Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

Channel Estimation 163and f D, filter = 333.3 Hz, where f D, filter corresponds to a velocity of v = 200 km/h. Abalanced design with approximately two-times oversampling is given with a pilot symbolspacing of N f = 6 in the frequency direction and of N t = 3 in the time direction.The resulting system parameters are summarized in Table 4-1. The chosen OFDM framestructure for pilot symbol aided channel estimation in two dimensions is illustrated inFigure 4-23.In the time direction, the last OFDM symbol with pilot symbols of the previous OFDMframe can be used for filtering. With a pilot spacing of 6 in the frequency direction,while starting and ending with a sub-carrier containing pilot symbols, a number of 511used sub-carriers per OFDM symbol is obtained and is considered in the following. Theresulting overhead due to pilot symbols is 5.6 %. With pilot symbols and data symbolshaving the same average energy, the loss in SNR V pilot due to pilot symbols is only0.3 dB for the defined multi-carrier scenario.The performance criterion for the evaluation of the channel estimation is the meansquare error, which is averaged over an OFDM frame. Thus, edge effects are also takeninto account. The information about the variance σ 2 required for the calculation of theautocorrelation matrix is assumed to be known perfectly at the receiver unless otherwisestated. In practice, the variance σ 2 can be estimated by transmitting a null symbol withoutsignal energy at the beginning of each OFDM frame (see Section 4.2.1). Alternatively,the auto-correlation function can be optimized for the highest σ 2 at which successful datatransmission should be possible.The mean square error of two-dimensional (2-D) filtering without model mismatchand two cascaded one-dimensional (2 × 1-D) filtering applied in a multi-carrier system ispresented and compared in the following. The mobile radio channel used has a uniformdelay power spectrum with τ max = 20 µs and a uniform Doppler power density spectrumwith f D,max = 333.3Hz.timefreq. 00 23data symbolpilot symboldata symbol of previous OFDMframe510pilot symbol of previous OFDMframe; used for channel estimationof actual OFDM frameT fr = 6.6 msFigure 4-23OFDM frame with pilot grid for channel estimation in two dimensions