Spread Spectrum

The Core Concept

Traditional radio transmits at a single frequency or narrow band. Spread spectrum takes the signal energy and spreads it across a wide frequency band — sometimes 10 to 1000 times wider than the minimum required bandwidth. The receiver uses a pseudorandom code to correlate the spread signal and recover the original data. This provides three key advantages:

• Anti-jamming: A narrowband jammer can only disrupt a small fraction of the spread signal energy. The receiver's correlation process suppresses the jammer by the processing gain.
• Low probability of intercept (LPI): The spread signal looks like noise to any receiver without the correct pseudorandom code. The signal power per unit bandwidth falls below the noise floor.
• Multipath resistance: The receiver can resolve and combine multipath components separated by more than one chip period, turning multipath from a problem into a diversity advantage.

The fundamental trade-off: spread spectrum uses more bandwidth than necessary, reducing spectral efficiency. The benefit is robustness — the system works in interference, jamming, and multipath environments where narrowband systems fail.

Processing Gain

The ratio of spread bandwidth to data rate is called processing gain (G_p) or spreading factor (SF):

G_p = B_spread / B_data = R_chip / R_data

In decibels: G_p(dB) = 10 × log₁₀(R_chip / R_data)

Practical examples:

• GPS C/A code: 1.023 Mcps / 50 bps = 20,460 → 43 dB processing gain
• 802.11b DSSS: 11 Mcps / 1 Mbps = 11 → 10.4 dB
• IS-95 CDMA: 1.2288 Mcps / 9.6 kbps = 128 → 21 dB
• Bluetooth: 1 Mcps / 1 Mbps = 1 → 0 dB (FHSS provides diversity, not processing gain)
• 3G W-CDMA: 3.84 Mcps / 12.2 kbps = 315 → 25 dB

Higher processing gain means better interference rejection but lower data rate for a given bandwidth. The system designer trades data rate for robustness.

Frequency Hopping (FHSS)

FHSS rapidly switches the carrier frequency among many channels according to a pseudorandom sequence known to both transmitter and receiver. At each hop, the transmitter and receiver retune simultaneously to the next frequency in the sequence. A jammer targeting one frequency only disrupts a fraction of the transmission.

Key parameters:

• Hop rate: Number of frequency changes per second — fast hopping changes frequency multiple times per data bit, slow hopping sends multiple bits per hop
• Hop set: The range of frequencies used — wider hop sets provide better jamming resistance
• Dwell time: How long the transmitter stays on each frequency before hopping
• Hop sequence: Pseudorandom permutation of frequencies — must be synchronized between transmitter and receiver

Military FHSS

• SINCGARS: Single Channel Ground and Airborne Radio System — 2,320 frequencies in 30–88 MHz band, 100–200 hops/sec, frequency hopping with data encryption. Standard US military tactical radio since the 1980s.
• Have Quick: UHF satellite communications anti-jam system — frequency hops across the UHF military band (225–400 MHz)
• JTIDS/MIDS: Joint Tactical Information Distribution System — uses TDMA with frequency hopping across 51 frequencies in L-band (960–1,215 MHz), up to 50 hops/sec

Commercial FHSS

• Bluetooth: 79 channels at 1 MHz each (2.402–2.480 GHz), hopping at 1,600 hops/sec (625 μs dwell time). Adaptive Frequency Hopping (AFH) avoids channels with interference (Wi-Fi). Uses a 7-bit master address to generate the hop sequence.
• 802.11 FHSS: Original Wi-Fi used 79 channels at 1 MHz each, hopping at 2.5 hops/sec (400 ms dwell). Achieved only 1–2 Mbps — replaced by DSSS (802.11b) which achieved 11 Mbps.

Direct Sequence (DSSS)

DSSS multiplies the data signal by a high-rate pseudorandom noise (PN) code called chips. Each data bit is XORed with the chip sequence, spreading the signal across the full chip bandwidth. The receiver despreads by correlating with the same chip sequence — the desired signal collapses back to the original bandwidth, while interference is spread and suppressed.

Transmitted signal: s(t) = data(t) × chip(t)
Despread: s(t) × chip(t) = data(t) × chip(t)² = data(t)

Because chip(t)² = 1 for binary chips (±1), the correlation process recovers the original data. Narrowband interference is spread across the chip bandwidth and suppressed by the processing gain.

Common DSSS Systems

• GPS C/A code: 1,023-chip Gold code at 1.023 Mcps, repeating every 1 ms. Each satellite uses a unique gold code. The 43 dB processing gain allows reception below the noise floor.
• 802.11b: 11-chip Barker sequence at 11 Mcps (1 Mbps) or CCK (Complementary Code Keying) at 5.5/11 Mbps. The Barker sequence provides 10.4 dB processing gain.
• 3G W-CDMA: 3.84 Mcps chip rate, variable spreading factors (4–512 chips per bit). Shorter spreading factors give higher data rates at lower processing gain.
• IS-95 CDMA: 1.2288 Mcps, 64-chip Walsh codes for channel separation, 42-bit long PN code for scrambling. 21 dB processing gain at 9.6 kbps voice.
• ZigBee (802.15.4): 32-chip pseudo-random sequence at 2 Mcps, giving 250 kbps data rate with 8 dB processing gain.

CDMA: Spread Spectrum for Multiple Access

CDMA (Code Division Multiple Access)uses spread spectrum to allow multiple users to share the same frequency band simultaneously. Each user is assigned a unique spreading code; the receiver correlates with the desired user's code to separate signals. Unlike FDMA (separate frequencies) or TDMA (separate time slots), CDMA allows all users to transmit at all times on the same frequency.

In IS-95 CDMA(Qualcomm, 1995), each voice user is assigned a 64-chip Walsh code from a set of 64 orthogonal codes. The 1.2288 Mcps chip rate with 64-chip codes gives a raw data rate of 19.2 kbps per channel. After forward error correction and repetition coding, 64 channels are multiplexed into the 1.2288 Mcps spread signal. The processing gain of 21 dB suppresses other users' signals.

The near-far problemis CDMA's greatest challenge: a user close to the base station can overwhelm signals from distant users. CDMA solves this with fast power control— each mobile adjusts its transmit power 800 times per second (1.25 ms rate) based on the base station's commands, ensuring all signals arrive at approximately equal power.

Hedy Lamarr: The Inventor

Actress Hedy Lamarr and composer George Antheil received US Patent 2,292,387 on August 11, 1942 for a "Secret Communications System." Their frequency-hopping idea used 88 frequencies (matching the 88 keys on a piano) and was intended to prevent Allied torpedoes from being jammed by Axis powers. Antheil's insight was using synchronized player-piano rolls as the hopping pattern controller — the same mechanical sequencer used in automatic player pianos.

The concept was ahead of its time. The mechanical implementation was impractical for missiles, and the Navy did not adopt the idea during WWII. Lamarr's patent expired in 1959 before she received any royalties. The technology was independently reinvented by military engineers in the 1950s. Lamarr was posthumously inducted into the National Inventors Hall of Fame in 2014.

Spread Spectrum Methods Comparison

Modern Applications

• GPS: All 31 GPS satellites transmit at L1 (1575.42 MHz) simultaneously. CDMA separates them — each satellite uses a unique Gold code. The 43 dB processing gain allows reception 20 dB below the noise floor.
• Wi-Fi: 802.11b used DSSS with Barker/CCK. 802.11a/g/n/ac/ax use OFDM (orthogonal frequency division), which is not spread spectrum per se but shares the wideband robustness principle.
• Bluetooth: FHSS with adaptive frequency hopping avoids Wi-Fi channels. BLE uses a simpler 40-channel FHSS at 2 MHz spacing.
• Cellular 3G: W-CDMA (UMTS) and CDMA2000 both use DSSS for multiple access. 4G LTE switched to OFDMA but retains spread-spectrum-like features (SC-FDMA uplink). 5G NR explores NOMA (Non-Orthogonal Multiple Access).
• RFID: Some UHF RFID anti-collision protocols use spread spectrum to enable hundreds of tags to respond simultaneously without collision.
• Ultra-Wideband (UWB): Intentional spread spectrum across 3.1–10.6 GHz using very short pulses (sub-nanosecond). Used for precise indoor positioning and high-speed short-range data transfer.