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Pilot-aided channel estimation is essential to orthogonal frequency division multiplexing systems and standards. Under the system setup that data and pilot waveforms are processed individually for enhancing the spectral efficiency of the composite waveform, pilot patterns are designed here to jointly optimize channel estimation on quasistatic multipath channels and provide extremely high spectral compactness by suppressing spectral sidelobes. Specifically, a general constraint on pilot pattern is developed to endow the pilot waveform with very small spectral sidelobes and thus compact spectrum. Using the constraint, systematic multiple-stage design procedures are proposed to develop the desired pilot patterns achieving Cramér Rao bound for channel estimation on quasistatic multipath channels while providing fast decaying spectral sidelobes. Among the demonstrated pilot patterns achieving optimum channel estimation, the pilot waveforms using \mathcal AI - and \mathcal BI -typed pilot patterns developed from the procedures are shown to exhibit higher spectral compactness than conventional pilot waveforms. Besides, \mathcal CI -typed pilot pattern that exploits extremely high spectral compactness without resort to channel estimation optimization is also developed. By sacrificing a slight loss in channel estimation, the pilot waveforms using \mathcal CI -typed pilot pattern are shown to exhibit spectrums approaching the Nyquist spectrum. [ABSTRACT FROM PUBLISHER]