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Spread Spectrum Concepts: FHSS, DSSS, and CDMA

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1. Fundamentals of Spread Spectrum

Spread Spectrum is a transmission technique where the bandwidth of the transmitted signal ($B_{ss}$) is intentionally expanded to occupy a much wider frequency spectrum than the minimum bandwidth ($B$) required by the original information signal:

The spreading is achieved by combining the original data with an independent, pseudo-random bit pattern called a Pseudo-Noise (PN) Code Sequence. At the receiver, the identical synchronized PN code is used to de-spread and recover the original data.

Core Motivations & Advantages:

1. Immunity to Jamming & Noise: Narrowband jamming signals only corrupt a tiny fraction of the spread spectrum energy and are suppressed during de-spreading.
2. Low Probability of Intercept (LPI): The signal power is diluted over such a wide band that it appears below the background thermal noise floor to eavesdroppers.
3. Multiple Access: Multiple users can transmit across the same frequency spectrum at the same time without interfering, using orthogonal PN codes (Code Division Multiple Access - CDMA).

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2. Frequency Hopping Spread Spectrum (FHSS)

In FHSS, the transmitter modulates data onto a carrier frequency that hops rapidly among many different frequencies across a wide band according to a pseudo-random sequence.

Architecture and Working:

• A Pseudorandom Code Generator produces a sequence of pseudo-random bits.
• A Frequency Synthesizer uses these bits to generate a carrier frequency that changes at regular intervals.
• The receiver has an identical PN generator synchronized with the transmitter so it hops to the exact same frequencies at the exact same time.

Slow Hopping vs. Fast Hopping:

• Slow Hopping: The carrier frequency remains constant for multiple data bits ($\text{Hop Rate} < \text{Bit Rate}$).
• Fast Hopping: The carrier frequency changes multiple times during the transmission of a single data bit ($\text{Hop Rate} > \text{Bit Rate}$).
• Standard Application: Bluetooth utilizes FHSS, hopping $1{,}600\text{ times per second}$ across 79 channels ($1\text{ MHz}$ wide each) in the $2.4\text{ GHz}$ ISM band to avoid Wi-Fi and microwave oven interference.

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3. Direct Sequence Spread Spectrum (DSSS)

In DSSS, each original data bit is multiplied directly by a higher-rate pseudo-random binary sequence called a Chipping Code (each bit in the spreading sequence is called a Chip).

• Chipping Rate: The chip rate ($R_c$) is much faster than the data bit rate ($R_b$). The ratio $\frac{R_c}{R_b}$ defines the Spreading Factor (Processing Gain):

• Barker Sequence (IEEE 802.11b):
  • Wi-Fi standard 802.11b uses an 11-chip Barker sequence: +1, -1, +1, +1, -1, +1, +1, +1, -1, -1, -1.
  • Spreads a $1\text{ Mbps}$ or $2\text{ Mbps}$ signal over a $22\text{ MHz}$ wide RF channel.
• De-spreading at Receiver:
  • The receiver multiplies the received signal by the identical synchronized Barker sequence.
  • Mathematical auto-correlation concentrates the dispersed data energy back into a narrow peak while spreading out any unwanted interference.

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4. Code Division Multiple Access (CDMA) & Walsh Codes

CDMA allows multiple transmitters to send information simultaneously over a single communication channel using Orthogonal Chip Codes (Walsh Sequences).

Mathematical Principles of CDMA:

• Represent bit 0 as $-1$ and bit 1 as $+1$. Silent (idle) is $0$.
• Each station $k$ is assigned an orthogonal chip sequence $C_k$ of length $N$ satisfying:

• When stations transmit simultaneously, their signals add linearly on the medium:

• To extract the data of station $i$, the receiver computes the normalized dot product:

Solved Numerical Example:

Let two stations A and B have 4-chip orthogonal codes:

• $C_A = [+1, +1, +1, +1]$
• $C_B = [+1, -1, +1, -1]$

1. Check Orthogonality:

2. Encoding:
   • Station A wants to send data bit 1 $\rightarrow d_A = +1$.

• Station B wants to send data bit 0 $\rightarrow d_B = -1$.

3. Combined Channel Signal:

4. Receiver Decoding for Station A:

5. Receiver Decoding for Station B:

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5. Comparison: FHSS vs. DSSS

Parameter	FHSS (Frequency Hopping)	DSSS (Direct Sequence)
Spreading Mechanism	Rapidly shifting carrier frequency	Multiplying data bits by high-rate chip sequence
Bandwidth Occupation	Narrow instant slice, hops across wide band	Occupies entire wide bandwidth continuously
Hardware Core	Frequency Synthesizer & PN generator	Correlator / Matched Filter & PN generator
Primary Standard	Bluetooth (IEEE 802.15.1)	Wi-Fi 802.11b, GPS, 3G CDMA (IS-95, UMTS)
Resistance to Multipath	Good (frequency diversity)	Excellent (Rake receiver isolates multipath delays)

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