Abstract: A method and modem for communicating serial input data over a transmission link are disclosed. Serial input data is partitioned into parallel data elements prior to rotation by an invertible linear mapping. Computationally efficient multi-rate wavelet filter banks are employed in a receiver for analyzing a received signal. Self-interference components are calculated in the receiver per sub-band and tap-weights for the filter banks are derived as a function over the range of self-interference values. A weighted sum is formed and subtracted from the delayed, received signal to eliminate the interference, and is removed from the recovered signal.

Abstract: Serial input data is partitioned into parallel data elements prior to rotation by an invertible linear mapping. The resulting frames of parallel signal elements are sequentially transmitted over the link. After receipt from the link, the signal is demodulated and assembled into frames of parallel signal elements which are de-rotated by an inverse linear mapping. The recovered parallel data elements are then re-assembled into serial output data. The linear mapping employs: 1) commuting rotation matrices for convolutionally rotating data vectors into signal vectors and vice-versa; 2) filter bank polyphase rotation matrices; or 3) computationally efficient multi-rate wavelet filter banks. Coefficients of the rotation matrix of the receiver are adaptively equalized to correct for transmission path distortion. A test signal may be inserted on the transmit side for receiver synchronization or link distortion characterization.