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

Channel Estimation 161Given the normalized filter bandwidths τ filter F s and f D, filter T s ′ , the sampling theoremrequires that the distance of the pilot symbols in the frequency direction isand in the time direction isN f 1τ filter F s, (4.64)1N t 2f D, filter T s′ . (4.65)An optimum sampling of the channel transfer function is given by a balanced designwhich guarantees that the channel is sampled in time and in frequency with the samesampling rate. A balanced design is defined as [36]N f τ filter F s ≈ 2N t f D, filter T ′s . (4.66)A practically proven value of the sampling rate is the selection of approximately twotimesoversampling to achieve a reasonably low complexity with respect to the filter lengthand performance. A practical hint concerning the performance of the channel estimationis to design the pilot grid such that the first and the last OFDM symbol and sub-carrierrespectively in an OFDM frame contain pilot symbols (see Figure 4-20). This avoids thechannel estimation having to perform channel prediction, which is more unreliable thaninterpolation. In the special case that the downlink can be considered as a broadcastingscenario with continuous transmission, it is possible to continuously use pilot symbols inthe time direction without requiring additional pilots at the end of an OFDM frame.4.3.4.2 OverheadBesides the mean square error of a channel estimation, a criterion for the efficiency ofa channel estimation is the overhead and the loss in SNR due to pilot symbols. Theoverhead due to pilot symbols is given by = N gridN c N s(4.67)and the SNR loss in dB is defined as( ) 1V pilot = 10 log 10 . (4.68)1 − 4.3.4.3 Signal-to-Pilot Power RatioThe pilot symbols S n ′ ,i ′ can be transmitted with higher average energy than the databearingsymbols S n,i ,n≠ n ′ ,i ≠ i ′ . Pilot symbols with increased energy are calledboosted pilot symbols [19]. The boosting of pilot symbols is specified in the DVB-T, LTE,and IEEE802.16x standards and achieves better estimates of the channel but reduces theaverage SNR of the data symbols. The choice of an appropriate boosting level for thepilot symbols is investigated in Reference [37].