System Model

The general time- and frequency-selective wireless channel model is considered in an OFDM system. The time and frequency selectivity, characterized by the multipath delay and relative motion between transmitter and receiver, are parametrized by the decay factor $\alpha$ in exponentially decaying power delay profile (EDPDP) and the velocity $v$ respectively.

In this webdemo, the pilot symbols are inserted in the time and frequency domain of OFDM signals, spaced by $N_{T}$ and $N_{F}$ respectively, to facilitate the channel estimation.

The relation between the transmitted signal $X(n,k)$ and received signal $Y(n,k)$ at the $n$-th subcarrier and $k$-th time instant in the frequency domain is given by

$$Y(n,k) = H(n,k)\cdot X(n,k) + Z(n,k),$$ provided that the cyclic prefix is longer than the channel duration.

At the receiver, the channel at the pilot positions can be estimated by

$$\hat{H}_{p}(n,k) = \frac{Y_{p}\left(n,k\right)}{X_{p}\left(n,k\right)} = H_{p}\left(n,k\right) + \frac{Z_{p}\left(n,k\right)}{X_{p}\left(n,k\right)}$$

Then the channel at the non-pilot positions can be estimated and interpolated by different methods. Three channel estimation methods are investigated in this webdemo,

**◆ Linear interpolation**

**◆ Least-squares (LS) with Legendre polynomials and eigen-functions**

**◆ Wiener/LMMSE interpolation**

The performance of all simulated schemes is investigated with QPSK modulation and block fading approach over EDPDP channel model based on Rayleigh fading.