In rectangularly-pulsed orthogonal frequency division multiplexing (OFDM) systems, constant-amplitude (CA) sequences are desirable to construct preamble/pilot waveforms to facilitate system parameter identification (SPI). Orthogonal CA sequences are generally preferred in various SPI applications like random-access channel identification. However, the number of conventional orthogonal CA sequences (e.g., Zadoff-Chu sequences) that can be adopted in cellular communication without causing sequence identification ambiguity is insufficient. Such insufficiency causes heavy performance degradation for SPI requiring a large number of identification sequences. Moreover, rectangularly-pulsed OFDM preamble/pilot waveforms carrying conventional CA sequences suffer from large power spectral sidelobes and thus exhibit low spectral compactness. This paper is thus motivated to develop several order-I CA sequence families which contain more orthogonal CA sequences while endowing the corresponding OFDM preamble/pilot waveforms with fast-decaying spectral sidelobes. Since more orthogonal sequences are provided, the developed order-I CA sequence families can enhance the performance characteristics in SPI requiring a large number of identification sequences over multipath channels exhibiting short-delay channel profiles, while composing spectrally compact OFDM preamble/pilot waveforms.