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In telecommunications, Filter Bank Modulation (FBM), also known as Multicarrier Modulation (MC), is a Frequency-division multiplexing transmission technique. This technique is generally used in digital high-data rate communication systems.

MC concepts
Multicarrier modulations idea was born in 1957 by M.L. Doelz. The baseline idea was quite simple. The high data-rate sequence is split into a series of K parallel low data-rate sequences. Following the FDM principle, the total bandwidth available is partitioned in K non-overlapping sub-channels. The sub-channels digital sequences are modulated with a digital modulation (e.g. PSK or QAM) and the obtained signals are summed together to yield the transmitted signal. If the sub-channel number is sufficiently high, the transmission medium frequency response is quasi-flat for each sub-channel. Thus, the equalization process can be simplified. A MC scheme is practically implemented with a filter bank structure. Oppositely from conventional FB theory, where an analysis bank is followed by a synthesis bank, in FBM the two banks are swapped. The transmitter is implemented with a synthesis bank and the receiver is implemented with an analysis bank.

Mathematically, the transmitted signal is expressed as

$$x(nT) = \sum_{k=0}^{K-1} \sum_{\ell=0}^{L-1} a^{(k)}(\ell N T) g(nT-\ell N T) e^{i 2 \pi n k/ K}$$, where L is transmitter block size (in symbols) and $g(nT)$ is the transmitter prototype pulse impulse response. At the receiver, the m-th received symbol in the i-th sub-channel is written as

$$z^{(i)}(m N T) = \sum_n x(nT) h(m N T - n T) e^{-i 2 \pi n i/ K} $$, where $h(nT)$ is the receiver prototype pulse impulse response.

Cyclic FBM
Generally, the filtering operations in the filter banks exploit the linear convolution operator. In 1997 a new idea has come: replace the linear convolution with the circular convolution. Cyclic filter banks have been introduced by Vaidyanathan. This new concept has been used to build a new type of multicarrier systems. Commons cyclic FBM schemes are CB-FMT, COQAM, SC-FDMA and GFDM.

CB-FMT
Cyclic Block Filtered Multitone Modulation is the cyclic-version of conventional Filtered Multitone Modulation, a multicarrier scheme proposed by G. Cherubini in 2000 for VHDSL. CB-FMT has been proposed by A. Tonello in 2008. In CB-FMT the prototype pulses have high frequency domain confinement and the banks are orthogonal.

COQAM
Cyclic Offeset-QAM is the cyclic-version of Offeset-QAM. In OQAM, the complex symbol is split into the real and the imaginary part. Furthermore, real and imaginary parts are staggered in time-domain between adjacent sub-channels. This idea was was conceived in 1967 by B.R. Saltzberg. The cyclic implementation has been proposed in 2014 by P. Siohan.

SC-FDMA
Single-carrier FDMA is born to improve OFDMA (multi-user version of OFDM). SC-FDMA scheme has been introduced by Myung, Junsung and Goodman in 2006 and it allows to reduce the peak-to-average power ratio.

GFDM
Generalized FDM is born to generalize the SC-FDMA scheme with pulse shaping. The scheme was introduced by Fettweis in 2009. Initially, the scheme was proposed for UHF TV bands.