FIELD

The present disclosure relates to systems and methods for use in wireless optical communications for use through high loss or noisy environments, for use over long ranges and/or for low power consumption. Such systems and methods may be of use for wireless optical communications generally and/or for navigation and/or positioning. BACKGROUND

Methods of wireless optical communication utilising parametric downconversion to simultaneously generate two photons are also known. However, such methods may rely on relatively complex transmitter and receiver arrangements. SUMMARY

It should be understood that any one or more of the features of any of the following aspects or embodiments may be combined with any one or more of the features of any of the other aspects or embodiments.

According to at least one aspect or to at least one embodiment there is provided a method for use in wireless optical communications comprising:

representing a value of a symbol of a digital signal as a corresponding characteristic series of optical pulses; and

wirelessly transmitting the series of optical pulses along an optical path.

Such a method may be suitable for use in wireless optical communications when a low signal to noise ratio (SNR) is present at an optical receiver. Such a method may be of use for wireless optical communications through a diffusing, highly absorbing, and/or scattering medium along which the optical path extends. The medium may, for example, comprise animal or human tissue. The tissue may be living or dead. Such a method may be of use for wireless optical communications through an environment such as a turbulent environment and/or a diffuse environment. Such a method may be of use for wireless optical communications in an underwater environment. Such a method may be of use for wireless optical communications communication through a vacuum or in space. Such a method may be of use for wireless optical communications through a noisy environment i.e. in the presence of a constant or varying background light level. Such a method may be of use for wireless optical communications over long distances. Such a method may be of use for wireless optical communications using low levels of optical power. Such a method may be of use for covert wireless optical communications.

The value of the symbol may be selected from a finite set of discrete values. The value of the symbol may be selected from a set of two discrete values, for example Ό' and .

Representing the value of the symbol of the digital signal as a corresponding characteristic series of optical pulses may comprise encoding the value of the symbol of the digital signal as the corresponding characteristic series of optical pulses.

The method may comprise:

representing a value of a further symbol as a corresponding further characteristic series of optical pulses; and

wirelessly transmitting the further series of optical pulses along an optical path.

The method may comprise representing a value of a further symbol as an absence of optical pulses, as an absent series of optical pulses, or as a zero amplitude series of optical pulses.

The method may comprise transmitting each optical pulse of the series of optical pulses with the same amplitude, power, duration, wavelength, intensity and/or polarisation.

The series of optical pulses may comprise one or more sets of optical pulses, and each optical pulse in each set of optical pulses is of the same power, duration, wavelength, intensity and/or amplitude.

The characteristic series of optical pulses corresponding to the value of the symbol may be periodic. The method may comprise representing the value of the symbol by a repetition period of the series of optical pulses.

The method may comprise representing the value of the symbol of the digital signal using pulse position modulation (PPM) of the optical pulses in the series of optical pulses.

The method may comprise representing the value of the symbol by the amplitude, intensity, power, duration, wavelength, and/or polarisation of the optical pulses.

The method may comprise representing the value of the symbol of the digital signal using pulse amplitude modulation (PAM) of the optical pulses in the series of optical pulses. The method may comprise representing the value of the symbol of the digital signal using on-off-keying (OOK) of the series of optical pulses.

The series of optical pulses may comprise 5, 100, 1000, 10,000 or more optical pulses.

Where the series of optical pulses comprises a plurality of sets of optical pulses, the method may comprise transmitting 5, 100, 1000, 10,000 or more optical pulses in each set of optical pulses.

The method may comprise detecting the series of optical pulses after wireless transmission of the series of optical pulses along the optical path to thereby generate a received signal.

The method may comprise determining the value of the symbol of the digital signal from the received signal.

The method may comprise comprising using single photon detection to detect the series of optical pulses and thereby generate the received signal.

The digital signal may comprise a plurality of symbols. The plurality of symbols may constitute a code. Each symbol of the digital signal may have the same duration.

The method may comprise wirelessly transmitting each optical pulse in the series of optical pulses along the same optical path.

The digital signal may comprise a plurality of symbols. The method may comprise:

representing, for each symbol of the digital signal, a value of each symbol as a corresponding characteristic series of optical pulses; and

wirelessly transmitting each series of optical pulses along the optical path.

Each series of optical pulses may have the same duration.

The method may comprise representing a value of at least one of the symbols of the digital signal as a series of zero amplitude optical pulses.

The method may comprise encoding information in the digital signal. The method may comprise encoding a clock in the digital signal. The method may comprise encoding information and a clock in the digital signal.

The method may comprise encoding a clock word in the digital signal. The clock word comprises a sequence of symbols which is repeated in the digital signal. The clock word, w _clk , may be defined by:

wclk = ^β _η ω ^β η ⁽² ' -" ^S _n ^(m

n n

B _n = ooTo ΐ ϊ The clock word, w _clk , may have a length of 2∑™ ₁ ^w bits.

The clock word may be defined as an inverse of the clock word, w _clk , defined above.

The clock word may comprise six bits. The clock word may comprise any one of the binary sequences 001101 110010, 010011 and 101100.

The method may comprise encoding an embedded clock, such as an anisochronous embedded clock, in the digital signal.

The method may comprise transmitting information. The method may comprise transmitting a clock. The method may comprise transmitting information and a clock. The method may comprise repeatedly transmitting a clock word. The method may comprise transmitting an embedded clock, such as an anisochronous embedded clock.

The use of a clock such as a clock word may advantageously be used to synchronise a received signal to the transmitted signal. The use of a clock such as a clock word may advantageously be used to identify which series of detected optical pulses relate to which symbol of the digital signal.

The method may comprise transmitting the digital signal as a bitstream, wherein each symbol in the bit stream is a bit, and each bit is transmitted with a series of optical pulses. The method may comprise transmitting the bitstream in frames. Each frame may comprise N _frame symbols. Each frame may comprise a clock word and a data word. The method may comprise transmitting each frame with the same clock word. The method may comprise transmitting a clock word at the beginning of each frame. Each clock word may comprise n _clk symbols. Each data word may comprise n _dat symbols.

The method may comprise collimating and/or focusing the series of optical pulses. This may advantageously increase the intensity of the transmitted optical pulses, which may advantageously increase the detectability of the series of optical pulses.

The method may comprise transmitting the series of optical pulses along a single optical path. The method may comprise transmitting different symbols of the digital signal along a single optical path. The method may comprise transmitting different symbols of the digital signal along different optical paths. For example, the series of optical pulses representative of the symbol of the digital signal may be transmitted along one optical path, and the further series of optical pulses representative of the further symbol of the digital signal may be transmitted along a further optical path. The optical path may extend through at least one of a solid, a liquid and a gas. The optical path may extend through a vacuum. The optical path may extend through space. The optical path may extend through air.

The optical path may extend through a scattering medium, such as a highly scattering medium. The optical path may extend through an organism such as a human or an animal. The optical path may extend through a living organism or a dead organism.

One skilled in the art will understand that the most appropriate method for representing the symbol of the digital signal in the series of optical pulses will depend on the particular method of optical communication, for example it will depend on the conditions set by the transmitter and receiver, and on the ambient conditions in which the method of communication is being carried out.

The method may comprise transmitting the series of optical pulses with low power. The method may comprise transmitting the series of optical pulses with a power of the order of W, mW or μ\Λ/. One skilled in the art will understand that the required power of the optical pulses will depend on the sensitivity of the receiver used to detect the optical pulses, on the medium through which the optical pulses are transmitted and/or on the presence of any background noise.

The method may comprise transmitting the series of optical pulses, wherein each of the optical pulses has an intensity below the ambient background light level. The method may comprise transmitting the series of optical pulses, wherein each optical pulse has an intensity of less than 10%, less than 50%, less than 100%, and/or less than 200% the intensity of the background light.

The method may comprise transmitting the digital signal at a symbol rate of 10kb/s, 100 kb/s, 1 Mb/s, or more. The method may comprise transmitting 10,000, 100,000, 1 ,000,000, or more series of optical pulses per second, where each series of optical pulses is representative of a different symbol of the digital signal. The method may comprise transmitting optical pulses at a rate of 1 MHz, 25 MHz or more.

The method may comprise using an optical transmitter to transmit the series of optical pulses. The optical transmitter may comprise an optical source. The optical transmitter may comprise a laser, such as a pulsed laser. The optical transmitter may comprise a non-coherent optical source. The optical transmitter may comprise an LED. The optical transmitter may comprise a gallium nitride (GaN) LED, an indium phosphide (InP) LED, a gallium arsenide (GaAs) LED, or an LED of a ternary or quaternary alloy of any of GaN, InP or GaAs. The optical transmitter may comprise a micro-LED. The optical transmitter may comprise an LED pixel of a micro-LED array.

The optical transmitter may comprise an electronic interface such as a CMOS control board to drive the optical source.

The method may comprise transmitting the series of optical pulses, wherein the optical pulses have a wavelength which correspond to low background levels. For example, the optical pulses may have a wavelength which at least partially overlaps with at least one of the Fraunhofer absorption lines in the solar spectrum.

The method may comprise generating an electrical data signal which is representative of the digital signal. The method may comprise using the electrical data signal to generate the series of optical pulses. The method may comprise using a transmitter field programmable gate array (FPGA) to generate the electrical data signal.

The method may comprise using an oscillator to generate an electrical waveform such as an electrical square wave or a stream of electrical pulses. The method may comprise using one or more logic circuits or logic gates to combine or modulate the electrical waveform using the electrical data signal to provide an electrical driving signal. The method may comprise applying the electrical driving signal to the electronic interface.

The method may comprise using a transmitter controller to control the transmission of the series of optical pulses, for example to control the optical transmitter. The transmitter controller may comprise a computer, such as a PC.

The method may comprise:

representing a value of a symbol of each digital signal of a plurality of digital signals as a corresponding characteristic series of optical pulses; and

wirelessly transmitting each series of optical pulses along a different optical path.

The method may comprise representing a value of at least one of the symbols of each digital signal by a series of zero amplitude optical pulses.

According to at least one aspect or to at least one embodiment there is provided a method for use in wireless optical communications comprising:

detecting a series of optical pulses after wireless transmission of the series of optical pulses along an optical path to thereby generate a received signal, wherein the series of optical pulses is representative of a value of a symbol of a digital signal; and determining the value of the symbol of the digital signal from the received signal. Such a method may be suitable for use in wireless optical communications when a low signal to noise ratio (SNR) is present at an optical receiver. Such a method may be of use for wireless optical communications through a diffusing, highly absorbing, and/or scattering medium along which the optical path extends. The medium may, for example, comprise animal or human tissue. The tissue may be living or dead. Such a method may be of use for wireless optical communications through an environment such as a turbulent environment and/or a diffuse environment. Such a method may be of use for wireless optical communications in an underwater environment. Such a method may be of use for wireless optical communications communication through a vacuum or in space. Such a method may be of use for wireless optical communications through a noisy environment i.e. in the presence of a constant or varying background light level. Such a method may be of use for wireless optical communications over long distances. Such a method may be of use for wireless optical communications using low levels of optical power. Such a method may be of use for covert wireless optical communications.

The method may comprise using single photon detection to detect the series of optical pulses and thereby generate the received signal.

Determining the value of the symbol of the digital signal from the received signal may comprise decoding the value of the symbol of the digital signal from the received signal.

The value of the symbol may be selected from a finite set of discrete values.

The value of the symbol may be selected from a set of two discrete values.

Each optical pulse of the series of optical pulses may be transmitted with the same amplitude, power, duration, wavelength, intensity and/or polarisation.

The series of optical pulses may be periodic. The value of the symbol may be represented by a repetition period of the series of optical pulses.

The method may comprise determining the repetition period of the detected series of optical pulses from the received signal and determining the value of the symbol of the digital signal from the determined pulse repetition period.

Detecting the optical pulses may comprise detecting the optical pulses using a single photon detector. The single photon detector may comprise or be a photomultiplier tube, a superconducting nanowire, and/or an image intensifier (micro- channel plates). The single photon detector may comprise or be a single-photon avalanche diode (SPAD). Detecting the optical pulses may comprise detecting fewer of the optical pulses in the series of optical pulses than are transmitted along the optical path.

The method may comprise correlating or autocorrelating the received signal. The method may comprise determining the value of the symbol of the digital signal from the correlation or autocorrelation of the received signal. The method may comprise determining the value of the symbol of the digital signal according to an amplitude of a peak in the correlation or autocorrelation of the received signal such as a peak in the correlation or autocorrelation of the received signal corresponding to the repetition period of the series of optical pulses.

The method may comprise determining the value of the symbol of the digital signal by comparing the amplitude of the peak in the correlation or autocorrelation of the received signal with a threshold amplitude.

The method may comprise selecting the threshold amplitude according to the environment through which the optical path extends. The method may comprise selecting the threshold amplitude according to the amount of background light or noise received. The method may comprise selecting the threshold amplitude according to the optical power with which the series of optical pulses are transmitted along the optical path.

The method may comprise determining the value of the symbol of the digital signal according to the presence or absence of a peak in the correlation or autocorrelation of the received signal. For example, the method may comprise determining the value of the symbol of the digital signal according to the presence or absence of a peak in the correlation or autocorrelation of the received signal such as a peak in the correlation or autocorrelation of the received signal corresponding to the pulse repetition rate of the series of optical pulses.

Such a method may advantageously allow the series of optical pulses to be distinguishable from background light and/or noise. The series of optical pulses may be distinguishable from constant and/or varying background light. Such a method may advantageously allow wireless optical communications through high loss environments, over long ranges and/or using low power consumption systems.

The method may comprise determining the value of the symbol of the digital signal from the received signal, wherein the value of the symbol of the digital signal is encoded on the series of optical pulses using pulse position modulation (PPM). The method may comprise determining the value of the symbol of the digital signal from the received signal, wherein the value of the symbol of the digital signal is encoded on the series of optical pulses using pulse amplitude modulation (PAM).

The method may comprise determining the value of the symbol of the digital signal from the received signal, wherein the value of the symbol of the digital signal is encoded on the series of optical pulses using on-off-keying (OOK).

The method may comprise receiving 5, 100, 1000, or more optical pulses in each series of optical pulses.

The method may comprise receiving the series of optical pulses after wireless transmission of each optical pulse along the same optical path.

The method may comprise receiving different spatial portions of the series of optical pulses on different optical detectors.

The method may comprise detecting a spatial portion of a first optical pulse of the series of optical pulses using a first optical detector and detecting a spatial portion of a second optical pulse of the series of optical pulses using a second optical detector.

The first and second optical pulses may be consecutive pulses of the series of optical pulses.

The method may comprise using an OR tree or an XOR tree to generate the received signal from the detected spatial portion of the first optical pulse and the detected spatial portion of the second optical pulse.

The method may comprise representing the value of the symbol of the digital signal as the corresponding characteristic series of optical pulses.

The method may comprise wirelessly transmitting the series of optical pulses along the optical path. The digital signal may comprise a plurality of symbols. The plurality of symbols may constitute a code. Each symbol of the digital signal may have the same duration.

The method may comprise:

detecting a further series of optical pulses after wireless transmission of the further series of optical pulses along the optical path to thereby generate a further received signal, wherein the further series of optical pulses is representative of a value of a further symbol of the digital signal; and

determining the value of the further symbol of the digital signal from the further received signal.

Each optical pulse of the further series of optical pulses may have a zero amplitude. The method may comprise:

detecting, for each symbol, a corresponding characteristic series of optical pulses representative of a value of each symbol of the digital signal after wireless transmission of each corresponding series of optical pulses along the optical path to thereby generate a received signal; and

determining the value of each symbol of the digital signal from the received signal.

Each series of optical pulses may have the same duration.

A value of at least one of the symbols of the digital signal may be represented by a series of zero amplitude optical pulses.

The method may comprise decoding information from the digital signal. The method may comprise decoding a clock from the digital signal. The method may comprise decoding information and a clock from the digital signal. The method may comprise decoding an embedded clock, such as an anisochronous embedded clock, from the digital signal.

The method may comprise decoding a clock word from the digital signal, wherein the clock word may be a sequence of symbols which is repeated in the digital signal.

The clock word, w _clk , may be defined by:

wclk = ^β _η ω ^β η ⁽² ' -" ^S _n ^(m

n n

B _n = ooTo ΐ ϊ The clock word, w _clk , may have a length of 2∑™ ₁ ^w bits.

The clock word may be defined as an inverse of the clock word, w _clk , defined above.

The clock word may comprise six bits. The clock word may comprise any one of the binary sequences 001101 1 10010, 010011 and 101100.

The use of a clock word may advantageously be used to synchronise the received signal to the transmitted digital signal. The use of a clock word may advantageously be used to determine which series of received optical pulses relate to which symbol of the digital signal.

The method may comprise locating each instance of the clock word in the determined values of the symbols of the digital signal. The method may comprise determining which series of optical pulses relate to the same symbol of the digital signal by relating determined values of the symbols of the digital signal to the location of the clock word. The method may comprise using the clock word to synchronise the receiver clock with the transmitter clock. This may advantageously allow the receiver to be synchronised with the received signal without communicating with the transmitter.

The method may comprise receiving the digital signal as a bitstream, wherein each symbol in the bitstream is a bit, and each bit corresponds to a series of optical pulses. The method may comprise receiving the bitstream in frames. Each frame may comprise Nframe symbols. Each frame may comprise a clock word and a data word. The method may comprise receiving each frame with the same clock word. The method may comprise receiving a clock word at the beginning of each frame. The method may comprise receiving a clock word comprising n _clk symbols. The method may comprise receiving a data word comprising n _dat symbols.

The method may comprise receiving different symbols of the digital signal in different frames.

The method may comprise determining which series of optical pulses relates to each symbol in the digital signal from the received series of optical pulses by knowing at least one of: the number of symbols N _frame in each frame; the number of symbols n _clk in the clock word; the number of symbols n _dat in the data word; and/or the duration of each symbol.

One skilled in the art will understand that the method for determining the value of the symbol of the digital signal from the series of optical pulses will depend on the particular method of optical communication, for example it will depend on the conditions set by the transmitter and receiver, and on the ambient conditions in which the method of communication is being carried out.

The series of optical pulses may have low power and/or intensity. The power of the optical pulses may be of the order of pW or nW. The method may comprise detecting the series of optical pulses, wherein the series of optical pulses have an intensity below the ambient background light level. The method may comprise detecting the series of optical pulses, wherein the series of optical pulses have an intensity of less than 10%, less than 50%, less than 100%, and/or less than 200% the intensity of the background light.

The method may comprise receiving the digital signal at a symbol rate of 10kb/s, 100 kb/s, 1 Mb/s, or more. The method may comprise detecting 10,000, 100,000, 1 ,000,000, or more series of optical pulses per second, where each series of optical pulses is representative of a different symbol in the digital signal. The method may comprise detecting optical pulses at a rate of 1 MHz, 25 MHz or more. The method may comprise:

detecting a plurality of series of optical pulses after wireless transmission of each series of optical pulses along a different optical path to thereby generate a corresponding plurality of received signals, wherein each series of optical pulses is representative of a value of a symbol of a corresponding digital signal; and

determining the value of the symbol of each digital signal from the corresponding received signal.

Such a method may allow the wireless transmission of different symbols along different optical paths i.e. multi-path propagation or spatial multiplexing.

The method may comprise representing a value of at least one of the symbols of each digital signal by a series of zero amplitude optical pulses.

According to at least one aspect or to at least one embodiment there is provided a method for use in wireless optical communications comprising:

representing a value of a symbol of a digital signal as a corresponding characteristic series of optical pulses;

wirelessly transmitting the series of optical pulses along an optical path, detecting the series of optical pulses after wireless transmission of the series of optical pulses along the optical path to thereby generate a received signal; and

determining the value of the symbol of the digital signal from the received signal.

Such a method may be suitable for use in wireless optical communications when a low signal to noise ratio (SNR) is present at an optical receiver. Such a method may be of use for wireless optical communications through a diffusing, highly absorbing, and/or scattering medium along which the optical path extends. The medium may, for example, comprise animal or human tissue. The tissue may be living or dead. Such a method may be of use for wireless optical communications through an environment such as a turbulent environment and/or a diffuse environment. Such a method may be of use for wireless optical communications in an underwater environment. Such a method may be of use for wireless optical communications communication through a vacuum or in space. Such a method may be of use for wireless optical communications through a noisy environment i.e. in the presence of a constant or varying background light level. Such a method may be of use for wireless optical communications over long distances. Such a method may be of use for wireless optical communications using low levels of optical power. Such a method may be of use for covert wireless optical communications.

The method may comprise transmitting the series of optical pulses with an optical transmitter. The method may comprise detecting the series of optical pulses with an optical receiver. The method may comprise transmitting optical pulses with a duration shorter than the dead time of the optical receiver. This may help to ensure that the optical receiver detects each received optical pulse at most once.

The optical transmitter may comprise an LED or a laser.

The optical receiver may comprise a single photon detector. The single photon detector may comprise or be a photomultiplier tube, a superconducting nanowire, and/or an image intensifier (micro-channel plates). The single photon detector may comprise or be a single-photon avalanche diode (SPAD). The optical receiver may comprise a single pixel of a SPAD array.

The SPAD may comprise silicon CMOS. The optical receiver may comprise embedded electronics, such as a transmitter field programmable gate array (FPGA). The embedded electronics may be configured to autocorrelate and/or demodulate the digital signal from the detected optical pulses.

The optical transmitter may comprise a plurality of optical sources or emitting pixels. The optical transmitter may comprise a micro-LED array.

The optical receiver may comprise a plurality of optical detectors or detecting pixels. The optical receiver may comprise an image sensor. The optical receiver may comprise a single photon detector array such as a SPAD array. The SPAD array may comprise silicon CMOS. The optical receiver may comprise embedded electronics, such as a transmitter field programmable gate array (FPGA). The embedded electronics may be configured to autocorrelate and/or demodulate the digital signal from the detected optical pulses.

The optical receiver may comprise a plurality of optical detectors, such as a plurality of SPADs. The plurality of SPADs may be connected to each other by an OR or XOR tree. The plurality of SPADs may be connected to the embedded electronics by an OR or XOR tree.

The embedded electronics may comprise multiple channels. Different channels of the embedded electronics may be connected or coupled to different optical detectors, such as different SPADs. This may provide multiple parallel outputs.

The method may comprise using multiple parallel outputs to determine the value of the symbol of the digital signal from the received signal. The method may comprise detecting a spatial portion of a first optical pulse using a first optical detector, and subsequently detecting a spatial portion of a second optical pulse using a second optical detector. The spatial portion of the second optical pulse may be detected by the second optical detector during the dead time of the first optical detector following detection of the spatial portion of the first optical pulse by the first optical detector. The use of multiple parallel outputs in this manner may allow optical pulses to be detected during the dead time of at least some of the optical detectors. This may increase the rate at which optical pulses can be detected, and therefore increase the rate at which data can be transmitted.

The method may comprise:

representing each value of each symbol of a plurality of digital signals as a corresponding characteristic series of optical pulses;

wirelessly transmitting each series of optical pulses along a different optical path;

detecting each series of optical pulses after wireless transmission of the series of optical pulses along the corresponding optical path to thereby generate a corresponding received signal; and

determining each value of each symbol of each digital signal from each received signal.

Such a method may allow the wireless optical communication of a plurality of digital signals over a plurality of different paths. This may provide an increase in communication speed.

According to at least one aspect or to at least one embodiment there is provided an optical transmitter for use in wireless optical communications, the optical transmitter being configured to:

represent a value of a symbol of a digital signal as a corresponding characteristic series of optical pulses; and

wirelessly transmit the series of optical pulses along an optical path.

The optical transmitter may comprise an optical source. The optical transmitter may comprise a laser, such as a pulsed laser. The optical transmitter may comprise a non-coherent optical source. The optical transmitter may comprise an LED. The optical transmitter may comprise a gallium nitride (GaN) LED, an indium phosphide (InP) LED, a gallium arsenide (GaAs) LED, or an LED of a ternary or quaternary alloy of any of GaN, InP or GaAs. The optical transmitter may comprise a micro-LED. The optical transmitter may comprise an LED pixel of a micro-LED array. The optical transmitter may comprise an electronic interface such as a CMOS control board to drive the optical source. The optical transmitter may comprise an electronic interface such as a CMOS control board to drive the optical source.

According to at least one aspect or to at least one embodiment there is provided an optical receiver for use in wireless optical communications, the optical receiver being configured to:

detect a series of optical pulses after wireless transmission of the series of optical pulses along an optical path to thereby generate a received signal, wherein the series of optical pulses is representative of a value of a symbol of a digital signal; and determine the value of the symbol of the digital signal from the received signal.

The optical receiver may comprise a single photon detector.

The single photon detector may comprise or be a photomultiplier tube, a superconducting nanowire, and/or an image intensifier (micro-channel plates). The single photon detector may comprise or be a single-photon avalanche diode (SPAD). The optical receiver may comprise a single pixel of a SPAD array.

The optical receiver may comprise a plurality of optical detectors or detecting pixels. The optical receiver may comprise an image sensor. The optical receiver may comprise a single photon detector array such as a SPAD array. The SPAD array may comprise silicon CMOS. The optical receiver may comprise embedded electronics, such as a transmitter field programmable gate array (FPGA). The embedded electronics may be configured to autocorrelate and/or demodulate the digital signal from the detected optical pulses.

The optical receiver may comprise a plurality of optical detectors, such as a plurality of SPADs. The plurality of SPADs may be connected to each other by an OR or XOR tree. The plurality of SPADs may be connected to the embedded electronics by an OR or XOR tree. The plurality of optical receivers may be integrated on a CMOS microchip.

The embedded electronics may comprise multiple channels. Different channels of the embedded electronics may be connected or coupled to different optical detectors, such as different SPADs. This may provide multiple parallel outputs.

According to at least one aspect or to at least one embodiment there is provided a system for use in wireless optical communications comprising: an optical transmitter and an optical receiver,

wherein the optical transmitter is configured to:

represent a value of a symbol of a digital signal as a corresponding characteristic series of optical pulses; and

wireless transmit the series of optical pulses along an optical path, and wherein the optical receiver is configured to:

detect the series of optical pulses after wireless transmission of the series of optical pulses along the optical path to thereby generate a received signal; and

determine the value of the symbol of the digital signal from the received signal.

The optical transmitter may comprise a laser, such as a pulsed laser. The optical transmitter may be a non-coherent light source. The optical transmitter may comprise an LED. The optical transmitter may comprise a gallium nitride (GaN) LED, an indium phosphide (InP) LED, a gallium arsenide (GaAs) LED, or an LED of a ternary or quaternary alloy of any of GaN, InP or GaAs. The optical transmitter may comprise a micro-LED. The optical transmitter may comprise an LED pixel of a micro-LED array.

The optical receiver may comprise a single photon detector. The single photon detector may comprise or be a photomultiplier tube, a superconducting nanowire, and/or an image intensifier (micro-channel plates). The single photon detector may comprise or be a single photon avalanche diode (SPAD). The optical receiver may comprise a single pixel of a SPAD array.

The optical receiver may have a dead time. The dead time may be the minimum time between consecutive photons the optical receiver is able to detect, for example, able to detect as discrete photons. The dead time may be the time the optical receiver takes to recover from a detection of a photon.

The optical receiver may comprise a plurality of optical detectors or detecting pixels. The optical receiver may comprise an image sensor. The optical receiver may comprise a single photon detector array such as a SPAD array. The SPAD array may comprise silicon CMOS. The optical receiver may comprise embedded electronics, such as a transmitter field programmable gate array (FPGA). The embedded electronics may be configured to autocorrelate and/or demodulate the digital signal from the detected optical pulses.

The optical receiver may comprise a plurality of optical detectors, such as a plurality of SPADs. The plurality of SPADs may be connected to each other by an OR or XOR tree. The plurality of SPADs may be connected to the embedded electronics by an OR or XOR tree.

The embedded electronics may comprise multiple channels. Different channels of the embedded electronics may be connected or coupled to different optical detectors, such as different SPADs. This may provide multiple parallel outputs.

The dead time of the optical receiver may be less than the time separation between optical pulses in the series of optical pulses. The optical transmitter may be configured to transmit optical pulses of a duration shorter than the dead time of the optical receiver. This may advantageously result in at most a single detection from the optical receiver for each transmitted optical pulse.

The system may comprise a transmitter controller. The transmitter controller may control the optical transmitter. The transmitter controller may comprise a computer, such as a PC. The transmitter controller may comprise transmitter electronics, such as a transmitter field programmable gate array (FPGA).

The system may comprise a receiver controller. The receiver controller may comprise a computer, such as a PC. The receiver controller may comprise receiver electronics, such as a receiver field programmable gate array (FPGA). The receiver controller and/or the receiver electronics may be embedded on a CMOS microchip, for example, on the silicon CMOS of the SPAD array. This may reduce size, cost and power consumption of the receiver controller and/or receiver electronics.

The system may comprise one or more optical elements. The optical element may be configured to collimate and/or focus the series of optical pulses from the transmitter on to the detector.

The optical transmitter may be configured to transmit or emit optical pulses of a wavelength which is detectable by the optical receiver.

The system may comprise a plurality of optical transmitters. The system may comprise a plurality of optical receivers. Each optical transmitter may be configured to transmit a plurality of optical pulses to a corresponding optical receiver. The plurality of optical transmitters may comprise a micro-LED array. The plurality of optical receivers may comprise a SPAD-array. The plurality of optical receivers may be integrated on a CMOS microchip.

BRIEF DESCRIPTION OF THE DRAWINGS

Systems and methods for use in wireless optical communications will now be described by way of non-limiting example only with reference to the drawings of which: Figure 1 shows a system for use in wireless optical communications;

Figure 2A shows a first method of encoding a digital signal using the system of Figure 1 , a corresponding received signal, and a time correlated histogram of the received signal;

Figure 2B shows a second method of encoding binary digital signal using the system of Figure 1 , a corresponding received signal, and a time correlated histogram of the received signal;

Figure 3(a) shows a mean correlation histogram for signals received using the system of Figure 1 for the case of a series of five 5ns optical pulses at 40 ns intervals; Figure 3(b) shows a mean correlation histogram for signals received using the system of Figure 1 for the case of a series of 100 5ns optical pulses at 40 ns intervals;

Figure 4A shows the Poissonian distributions for signal and noise correlation counts for five pulse repetitions based on the mean correlation histogram of Figure 3(a);

Figure 4B shows the Poissonian distributions for signal and noise correlation counts for 100 pulse repetitions based on the mean correlation histogram of Figure 3(b);

Figure 4C shows the calculated overlap of Poisson distributions with increasing repetitions using the system of Figure 1 including the overlap of the Poisson distributions from Figures 4A and 4B; Figure 4D shows the Poisson distribution overlap for 100 pulse repetitions using the system of Figure 1 , with varying received photons per pulse;

Figure 5A shows the relationship between data transfer rate, bit error rate (BER), and detected photons per optical pulse using the system of Figure 1 and the encoding method of Figure 2A; Figure 5B shows the relationship photons detected per bit and data transmission rate for a fixed BER using the system of Figure 1 and the encoding method of Figure 2A;

Figure 6 shows the relationship between BER and the received power of the plurality of optical pulses using the system of Figure 1 and the encoding method of Figure 2A; Figure 7 shows the effect of background light on the BER using the system of

Figure 1 and the encoding method of Figure 2A;

Figure 8 shows another system for use in wireless optical communications; Figures 9A illustrates a method of embedding a clock into a bitstream using the system of Figure 8;

Figure 9B illustrates symbol-level synchronisation using the system of Figure 8; Figure 10 shows BER against received signal power for a real time link using the system of Figure 8 and the encoding method of Figure 2A;

Figure 11 shows a method for use in wireless optical communications along multiple optical paths; and

Figure 12 shows an alternative method of encoding a symbol of a digital signal using a series of optical pulses.

DETAILED DESCRIPTION OF THE DRAWINGS

Figure 1 shows a system 105 for use in wireless optical communications. The system 105 includes an optical transmitter in the form of a single LED pixel 122 of a GaN micro-LED array mounted on a CMOS control board 120, an optical element in the form of a lens 130, and an optical detector in the form of a single photon avalanche diode (SPAD) module 135. The system 105 further includes transmitter electronics in the form of a transmitter field programmable gate array (FPGA) 110 and a transmission circuit 112, receiver electronics in the form of an oscilloscope 140, and a controller in the form of a personal computer (PC) 115. The transmission circuit 112 comprises an oscillator 114 and an AND gate 116. The PC 115 is configured for communication with the FPGA 110 and the oscilloscope 140.

Also shown in Figure 1 is a background light source 125 which is configured to emit 450 nm light to simulate background light to allow the performance of the optical system 105 to be measured in the presence of noise. Similarly, a graded neutral density (ND) wheel 131 is used to control the intensity of light incident on the SPAD module 135 to simulate transmission loss. It should be understood that neither the background light source 125 nor the graded neutral density (ND) wheel 131 form part of the system 105. Similarly, neither the background light source 125 nor the graded neutral density (ND) wheel 131 are required for implementing a method for use in wireless communications.

The micro-LED pixel 122 is 100 ^χ 100 μηι square and part of a 16 ^χ 16 array of micro-LED pixels mounted on the CMOS control board 120. The micro-LED pixel 122 has a 405 nm emission wavelength. The micro-LED array is fabricated in flip chip format, and bump-bonded onto the CMOS control board 120.

The LED pixel 122 output is collimated with the lens 130 and transmitted through the graded neutral density (ND) wheel 131. This permits control of the amount of light reaching the SPAD module 135. The LED pixel 122 and the SPAD module 135 are 15 cm apart. The LED pixel 122 is imaged onto a circular detector active area of diameter 20 μηι of the SPAD module 135. As the image of the LED pixel 122 is approximately a 7 mm square, only a small portion of the light is imaged on to the SPAD active area. This means the received light is of exceptionally low power, on the order of tens of pW.

The SPAD detector 135 has a dead time of 35 ns, and a typical dark count rate of 25 Hz. The SPAD module 135 outputs a 3 V logic signal indicating photon counts. This logic signal is sent to the oscilloscope 140, and collected by the computer 115 for offline decoding of the detected signal.

In use, the FPGA 1 10 and the transmission circuit 1 12 drive the LED pixel 122 so as to wirelessly transmit a series of optical pulses to represent one or more symbols of a binary code. Specifically, the computer 115 instructs the FPGA 110 to produce a data signal 1 11 which is sent to the transmission circuit 112. The oscillator 114 produces a signal of square waves 1 13 with a period of 40 ns. The AND gate 116 combines the data signal 1 11 with the signal of square waves 1 13 to provide a driving signal 121 which is sent to the CMOS control board 120 of the micro-LED array. The CMOS control board 120 allows the LED pixel 122 to be modulated in a pulsed mode, triggered by a falling edge of the driving signal 121. As will be described in more detail below, the LED pixel 122 transmits a symbol of a digital signal as a series of optical pulses.

The SPAD detector 135 generates a time correlated signal from the detection of the series of optical pulses. The dark counts and counts from the background light are not time correlated. Analysis of the SPAD detector response to incoming light over an interval [-t _t , t _t ] shows that the correlation count density function g(r)dt' of recording two subsequent SPAD counts with temporal separation in the interval [τ, τ + dt'] is given by:

Here / ^" (t) is the probability distribution of SPAD pulses, which is determined by the optical signal from the transmitter. If an optical source transmits pulses with a time separation of T, g( ) will show a peak at τ = T, as the probability of observing SPAD pulses separated by T is increased. Equation (1) is the autocorrelation of f(t), so it is expected that peaks in g( ) would have a width of 2t _pulse , where t _pulse is the width of the optical pulse. It is important that T > τ _α , where τ _α is the dead time of the SPAD, as otherwise the SPAD would not recover from the first pulse in time to detect the second, and it would be impossible to see a correlation count. The presence and/or temporal position of peaks in g( ) directly depends on the sequence of optical pulses from the transmitter, and therefore can be used as a means of transmitting data.

In reality, the SPAD output is not a continuous probability distribution, but a series of discrete photon detection events. These events can occur due to the optical pulses from the LED pixel 122, background photons from background LED 125, or dark counts. The SPAD output signal will be sampled over a time period, into time bins t _ir i = 1, ... , N _S , where N _s is the total number of time bins. Each bin contains a number of counts f _t . If these bins are chosen to be smaller than τ _α , ft will only have values of 0 or 1. Correlation time will also be discretised into Tj,j = 1, ... , N _T . For a single pair of pulses a correlation either is or is not detected. This single correlation is indistinguishable from a random correlation of counts, so the series of optical pulses must comprise many pulses to produce a usable histogram of correlation counts. If correlation time bin size is chosen as an integer multiple of sampling bin size, τ _Μη = kt _bin , we can define indices for start and stop indices for correlating across i as:

(2) nstart

nstop — ⁿ start + 1 (3)

The function g( j) can be expressed in the discrete form as:

ΛΛ _Γ - n stop fe-l

5 '1( ^τ 7 ^' ) ⁼ ^ ^ ί ί+ n _start + (7-l)fe+i

i=i i=o

As fi is a binary value, and the output from the SPAD is a transistor-transistor logic (TTL) signal, the summation could be implemented with simple logic circuits.

Encoding data in g( j) has the potential to allow data transfer at exceptionally low light levels. In order to detect correlations, the receiver requires, and may be limited to detection of a single photon from each optical pulse. Such conditions allow average received power to be extremely low, in the range of pW. This would be suitable for systems where optical losses within the channel are high, such as through water or over long range. Equivalently, the scheme would be appropriate for low power systems. The data rate is expected to be relatively modest, as the optical signal must be repeated several times in order to generate a distinguishable signal in g( j) .

There are several potential ways to encode data in to g( j). Figure 2A shows a method of encoding a binary signal using a Pulse Position Modulation (PPM) method in the form of on-off keying (OOK). Data can be encoded using a single pulse time separation. To transmit the symbol , pulses of width t _pulse are transmitted continuously with a fixed time separation T, so g( j) will show a peak at τ = T. To transmit the symbol Ό', no pulses are transmitted, giving no peaks in g( j). The presence or absence of the peak at τ = T carries the data. Specifically, a first symbol of the digital signal is represented as a characteristic series of optical pulses 205a, a second symbol Ό' of the digital signal is represented as an absence of optical pulses, and a third symbol of the digital signal is represented as a characteristic series of optical pulses 205b. Figure 2A also shows the signal 210 generated by the SPAD module 135, and histograms 215 of the signal 210 generated by the SPAD module 135. The LED pixel 122 transmits the optical pulses of each series of optical pulses 205a, 205b with a time separation of 40 ns. As t _pulse is 5 ns, and the detector dead time is 35 ns, only one photon can possibly be detected from each pulse. In reality the detection rate is less than one photon per pulse, and some of the optical pulses in the series of optical pulses 205a, 205b are not detected by the SPAD module 135. For example, an optical pulse may be incident on the SPAD module 135 during the dead time following the detection of background light. The SPAD signal 210 is a series of apparently random photon count events, with high timing accuracy. When time correlation is performed over a data interval, the histograms 215 show peaks 216 at 40 ns intervals for transmission of a . The histograms 215 show a second peak 217 at 80 ns intervals for transmission of a , as every second optical pulse is separated in time by 80 ns. No peaks are determined for transmission of a Ό', as there are no optical pulses transmitted, and background light and dark counts are uncorrelated at these time scales. Applying a threshold to the histogram bin generated for each symbol at a delay 40 ns allows decoding of a binary stream.

Figure 2B shows a slightly different a Pulse Position Modulation (PPM) method for encoding the same binary signal. To transmit the symbol , pulses of width t _pulse are transmitted continuously with a fixed time separation T and g( _j ) shows a peak at τ = T. To transmit the symbol Ό', pulses are transmitted with a time separation of 2T, giving a peak in g( _j ) at T = 2T. As in the method of Figure 2A, the presence or absence of the peak at τ = T carries the data. Specifically, a binary value is encoded as a series of optical pulses 220 with a time separation of 40 ns, as before. However, a binary value Ό' is encoded as a series of optical pulses 225 with a time separation of 80 ns. The correlation peak 227 at 80 ns is now always present, and the binary signal is determined from the presence or absence of the correlation peak 226 at 40 ns.

In a more complex transmission scheme involving multiple time intervals, there may be many additional correlation peaks at relevant time intervals. It is important to consider potential overlaps in the correlation peaks when decoding the digital signal.

The maximum data rate of the communication system 105 is determined by the number of pulse pair repetitions required to obtain a distinguishable correlation peak in the g( ) histogram. Figure 3(a) shows a mean correlation histogram for signals generated using five repetitions (i.e. signals generated from multiple measurements, wherein each measurement uses a series of five optical pulses). Similarly, Figure 3(b) shows a mean correlation histogram for signals generated using 100 repetitions (i.e. signals generated from multiple measurements, wherein each measurement uses a series of 100 optical pulses). In both cases, the series of optical pulses used to represent a binary are 5 ns pulses at 40 ns intervals. As correlation detection is a statistical process, the histograms shown are generated from the mean of 1500 measurements. The background counts are very low, at a rate of approximately 600 Hz. This includes both dark counts within the detector, and ambient light. The average count rate from the SPAD module 135 during photon transmission was 1.07 ^χ 10 ⁷ , meaning 32.8 pW was incident on the SPAD module 135, once detection efficiency is accounted for.

In order to differentiate a transmitted signal from background correlations, a threshold must be specified at an integer level. For five optical pulse repetitions, on average, the SPAD module 135 does not detect a single correlation, as the mean number of correlations at 40 ns is below 1 , making it impossible to specify a threshold. However, for 100 optical pulse repetitions, an average of 13.83 correlations are detected. A series of optical pulses comprising 100 optical pulses therefore results in an easily detectable correlation peak and a threshold of two correlations would be sufficient to clearly identify the presence of the series of optical pulses, as it is highly unlikely that more than one background correlation will occur at 40 ns with such a low background photon count rate. A signal-to-noise ratio (SNR) may be defined to quantify how the number of repetitions affects signal levels.

Conventional SNR can be defined as in Equation 5, where N _signa i is average signal correlation counts and N _noise is average noise correlation counts.

^signal

SNR = 10 log _w

N-no ise

As number of pulse repetitions increases, both N _signal and N _noise will increase at linear rates. This results in a constant SNR, which does not reflect the observed increase in distinguishability of signal correlations with increasing pulse repetitions.

Instead, it is more useful to consider the statistical distribution of correlation counts for signal and noise. Correlation counts should follow a Poissonian distribution, as they are discrete independent events. Figures 4(a) and 4(b) show the Poissonian distribution for signal and noise for five and 100 repetitions. The mean correlation count values of signal and noise are taken as the correlation counts in the 40 and 60 ns histogram bins respectively, from the data in Figures 3(a) and 3(b). For five repetitions, the probability distribution for signal and noise are strongly overlapping. This correlation count peak due to signal transmission is difficult to distinguish from a correlation count peak due to random background and dark counts. At 100 repetitions, the overlap of signal and noise distributions is significantly reduced, making distinction much easier.

A histogram threshold equates to a point along the x-axis of the distribution plots of Figure 4A. Evidently a threshold point of 2 correlation counts at five repetitions would result in many signal correlation peaks being rejected as noise, whereas at 100 repetitions the majority of signal correlation peaks would be correctly identified, and noise correlation peaks rejected.

Distinguishability between signal and noise is well represented by the overlap of the Poisson distributions for signal and noise. Figure 4C shows the calculated overlap of the distributions, defined by:

(6) overlap = ^ Ps(k)P _n (k)

kk-=o

ke ^~ (7)

P(k) =

k\ where P _s (k) and P _n (k) are the probability of k correlation counts occurring for mean λ signal and noise correlation counts respectively.

As the overlap of the probability distributions decays exponentially with increasing pulse repetitions, it is a more useful metric for distinguishability than conventional SNR. The rate of decay of the overlap will depend on the received signal power. Figure 4C is valid for a received power of 5.21 pW. Higher received power would result in a steeper decay, and lower received power in a more shallow decay.

In addition to number of repetitions, the Poisson distribution overlap of the signal and noise will also depend on the number of photons detected from each pulse. As the pulses used are shorter than the dead time of the SPAD, the maximum number of photons that can be detected is one. By varying received power with the neutral density wheel 131 , histograms, Poisson distributions and the overlap can be determined as a function of detected photons per pulse, rather than pulse repetitions. Figure 4D shows the Poisson distribution overlap for 100 optical pulse repetitions, with varying received photons per pulse. The mean correlation counts λ in the distributions P(k) follow λ = p _ph N _rep where p _ph is the probability of detecting a photon from a single pulse, and N _rep is the number of pulse repetitions.

It is desirable to minimise the time separation between pulses to increase the data transmission rate. The response of the SPAD module 135 imposes a lower limit on this separation, due to the dead time τ _α . For the time correlation histogram to resolve the correlation peak, the pulses must be at least t _pulse + τ _α apart. Therefore the data transmission rate follows the equation:

where N _rep is the number of pulse repetitions required to see a distinguishable peak in the correlation histogram. In reality, N _rep strongly depends on received power. Higher power increases the probability of photon detection for each pulse, increasing the probability of detecting a correlation and in turn decreasing the number of repetitions required.

Decreased received power will decrease the probability of detecting correlation, and therefore require more pulse repetitions to achieve the same Poisson distribution overlap and therefore the same distinguishability between signal and noise.

Figure 5A shows the bit error rate (BER) as a function of received average signal power for the transmission of a pseudo-random bit sequence (PRBS) of 10 ⁴ bits using the system 105 of Figure 1 and the encoding method of Figure 2A. The neutral density filter wheel 131 was used to control the received power or equivalently, photon detection probability. Figure 5A shows higher transmission rates require more received power to achieve the same BER.

As shown in the SNR details, it is extremely unlikely to detect a noise correlation. On transmission of a Ό', no pulses are sent, meaning only noise correlations will be present. Bit errors arise almost exclusively from missed correlation counts on transmission of a rather than noise correlations on transmission of Ό'. Therefore, a decision threshold of 2 counts applied to the correlation histograms provides the lowest BER values. At 10 pW of average power, a data rate of 100 kb/s is possible with a BER of less than 10 ^~4 . Received optical power can be reduced at the expense of data rate. A data rate of 10 kb/s can be achieved with 3 pW. It is worth noting that the average power emitted from the LED 122 is 3.40 μ\Λ/, permitting a large amount of optical attenuation in the channel. Emitted power could also be adjusted by changing the pulse energy, through control of the driving conditions. Higher pulse energy would permit longer range or higher loss, while lower energy would permit an energy efficient short range system.

Figure 5B shows detected photons per bit for different data transmission rates, at the level required for a BER of less than 10 ^"4 using the system 105 of Figure 1 and the encoding method of Figure 2A. The 100 kb/s data transmission is achieved by transmitting each bit with an average of 32 received photons. After correcting for detector efficiency of the

SPAD module 135, this equates to 9.81 ^χ 10 ^~17 J incident on the detector per bit. This exceptionally low energy demonstrates the suitability of the transmission scheme in low power or high loss systems. The commercial SPAD module 135 has a detection efficiency of

16% for 405 nm light. Using a wavelength and SPAD optimised for efficient photon detection would allow further reductions in energy received per bit.

There is a clear trend in Figure 5B, arising from the relationship between correlation counts, received power and data rate. The number of signal correlations depends on the square of received power, as the probability of detecting a single photon scales linearly with power. As both a trigger photon and correlated photon must be detected, the probabilities must multiply.

In addition, the number of signal correlations depends inversely on the data rate

^R data, ^as this dictates how many times the pulses are repeated. In order to reach a given target BER, a certain constant number of signal correlation counts must be reached, meaning (ph/s) ² oc R _data . As photons per bit is simply the required photons per second divided by data rate, then:

1 (9) photons per bit oc —==

sj Rdata The data in Figure 5B is fitted with this relationship. While efficiency would improve as data rate increases, there are some fundamental limits. The first is that it would be impossible to have an efficiency of less than 1 photon per bit, as no correlations at all would be detected. This also could be thought of as a somewhat fundamental physical limit. As information is encoded only in the presence or absence of photons, without exploiting quantum properties, it would be impossible to transmit more than a single bit with a single photon. More practical limitations arise from the transmission scheme employed. As the pulses are repeated every 40 ns, the data rate could not be increased beyond 25 Mb/s. Ultimately this limitation comes from the SPAD used, as the dead time restricts pulse separation. Further limitations may occur due to SPAD saturation, detection efficiency, and maximum LED output power.

Figure 6 shows BER curves for a data transmission rate of 50 kb/s for different levels of DC background light emitted at 450 nm from the background LED 125 using the system 105 of Figure 1 and the encoding method of Figure 2A. The data of Figure 6 was generated by placing the background LED 125 within a few centimetres of the LED pixel 122 and directing the background LED 125 towards the SPAD module 135, as shown in Figure 1.

The background counts were controlled by controlling the driving current for the background LED 125. As background counts increase, the probability of detecting noise correlations increases. The threshold applied to the correlation histogram must then be increased to avoid erroneous detection of Ό' symbols from background correlations. This means higher received average power is required to obtain the same BER for higher background levels.

The DC background conditions are detailed in Table 1. For comparison, a received signal power of 10 pW corresponds to 3.26 x 10 ⁶ counts.

Table 1 : Background conditions, and required correlation thresholds for the BER curves in Figure 6.

Figure 6 shows that increasing levels of background counts increases the received power required to obtain a BER of less than 10 ^"4 . However, the power requirements are still very low. Even with a background count rate of 10 ⁷ , less than 16 pW is required.

This background illumination level is somewhat extreme, as normal room lighting in this setup gives a background count rate of 2.33 x 10 ⁵ .

In addition to continuous background light, the modulation scheme is robust to AC or modulated background signals. This is due to the data being encoded in the temporal correlation, rather than intensity of received light. A conventional pseudorandom OOK signal will have varying intensity, however it will not have a strongly varying temporal correlation.

Figure 7 shows BER curves for a data transmission rate of 50 kb/s for AC background signals modulated at different frequencies using the system 105 of Figure 1 and the encoding method of Figure 2A. Detected correlation counts depend on the square of received power, therefore a high modulation rate background should interfere in the same manner as a DC signal at the root-mean-squared (RMS) of its count rate. For this reason, the background signals used to generate the BER curves of Figure 7 maintain similar RMS photon count rates for comparison to DC measurements.

The background optical signal was generated using the background LED 125, modulated with a transistor. The background LED 125 had a modulation bandwidth of 15.9 MHz, and was within a few centimetres of the LED pixel 122. The background LED 125 was modulated with a pseudo random binary sequence (PRBS). This effectively simulated operation of the correlation link in an environment with conventional optical wireless communication links. The background conditions are detailed in Table 2.

Table 2: AC background conditions, and required correlation thresholds for BER curves of Figure 7.

Figure 7 shows two distinct groups of results. The high background modulation rates of 1 and 10 MHz show very similar curves to DC conditions. This can be attributed to 2 factors. Firstly, the background signal completes many cycles within a single bit period of the correlation link, making the modulation of the background less significant. Secondly, the dead time of the SPAD module 135 restricts the number of photons that can be detected per background cycle. This reduces the difference between a high and low level, further making the background signal act like DC interference.

When the background modulation rate is close to the correlation link data rate, the

BER performance is slightly worse, though all conditions reach a BER of less than 10 ^"4 for less than 16 pW. This reduction in performance occurs as the background signal is now generating different levels of noise correlations from one bit period to the next. This makes it more difficult to choose a suitable correlation threshold, and increases the BER. Nevertheless, the correlation link still shows exceptional low power performance even with high power background interference.

For a background signal to have significant influence on the transmission link, it would have to not only be correlated at the appropriate time interval, but also have that correlation vary significantly over time to impose an unwanted correlated data signal instead of just constant correlated background. For this reason, it may be possible to implement this transmission scheme simultaneously with a high data rate, high power optical link. This could be useful for a bi-directional link, with high data rate download and low data rate upload, similar to home internet connections. Alternatively, this may be useful for a long range, low data rate link, combined with a shorter range, higher data rate link. With arrays of LED pixels under CMOS control, this system could be implemented in a single device.

The system 105 uses offline decoding. The output from the SPAD module 135 is collected with the oscilloscope 140, and the traces repeated many times to build a data sequence long enough for BER analysis. In addition, the oscilloscope 140 is triggered from the transmitting FPGA 110, thereby avoiding any requirement for the transmitter and receiver to be synchronised.

Figure 8 shows an alternative system 805 which includes a transmitter 806 and a receiver 807. The system 805 is configured for wireless optical communications using real-time decoding to permit synchronisation of the transmitter 806 and receiver 807. The transmitter 806 includes an optical transmitter in the form of a single LED pixel 822 of a GaN micro-LED array mounted on a CMOS control board 820, and an optical element in the form of a lens 830. The receiver 807 includes an optical detector in the form of a single photon avalanche diode (SPAD) module 835. The transmitter further includes transmitter electronics in the form of a transmitter field programmable gate array (FPGA) 810, and a transmitter controller in the form of a PC 815 for controlling the transmitter FPGA 810. The receiver 807 further includes receiver electronics in the form of a receiver field programmable gate array (FPGA) 840, and a receiver controller in the form of a PC 845 for collecting the output from the receiver FPGA 840.

Also shown in Figure 8 is a graded neutral density (ND) wheel 831 in an optical path 832 between the transmitter 806 and the receiver 807. The graded neutral density (ND) wheel 831 is used to control the intensity of light incident on the SPAD module 835 to simulate transmission loss. It should be understood that the graded neutral density (ND) wheel 831 does not form part of the system 805, and is not required for implementing a method for use in wireless communications.

The micro-LED pixel 822 is 100 ^χ 100 μηι square and part of a 16 ^χ 16 array of micro-LED pixels mounted on the CMOS control board 820. The micro-LED pixel 822 has a 405 nm emission wavelength. The micro-LED array is fabricated in flip chip format, and bump-bonded onto the CMOS control board 820.

The LED pixel 822 output is collimated with the lens 830 and transmitted through the graded neutral density (ND) wheel 831. This permits control of the amount of light reaching the SPAD module 835. The LED pixel 822 and the SPAD module 835 are 15 cm apart. The LED pixel 822 is imaged onto a circular detector active area of diameter 20 μηι of the SPAD module 835. As the image of the LED pixel 822 is approximately a 7 mm square, only a small portion of the light is imaged on to the SPAD active area. This means the received light is of exceptionally low power, on the order of tens of pW.

The SPAD detector 835 has a dead time of 35 ns, and a typical dark count rate of 25 Hz. The SPAD module 835 outputs a 3 V logic signal indicating photon counts. This logic signal is sent to the receiver FPGA 840, which determines the symbols of the digital signal and outputs the digital signal to the PC 845.

In use, the transmitter FPGA 810 drives the LED pixel 822 so as to wirelessly transmit a series of optical pulses to represent one or more symbols of a binary code. Specifically, the computer 815 instructs the transmitter FPGA 810 to produce a driving signal 821 which is directly sent to the CMOS control board 820 with the need of extra logic circuitry. The driving signal 821 represents the digital signal in frames, with a 6 bit clock word at the start of every frame. The CMOS control board 820 allows the LED pixel 822 to be modulated in a pulsed mode, triggered by a falling edge of the driving signal 821. The LED pixel 822 transmits the binary code by transmitting a series of 5 ns optical pulses separated by 40 ns to represent the binary symbol , and by not transmitting any optical pulses to represent a binary symbol Ό'. The SPAD module 835 detects the optical pulses from the LED pixel 822 and outputs the 3 V logic signal indicating photon counts to the receiver FPGA 840, which determines the symbols of the binary code from the logic signal from the SPAD module 835. The FPGA 840 also detects the clock word from the logic signal, and uses the clock word to synchronise the receiver clock to the transmitter clock. The clock synchronisation removes the need for a trigger from the transmitter 806. Due to limitations from the transmitter and receiver FPGA boards 810, 840, the achievable data rates with the realtime setup are limited to 20 kb/s.

As described in more detail below, the system 805 allows a synchronisation system to be implemented, involving data transmission frames consisting of a 6 bit clock word and 32 data bits. A carefully chosen clock word, O01101', allows both frame level and symbol level synchronisation of data streams. Frame level synchronisation is attained by searching the received data stream for the clock word. Symbol level synchronisation requires calculation of the phase offset between the transmitted and received symbols. This is done using the correlation counts received for the clock word, as any phase offset will increase counts on transmission of Ό' and decrease counts for . In addition, the repetitive nature of the clock word allows calculation of an appropriate threshold for OOK transmission.

As described in more detail below with reference to Figures 9A and 9B, the synchronisation system uses an anisochronous embedded clock with OOK encoding, which allows the sampling rate to be the same as the symbol rate. Figure 9A shows a bitstream 905 in which the data is divided into M frames, where each frame is of bit length ^N frame , ^an d ^eacn frame comprises a clock word of bit length n _clk , and a data word of bit length n _dat . For error free transmission (BER = 0), the probability P _err that the clock is erroneously synchronized to a randomly occurring replica of the clock word in the bitstream is:

P (n n Af) - Ρ( ^η ^ ^η ^ ^Μ > (10)

1 + P(n _clk , n _dat , M)

where p(n _clk , n _dat , M) is the average number of false clock word sequences in the bitstream. It can be calculated recursively:

P (n _clk , n _dat < n _clk , M) = 0 (11.1)

1 (11.2)

P(n _clk , n _dat = n _clk , M) =

2 ⁿ clkM P(.n _clk , n _dat > n _clk , M) (11.3)

= ^{1 +} ( ⁿ ik> ⁿ dat - n _c i _k , ))

Equations 11.1 - 11.3 above are valid for error free transmission (BER = 0). For these equations to be valid requires careful selection of the clock word. Namely, the clock word has to be chosen such that part of the clock word cannot be completed to a replica of the clock word by adding matching data bits in the data word before/after the clock word. An unwise choice (e.g. Ό10 0 ) would yield a larger p(n _c i _k , n _dat , M) than calculated in Equations 13.1 - 13.3. Specifically, the clock word should be selected such that a greater proportion of the sequence of the clock word must be present in the data word before the clock word is erroneously detected in the data word. For example, if the clock word were 111111', transmission of a as the first bit in the data word could result in erroneous detection of the clock word 1 bit late i.e. the clock word may be erroneously detected as the last five bits of the actual clock word and the first bit of the actual data word. '111111' is therefore a poor clock word. In contrast, the clock word Ό0110 must be present in the data word before the clock word is erroneously detected in the data word, and Ό01101' is therefore a good clock word.

The frame-level synchronisation variables n _clk , n _clk and M should be chosen such that P _err calculated with Equations 10 and 11.1 - 11.3 matches the target BER of the system. A compromise may be found between minimising M x N _frame for faster clock synchronisation, and maximising n _dat /n _cife for increasing the data transmission rate. For example, if n _clk = 6, n _clk = 32 and M = 6, then P _err = 3.9 ^χ 10 ^"10 . This allows frame-level synchronisation on the basis of 228 transmitted bits.

In addition to synchronising the transmitter and receiver on a frame level, it is necessary to synchronise on a symbol level. Figure 9B shows a transmitted clock bit, and the received symbol due to a phase offset between the transmitter and the receiver.

Let r _x (t) be the received correlation counts at receiver time-frame t. Let be the correlation counts corresponding to a transmitted under perfect clock synchronisation and the correlation counts corresponding to a transmitted Ό' under perfect clock synchronisation. Then the received correlation counts at time frames t _t , ... , t ₅ in Figure 9B are:

(12.1) r _x t ₂ ) = p - r^ + (1 - p)

r _x t ₃ ) = r _x ⁽¹⁾

r _x (t ₄ ) = (1 - p)r _x ⁽¹⁾ + p ^■

¾(t ₅ ) = p - ^r * ⁽¹⁾ + (i - p)

P ε [0,1)

Here, p is a parameter that is directly related to the phase offset between the two clocks. If p = 0, then the transmitter and receiver clocks are perfectly synchronised. If p ≠ 0, p can be used to determine by how much the receiver phase needs to be corrected to achieve synchronisation. One skilled in the art will understand how this series of equations (12.1 - 12.5) should be extended for longer clock words.

Due to the variability in the receiver counts, it is advisable to use more than one repeat of the clock word to measure p, and The greater the number of frames used to achieve synchronisation, the more accurately the phase shift can be determined. For example, if an accuracy of 15° is required in the calculated phase shift using a 6-bit long clock word, 25 frames should be used. Longer clock words can achieve the same precision with fewer frames.

If several clock word repetitions are used to determine and then their variances and can be determined at the same time. An OOK threshold r _00K that discriminates between whether a given is a Ί ' or a Ό' can be found by:

TOOK = \ (r∞ - + + ^{(1 3)}

This allows continuous adaptation of the OOK threshold during each symbol-level synchronisation, which can account for a changing background level.

Simultaneous frame-level and symbol-level synchronization can be achieved by searching the detected signal for the periodic occurrence of the 5-symbol pattern given by Equations 12.1 - 12.5 in the stream of received counts, with a period N _frame .

If the phase offset measured by p is found to be excessively large, it may be indicative that both symbol- and frame-level synchronization has been lost, and that the above synchronisation process can be triggered to re-establish synchronisation.

As shown in Figure 10, the system 805 of Figure 8 performs real-time synchronization of data transmissions at 10 kb/s and 20 kb/s, with low background conditions. The BER result for offline transmission is also plotted in Figure 10 for comparison. The live transmission has some reduction in performance, which is to be expected as the synchronisation is no longer artificially set as perfect. However, the system 805 still reaches a BER of less than 10 ^"4 with less than 6 pW of received power, for 20 kb/s. It should also be noted that the data rates quoted here include transmission of the clock word. This 18.75% overhead reduces useful data transfer to 8.42 and 16.84 kb/s for 10 kb/s and 20 kb/s links respectively.

Figure 1 1 shows a system 1005 for use in a method of optical communications. The system 1005 includes a first optical transmitter 1010a, a second optical transmitter 1010b, a first optical receiver 1015a and a second optical receiver 1015b. The digital signal 1020 is split and transmitted in two independent optical paths 1025a-b. The first optical transmitter 1010a transmits a first portion 1030a of the digital signal 1020 along a first optical path 1025a. The first portion 1030a of the digital signal 1020 is receiver by the first optical receiver 1015a. The second optical transmitter 1010b transmits a second portion 1030b of the digital signal 1020 along a second optical path 1025b. The second portion 1030b of the digital signal 1020 is receiver by the second optical receiver 1015b. The first and second portions 1030a-b are combined to create the complete received signal 1035. This system 1005 can increase the data transmission rate of the method, as multiple channels are used to communicate the digital signal 1020. One skilled in the art will understand that any number of channels may be used, and that the data transmission rate will increase with the number of communication channels.

The optical transmitters may be individual pixels of a micro-LED array, with each LED pixel communicating part of a digital signal along a different optical path. The receiver could be a SPAD array, with each pixel in the SPAD array corresponding to an individual LED pixel in the micro-LED array. With an area detector such at this, the communication method could be combined with other SPAD detector functionality such as measurement of intensity, time of flight measurement, or imaging.

Figure 12 shows an alternative method of encoding a symbol of a digital signal in a series of optical pulses, which series includes a first set of optical pulses each having an amplitude p ₀ and a second set of optical pulses each having an amplitude p _P interleaved with the first set of optical pulses, wherein the first and second sets of optical pulses each have a repetition period of r _rep .

Each pulse of the second set of optical pulses is transmitted a time T after a corresponding pulse of the first set of optical pulses. The time correlation between the optical pulses in the series of optical pulses can be used to distinguish the series of optical pulses from any other detected signals, such as background light. The time correlation between the optical pulses in the series of optical pulses can be distinguished by sampling the optical pulses received over a time T _s , and then binning the times of arrival into time bins of t _t . This binning will produce correlation peaks at time T and time r _rep . Provided time r _rep is not a multiple of time T, the presence or absence or either or both of these correlation peaks can be used to transmit data. One or more further sets of optical pulses may be interleaved with the first set of optical pulses. Each pulse of each further set of optical pulses may be transmitted a corresponding delay time T _t after a corresponding pulse of the first set of optical pulses. Binning may then produce correlation peaks at times 7 , T ₂ , T ₃ etc. and at time T _rep . Provided time r _rep is not a multiple of any of times 7 , T ₂ , T ₃ etc., the presence or absence of any of the correlation peaks at times r _rep , 7 , T ₂ , T ₃ etc. can be used to represent different symbols of a binary code or different values of a non-binary symbol. It is also possible to encode a symbol of a digital signal in the relative amplitudes of the optical pulses according to the Pulse Amplitude Modulation (PAM) scheme shown in Figure 12. An autocorrelation at time T can only be recorded if an optical pulse of amplitude p ₀ is detected, followed by an optical pulse of amplitude p _P . An autocorrelation at time r _rep can be recorded if an optical pulse of amplitude p ₀ is detected, followed by another optical pulse of amplitude p ₀ . An autocorrelation at time r _rep can also be recorded if an optical pulse of amplitude p _P is detected, followed by another optical pulse of amplitude p _P . As a consequence of the difference in the amplitudes p ₀ and p _P , one of skill in the art will understand an autocorrelation peak at time r _rep will have a greater amplitude than the autocorrelation peak at time T. The symbol of the digital signal can then by decoded from the relative amplitudes of the autocorrelation peaks.