Chirp Spread Spectrum (CSS)

The core of CSS is a linear chirp, where the instantaneous frequency increases (up-chirp) or decreases (down-chirp) linearly with time over a defined bandwidth B and symbol duration T.

• Time-Bandwidth Product (BT): The product of sweep bandwidth and duration defines the processing gain. A higher BT means greater resilience to interference.
• Chirp Rate: The constant rate of frequency change, calculated as B/T, measured in Hz/s.
• The baseband waveform is a complex exponential with quadratic phase: s(t) = exp(jπμt²) where μ is the chirp rate.

CSS systems encode information by modulating the chirp's parameters, not its amplitude or phase.

• Binary Chirp Keying: The simplest form uses an up-chirp for binary '1' and a down-chirp for binary '0'. These two signals are near-orthogonal.
• Differential CSS: Data is encoded in the phase difference between consecutive chirps, commonly used in the IEEE 802.15.4a standard.
• Chirp Position Modulation: The symbol is determined by a deliberate time-shift applied to the chirp within the symbol period.

The receiver uses a matched filter to compress the received chirp into a narrow pulse, concentrating its energy in time.

• Compression Ratio: Equal to the Time-Bandwidth Product (BT). A chirp with BT=100 is compressed to 1/100th of its original duration.
• Range Resolution: The compressed pulse width determines the ability to resolve two closely spaced signal paths, critical for radar and multipath mitigation.
• The matched filter for an up-chirp is a down-chirp, and vice-versa, implementing a convolution that de-spreads the signal.

A key advantage of CSS over other spread spectrum techniques is its inherent resilience to Doppler frequency shifts caused by relative motion between transmitter and receiver.

• A Doppler shift simply translates the chirp in frequency, which manifests as a small timing offset at the matched filter output rather than a complete decorrelation.
• This property makes CSS ideal for high-mobility applications like aerospace telemetry and underwater acoustic communications.
• The ambiguity function of a linear chirp exhibits a ridge-like shape, coupling time delay and frequency shift.

CSS provides robust protection against both narrowband and broadband interference through its processing gain.

• Narrowband Jamming: The matched filter spreads a narrowband interferer's energy over time while compressing the desired chirp, effectively suppressing the jammer by the compression ratio (BT).
• Multipath Fading: By resolving multipath components as distinct compressed pulses, a rake receiver architecture can coherently combine them, exploiting time diversity.
• Co-channel Interference: Chirps with different chirp rates are quasi-orthogonal, allowing multiple users to share the same band simultaneously.

The most widespread commercial implementation of CSS is LoRa (Long Range), a proprietary physical layer owned by Semtech.

• LoRa uses a variant called Frequency Shift Chirp Modulation (FSCM) where cyclic time-shifts of a continuously repeating up-chirp encode the symbol.
• Spreading Factor (SF): Defines the number of chips per symbol (2^SF). Higher SF increases sensitivity and range at the cost of data rate.
• LoRa's high sensitivity (down to -148 dBm) makes it the de facto standard for low-power wide-area networks (LPWANs).