1. A signal transmitting apparatus for an orthogonal frequency division multiplexing (OFDM) system, comprising: a receiver, configured to receive and expand an orthogonal frequency-divided multiplexed signal in accordance with a dynamic range function; and a transmitter in communication with said receiver configured to compress the expanded orthogonal frequency-divided multiplexed signal and transmit the resulting compressed signal; wherein said receiver and said transmitter together comprise a compander and said dynamic range function comprises a conversion of a Rayleigh amplitude distribution, said Rayleigh amplitude distribution comprising a plurality of Rayleigh distributed signal amplitude values, to a piecewise linear distribution which optimally matches the Rayleigh amplitude distribution up to a cutoff amplitude value, and wherein said piecewise linear distribution is determined by defining and solving a constrained optimization problem using Lagrange multipliers.