very low SNR. Different spreading factors are quasi-orthogonal, so a single gateway can simultaneously receive signals at SF7 through SF12 on the same frequency channel, with each SF occupying a different time-bandwidth space. The key engineering trade-off is that higher SF increases range (better sensitivity) but decreases data rate and increases time-on-air, which affects battery life and regulatory duty-cycle compliance.

CSS / LoRa Key Equations

Symbol Duration:
T_s = 2^SF / B [seconds]

Bit Rate:
R_b = SF · B / 2^SF · CR [bps, CR = coding rate 4/5 to 4/8]

Processing Gain (approximate):
G_p ≈ 10 · log₁₀(2^SF / SF) [dB]

Where SF = spreading factor (7 to 12), B = bandwidth (125/250/500 kHz), CR = forward error correction coding rate. At SF12 with 125 kHz BW and CR 4/5: T_s = 32.77 ms, R_b = 293 bps, G_p ≈ 25.1 dB.

LoRa Spreading Factor Performance

SF	Bit Rate (125 kHz)	SNR Sensitivity	Time-on-Air (50 B)	Approx. Range
SF7	5,470 bps	-7.5 dB	72 ms	2 to 5 km
SF8	3,125 bps	-10 dB	134 ms	3 to 7 km
SF9	1,758 bps	-12.5 dB	247 ms	4 to 9 km
SF10	977 bps	-15 dB	452 ms	5 to 11 km
SF11	537 bps	-17.5 dB	824 ms	7 to 13 km
SF12	293 bps	-20 dB	1,483 ms	10 to 15 km

Common Questions

Frequently Asked Questions

How does CSS encode data in frequency chirps?

The channel bandwidth is divided into 2^SF frequency bins. Each symbol starts an up-chirp at one of these frequencies, sweeps to the upper edge, wraps to the lower edge, and continues back to start. The receiver multiplies by a conjugate down-chirp (de-chirping), converting each symbol into a single tone. An FFT of size 2^SF identifies the peak bin, completing demodulation with inherent resilience to multipath and Doppler.

What is the trade-off between spreading factor, range, and data rate?

Each SF step adds roughly 2.5 dB of processing gain (30% more range) but doubles symbol duration, halving data rate. SF7 at 125 kHz gives 5.5 kbps and -7.5 dB SNR sensitivity. SF12 drops to 0.3 kbps but reaches -20 dB, enabling 15+ km rural links. Gateway receivers demodulate all SFs simultaneously because each SF is orthogonal to the others.

How does CSS compare to direct-sequence spread spectrum?

Both spread signals for processing gain, but CSS uses frequency chirps that are Doppler-tolerant and synchronize easily via FFT, while DSSS requires tight chip-level timing. CSS handles multipath better (reflections appear as additional FFT bins) but supports fewer simultaneous users (6 SFs vs unlimited PN codes). DSSS supports full CDMA; CSS relies on SF orthogonality.

Related Terms

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