OFDM transmitter and receiver

Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation in which a high-rate data stream is split into N low-rate streams, and each is sent on a separate subcarrier. The subcarriers are spaced at Δf = 1/T_s (T_s = OFDM symbol time), so they are orthogonal and their spectra can overlap without interference. Because each subcarrier carries a slow symbol, the channel looks flat on each subcarrier, which removes the need for a complex equalizer. It is used in Wi-Fi, LTE, 5G NR, DVB-T and WiMAX.

OFDM transmitter

bits → [Channel  ] → [Symbol  ] → [S/P] → [IFFT ]
       [coding + ]   [mapping ]           [N-pt ]
       [interleave]  [QAM/PSK ]              |
                                              v
 RF ← [Up-conv/] ← [DAC] ← [P/S] ← [Add cyclic ]
      [  PA    ]                    [ prefix   ]

1. Coding and interleaving – adds FEC and spreads burst errors.
2. Symbol mapping – groups bits into QPSK/16-QAM/64-QAM symbols X_k.
3. Serial-to-parallel (S/P) – splits the symbol stream into N parallel streams, one per subcarrier; pilots are also inserted.
4. IFFT – N-point IFFT does the multicarrier modulation in one step: x(n) = (1/N) Σ X_k e^(j2πkn/N). It turns frequency-domain symbols into a time-domain OFDM symbol.
5. Parallel-to-serial (P/S) – forms one time sequence.
6. Cyclic prefix (CP) – the last part of the symbol is copied to its front. CP length is greater than the channel delay spread, so it absorbs ISI and keeps subcarriers orthogonal.
7. DAC, up-conversion and power amplifier – produce the RF signal.

OFDM receiver

RF → [Down-conv] → [ADC] → [Remove CP] → [S/P]
                                           |
                                           v
 bits ← [Decode/  ] ← [Demap] ← [P/S] ← [Equalize] ← [FFT]
        [deinterl.]                     [1-tap  ]

1. Down-conversion and ADC – baseband samples; time and frequency synchronization are done here.
2. Remove CP – the prefix, which holds the ISI, is discarded.
3. S/P and FFT – the N-point FFT separates the subcarriers: Y_k = H_k X_k + noise.
4. One-tap equalizer – each subcarrier is divided by its channel estimate H_k (found from pilots).
5. P/S, demapping, deinterleaving and decoding – recover the original bits.

Key points

• Long symbol duration + CP gives strong resistance to multipath and ISI.
• FFT/IFFT make the system cheap to build.
• Drawbacks: high peak-to-average power ratio (PAPR) and sensitivity to frequency offset and Doppler.