--- title: "OFDM transmitter and receiver" subject: "Wireless Communication" chapter: 4 key: "semester_7/wireless_communication:ofdm-transmitter-receiver" source: https://www.bctengineer.com/q/semester_7/wireless_communication/ofdm-transmitter-receiver site: BCT Engineering --- # OFDM transmitter and receiver Wireless Communication · Chapter 4: Modulation and Demodulation in Mobile Communication - Asked in: 2082 Baisakh, 8 marks; 2080 Bhadra, 8 marks; 2078 Chaitra, 8 marks; 2074 Bhadra, 8 marks; 2071 Magh, 8 marks (asked 5 times) - 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-transmitter-receiver - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-4 ## Question With block diagrams, describe the working principle of OFDM transmitter and receiver. ## Short answer OFDM splits data into N parallel streams on orthogonal subcarriers spaced 1/Ts, using IFFT at transmitter and FFT at receiver. Cyclic prefix longer than delay spread absorbs ISI. Receiver removes CP, does FFT, one-tap equalization, demapping, decoding. ## Answer **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 ```text 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 ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Subcarrier spacing in OFDM is chosen as: A. 1/T_s so subcarriers are orthogonal B. Much larger than 1/T_s C. Equal to the symbol rate squared D. Random Answer: A. Delta f = 1/T_s makes spectra overlap without interference. (Key point: Orthogonality) 2. What does the transmitter IFFT do? A. Converts the time-domain signal to frequency B. Modulates all subcarriers at once, giving a time-domain OFDM symbol C. Adds the cyclic prefix D. Decodes bits Answer: B. The N-point IFFT turns frequency-domain symbols X_k into one time-domain OFDM symbol. (Key point: Role of IFFT) 3. Why must the cyclic prefix be longer than the channel delay spread? A. To raise power B. To absorb ISI and keep subcarriers orthogonal C. To reduce the FFT size D. To remove Doppler Answer: B. The CP holds the ISI, which is discarded at the receiver, preserving orthogonality. (Key point: Cyclic prefix) 4. After the FFT, equalization needs only: A. A long time-domain filter B. One complex division per subcarrier by H_k C. A RAKE receiver D. No channel estimate Answer: B. Y_k = H_k X_k + noise, so each subcarrier is divided by its estimate H_k found from pilots. (Key point: One-tap equalizer) ## Related in Wireless Communication - [Spread spectrum and DSSS transmitter/receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspread-spectrum-dsss-tx-rx) — Wireless Communication, chapter 4 - [OFDM transmitter](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aofdm-transmitter) — Wireless Communication, chapter 4 - [OFDM receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aofdm-receiver) — Wireless Communication, chapter 4 - [OFDM transmitter side, advantages and disadvantages](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aofdm-transmitter-advantages) — Wireless Communication, chapter 4 - [DPSK transmitter/receiver and PN sequence](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adpsk-pn-sequence) — Wireless Communication, chapter 4 - [OQPSK transmitter/receiver and π/4-QPSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aoqpsk-pi4-qpsk) — Wireless Communication, chapter 4 ## Related in other subjects - [Stereo FM transmitter and receiver; output of mono receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Astereo-fm-mono-receiver) — Communication Systems, chapter 3 - [Why DPCM over PCM; DPCM transmitter and receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adpcm-preferred-transmitter-receiver) — Communication Systems, chapter 4, asked 2× - [Working principle of analog spectrum analyzer](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aanalog-spectrum-analyzer) — Communication Systems, chapter 1 - [FDM and TDM with block diagrams](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultiplexing-fdm-tdm-block) — Telecommunications, chapter 3