【Practical Exercise】Principles of OFDM and MATLAB Simulation

# 1. Basic Theory of OFDM

Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation technique that divides a wideband signal into multiple narrowband subcarriers, with each subcarrier carrying an independent data stream. The advantages of OFDM include strong resilience to frequency-selective fading, high spectral efficiency, and straightforward implementation.

An OFDM system consists of a modulator and a demodulator. The modulator maps the input data stream onto multiple subcarriers and synthesizes a wideband signal using IFFT (Inverse Fast Fourier Transform). The demodulator decomposes the wideband signal into subcarrier signals using FFT (Fast Fourier Transform) and then demodulates each subcarrier signal to restore the original data stream.

# 2. OFDM Signal Processing

### 2.1 OFDM Modulation and Demodulation

OFDM modulation and demodulation are critical processes in an OFDM system. Modulation maps digital data onto OFDM symbols, while demodulation recovers digital data from OFDM symbols.

#### 2.1.1 IFFT and FFT Operations

**Modulation:**

* Input: Digital data sequence
* Output: OFDM symbol

The modulation process uses an Inverse Fast Fourier Transform (IFFT) to convert the digital data sequence into OFDM symbols. The IFFT maps the data sequence onto a series of orthogonal subcarriers, with each subcarrier carrying a data symbol.

**Demodulation:**

* Input: OFDM symbol
* Output: Digital data sequence

The demodulation process uses a Fast Fourier Transform (FFT) to recover the digital data sequence from OFDM symbols. The FFT decomposes the OFDM symbol into its constituent subcarriers and extracts the data symbols from each subcarrier.

#### 2.1.2 Windowing and De-windowing

**Windowing:**

Prior to modulation, windowing is applied to the data sequence to reduce spectral leakage. The windowing function is a smooth function that gradually attenuates at the edges of the data sequence. This helps to suppress interference between adjacent subcarriers.

**De-windowing:**

After demodulation, de-windowing is applied to the OFDM symbols to restore the original data sequence. The de-windowing function is the same as the windowing function but applied to the end of the OFDM symbols. This helps to remove distortion introduced by windowing.

### 2.2 OFDM Channel Estimation

Channel estimation is another important process in an OFDM system. The goal of channel estimation is to determine the characteristics of the wireless channel to compensate for channel distortion.

#### 2.2.1 Pilot Sequence Design

The pilot sequence is a set of known symbols used for channel estimation. The pilot sequence is embedded within OFDM symbols and is distributed across the frequency band.

#### 2.2.2 Minimum Mean Square Error Channel Estimation

The Minimum Mean Square Error (MMSE) channel estimation is a widely used channel estimation algorithm. The MMSE algorithm uses the pilot sequence and received OFDM symbols to estimate the channel. It operates by minimizing the mean square value of channel estimation errors.

### 2.3 OFDM Equalizati