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

164 Implementation IssuesTable 4-1Parameters for pilot symbol aided channel estimation in two dimensionsParameterBandwidthCarrier frequencyOFDM frame durationB = 2MHzf c = 1.8 GHzT fr = 6.6msOFDM symbols per OFDM frame N s = 24FFT size 512OFDM symbol duration T s = 256 µsCyclic prefix duration T g = 20 µsSub-carrier spacingNumber of used sub-carriers 511Pilot symbol distance in frequency directionF s = 3.9kHzN f = 6Pilot symbol distance in time direction N t = 3Delay filter bandwidth τ filter = 20 µsDoppler filter bandwidthFilter characteristicf D, filter = 333.3HzValueWiener filter with and without model mismatchIn Figure 4-24, the mean square error (MSE) versus the SNR for 2-D filtering withoutmodel mismatch with different numbers of filter taps is shown. The corresponding resultsfor 2 × 1−D filtering are presented in Figure 4-25. It can be observed in both figures thatthe mean square error decreases with increasing numbers of taps. The mean square errorpresented with 2-D filtering using 100 taps can be considered as a lower bound. In thecase of 2-D filtering, 25 taps seems to be reasonable with respect to mean square errorperformance and complexity. In the case of 2 × 1−D filtering, 2 × 5 taps is a reasonablechoice. A further increase of the number of taps only reduces the mean square errorslightly. Moreover, with 2 × 5 taps, the performance with 2 × 1−D filtering is similar tothe performance with 2-D filtering with 25 taps. Based on these results, 2 × 1−D filteringwith 2 × 5 taps is chosen for channel estimation in this section.In the following, the focus is on the degradation due to model mismatch in the filterdesign. In the first step, the mean square error of the defined channel estimation in differentCOST 207 channel models versus the SNR is shown in Figure 4-26 for 2 × 1−D filteringwith 2 × 5 taps. The velocity of the terminal station is equal to 3 km/h. As a reference,the mean square error curve without model mismatch is given. The presented channelestimation provides a better performance in channels with a large delay spread than inchannels with a low delay spread. The reason for this effect is that a channel with a delaypower density spectrum that matches more closely with that chosen for the filter designalso matches more closely to the performance without model mismatch and, thus, showsa better mean square error performance.