| Orthogonal frequency-division multiplexing (OFDM) has been considered for various broadband, high-data-rate transmission systems. However, it is well known that these systems exhibit high peak-to-average power ratio (PAR). We introduce a novel approach to reduce the peak power using constellation shaping. We propose three methods—hyperspherical, hyperdiamond, and algebraic shaping. Hyperspherical and hyperdiamond shaping use shell mapping to efficiently encode and decode the constellation points. For algebraic shaping, we introduce a method for encoding and decoding multidimensional frequency-domain constellation points within the boundary using group generators.; For high rate systems, the hyperspherical and hyperdiamond shaping reduce the unclipped peak power by 5 to 7 dB with no loss of data rate and with a symbol error rate that is virtually identical to that of conventional systems. With a clipping rate of 10−8, they still provide up to 2.8 dB of peak-power reduction. Algebraic shaping reduces the unclipped peak power by 8 to 10 dB and about 2.9 dB at a clipping rate of 10−8 for 16-channel systems. Moreover, algebraic shaping asymptotically provides an unlimited amount of peak-power reduction as the number of channels and the constellation size increase. It also approaches the PAR characteristics of a single-carrier system (such as QAM or PAM) as the number of constellation points per channel increases. In addition, we present an O( N log2N) algorithm using a discrete Hadamard transform-based OFDM and introduce a method for incorporating arbitrary lattice codes inside the shaped boundary. |
