9. Spread Spectrum: Hide and Seek with Cryptographic Codes

Spread spectrum spreads a narrow-band signal over a much wider bandwidth, then despreads at the receiver. The signal is buried below the noise floor, but the despreading reveals it. Counter-intuitively, this both defeats jammers and lets multiple users share a channel.

Whisper-with-a-secret-code analogy. Imagine you and a friend agree to communicate at a noisy concert. You decide to whisper but in a secret rhythm only you both know. Anyone listening hears only random noise; only your friend, listening for the rhythm, can pull your message out of the chaos. Spread spectrum is exactly that: a signal disguised as noise to anyone without the code.

9.1 Direct-sequence spread spectrum (DSSS)

Multiply the data symbols by a fast pseudo-noise (PN) sequence at chip rate $R_c \gg R_b$. Each data bit becomes $G = R_c / R_b$ chips. The transmitted spectrum spreads to a bandwidth $\sim R_c$.

At the receiver, multiply again by the same PN sequence. The data despreads back to its original bandwidth, while any narrow-band interferer gets spread by the multiplication, dropping its in-band power by the processing gain $G$:

$G_p = 10 \log_{10}(R_c / R_b) \text{ dB.}$

GPS L1 C/A: data rate 50 bps, chip rate 1.023 Mcps. Processing gain $G_p = 10 \log_{10}(1.023 \times 10^6 / 50) = 43$ dB. Plus the integration over many bits in the navigation message. The signal as received at the surface of the Earth is about 30 dB below the thermal noise floor in the receiver's front-end bandwidth, yet correlation lifts it out reliably.

9.2 Frequency-hopping spread spectrum (FHSS)

Instead of spreading over a wide spectrum simultaneously, hop the carrier across many narrow channels under control of a PN sequence. The transmitter and receiver hop in lockstep; eavesdroppers without the code see only brief blips on each channel and cannot reassemble the message. Bluetooth Basic Rate hops at 1600 hops per second across 79 channels in the 2.4 GHz band. Military radios (HAVE QUICK, SINCGARS) hop hundreds of times per second across hundreds of MHz.

9.3 CDMA: spread spectrum as multiple access

If different users have different (orthogonal) PN codes, they can share the same time and frequency simultaneously. The receiver despreads with user $k$'s code; user $j$'s signal does not despread (because the cross-correlation between codes is small) and contributes only as low-level interference. Code-Division Multiple Access (CDMA, IS-95, then UMTS WCDMA) used this idea to share spectrum among hundreds of users at once. GPS uses CDMA across satellites: each satellite has a unique 1023-chip Gold code, and the receiver despreads each separately.

9.4 Jamming margin

A jammer with power $J$ in the receiver's band can be tolerated up to a jamming margin of roughly $G_p - (E_b/N_0)_\text{required}$ dB. So a 43 dB processing gain GPS receiver, requiring 10 dB of $E_b/N_0$, can tolerate a jammer 33 dB above the signal in its band. Spread spectrum is the canonical anti-jam waveform for exactly this reason. Military GPS (M-code) extends this with stronger codes and adaptive nulling antennas.

Hardware-security tie-in. Spread spectrum is anti-jam, but it is not anti-tamper. A spoofer who knows the PN code can synthesize a fake signal that despreads correctly and overrides the genuine satellites; this is the family of GPS-spoofing attacks. The 2011 Iranian capture of an RQ-170 drone and the 2017 Black Sea ship-AIS spoofing incidents both exploit the open knowledge of civil-GPS codes. Encrypted military codes are far harder to spoof, illustrating that the same spectrum-spreading tool is both protection and surface area.