A communications device includes communication data and a training sequence corresponding to a preamble. A modulation and mapping circuit modulates the communications data and training sequence into a plurality of multiple subcarriers that are orthogonal to each other to form an OFDM communications signal having modulated subcarriers carrying the communications data forming a data payload and modulated subcarriers forming the preamble. A pseudo-random signal generator is operative with the modulation and mapping circuit and generates pseudo-random signals based on an encryption algorithm for frequency hopping each subcarrier at an OFDM symbol rate. The modulation and mapping circuit applies a quadratic modulation to the subcarriers carrying the training sequences to produce a low peak-to-average power ratio (PAPR) preamble with a PAPR value of approximately 2.6 decibels (dB).