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

Channel Estimation 169in order to reduce the noise. Without filtering in either the frequency or time domain, theBER performance of differential modulation is obtained. Based on the obtained channelestimate Hˆn,i−1 , the received symbols R n,i are equalized according toU n,i = G n,i R n,i , (4.70)whereG n,i = f( ˆ H n,i−1 ) (4.71)is an equalization coefficient depending on the previous channel estimate Hˆn,i−1 .Inorderto achieve a reliable estimation of the transmitted sequence, the error correction capabilityof the channel coding is used. The bit sequence at the output of the channel decoder is reencodedand re-modulated to obtain reliable estimates Ŝ n,i−1 of the transmitted sequenceS n,i−1 . These estimates are fed back to obtain a channel estimate Hˆn,i−1 , which is usedfor the detection of the following symbol S n,i . With decision directed channel estimationthe channel estimates are updated symbol-by-symbol.Decision directed channel estimation can reduce the amount of reference data requiredto only an initial OFDM reference symbol. This can significantly reduce the overheaddue to pilot symbols at the expense of additional complexity [28]. The achievable estimationaccuracy with decision directed channel estimation including FEC decoding iscomparable to pilot symbol aided channel estimation and with respect to BER outperformsclassical differential demodulation schemes [56]. Classical differential modulationschemes can also benefit from decision directed channel estimation where the correlationsin time and frequency of previously received symbols are filtered and used for estimationof the actual ˆ H n,i .4.3.8 Blind and Semi-Blind Channel EstimationThe cyclic extension of an OFDM symbol can be used as an inherent reference signalwithin the data, enabling channel estimation based on the cyclic extension [34, 64, 88].Since no additional pilot symbols are required with this method in OFDM schemes, thiscan be considered as blind channel estimation. The advantage of blind channel estimationbased on the cyclic prefix is that this channel estimation concept is standard-compliantand can be applied to all commonly used OFDM systems that use a cyclic prefix.A further approach of blind detection without the necessity of pilot symbols for coherentdetection is possible when joint equalization and detection is applied. This is possible bytrellis decoding of differentially encoded PSK signals [52] where the trellis decoding canefficiently be achieved by applying the Viterbi algorithm. The differential encoding canbe performed in the frequency or time direction, while the detector exploits correlationsbetween adjacent sub-carriers and/or OFDM symbols. These blind detection schemesrequire a low number of pilot symbols and outperform classical differential detectionschemes. The complexity of a blind scheme with joint equalization and detection is higherthan that of differential or coherent receivers due to the additional implementation of theViterbi algorithm.Statistical methods for blind channel estimations have also been proposed [34] which,however, require several OFDM symbols to be able to estimate the channel and might fail