Ultra high speed communications system with finite rate of innovation

Abstract

A finite rate of innovation (FRI) communications system includes a reference signal generator, an FRI modulator configured to apply an FRI kernel and encode information onto the reference signal, and a transmitter configured to transmit the encoded signal. The FRI kernel is one of a sinc function kernel or a Gaussian kernel. A receiver unit is configured to receive an encoded signal, convert the encoded signal into a digital signal, and demodulate and recover information from finite rate of innovation parameters in the digital signal.

Claims

1. A finite rate of innovation (FRI) communications system comprising: a reference signal generator; an FRI modulator configured to apply an FRI kernel and encode information onto the reference signal; and a transmitter configured to transmit the encoded signal, wherein the FRI kernel is one of a sinc function kernel or a Gaussian kernel.

2. The FRI communications system of claim 1, wherein the reference signal generator generates a radio frequency signal.

3. The FRI communications system of claim 1, wherein the reference signal generator generates an optical signal and the FRI kernel is a Gaussian kernel.

4. The FRI communications system of claim 1, further comprising: a receiver configured to receive an encoded signal; an analogue-to-digital converter configured to convert the encoded signal into a digital signal; and a demodulator configured to recover information from finite rate of innovation parameters in the digital signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a block diagram of an exemplary radio-frequency FRI communication system.

(2) FIG. 2 shows a block diagram of an exemplary optical communication system.

DETAILED DESCRIPTION

(3) FRI signals differ from conventional communications systems as they are not bandlimited. Instead they possess a quality known as innovations; it is this quality that is finite per unit time. The equation below shows an illustrative form of FRI signals

(4) $\begin{array}{cc}x\left(t\right)=\underset{n\in Z}{\overset{}{.Math.}}\underset{r=0}{\overset{R}{.Math.}}{c}_{\mathrm{nr}}\delta \left(\frac{t-t_n}{T}\right)& \left(4\right)\end{array}$

(5) Above C.sub.nr are scalar coefficients, δ(t) is the dirac delta function and t.sub.n are time instants. The degrees of freedom present in the signal are C.sub.nr and t.sub.n: i.e., this is where the information is encoded or “stored” in the signal. Note that while δ(t) is highly localized in time, it is not band limited. Define a function C.sub.x(τ.sub.a, τ.sub.b) which counts the degrees of freedom on an interval from τ.sub.a to τ.sub.b. The rate of innovation of a signal is defined as

(6) $\begin{array}{cc}\rho =\underset{\tau .fwdarw.\infty }{\lim }\frac{1}{\tau }{C}_x\left(-\frac{\tau }{2},\frac{\tau }{2}\right)& \left(5\right)\end{array}$

(7) Only p measurements per unit time are necessary to fully represent a signal with a finite rate of innovation. The implications of this statement are that relative to bandlimited signals, FRI signals contain more information per measurement. The challenge behind measuring FRI signals is that they require non-bandlimited sampling kernels; non-bandlimited sampling kernels are not practical to implement in real-world digital receivers.

(8) An exemplary embodiment realizes a real-world RF FRI communications system by modulation of the RF signal with either a sinc function kernel or a Gaussian kernel. The equations below show archetypes for the sinc kernel and the Gaussian kernel respectively.

(9) $\begin{array}{cc}\varphi \left(t\right)=\sin c\left(\frac{t}{T}\right)& \left(6\right)\\ \varphi \left(t\right)=\exp \left(\frac{-t^2}{2{\sigma }^2}\right)& \left(7\right)\end{array}$

(10) The FRI modulator realizes the sinc kernel through amplitude and phase modulation. The FRI modulator realizes the Gaussian kernel through amplitude modulation.

(11) The remainder of the RF FRI system utilizes standard RF components. Recovery of the information is performed through standard methods, for example the annihilator method or noisy spectral estimation techniques.

(12) FIG. 1 shows a block diagram of an exemplary RF FRI communications system 100. At block 102, a local oscillator generates a reference clock source. At block 104, an upconverter provides RF reference derived from the clock source. At block 106, the FRI modulator applies an FRI kernel to pulse-position modulation (PPM) and encodes information onto the RF signal. A TX aperture 110 couples transmitter 108 to channel (antenna for OTA applications) 112. A media is used as a channel 112 between TX and RX subsystems (atmosphere for OTA applications). An RX aperture 114 couples the channel 112 to the receiver (antenna for OTA applications). A bandpass filter 116 is used for bandwidth limiting and anti-aliasing. An analog-to-digital converter (ADC) 118 converts the received analog signal into a digital signal. A demodulator 120 recovers information from the digital signal.

(13) Another exemplary embodiment includes a real-world Optical RFI communications system using spatial modulation of the Optical signal by slewing the positioning optics, such as with a fast steering mirror (FSM), of the transmitter. As the gain of an optical beam is Gaussian spatially, the consequence of slewing the FSM is imposing a Gaussian kernel onto the time domain at the receiver.

(14) The remainder of the Optical RFI system may utilize standard optical components. Recovery of the information is performed through standard methods, for example the annihilator method or noisy spectral estimation techniques.

(15) FIG. 2 shows a block diagram of an Optical RFI communications system 200. At block 202, a local oscillator generates a reference clock source. At block 204, an optical source generates CW tone at optical wavelength from a clock source. An optical transmitter 206 (e.g., an Erbium-doped fiber amplifier (EDFA) may be used) amplifies the optical source 204. TX optics 208 (e.g., an FSM) steer the optical beam. The optics 208 may be actuated by actuator 209, configured to actuate the optics according to the Gaussian kernel discussed above. At block 210, TX aperture (lenses for OTA applications) couples transmitter modules to channel 212. At block 212, a media is used as a channel between TX and RX subsystems (atmosphere for OTA applications). At block 214, an RX aperture couples the channel to the receiver (lenses for OTA applications). At block 216, an optical filter is used for spectral limiting. At block 218, RX optics steers the optical beam (e.g., an FSM). At block 220, a photodiode/transimpedance amplifier (TIA) develops a digital signal from the optical signal (e.g., an avalanche photodiode (APD) and TIA). At block 222, a demodulator recovers information from the digital signal.

(16) Exemplary systems provide greater data throughput using lower bandwidth signals than existing communication systems. Exemplary systems are the first practical high-speed communications systems implementing a FRI process. Further, exemplary systems could also provide ultra-high quality time transfer between devices.

(17) Although the invention has been shown and described with respect to a certain embodiment or embodiments, it is obvious that equivalent alterations and modifications will occur to others skilled in the art upon the reading and understanding of this specification and the annexed drawings. In particular regard to the various functions performed by the above described elements (components, assemblies, devices, compositions, etc.), the terms (including a reference to a “means”) used to describe such elements are intended to correspond, unless otherwise indicated, to any element which performs the specified function of the described element (i.e., that is functionally equivalent), even though not structurally equivalent to the disclosed structure which performs the function in the herein illustrated exemplary embodiment or embodiments of the invention. In addition, while a particular feature of the invention may have been described above with respect to only one or more of several illustrated embodiments, such feature may be combined with one or more other features of the other embodiments, as may be desired and advantageous for any given or particular application.