DSP in Communications
Every Wi-Fi packet, every 5G frame — decoded by a chain of DSP algorithms running at billions of operations per second inside a chip smaller than a fingernail.
OFDM: Many Narrow Channels
Split the bandwidth into hundreds of narrow subcarriers. Each one sees a flat channel — no equalization filter needed, just one complex division.
The IDFT is the Transmitter
The time-domain OFDM symbol is literally the Inverse DFT of the frequency-domain symbol vector — computed in O(N log N) by the IFFT.
Cyclic Prefix
Copy the last L samples to the front. This converts the channel's linear convolution into circular convolution, which is diagonal in the DFT domain.
- Eliminates inter-symbol interference (ISI) from multipath
- CP length ≥ channel delay spread (typically 16–160 samples)
- Cost: wasted bandwidth — CP carries no new data
- Transforms the channel into a set of independent scalars per subcarrier
Timing & Frequency Lock
Pilot Subcarriers
- Pilots: known symbols inserted at fixed subcarrier positions
- Channel at pilot = received ÷ known → H̃[k] at pilot frequencies
- Interpolate between pilots to get Ĥ[k] for all data subcarriers
- Track channel variations over time with least-squares or Wiener filter
- Overhead trade-off: more pilots = better estimate but less data throughput
One Division per Subcarrier
ZF: divide by Ĥ[k]. Simple but amplifies noise on faded subcarriers.
MMSE: adds noise regularization — optimal when SNR is known.
FEC Decoding
OFDM Receive Chain
- ADC — digitize at Nyquist rate
- Sync — preamble correlation, CFO correction
- CP Remove — strip cyclic prefix
- FFT — recover frequency-domain subcarriers
- Channel Eq. — per-subcarrier complex division
- FEC Decode — soft LLR decoding to bits
Machine Learning Meets DSP
Neural network signal classifiers, learned filters, and where data-driven methods extend — and where they still can't replace classical DSP.