# US 10,771,304 B2 · Devices and methods using the hermetic transform for transmitting and receiving signals using multi-channel signaling

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- Number: US 10,771,304 B2
- Document ID: US10771304B2
- Status: Granted
- Kind: B2
- Application number: 16/256,624
- Filed: 2019-01-24
- Published: 2019-06-06
- Granted: 2020-09-08
- Earliest claimed: 2016-02-26
- Assignees: VertoCOMM, Inc.
- Applicants: VertoCOMM, Inc.
- Inventors: Harvey C. Woodsum
- Web page: https://patentgrep.com/patent/US10771304B2

## CPC

- H04L 27/2663: {Coarse synchronisation, e.g. by correlation}
- H04L 25/03012: {operating in the time domain (H04L25/03165, H04L25/03178 take precedence)}
- H04L 27/2639: {Modulators using other transforms, e.g. discrete cosine transforms, Orthogonal Time Frequency and Space [OTFS] or hermetic transforms}
- H04L 27/26532: {Demodulators using other transforms, e.g. discrete cosine transforms, Orthogonal Time Frequency and Space [OTFS] or hermetic transforms}
- H04L 27/2656: {Frame synchronisation, e.g. packet synchronisation, time division duplex [TDD] switching point detection or subframe synchronisation}
- H04L 27/367: {using predistortion}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

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.

## Claims

### Claim 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.

### Claim 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.

### Claim 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.

### Claim 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.