Frequency-Division Multiplexing (FDM)

The Concept of FDM

Frequency Division Multiplexing (FDM) is one of the classic techniques for sharing a single communication medium among multiple independent signals. The total available bandwidth of a channel is divided into a series of smaller, non-overlapping frequency sub-channels. Each of these sub-channels is then assigned to a separate user or data stream.

Broadcast radio illustrates this frequency separation. Stations transmit in assigned frequency channels, and a receiver selects one channel with a tuned filter while rejecting the others.

FDM process: baseband to broadband

The process of combining multiple signals using FDM involves a series of steps at the transmitter (multiplexing) and receiver (demultiplexing).

Transmitter Side (Multiplexing)

1. Input Signals: We start with multiple independent input signals. Typically, these are baseband signals, such as voice channels with a nominal baseband width of 4 kHz.
2. Modulation: Each baseband signal is used to modulate a unique, high-frequency carrier wave. For example, signal 1 modulates a carrier at frequency $f_{c1}$, signal 2 modulates a carrier at $f_{c2}$, and so on. Amplitude modulation (AM), particularly Single-Sideband (SSB), is often used to conserve bandwidth.
3. Filtering: After modulation, band-pass filters are used to select the desired portion of the modulated signal (e.g., just the upper sideband in SSB) and to limit energy in adjacent channels.
4. Combining: Finally, all the modulated and filtered signals are summed together electrically to create a single, wideband composite FDM signal, which is then sent into the transmission medium.

Receiver Side (Demultiplexing)

1. Filtering: The incoming composite FDM signal is fed into a bank of band-pass filters. Each filter is precisely tuned to one of the carrier frequencies ($f_{c1}, f_{c2}, ...$) and only allows its designated channel to pass through, effectively separating the signals.
2. Demodulation: Each separated signal is then individually demodulated. This process removes the high-frequency carrier, shifting the signal's spectrum back down to its original baseband range (e.g., 0 to 4 kHz).
3. Final Filtering: Low-pass filters are used to clean up the demodulated signals, removing any unwanted high-frequency artifacts left over from the demodulation process.
4. Output Signals: The original baseband signals are now recovered and sent to their respective destinations.

Analog telephone FDM hierarchy

FDM formed the basis of long-distance analog telephone systems for decades. These systems used a standardized hierarchy to combine thousands of voice calls on a single coaxial cable.

• Base Channel: A single voice channel used a nominal 4 kHz channel spacing. The 0.3 to 3.4 kHz speech band occupied about 3.1 kHz; the remaining interval provided room for filter transition and channel separation.
• Basic group (or primary group): The first level of multiplexing combined 12 voice channels using FDM to occupy the frequency range of 60-108 kHz.
• Supergroup: The next level combined five Channel Groups (5 x 12 = 60 voice channels).
• Mastergroup: In the ITU-T hierarchy, five Supergroups formed a 300-channel mastergroup (5 x 60 = 300). Some North American carrier systems combined ten Supergroups into a 600-channel mastergroup.

The hierarchy let carriers scale network capacity by combining groups into progressively larger composite signals for long-haul transmission.

Key Concepts and Trade-offs

• Guard Bands:To prevent signals from adjacent sub-channels from interfering with each other, small, unused frequency gaps known as guard bands are left between them. Guard bands are necessary and reduce the efficiency of bandwidth use.
• Analog and digital: FDM can combine analog signals or digitally modulated signals. In conventional analog FDM, multiplexing acts on continuous waveforms; digital multicarrier systems such as OFDM apply the same frequency-separation principle with discrete processing.
• FDM and WDM: Wavelength-Division Multiplexing (WDM) applies the same channel-separation idea in optical fibers. It assigns each channel a wavelength, commonly specified in nanometres, whereas FDM assigns frequency bands, commonly specified in MHz or GHz. In both cases, the channels occupy distinct spectral regions.
• Rigid Allocation: A primary drawback of classic FDM is its rigid resource allocation. Each user is assigned a fixed bandwidth slice, which remains reserved for them even if they are not actively transmitting data. This can be inefficient compared to the dynamic allocation used in packet-switched networks.