System and Channel Model

The following demonstration shows the performance of various channel equalizers.

A BPSK signal ($+1,-1$) is transmitted over a frequency-selective channel with FIR impulse response $$h_1(k)=\frac{8}{\sqrt{125}} \cdot \left[1, -\frac{3}{4}, -\frac{5}{8}\right]$$ or $$h_2(k)=\frac{4}{\sqrt{21}} \cdot \left[1, \frac{1}{2}, -\frac{1}{4}\right] \text{ ,}$$ respectively. Additionally, the receive signal is corrupted by AWGN with variance $\sigma^2$.

At the receiver side equalization is performed with either FIR, IIR or non-linear equalizers and the signal-to-interference-and-noise ratio (SINR) as well as the bit error rate (BER) is measured.

__The following equalizers are implemented: __

**IIR:** ideal (ZF-ideal)

**FIR:** truncated zero-forcing (ZF-trunc), optimum zero-forcing (ZF-trunc-opt), minimum mean squard error (MMSE) = ZF-opt + noise consideration

**Non-linear:** decision feedback (DF)

In the following demo slide, the BER and SINR are always calculated based on 10,000 BPSK symbols. Furthermore, only the real component of noise is considered in the definition of the Signal to Noise Ratio (SNR, $\frac{E_{s}}{N_0}$), i.e. $N_{0}=\sigma_{n}^{2}$, with $\sigma_{n}^{2}$ being the noise power density per real component.