This invention provides a method for increasing the data rates supported by WiFi, WiMax, LTE communications using OFDM and SC-OFDM data symbol waveforms, by using quadrature layered modulation QLM which layers communications channels with a differentiating parameter for each layer that enables a demodulation algorithm to recover the data symbols in each layer, and supports higher data symbol rates then allowed by the Nyquist rate. A maximum likelihood (ML) QLM demodulation algorithm supports data rates to 4.75×57=271 Mbps compared to the current OFDM WiFi standard 57 Mbps with similar increases for WiMax, LTE. Multi-scale (MS) coding can be implemented to spread each data symbol over the OFDM band and over the 4 μs data packet to optimize BER performance. Computationally efficient signal processing for transmit and receive for OFDM and SC-OFDM are disclosed and Matlab direct error count Monte Carlo bit error rate simulations are evaluated to predict performance.