Spread Spectrum Concepts: FHSS, DSSS, and CDMA

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:

B_{ss} \gg B

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.

                  SENDER                                              RECEIVER
            +-----------------+                                 +-----------------+
  Data ───> |  Modulator /    | ===> Transmitted Signal ====>   |  Demodulator /  | ───> Data
  Signal    |  Spreading Unit |        (Spread BW: Bss)         | De-spreading    |
            +-----------------+                                 +-----------------+
                     ^                                                   ^
                     |                                                   |
            [ PN Code Generator ]                               [ Synchronized PN Gen ]

Core Motivations & Advantages:

Immunity to Jamming & Noise: Narrowband jamming signals only corrupt a tiny fraction of the spread spectrum energy and are suppressed during de-spreading.
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.
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).

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.

 Frequency
    ^
 f4 |            [ Hop 2 ]
 f3 |                                        [ Hop 5 ]
 f2 |   [ Hop 1 ]               [ Hop 4 ]
 f1 |                       [ Hop 3 ]
    +----------------------------------------------------> Time

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.

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).

 Data Bit:        [   1   ]                   [   0   ]
                  +-------+                   +-------+
                  |       |                   |       |
                  |       +-------------------+       +--------

 Chipping Code:   1 0 1 1 0 1 0 0 1 1 0       1 0 1 1 0 1 0 0 1 1 0
 (11-bit Barker)  + - + + - + - - + + -       + - + + - + - - + + -

 Transmitted:     1 0 1 1 0 1 0 0 1 1 0       0 1 0 0 1 0 1 1 0 0 1
 (XOR Result)     (Same as chipping code)     (Inverted chipping code)

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):

\text{Processing Gain } (G_p) = 10 \log_{10}\left(\frac{B_{ss}}{B}\right)\text{ dB}

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.

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:

C_i \cdot C_j = 0 \quad (\text{for } i eq j \text{ — Orthogonal})

C_i \cdot C_i = N \quad (\text{Self Inner Product})

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

S = \sum_{k=1}^{n} d_k \cdot C_k

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

d_i = \frac{S \cdot C_i}{N}

Solved Numerical Example:

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

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

Check Orthogonality:

C_A \cdot C_B = (1)(1) + (1)(-1) + (1)(1) + (1)(-1) = 1 - 1 + 1 - 1 = 0 \quad \checkmark

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

S_A = (+1) \times [+1, +1, +1, +1] = [+1, +1, +1, +1]

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

S_B = (-1) \times [+1, -1, +1, -1] = [-1, +1, -1, +1]

Combined Channel Signal:

S = S_A + S_B = [0, +2, 0, +2]

Receiver Decoding for Station A:

S \cdot C_A = (0 \times 1) + (2 \times 1) + (0 \times 1) + (2 \times 1) = 4

d_A = \frac{4}{4} = +1 \implies \text{Data Bit } 1 \quad \checkmark

Receiver Decoding for Station B:

S \cdot C_B = (0 \times 1) + (2 \times -1) + (0 \times 1) + (2 \times -1) = -4

d_B = \frac{-4}{4} = -1 \implies \text{Data Bit } 0 \quad \checkmark

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)

6. Key Exam Questions & Takeaways

What is a Pseudo-Noise (PN) sequence?
- A deterministic binary sequence generated by a mathematical algorithm (e.g., Linear Feedback Shift Registers) that appears random to unauthorized observers but repeats deterministically and is known to both transmitter and receiver.
State two benefits of Spread Spectrum in commercial and military systems.
- Immunity against intentional hostile jamming and ambient radio interference.
- Enabling multiple access (CDMA) on identical frequencies with orthogonal codes without collision.
What is Processing Gain?
- The ratio of the spread spectrum signal bandwidth to the original baseband information bandwidth ( $G_p = B_{ss} / B$ ). Higher processing gain yields higher noise rejection.

Concepts on Spread Spectrum