Devices and methods using the hermetic transform for transmitting and receiving signals using multi-channel signaling
According to an exemplary embodiment, a method of making a Hermetic transform to mitigate noise comprises: receiving over a channel signal frames comprising predetermined data and gaps comprising noise; framing the predetermined data; constructing a set of linear equations which relate a transfer function matrix of the channel to the predetermined data; determining the transfer function matrix by inverting the linear equations using a first pseudo inverse matrix; incorporating transfer function matrix into linear equations for a hermetic transform; and determining the hermetic transform using a second pseudo inverse matrix based on the predetermined data and the noise.
1. A method for spectral compacting, the method comprising:
generating a set of orthogonal basis signals;
modulating each of the basis signals with a complex modulation based on a constellation of complex symbols to produce modulated basis signals;
summing the modulated basis signals to produce a frame of signal data;
applying a matrix transformation to the frame of signal data to produce a reduced bandwidth frame of signal data comprising non-orthogonal basis signals; and
transmitting the reduced bandwidth frame of signal data.
2. An apparatus for spectral compacting, the apparatus comprising:
a processor configured to:
generate a set of orthogonal basis signals;
modulate each of the basis signals with a complex modulation based on a constellation of complex symbols to produce modulated basis signals;
sum the modulated basis signals to produce a frame of signal data; and
apply a matrix transformation to the frame of signal data to produce a reduced bandwidth frame of signal data comprising non-orthogonal basis signals; and
a transmitter configured to transmit the reduced bandwidth frame of signal data.
3. A method for spectral de-compacting, the method comprising:
receiving a reduced bandwidth frame of signal data comprising non-orthogonal basis signals modulated with a complex modulation based on a constellation of complex symbols;
applying an inverse transformation of a matrix transformation to the frame of signal data to produce a de-compacted frame of signal data comprising orthogonal basis signals modulated with the complex modulation; and
applying a transformation to the de-compacted frame of signal data to remove the complex modulation and extract the constellation of complex symbols.
4. An apparatus for spectral de-compacting, the apparatus comprising:
a receiver configured to receive a reduced bandwidth frame of signal data comprising non-orthogonal basis signals modulated with a complex modulation based on a constellation of complex symbols; and
a processor configured to:
apply an inverse transformation of a matrix transformation to the frame of signal data to produce a de-compacted frame of signal data comprising orthogonal basis signals modulated with the complex modulation; and
apply a transformation to the de-compacted frame of signal data to remove the complex modulation and extract the constellation of complex symbols.