OFDM Channel Estimation and Equalization in MATLAB

This document explains channel estimation and equalization techniques for OFDM-based systems using MATLAB. When a transmitted packet travels through a wireless channel, it is susceptible to impairments and corruption, leading to a higher bit error rate (BER). To mitigate these effects, channel correction techniques are employed.

Typically, a preamble is added to the information packet before transmission. In the figure below, PS1 and PS2 represent two preamble symbols, while D1 to Dn are the data symbols.

Channel correction or equalization is performed in two main steps: preamble-based channel estimation and equalization, followed by pilot subcarrier-based phase rotation of the data symbols. The figure depicts four pilot carriers embedded in the data symbol D1. This arrangement is consistent across all data symbols.

Steps for Channel Estimation and Equalization

Here’s a breakdown of the channel estimation and equalization process:

STEP 1: Time Domain Channel Estimation

The received preamble samples are divided by the reference preamble symbol 1 (PS1). This provides the channel response in the time domain for preamble symbol 1.

STEP 2: Deconvolution

The entire received packet is deconvolved using the channel response obtained in STEP 1.

STEP 3: FFT and Phase Rotation Estimation

An FFT is performed on the entire packet. Then, the phase rotation is determined using the pilots embedded within data symbols D1 to Dn. The average phase rotation of all four pilots is calculated.

STEP 4: Symbol Rotation

The values of data symbol 1 are rotated using the average phase rotation calculated in STEP 3.

STEP 5: Iterative Phase Correction

Steps 3 and 4 are repeated for each data symbol (e.g., D2, D3,…Dn). The phase rotation is determined for each data symbol using its respective pilot carriers, and each symbol is derotated accordingly.

estimated_pilots=angle(received_D1_symbol_pilots([P1 P2 P3 P4])./(Reference_pilots));

%%%%%%%%%%
%%Rotating symbol accordingly
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Data_symbols_rotated = Data_symbols_after_equalization*exp(-i*mean(estimated_pilots));

This method of channel estimation is also known as the Least Squares (LS) method.