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 Tsym.
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 Tsym. 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) = ∑ā ∑ā sā[n] · g(t − nT) · e^{j2ĻmĪf t}
- sā[n] – symbol on subcarrier m at time index n
- g(t) – prototype filter with good spectral localization
- T – symbol duration
- Īf = 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