# METHODS AND SYSTEMS FOR MODULATING AND DE-MODULATING DATA

Methods and systems for modulating and demodulating data in systems is described. An Inverse Fast Fourier Transform (FFT) can be applied to complex-valued symbols that represent bit groups. The FFT can be replaced with a Fast Accurate Fourier Transform (FAFT) that can comprise variable size signal windows.

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**Description**

**CROSS-REFERENCE TO RELATED APPLICATIONS**

This application is a continuation application to U.S. application Ser. No. 16/845,613, filed Apr. 10, 2020, which claims priority to U.S. Provisional Application No. 62/831,939, filed Apr. 10, 2019, which are incorporated by reference in their entireties.

**BRIEF DESCRIPTION OF THE DRAWINGS**

**DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION**

Modern communication systems can rely on an Orthogonal Frequency Division Multiplexing (OFDM) scheme and other similar methods to encode digital data on multiple carrier frequencies. Every OFDM symbol of length T can have K sub-carriers that are 1/T apart from each other to ensure orthogonality even if the sub-carriers partially overlap. A specific sub-carrier can be associated with a complex-value number belonging to a Quadrature Amplitude Modulation (QAM) constellation that can encode groups of digital bits according to a predefined convention (frequency domain). Then, at the transmitter side, the sequence of complex values can be modulated using the Inverse FFT in order to get a signal in the time domain that can be transmitted as an electromagnetic wave. At the receiver side, the Fast Fourier Transform (FFT) can be used to recover the data in the frequency domain which can then be interpreted according to the QAM constellation to obtain the original sequence of bits.

As the transmission capacity requirements increase, the FFT size can become a problem. The higher the data rate of transmission, the larger the required FFT size can be. However, larger FFT sizes can carry proportionally less useful information due to the conventional padding with zeros. This strategy, called zero padding (ZP), may be necessary to increase the sampling rate in the time domain of the actual signal that will be transmitted by the antenna.

Although this zero padding may help with issues related to the interference (including the Inter-Symbol Interference) and signal synchronization, the cost may be a significant reduction of the ratio of useful transmitted data to less than a half. Moreover, this cost may be compounded by the higher demand of computational resources in terms of memory and processing time.

Therefore, conventional zero padding of ever larger parts of OFDM carriers can lead to a severe reduction of the proportion of useful transmitted data, which can translate into a loss of efficiency and a higher computational costs.

In order to reduce the ratio between zero padding (ZP) and the actual data that conform an OFDM symbol, a FFT variant called Fast Accurate Fourier Transform (FAFT) can be used. The Fast Accurate Fourier Transform (FAFT) is a Fast Fourier Transform (FFT) modification that can be applied in many engineering fields such as telecommunications. For example, the FAFT can be used where the digital modulation/demodulation systems are based on the orthogonal frequency division multiplexing (OFDM) method.

In contrast to the standard FFT, the FAFT can have a tunable frequency window that can reduce the need for zero padding. The FAFT can also be more versatile because it can have independent variable windows in both time and frequency. This advantage can reduce the ability to introduce zero padding with a consequent increase of efficiency for higher data transmission rates.

Conventional OFDM systems based on FFT can require ZP to increase the sampling rate in a time domain signal. In this embodiment, the data modulation on the transmitter side can be carried out by the inverse FAFT, which can be capable to reduce ZP to only a few carriers in the frequency domain while getting the same sampling rate in the time domain. As in the conventional OFDM system, the output of the inverse FAFT can be processed copying a small section of the tail of the modulated data to the beginning according to a Cyclic Prefix (CP) scheme, which can be a guard interval devised to protect the signal from Inter-Symbol Interference. As a final step in the source side, the signal can be turn into an electromagnetic wave that can be transmitted to the receptor.

On the receiver side, the CP can be removed as in the conventional OFDM system but the remaining part can be demodulated using the FAFT with the same window employed by the transmitter when applying the inverse FAFT. The demodulated data can also be absent from large ZP carriers that can otherwise be required by standard OFDM systems using the FFT. From this point, in some embodiments, the same standard methods can be employed to estimate the channel, equalize the signal, and de-map the sequence of complex numbers using the QAM constellation retrieving the original data bits.

The FAFT can be suitable for the numerical evaluation of signals where a significant fraction of the carriers is zero. So, for example, a conventional FFT applied to a 4096-QAM OFDM system can require more ZP to get a signal resolution, as compared to the FAFT method.

Moreover, some aspects of the disclosure can be used to increase the data rate transmission for low and extremely low frequency communications exploiting the higher resolution provided by FAFT, which may allow for extra-fine signal modulation. For example, the FAFT spectrum in

In addition to applications in telecommunications, FAFT can be used to perform signal analysis with higher spectral resolution. One example case is the achievement of higher precision measurements using Doppler-effect radars where the resolution of frequencies is important. The higher resolution, which can be provided by FAFT, can be directly used to detect finer displacements of frequency, thus helping enhance current Doppler radars. An example of the frequency resolution of two signals produced by FAFT is shown in

A second example application relying on the higher resolutions provided by FAFT can be the construction of digital-signal watermarking that could be used in images, video or music. This type of application can introduce finer spectral features that may be otherwise overlooked by standard FFT algorithms. As it happens with the Doppler effect, FAFT can be used to distinguish two different signals that are otherwise not differentiated by FFT.

Moreover, the FAFT can offer better resolution to improve low frequency data transmissions. The FAFT variable window size can also increase the detail at which low frequency data transmissions are modulated, allowing better data rates.

Consequently, the resolution of this plot may be significantly lower and may not be able to be improved without extensive zero padding in the original time domain signal.

**Basic OFDM Pseudo-Code**

The pseudo-code example in

## Claims

1. A method for modulating and demodulating data, comprising:

- applying an Inverse Fast Fourier Transform (FFT) to complex-valued symbols that represent bit groups;

- replacing the FFT with a Fast Accurate Fourier Transform (FAFT) that comprises variable size signal windows

**Patent History**

**Publication number**: 20220123982

**Type:**Application

**Filed**: Dec 30, 2021

**Publication Date**: Apr 21, 2022

**Applicant**: Arctan, Inc. (Arlington, VA)

**Inventors**: Renan Andres CABRERA LAFUENTE (Arlington, VA), Oscan Roberto CABRERA LAFUENTE (Arlington, VA)

**Application Number**: 17/565,892

**Classifications**

**International Classification**: H04L 27/26 (20060101);