System and method for communicating data using efficient fast fourier transform (fft) for orthogonal frequency division multiplexing (ofdm)

A system for communicating data, comprising:

• a transmitter for transmitting a communications signal that carries communications data and comprising
• a forward error correction encoder for applying a forward error correction code to communications data as data symbols;
• a modulator for approximating the frequencies of sine/cosine basis waveforms using complex exponential functions corresponding to square type waveforms and adding and subtracting the complex exponential functions to generate an orthogonal frequency division multiplexed (OFDM) communications signal as a plurality of N data subcarriers that carry communications data and mapped as data symbols into a quadrature amplitude modulation (QAM) scheme;
• and
• a receiver for receiving the OFDM communications signal and comprising
• a demodulation circuit for demodulating the OFDM communications signal using logical shifts of multiples of +/−2p based on complex exponential functions corresponding to sine/cosine basis waveform approximations to extract amplitude and phase values from a plurality of N data subcarriers within the OFDM communications signal and demapping the signal as data symbols;
• and
• a circuit for decoding the signal and obtaining the communications data.

A method for communicating data, which comprises:

• distributing communications data over multiple subcarriers that are orthogonal to each other by approximating the frequencies of sine/cosine basis waveforms using complex exponential functions corresponding to square type waveforms and adding and subtracting the complex exponential functions to generate an orthogonal frequency division multiplexed (OFDM) communications signal as a plurality of N data subcarriers that carry communications data;
• transmitting the OFDM communications signal over a communications channel;
• receiving the OFDM communications channel within a receiver;
• and
• demodulating the OFDM communications signal by using logical shifts of multiples of +/−2P based on complex exponential functions corresponding to sine/cosine basis waveform approximations to extract amplitude and phase values from a plurality of N data subcarriers.