Why use a cyclic prefix?

It absorbs the channel delay spread so each subcarrier sees a complex gain H[k] instead of inter-symbol interference between OFDM symbols.

What happens if CP is too short?

The multipath tail leaks into the FFT window from the previous samples, destroying orthogonality and rotating/spreading constellation points.

OFDM Subcarriers

IFFT subcarriers with cyclic prefix, multipath delay tap, one-tap ZF, and constellation distortion when CP is too short.

About this model

Orthogonal frequency-division multiplexing (OFDM) places QPSK or 16-QAM symbols on IFFT bins so subcarriers are orthogonal over the symbol period. A cyclic prefix longer than the multipath delay converts linear convolution into circular convolution, enabling a one-tap equalizer per subcarrier. If the CP is shorter than the delay, residual ISI/ICI smears the constellation and raises EVM.

Who it's for: Digital communications, wireless systems, and electrical engineering courses covering multicarrier modulation.

Key terms

OFDM
IFFT
Cyclic prefix
Multipath
Subcarrier
Zero-forcing equalizer
EVM

How it works

OFDM packs data onto many orthogonal IFFT subcarriers and guards each symbol with a cyclic prefix. Watch the constellation stay clean when the CP covers multipath delay — and smear when it does not.

Key equations

x = IFFT(X) · TX = [x_tail (CP) | x]

Multipath: y[n] = x[n] + a x[n−d] + noise

If CP ≥ d: circular conv → Y[k] = H[k] X[k] (1-tap ZF)

Frequently asked questions

Why use a cyclic prefix?: It absorbs the channel delay spread so each subcarrier sees a complex gain H[k] instead of inter-symbol interference between OFDM symbols.
What happens if CP is too short?: The multipath tail leaks into the FFT window from the previous samples, destroying orthogonality and rotating/spreading constellation points.

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Frequently asked questions