---
title: "OFDM receiver"
subject: "Wireless Communication"
chapter: 4
key: "semester_7/wireless_communication:ofdm-receiver"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/ofdm-receiver
site: BCT Engineering
---

# OFDM receiver

Wireless Communication · Chapter 4: Modulation and Demodulation in Mobile Communication

- Asked in: 2080 Chaitra, 4 marks
- Video: [OFDM Implementation Explained Visually!](https://www.youtube.com/watch?v=VwnUuBshXGw) — Wireless Explained
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/ofdm-receiver
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-4

## Question

Explain OFDM receiver in brief.

## Short answer

The OFDM receiver down-converts, samples, synchronizes, and removes the cyclic prefix, then uses an N-point FFT to separate orthogonal subcarriers. Channel estimates from pilots allow one-tap equalization per subcarrier, followed by P/S conversion, demapping, and decoding. This avoids complex time-domain equalization.

## Answer

The **OFDM receiver** reverses the steps of the transmitter. It uses an FFT to separate the orthogonal subcarriers, after which each subcarrier sees a flat channel and is equalized with one complex gain.

```text
RF->[Down-conv]->[ADC]->[Sync]->[Remove]->[S/P]
                                 [ CP   ]    |
                                             v
bits<-[Decode]<-[Demap]<-[P/S]<-[1-tap EQ]<-[FFT]
                                   ^
                            [Channel est.]
                            [from pilots ]
```
1. **Down-conversion and ADC** – RF to complex baseband samples.
2. **Synchronization** – finds the symbol start and corrects carrier frequency offset (often using the CP or preambles).
3. **Remove cyclic prefix** – discards the guard part that contains ISI from the previous symbol.
4. **S/P and N-point FFT** – converts the time samples back to subcarrier symbols: Y_k = H_k X_k + N_k.
5. **Channel estimation and equalization** – H_k is estimated from pilots and X̂_k = Y_k / H_k (zero-forcing) per subcarrier.
6. **P/S, demapping, deinterleaving and decoding** – recover the bit stream.

Because equalization is one division per subcarrier, the receiver is far simpler than a time-domain equalizer for the same multipath channel.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does the FFT in the OFDM receiver do?
   A. Adds the cyclic prefix
   B. Generates the PN code
   C. Maps bits to QAM symbols
   D. Converts the time samples back into subcarrier symbols Y_k = H_k X_k + N_k
   Answer: D. The FFT reverses the transmitter's IFFT and separates the orthogonal subcarriers, each seeing a flat channel. (Key point: FFT role)

2. Why is the cyclic prefix discarded before the FFT?
   A. It contains ISI from the previous symbol
   B. It carries the pilot data needed for the FFT
   C. It is used to amplify the signal
   D. It contains the channel gain H_k
   Answer: A. The CP is a guard part longer than the delay spread; it absorbs ISI, so removing it leaves an ISI-free symbol. (Key point: CP removal)

3. How is each subcarrier equalized in the OFDM receiver?
   A. A long time-domain FIR equalizer with many taps
   B. A one-tap zero-forcing division X_k = Y_k / H_k using H_k estimated from pilots
   C. A Viterbi equalizer across all subcarriers
   D. A RAKE receiver with M fingers
   Answer: B. Each subcarrier is flat, so a single complex division suffices, far simpler than time-domain equalization. (Key point: Equalization)

## Related in Wireless Communication

- [OFDM transmitter and receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aofdm-transmitter-receiver) — Wireless Communication, chapter 4, asked 5×
- [OFDM transmitter](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aofdm-transmitter) — Wireless Communication, chapter 4