Orthogonal Frequency Division Multiplex

OFDM is a common multi-carrier modulation scheme. OFDM is most often implemented in the discrete-time domain and therefore the complexity is reduced by using the Fast Fourier Transform (FFT). The number of subcarriers is called $N_{sub}$. For a discrete signal a single OFDM symbol in the baseband is given as $$x_m = \frac{1}{\sqrt{N_{sub}}}\sum_{n=0}^{N_{sub}-1}s_{0,n}e^{j2\pi \frac{nm}{N_{sub}}} \qquad m=0,..,N_{sub}-1 \label{eq:FFT}$$ Hereby is $s_{0,n}$ a QAM symbol and m is the discrete-time index with respect to the output of FFT, thus defines the baseband bandwidth $B=1/T_m=N_{sub}/T_s$, with $t=m T_m$.$k$ is the discrete-time index at OFDM symbol level, with $t=k T_s$ and $T_s=N_{sub} T_m$. $n$ is the discrete frequency index.

The blockdiagramm of the transmission link is given as

Hereby to note is that a Rayleigh fading channel was used with 0dB gain. Therefore the channel coefficients are given as $$h_k \sim \mathcal{N}\left(0,\frac{1}{L+1}\right). \label{eq:channel_tab_eq}$$

For testing the implemented script, a given channel $$H_1(z) = 1 + z^{-1} - \frac{1}{2}z^{-2} \label{eq:givenchannel}$$ was used.