GFDM (Generalized Frequency Division Multiplexing)

1. What is GFDM?

GFDM is a flexible multi-carrier modulation scheme extending OFDM. It was developed for 5G and beyond networks to improve spectral efficiency, reduce out-of-band emissions, and lower PAPR.

• Block-based structure: Transmits data in blocks of K subcarriers and M time slots (symbols).
• Flexible pulse shaping: Each subcarrier can use a filter g(t) to reduce interference.
• Cyclic prefix (CP): Used to combat multipath interference, like in OFDM.
• Circular filtering: Filters are circularly convolved with the data, simplifying FFT-based implementation.

2. GFDM Signal Model

Discrete-time transmitted GFDM signal:

x[n] = Σₖ₌₀ᴷ⁻¹ Σₘ₌₀ᴹ⁻¹ dₖ,ₘ · g[(n − mK) mod N] · e^(j 2 π (k/K) n),
n = 0,1,...,N−1

      

Where:

• dₖ,ₘ = data symbol at subcarrier k and time slot m
• g[n] = prototype filter of length N = K · M
• K = number of subcarriers
• M = number of subsymbols per subcarrier

Notes:

• If g[n] is rectangular → GFDM reduces to OFDM.
• Flexible g[n] reduces out-of-band emissions and improves spectral efficiency.

Matrix Form

GFDM can also be represented as a matrix equation:

x = A · d

      

Where:

• d = K × M data vector
• A = N × K·M modulation matrix from circularly shifted and frequency-shifted pulse shapes
• x = transmitted time-domain block

3. Key Differences: GFDM vs Traditional FDM/OFDM

Feature	Traditional FDM / OFDM	GFDM
Pulse shaping	Rectangular (rect) pulses; high out-of-band emissions	Flexible pulse g[n] per subcarrier; low OOB
Subsymbol structure	One symbol per subcarrier per FFT interval	Multiple subsymbols (M) per subcarrier in one block
Circular filtering	No	Yes, allows overlapping pulses without interference
PAPR	High	Lower due to pulse shaping and overlapping
Flexibility	Fixed FFT size, rectangular pulses	Tunable K, M, filters, CP; supports non-orthogonal multiplexing
Spectral efficiency	Moderate	High; supports fragmented spectrum efficiently
Orthogonality	Strictly maintained	Can be non-orthogonal; requires interference cancellation

4. Advantages of GFDM

• Reduced out-of-band emissions → better for dynamic spectrum access
• Flexible time-frequency allocation → suitable for fragmented spectrum
• Lower PAPR → efficient power amplification
• Compatible with 5G/6G → supports URLLC, IoT, and underwater optical communications

OFDM: Rectangular pulses in time → sinc-shaped spectrum → high side-lobes.
GFDM: Pulse-shaped subcarriers → overlapping in time and frequency → smooth spectrum.

Further Reading