Spread Spectrum Intro

Spread spectrum is a transmission technique in which the signal bandwidth is intentionally expanded far beyond the minimum required to transmit the information. This deliberate bandwidth expansion provides robustness against jamming, interception, and interference, making it foundational in military communications, CDMA cellular networks, and modern wireless standards.

Core Concept Explanation

In conventional narrowband communication, the signal occupies a bandwidth just sufficient to carry the data. Spread spectrum deliberately uses a bandwidth many times larger. The spreading is achieved by modulating the data signal with a high-rate **pseudorandom noise (PN) code** before transmission. Because the receiver knows this PN code, it can despread and recover the original data. An unintended receiver, lacking the code, sees only a noise-like wideband signal.

The key advantage of spreading is that the transmitted power is distributed over a large bandwidth. This makes the power spectral density (PSD) extremely low, often below the noise floor. Consequently, the signal is difficult to detect (low probability of intercept) and difficult to jam with narrowband interference. A narrowband jammer concentrates power at one frequency, but after despreading at the receiver, the jammer energy is spread and filtered out while the desired signal is reconstructed.

Two primary spread spectrum techniques exist: Direct Sequence Spread Spectrum (DSSS) and Frequency Hopping Spread Spectrum (FHSS). DSSS multiplies the data with a PN chip sequence directly in the time domain. FHSS hops the carrier frequency in a pseudorandom pattern. Both share the same fundamental goal — making the signal appear noise-like to unauthorized parties.

Mathematical Expression

The most important metric in spread spectrum is the **processing gain (PG)**, also called the spreading gain. It quantifies how much the system suppresses interference after despreading. Processing gain is defined as the ratio of the spread signal bandwidth to the original data bandwidth. Equivalently, it equals the ratio of the chip rate to the data bit rate. In decibels, processing gain is expressed as 10 times the log of this ratio.

If the chip rate is Rc chips per second and the data rate is Rb bits per second, then the processing gain PG equals Rc divided by Rb. A higher PG means more spreading, greater jam resistance, and better covert operation. The **jamming margin** quantifies how much jamming power the system can tolerate while maintaining acceptable performance, and it depends directly on the processing gain and the required signal-to-noise ratio.

Given:
Data bit rate Rb = 10 kbps
Chip rate Rc = 10 Mcps (10 × 10^6 chips per second)
Required minimum SNR at receiver = 10 dB

Why this formula applies:
Processing gain measures spreading ratio; jamming margin uses PG to find tolerable jammer power.

Formula:
PG = Rc / Rb
PG_dB = 10 log10(PG)
Jamming Margin (dB) = PG_dB - Required SNR_dB

Substitution:
PG = (10 × 10^6) / (10 × 10^3) = 1000
PG_dB = 10 log10(1000) = 30 dB
Jamming Margin = 30 dB - 10 dB

Calculation:
PG = 1000
PG_dB = 30 dB
Jamming Margin = 20 dB

Final Answer:
Processing Gain = 30 dB, Jamming Margin = 20 dB
The system can tolerate jammer power 100 times the signal power.

Practical Understanding

Processing gain is the single most important design parameter in spread spectrum. In CDMA-based cellular systems such as IS-95 and WCDMA, processing gain allows multiple users to share the same frequency band simultaneously, each assigned a unique PN code. The receiver uses matched filtering against the known code to extract one user's signal while treating all other users as noise-like interference.

Low probability of intercept (LPI) makes spread spectrum attractive in military radios. Because the PSD falls below ambient noise, a surveillance receiver scanning the spectrum cannot easily detect the transmission. Anti-jam (AJ) capability arises because a narrowband jammer is itself despread and filtered. GPS signals operate at power levels well below the noise floor and rely entirely on processing gain for demodulation at the receiver.

Exam Tip: GATE frequently asks to calculate processing gain given chip rate and bit rate. Remember PG = Rc/Rb and jamming margin = PG_dB minus required SNR in dB. Also note: doubling the chip rate doubles PG, adding 3 dB to jamming margin.

Quick Revision

• Spread spectrum expands signal bandwidth far beyond data bandwidth using a PN code, making signals noise-like.
• Processing gain PG = Rc/Rb. In dB: PG_dB = 10 log10(Rc/Rb). Higher PG means better jam resistance.
• Jamming margin = PG_dB minus minimum required SNR_dB. It tells how much jammer power can be tolerated.
• Low probability of intercept (LPI) arises because spread signal PSD falls below noise floor.
• Two main types: DSSS (time-domain PN multiplication) and FHSS (frequency hopping).
• CDMA is built on DSSS — multiple users share same band with orthogonal or near-orthogonal PN codes.
• Trap: Do not confuse chip rate with bit rate. Chip rate is always much higher than bit rate in spread spectrum.