Comparison of low complexity OFDM channel estimation techniques

Abstract—We address pilot-symbol aided channel esti-mation (PACE) for OFDM. To reduce the complexity ofthe optimum minimum mean squared error (MMSE) es-timator, two sub-optimum estimators are investigated. First,an estimator utilizing an FIR filter of reduced length. Thefilter coefficients are determined according to a Wiener filterwith model mismatch, i.e. the channel conditions which areassumed to compute the filter weights are chosen accordingto a typical scenario, and may be different from the actualchannel. Second, channel estimation based on the discreteFourier transform (DFT) is considered. By utilizing the fastFourier transform (FFT) algorithm, interpolation, which isan integral part of PACE, can be performed very efficiently.However, the DFT-based estimator is very sensitive to thechosen channel model. The performance significantly de-grades if the channel is non-sample spaced, i.e. the channeltap delays are not multiples of the sampling duration. I. I NTRODUCTION Multi-carrier modulation, in particular orthogonal fre-quency division multiplexing (OFDM) [1], has been suc-cessfully applied to a wide variety of digital communica-tions systems. For the transmission of large data rates itssuperior performance in transmission through dispersivechannels is a major advantage.Transmitting a radio signal over a multipath fadingchannel, the received signal will have unknown amplitudeand phase variations. In order to coherently detect thereceived signal, accurate channel estimation is essen-tial. We focus on pilot-symbol aided channel estimation(PACE), where a subset of the transmitted subcarriersis reserved for transmitting pilot symbols. In order toobtain an estimate for subcarriers which carry information,interpolation between pilot symbols is required.The optimum solution for PACE is given by the Wienerinterpolation filter (WIF). Unfortunately, an optimum WIFmay be too complex for practical implementation. Thereason is that the optimum WIF is of large dimensionand requires knowledge about the channel statistics. Com-putation of the filter coefficients “online”, i.e. duringoperation, is of significant computational complexity. Asan alternative, a WIF with reduced dimension and modelmismatch has been proposed [2]. In this case the WIFis matched to a typical worst case scenario, so the filtercoefficients can be precomputed and stored.In [3] DFT-based channel estimation in the time domainwas examined. Such a time domain estimator (TDE) canbe implemented very efficiently using the FFT. However,the performance of the TDE was shown to be verysensitive to the chosen channel model [3]. That is, whetherthe channel is sample spaced, i.e. the channel tap delaysare multiples of the sampling duration. A non-samplespaced channel, which appears to be a more realisticmodel for a wireless OFDM system, does result in anerror floor.Interpolation between pilot symbols, which is an essen-tial part of PACE, can be performed very efficiently byDFT-based interpolation [4]. While the discussion in [4]was limited to the sample spaced channel, we addressDFT-based channel estimation and interpolation for thenon-sample spaced channel.For multi-carrier systems the observed channel is typ-ically correlated in two dimensions, frequency and time.Although the discussion in this paper is limited to channelestimation in frequency direction over one OFDM symbol,such a one dimensional estimator can be extended to twodimensional channel estimation by using two cascadedone dimensional estimators [2].The remainder of this paper is structured as follows:the OFDM system and the used channel model are brieflydescribed in section II. After introducing the concept ofPACE in section III, the Wiener interpolation filter andthe DFT-based time domain estimator are derived in sec-tion IV and section V, respecively; and their performanceis compared in section VI.II. S