A method of modulating communications signals, such as optical fiber, wired electronic, or wireless signals in a manner that facilitates automatic correction for the signal distortion effects of echoes and frequency shifts, while still allowing high rates of data transmission. Data symbols intended for transmission are distributed into N×N matrices, and used to weigh or modulate a family of cyclically time shifted and cyclically frequency shifted waveforms. Although these waveforms may then be distorted during transmission, their basic cyclic time and frequency repeating structure facilitates use of improved receivers with deconvolution devices that can utilize the repeating patterns to correct for these distortions. The various waveforms may be sent in N time blocks at various time spacing and frequency spacing combinations in a manner that can allow interleaving of blocks from different transmitters. Applications to channel sounding/characterization, system optimization, and also radar are also discussed.