Filter Bank Multicarrier (FBMC)

Filter Bank Multicarrier (FBMC) is an advanced multicarrier modulation technique designed to overcome the spectral inefficiencies and interference issues of OFDM.

Motivation: Limitations of OFDM

In an OFDM system, the transmitter uses an Inverse Fast Fourier Transform (IFFT) and the receiver uses a Fast Fourier Transform (FFT) to process multiple subcarriers. Each OFDM symbol occupies a duration denoted by T_sym.

OFDM is a multicarrier modulation technique where a high data-rate stream is divided into multiple parallel low data-rate streams. To mitigate inter-symbol interference (ISI) caused by multipath fading, the total bandwidth B is divided into N narrow sub-bands.

However, a major drawback of OFDM is that the subcarrier filters generated by the IFFT/FFT process have poor spectral containment. The frequency response of each subcarrier resembles a sinc function, which has high side-lobes.

As a result, each subcarrier leaks energy into adjacent subcarriers, leading to out-of-band emissions and interference with neighboring users or channels.

Additionally, OFDM requires the insertion of a cyclic prefix (CP) along with the useful symbol duration T_sym. While CP helps combat ISI, it reduces bandwidth efficiency.

Core Idea of FBMC

FBMC addresses the above OFDM limitations by replacing the FFT-based rectangular subcarrier shaping with a digital filter bank.

In FBMC, each subcarrier is passed through a well-designed prototype filter that provides excellent spectral localization. These filters are sharp in frequency, significantly reducing side-lobes and interference between adjacent subcarriers.

Due to this strong spectral containment, FBMC typically does not require a cyclic prefix, leading to improved bandwidth efficiency compared to OFDM.

Mathematical Representation of FBMC Signal


x(t) = ∑ₙ ∑ₘ sₘ[n] · g(t − nT) · e^{j2πmΔf t}

sₘ[n] – symbol on subcarrier m at time index n
g(t) – prototype filter with good spectral localization
T – symbol duration
Δf = 1/T – subcarrier spacing

FBMC Packet Structure

Unlike FDMA or OFDM, FBMC packets are not confined to rigid frequency slots. Subcarriers overlap in frequency but remain distinguishable due to filtering.


| Subcarrier 0 | ~~~~~~ |
| Subcarrier 1   | ~~~~~~ |
| Subcarrier 2     | ~~~~~~ |
| Subcarrier 3       | ~~~~~~ |

This overlapping is controlled and does not result in harmful interference, unlike the sinc-shaped leakage seen in OFDM.

Advantages of FBMC

Excellent spectral containment
No cyclic prefix overhead
Low out-of-band emissions
High bandwidth efficiency
Robust against adjacent-channel interference

Applications of FBMC

5G and beyond (6G) waveform research
Cognitive radio systems
Fragmented spectrum access
High-efficiency multicarrier communications

Search This Blog