Frequency Division Multiplexing (FDM)

Frequency Division Multiplexing: Sharing by Frequency

Frequency Division Multiplexing is the oldest and most intuitive multiplexing technique — it assigns each user a different frequency band within the total available bandwidth. Just as different radio stations broadcast on different frequencies without interfering with each other, FDM allows multiple signals to share the same physical medium simultaneously by occupying non-overlapping frequency ranges.

The Concept

Think of it this way: a highway has painted lane markings separating traffic into lanes. In FDM, the "lanes" are frequency bands, and the "paint" is guard bands (unused frequency gaps) that prevent adjacent channels from interfering. Each signal travels in its own frequency lane, independently of all others.

Key principle: Different frequency signals sharing the same medium do not interact (assuming linearity). The receiver uses a bandpass filter tuned to its assigned frequency to extract the desired signal and reject all others.

How FDM Works

At the transmitter (Multiplexer):

1. Each input signal occupies baseband (0 to fm Hz)
2. Each signal modulates a different carrier frequency (f₁, f₂, f₃, ...)
3. Modulated signals are summed together into a composite wideband signal
4. Composite signal transmitted over the shared channel

At the receiver (Demultiplexer):

1. Composite signal received
2. Bandpass filters tuned to each carrier frequency separate the channels
3. Each filtered signal is demodulated to recover the original baseband signal
4. Individual signals delivered to their respective outputs

Bandwidth Requirements

For N channels, each with bandwidth W:

Minimum total bandwidth (ideal): B_total = N × W

Practical bandwidth (with guard bands): B_total = N × W + (N-1) × G

Where G is the guard band width between adjacent channels.

Example — Analog telephone FDM:

• Each voice channel: 4 kHz bandwidth (300-3400 Hz speech + guard)
• 12 channels form one "group": 12 × 4 = 48 kHz (60-108 kHz)
• 5 groups form one "supergroup": 5 × 48 = 240 kHz (312-552 kHz)
• 10 supergroups form one "mastergroup": 2.4 MHz

Guard Bands: The Necessary Waste

Guard bands are empty frequency gaps between adjacent channels that prevent spectral overlap and inter-channel interference (crosstalk):

Why needed:

• Practical filters have non-zero transition bandwidth (cannot cut off instantly)
• Oscillator drift may shift signal frequencies slightly
• Non-linearities generate spectral regrowth beyond allocated bandwidth

Trade-off: Larger guard bands → better isolation but worse spectral efficiency. Typical guard band = 10-25% of channel bandwidth.

OFDM's breakthrough: By making subcarriers mathematically orthogonal, OFDM eliminates the need for guard bands entirely — subcarriers can overlap without interference, achieving 100% spectral efficiency.

FDM Applications

AM/FM Radio Broadcasting:

• AM: 540-1600 kHz, each station gets 10 kHz bandwidth
• FM: 88-108 MHz, each station gets 200 kHz bandwidth
• All stations broadcast simultaneously — your radio's tuner is the demultiplexer

Cable Television:

• Each TV channel occupies 6 MHz (NTSC) or 8 MHz (DVB)
• Entire 50-860 MHz cable spectrum divided into channels
• 100+ TV channels multiplexed on one coaxial cable

ADSL (Digital Subscriber Line):

• Telephone line bandwidth divided into:
• Voice: 0-4 kHz (traditional POTS)
• Upstream data: 25-138 kHz
• Downstream data: 138 kHz - 1.1 MHz
• Within data bands: 256 subcarriers of 4.3125 kHz each (OFDM)

4G LTE and 5G (OFDMA):

• Total bandwidth (e.g., 20 MHz) divided into subcarriers
• Resource blocks of 12 subcarriers × 7 OFDM symbols assigned to users
• Both frequency and time are divided — FDM + TDM hybrid

Advantages of FDM

1. Simplicity: Conceptually straightforward — just use different frequencies
2. Simultaneous access: All users transmit/receive continuously (no waiting for time slots)
3. Analog-friendly: Works with analog signals directly (no digitization needed)
4. Low latency: No buffering or time-slot waiting required
5. Scalability: Adding users means allocating new frequency bands

Disadvantages of FDM

1. Guard band waste: 10-25% of spectrum lost to guard bands
2. Expensive filters: Precise bandpass filters needed at receiver
3. Intermodulation: Non-linear amplifiers create sum/difference frequencies that cause interference
4. Inflexible allocation: Fixed channel bandwidth cannot adapt to varying user needs
5. Cross-talk: Imperfect filters allow signal leakage between channels

OFDM: FDM Perfected Through Digital Signal Processing

Orthogonal FDM represents the modern evolution of classical FDM:

• Subcarriers spaced at exactly 1/Ts (reciprocal of symbol time)
• Orthogonality allows spectral overlap without interference
• Implemented efficiently using Inverse FFT (at transmitter) and FFT (at receiver)
• Cyclic prefix handles multipath without inter-symbol interference

OFDM combines FDM's advantage (frequency-domain separation) with digital processing's flexibility and precision. It is the foundation of WiFi, LTE, 5G, and digital broadcasting.

Comparison with Other Multiplexing

Key Takeaways

1. FDM assigns each user a unique frequency band, allowing simultaneous transmission on a shared medium separated by frequency-selective filtering.
2. Guard bands prevent inter-channel interference but waste 10-25% of available spectrum.
3. OFDM eliminates guard band waste through mathematical orthogonality, achieving maximum spectral efficiency via FFT processing.
4. FDM is the basis of radio broadcasting, cable TV, DSL, and (as OFDMA) modern cellular networks.
5. The key trade-off is between channel isolation (wider guard bands) and spectral efficiency (narrower guards).
6. Intermodulation distortion from non-linear amplifiers is FDM's primary impairment, generating unwanted frequency products that corrupt adjacent channels.