Modulation and equalization in an orthonormal time-frequency shifting communications system

A method of receiving data, comprising:

• receiving, on one or more carrier waveforms, signals representing a plurality of data elements of an original data frame wherein each of the data elements are represented by cyclically time shifted and cyclically frequency shifted versions of a known set of waveforms;
• generating, based upon the signals, a received data frame having a first dimension of at least N elements and a second dimension of at least N elements, where N is greater than one and where each element of the received data frame includes a contribution from each of a plurality of elements of the original data frame;
• wherein the first dimension corresponds to a frequency shift axis and the second dimension corresponds to a time shift axis;
• performing, using a decoding matrix, an inverse transformation operation with respect to elements of the received data frame so as to yield a non-transformed matrix;
• and
• generating, based upon the non-transformed matrix, a recovered data frame comprising an estimate of the original data frame.

A data transmitter, comprising:

• an input port;
• an output port;
• a processor;
• a memory including program code executable by the processor, the program code including:
• code for receiving, at the input port, a set of data elements;
• code for arranging the set of data elements into an original data frame having a first dimension of N elements and a second dimension of N elements, where N is greater than one;
• code for transforming the original data frame in accordance with a transformation matrix to form a first transformed data matrix having at least N2 transformed data elements wherein each of the transformed data elements is based upon a plurality of the data elements of the original data frame and wherein a first dimension of the first transformed data matrix corresponds to a frequency shift axis and a second dimension corresponds to a time shift axis;
• code for forming a permuted data matrix by permuting at least a portion of the elements of the first transformed data matrix so as to shift the at least a portion of the elements with respect to the time shift axis;
• code for transforming the permuted data matrix using a frequency-shift encoding matrix to form a transmit frame;
• and
• code generating a modulated signal in accordance with elements of the transmit frame.

A data receiver, comprising:

• a processor;
• a memory including program code executable by the processor, the program code including:
• code for facilitating receiving, on one or more carrier waveforms, signals representing a plurality of data elements of an original data frame wherein each of the data elements are represented by cyclically time shifted and cyclically frequency shifted versions of a known set of waveforms;
• code for generating, based upon the signals, a received data frame having a first dimension of at least N elements and a second dimension of at least N elements, where N is greater than one and where each element of the received data frame includes a contribution from each of a plurality of elements of the original data frame;
• wherein the first dimension corresponds to a frequency shift axis and the second dimension corresponds to a time shift axis;
• code for performing, using a decoding matrix, an inverse transformation operation with respect to elements of the received data frame so as to yield a non-transformed matrix;
• and
• code for generating, based upon the non-transformed matrix, a recovered data frame comprising an estimate of the original data frame.

A non-transitory computer readable medium including program instructions for execution by a processor in a data transmitter, the program instructions comprising instructions for causing the processor to:

• receive, at an input port of the data transmitter, a set of data elements;
• arrange the set of data elements into an original data frame having a first dimension of N elements and a second dimension of N elements, where N is greater than one;
• transform the original data frame in accordance with a transformation matrix to form a first transformed data matrix having at least N2 transformed data elements wherein each of the transformed data elements is based upon a plurality of the data elements of the original data frame and wherein a first dimension of the first transformed data matrix corresponds to a frequency shift axis and a second dimension corresponds to a time shift axis;
• form a permuted data matrix by permuting at least a portion of the elements of the first transformed data matrix so as to shift the at least a portion of the elements with respect to the time shift axis;
• transform the permuted data matrix using a frequency-shift encoding matrix to form a transmit frame;
• and
• generate a modulated signal in accordance with elements of the transmit frame.

A non-transitory computer readable medium including program instructions for execution by a processor in a data receiver, the program instructions comprising instructions for causing the processor to:

• facilitate receiving, on one or more carrier waveforms, signals representing a plurality of data elements of an original data frame wherein each of the data elements are represented by cyclically time shifted and cyclically frequency shifted versions of a known set of waveforms;
• generate, based upon the signals, a received data frame having a first dimension of at least N elements and a second dimension of at least N elements, where N is greater than one and where each element of the received data frame includes a contribution from each of a plurality of elements of the original data frame;
• wherein the first dimension corresponds to a frequency shift axis and the second dimension corresponds to a time shift axis;
• perform, using a decoding matrix, an inverse transformation operation with respect to elements of the received data frame so as to yield a non-transformed matrix;
• and
• generate, based upon the non-transformed matrix, a recovered data frame comprising an estimate of the original data frame.