Linearly Equalize QPSK-Modulated Signal in Simulink

Apply linear equalization using the least mean squares (LMS) algorithm to recover QPSK symbols passed through an AWGN channel.

The slex_lineq_qpsk_signal model generates an M=4 sequence using the Random Integer Generator block. The sequence is modulated with the M-PSK Modulator Baseband block, filtered with the Discrete FIR Filter block, and then impaired with the AWGN block. The Linear Equalizer block equalizes the data sequence, the data is demodulated with the M-PSK Demodulator Baseband block, and the bit error rate is computed. The signal path out of the modulator is split to a Selector block, which provides the first 1000 symbols of the modulated signal to the equalizer as an initial training sequence.

No delay is introduced between the transmitted and received signal becasue the maximum tap value is the first tap of the discrete FIR filter and the equalizer referecne tap is 1. The equalizer converges after around 1000 symbols so this value is used for the computation delay of the Error Rate Calculation block.

The computed error rate is displayed and plots show the equalized constellation, equalized tap weights, and signal error magnitude.

Computed error rate = 0.0024444