Patent Application
20180309477
Virtually all sequence-based spread spectrum systems are based on the interpretation of a stream of independent and identically distributed (iid) random variables translated to discrete phase words. These phase words are subsequently combined as a time series into a bandlimited spread spectrum communications signal, and traditionally combined via spreading operations with phase-shift keying (PSK)-based data words. In direct sequence spread spectrum (DSSS) modulations, the discrete phase words are typically selected as 2-ary or 4-ary PSK-based spread modulations, effectively representing a higher rate version of a standard BPSK or QPSK modulation. In chaotic sequence spread spectrum (CSSS) modulations, the discrete phase words may be represented as arbitrary-phase modulations that are drawn as nearly random points on the unit circle, representable by phases such as 28-ary up to 216-ary PSK modulations. The increased order of the representative PSK modulation produces a whiter overall spectral response. Ignoring windowing effects, the spectral content can be approximated as consisting of concentrations of energy represented by the phase difference between each successive iid phase word (instantaneous frequency being approximated as the rate of change of phase within the chosen chip periods), which if drawn from a uniform distribution, will also be uniform, and therefore generate an approximately white communications signal.
Disclosed herein is a candidate arbitrary-phase spread spectrum modulation technique and associated apparatus that offers similar performance to spread continuous phase modulation (CPM) or CSSS waveform techniques, yet offers additional capabilities for programming a chosen frequency domain spectra into the resulting spread spectrum signal. The proposed chaotic-FSK waveform may be derived from high-order sequence-based spread spectrum signals, with multi-bit resolution chaos-based sequences defining incremental phase words, enabling real-time efficient generation of practically non-repeating waveforms. A result of the C-FSK formulation is a parameterized hybrid modulation capable of acting like a traditional sequence-based spread spectrum signal or a traditional frequency shift keying signal depending on chosen parameters. As such, adaptation in this modulation may be easily implemented as a time-varying evolution, increasing the security of the waveform while retaining many efficiently implementable receiver design characteristics (no MLSE algorithms required) of traditional PSK modulations. Most importantly, the chaotic-FSK modulation enables selective frequency controls that color the resulting frequency spectrum of the transmitted signal into a non-white, or equivalently non-uniform, communications signal that can mitigate the impact of interfering signal operating within its band.
In one aspect the disclosure relates to an apparatus for generating a communications signal. The apparatus includes a pseudorandom number generator for providing a sequence of pseudorandom phase words. A mapping module includes a color mapping table containing phase value information. The mapping module is configured to provide an output phase word sequence by phase mapping the sequence of pseudorandom phase words in accordance with the phase value information. A modulator is operative to generate the communications signal using the output phase word sequence wherein a frequency domain spectra of the communications signal is determined in accordance with the phase value information.
In another aspect the disclosure relates to a transmitter including an encoder for generating encoded data symbols based upon input data provided by a data source. The transmitter further includes a communications signal generator having a pseudorandom random number generator for providing a sequence of pseudorandom phase words. The communications signal generator further includes a mapping module including a color mapping table containing phase value information. The mapping module is configured to provide an output phase word sequence by phase mapping the sequence of pseudorandom phase words in accordance with the phase value information. The communications signal generator also includes a modulator operative to generate a spreading sequence using the output phase word sequence wherein a frequency domain spectra of the spreading sequence is determined in accordance with the phase value information. A transmit signal generator is operative to generate a transmit signal by spreading the encoded data symbols using the spreading sequence.
The disclosure is also directed to a transceiver apparatus including a receiver including a channel state information module configured to provide channel state information based upon a received signal. A color mapping table stores phase value information wherein the phase value information is determined based at least in part upon the channel state information. A communications signal generator is configured to generate a communications waveform. The communications signal generator includes a mapping module operative to introduce a selected frequency domain spectra into the communications waveform in accordance with the phase value information.
The disclosure also pertains to a method for generating a communications signal. The method includes providing a sequence of pseudorandom phase words. The method further includes generating a color mapping table containing phase value information. An output phase word sequence is provided by phase mapping the sequence of pseudorandom phase words in accordance with the phase value information. The method further includes generating the communications signal using the output phase word sequence wherein a frequency domain spectra of the communications signal is determined in accordance with the phase value information.
In yet another aspect the disclosure relates to a method which includes generating encoded data symbols based upon input data provided by a data source. The method further includes providing a sequence of pseudorandom phase words and generating a color mapping table containing phase value information. An output phase word sequence is provided by phase mapping the sequence of pseudorandom phase words in accordance with the phase value information. A spreading sequence is generated using the output phase word sequence wherein a frequency domain spectra of the spreading sequence is determined in accordance with the phase value information. A transmit signal is generated by spreading the encoded data symbols using the spreading sequence.
The disclosure is also concerned with a method which includes providing channel state information based upon a received signal. The method further includes storing phase value information wherein the phase value information is determined based at least in part upon the channel state information. A communications waveform is generated, in accordance with the phase value information, to have a selected frequency domain spectra determined by the phase value information.
The present invention is described with reference to the accompanying drawings. In the drawings, like reference numbers indicate identical or functionally similar components.
Disclosed herein are embodiments of a chaotic frequency shift keying (CFSK) modulation system and technique useful in generating a spread spectrum communication signal having a tailored or, equivalently, “colored” frequency spectra. The disclosed arbitrary-phase spread spectrum modulation technique offers the opportunity to effectively program a chosen frequency domain spectra into a spread spectrum communication signal produced using the proposed chaotic-FSK waveform as a spreading signal. The chaotic-FSK waveform may be derived from a sequence of multi-bit phase words produced by a pseudorandom number generator. More particularly, the pseudorandom multi-bit phase words may undergo a color mapping process to define a sequence of incremental phase words, thereby enabling real-time efficient generation of practically non-repeating waveforms. As is discussed below, such chaotic-FSK waveforms facilitate a parameterized hybrid modulation scheme capable of acting like a traditional sequence-based spread spectrum signal or a traditional frequency shift keying signal depending on chosen parameters. As such, adaptation in the disclosed modulation scheme may be easily implemented as a time-varying evolution, increasing the security of the waveform while retaining many efficiently implementable receiver design characteristics (i.e., no maximum likelihood sequence estimation, MLSE, algorithms required) of traditional PSK modulations.
Before describing the details of the present chaotic sequence based frequency shift keying spreading techniques, it will be helpful in understanding an exemplary communication environment in which the disclosed techniques may be utilized.
Attention is now directed to
Data source 118 may be implemented as an interface though which an externally-provided input signal is received. During operation of the transmitter 102, data source may supply bits of data to the encoding subsystem 110 at a specified data rate.
The encoding subsystem 110 may conventionally encode the data provided by the data source 118 and format the encoded data into symbols. For example, the encoded data may be formatted into phase shift keyed (PSK) symbols (e.g., QPSK symbols). The encoding subsystem may also include conventional sample rate matching structures so that a sample rate of the PSK symbol data matches that of a digital chaotic-FSK sequence generated by the chaotic sequence generator 108 in the manner described hereinafter.
The spread spectrum modulator 106 includes a complex multiplier 120 operative to perform complex-valued digital multiplication operations using the encoded digital symbol data from the encoding subsystem 110 and the digital chaotic-FSK sequence provided by the chaotic sequence generator 108. The output of the complex multiplier yields a digital IF signal which may be characterized as a spread spectrum chaotic-FSK signal. It will be appreciated that increasing the ratio between the period of the encoded symbol data and the sample period of the chaotic-FSK sequence increases the associated spreading gain.
Within the DAC/RF subsystem 114, the spread spectrum chaotic-FSK signal may be conventionally interpolated, converted to analog form using a digital to analog converter (DAC), and upconverted in frequency to an RF signal. The RF signal may then be amplified and transmitted as a spread spectrum communication signal using an antenna 126.
As shown, each receiver 104 includes a spread spectrum demodulator 136 having a chaotic sequence generator 138 essentially identical to the chaotic sequence generator 108 within the transmitter 102. Each receiver 104 also includes an RF front end subsystem 140 and a decoding subsystem 144.
After being received by antenna 148 of receiver 104, the spread spectrum communication signal communicated from the transmitter 102 is provided to the RF front end subsystem 140 in which it may be conventionally amplified, downconverted in frequency to an IF, filtered and converted to a digital signal using an analog to digital (A/D) converter. Additionally, although not shown, the RF front end subsystem 140 may be configured to include a frequency selective equalizer that pre-processes the received signal before passing to the spread spectrum demodulator 136.
The spread spectrum demodulator 136 may be configured for de-spreading the transmitted spread spectrum communication signal after processing by the RF front end subsystem 140. This de-spreading may be effected by correlating the received signal with a replica of the chaotic-FSK signal generated at the transmitter 102. To this end, the demodulator 136 includes a correlator 154, a peak detector 156, a complex multiplier 150 configured for complex multiplying digital words provided by the RF front end subsystem 140 by digital words defining the chaotic-FSK signal produced by the chaotic sequence generator 138.
A correlator 154 is configured for correlating the received baseband chaotic-FSK signal with a digital signal based upon an output of the chaotic sequence generator 138. The sequence values provided from the chaotic sequence generator 138 to the correlator 154 are used to define an acquisition preamble that is used to discriminate the presence of an incoming signal preamble (or other known signal content). Following the correlator 154 is a peak detector 156 that translates the outputs of the correlator 154 to determine the presence and timing of the incoming signal preamble. Not shown are optional phase, frequency, and timing tracking loops that follow traditional sequence-based spread spectrum communications receiver designs. Upon detection of a preamble by the peak detector 156, timing, frequency, and phase information are provided to the chaotic sequence generator 138, which may be configured to correct for those observed offsets. The chaotic sequence generator 138 then produces a complex conjugate of the spreading signal, modified for the phase, frequency, and timing offsets as appropriate for communication to the complex multiplier 150. Following the complex multiplier 150 is an accumulate & dump circuit 158 that assists with translation from despread spread spectrum chips into data symbols. During steady state operation of the receiver 104, the output produced by the integrate & dump circuit 158 corresponds to “soft decisions” of PSK symbols. These PSK soft decisions may be provided to the decoder 144, which is configured to render final decisions with respect to each soft decision and thereby produce a recovered symbol stream. The recovered symbol stream may then be conventionally decoded into recovered data 164 corresponding to an estimate of the input data provided by the data source 118. Although not shown, traditional mechanisms for data frame verification like cyclic redundancy checks (CRC) or forward error correction (FEC) processing may be inserted into the decoder's 144 processing to improve error rate performance.
As noted above, embodiments of a chaotic frequency shift keying (CFSK) modulation system and technique may be useful in generating a spread spectrum communication signal having a “colored” frequency response selected in accordance with, for example, channel conditions or other criteria. In one aspect, the disclosed embodiments facilitate coloring or otherwise programming a desired frequency response within a chaotic spreading signal by using an accumulator element to aggregate phase differences between pseudorandom spreading chips provided by, for example, a PRNG. As is discussed below, this hardware structure of a PRNG and an accumulator may be easily extended to enable color mapping information to determine the frequency response characteristics of the chaotic spreading signal provided at the output of the structure.
Accordingly, presented herein is a candidate reinterpretation of the 2k-ary PRNG output as an iid phase word to instead be an accumulated phase increment whose sum rolls over uniformly on each new PRNG value. By so doing, easy additions may be incorporated to programmably define a spread spectrum output signal that contains tailored/colored frequency responses, which cannot be achieved when phase words are taken as uniformly distributed iid entities. The ability to uniquely color the spectrum of the output signal offers new advantages for optimizing transmission in a non-white or frequency dispersive channel as well as mitigating interference observed in the channel.
This Section II introduces a foundational framework for the chaotic frequency shift keying (CFSK) modulation concept and includes a discussion of methods to increase the adaptability in the CFSK spreading process. This is followed by an analysis of the CFSK techniques, including extensibility to optimized implementation on different types of hardware platforms in Section III; a proof-of-concept fixed-point implementation of the CFSK modulator was constructed in Simulink and subsequently translated into Verilog for verification on an Altera Cyclone V FPGA.
Attention is now directed to
As shown in
As shown, the color mapping module 240 includes a color mapping unit 244 containing and an accumulator structure 248. The color mapping module 240 contains a color mapping table of phase pre-mapping mapping values. In one respect the accumulator structure 248 represents an interpretation of the output of the PRNG 234 as an additive phase increment/instantaneous frequency word, acting much like a variable-input numerically controlled oscillator (NCO). In these scenarios, the bulk signal properties are identical to the multi-bit resolution style CSSS signals. In other embodiments the color mapping table of the color mapper 244 comprises an adaptable array of values representative of a surjective mapping from the input GF(2k) domain onto a chosen subset of values.
In yet other embodiments, the output of the PRNG 234 represents a sequence of phase difference values (derivative of phase). In this embodiment the color mapping module 240 further includes an integrator operative to perform an integration of the sequence of phase difference values (with the recognition that phase is circularly symmetric). In this way the color mapping module 240 synthesizes a phase stream that is subsequently employed to modulate the spreading chips generated by spread spectrum modulator 260.
As mentioned above, the color mapping table of the color mapper 244 may comprise an adaptable array of values representative of a surjective mapping from the input GF(2k) domain onto a chosen subset of values. A few scenarios for this surjective mapping include (1) uniform definition of the color mapping table to be a single phase value, producing a continuous wave (CW) signal, (2) subdivision of the 2k memory entries of the color mapping table of the color mapper 244 into a discrete number of M allowable phases, establishing a discrete number of phase steps (instantaneous frequency content) that are reflective of a traditional M-ary frequency shift keying (FSK) modulation where each symbol in the FSK constellation may be arbitrarily weighted, (3) non-uniform definition of the color mapping table to uniquely allocate frequency content into specific bins, (4) a time-varying programmable set of phase values that achieve any of the previously described modes or newly developed ones, (5) an externally or internally driven swap between parallel instantiated phase word tables, and/or (6) a rapid spread bandwidth expansion/contraction selection. These scenarios are further described below.
A. CW Signals
The color mapper 244 may be configured to act as a straightforward continuous input (at any chosen center frequency) to the accumulator structure 248, truly acting as a numerically controlled oscillator. This function may be used as a pilot tone, a time-adapted CW pulse (an FSK modulation with variability in symbol durations), and/or as a test tone signal for obtaining detailed characterization of the output chain.
B. Static FSK
By sub-dividing the 2k allowable phase outputs into a discrete set, an M-ary FSK signaling set may be assumed, where each FSK pulse occurs over a single or defined number of chip durations. As such, the CFSK modulator 260 may be configured for traditional FSK signals, yet still be synchronized to the underlying spreading sequence generator.
C. Dynamic FSK
By dividing the 2k allowable phase outputs over a much larger discrete set, and specifically in a non-uniform manner, allowing discrete control of the unfiltered power spectral density of the resulting spectrum, under the assumption of a uniformly distributed input. Filtering of these interleaved FSK “chips” will distort the spectrum in a manner that limits the nulls in unselected bins, but does enable coarse shaping of the signal spectrum in a way to avoid interferers and/or optimally equalize the spread signal in a frequency dispersive propagation environment.
Attention is now directed to
More extreme shaping may also be performed, although in one embodiment the core assumption of “shaping” is that the total power is conserved, so accentuating half a band by 3 dB represents a null in the other half of the band. The traditional correlation process of despreading remains identical, leading to no additional losses. Note that the signal spectrum shown in
D. Programmable Color Maps
By enabling the color mapping to be a time-varying vector of phase words, (1) a CW signal may be converted to a short duration arbitrary phase chirp signal, (2) the static FSK symbol set/center frequencies may be re-defined, and/or (3) the chosen frequency spectra of a dynamic FSK model may be changed to meet observed changes in propagation or interferers. This programmable characteristic may be updated periodically, based on an external pseudorandom process, and/or on a burst-by-burst basis, offering additional waveform entropy. The most common anticipated use for the adaptation is coupling with an RF interference (RFI) measurement/scanning receiver that now permits re-shaping of the signal in addition to changing channels as part of a dynamic spectrum access algorithm.
In one embodiment, the color mapper 244 may be swapped to occur after the accumulator structure 248, enabling better timing/code synchronization between two end points, since the intervals over which the phase words accumulate should be perfectly aligned at the transmitter 102 and receiver 104.
E. Selectable Color Maps
Another bandwidth-preserving mechanism is to employ multiple color mapping tables within the color mapper 244 and to then select between them based on, for example, some portion of the k-bit output of the PRNG 234, an externally provided control signal (periodic or nonperiodic), or an externally provided PRNG source. Selection between these color mapping tables may also be data dependent, allowing integration of CFSK spreading mechanisms with carrier shift keying (CSK) modulations.
In the implementations discussed above, the waveforms retain the constant envelope characteristic, making them power efficient from a transmission perspective, and the arbitrary phase behavior that lends security from an unintended recipient (on par with the quality of the k-bit PRNG). Correlation processing using a coherent replica of the signal inside the receiver 104 remains a robust option on par with traditional correlation techniques applied to sequence-based spread spectrum. In other embodiments amplitude shaping or mapping may also be applied to, for example, increase security.
For example, attention is now directed to
F. Spreading Bandwidth Expansion and Contraction
In one embodiment variable-bandwidth controls may also be applied to the overall spreading sequence. By incorporating a gain term (δ≤1) after the color mapper (or equivalently within the color mapping values), the instantaneous bandwidth of the signal may be constrained to δ% of the overall bandwidth; i.e. each successive incremental phase word will use a non-complete portion of the overall available spectrum when viewed at the chip rate. By making this δ term an externally controlled parameter, the bandwidth may be varied on a symbol-by-symbol basis (total energy per symbol is conserved), enabling yet another free parameter for encoding data into the spread signal.
Another implementation of variable-bandwidth controls using the gain word is to periodically slew the bandwidth of a spread spectrum communications signal, reducing its signature under rate line detection techniques. Choosing a value of δ>1 results in periodic aliasing of the phase increments (rollover within the accumulator), and equivalently an aliasing of the spectrum, yet may also be used.
The resulting waveform produced by applying variable-bandwidth controls to the spreading sequence will remain constant envelope and present similar computational challenges for reception as a CPM signal. Most notably, the phase of the resulting signal accumulates through the duration of a symbol, allowing the option for an accumulator reset (to a known, optionally PN-driven, phase value) between symbols to eliminate most of the CPM-required MLSE processing. With the arbitrary phase nature of the resulting signals, time-domain cross-correlations between signals of different scaled bandwidths will quickly devolve into phase incoherent entities (amplitude scaling will remain coherent if employed) giving solid orthogonality, even though they can start on symbol boundaries at similar values.
With respect to the six CFSK variants identified above, it is noted that the chosen instantaneous frequency components will naturally blur when passed through an interpolation and/or band limiting filter. As such, the programmability of the frequency spectra observed at a symbol level, or any other long-term observation, will be inherently limited in its variation. In other embodiments these transitions could potentially be made tighter by using different types of band limiting filters.
Referring again to
The receiver 104 may be informed of the particular color mapping table utilized by the color mapper 244 by, for example, including this color mapping table information within the preamble of one or more data packets or within a system overhead message. In one embodiment the receiver 104 is configured to store multiple color mapping tables and to select one of these for use during demodulation based upon the color mapping table information received in the chaotic-FSK signal produced by the modulator 260.
The precision of the output of the color mapper 244 is a flexible parameter, preferably chosen with a dynamic range that exceeds resolution provided by k. In cases (a)-(e) of section II, the resolution of the phase word value, and the resulting size of the accumulator structure 248, may be comparable without any loss of performance. The final case (f) of an optional gain term requires consideration of the level of precision desired in the PN/data driven scaling (
To validate the CFSK modulation model, a fixed point model (k=8) was implemented in Simulink using the HDL Coder block set, and subsequently translated into Verilog for prototype hardware deployment on an Altera Cyclone V SX FPGA. Relative to the resources available in the FPGA, the added logic is negligible (one 256-entry block RAM and an 8-bit accumulator). This CFSK mode was then coupled with a burst-mode high-order PSK signaling (HOPS) modem and validated both in Simulink and via the hardware prototype to yield similar communications performance to the traditional sequence-based spread spectrum modulations, yet with the ability to coarsely tune the frequency spectrum.
Attention is now directed to
In another embodiment the receiver subsystem of the transceiver 610 is configured to derive channel state information (CSI) using a signal transmitted by antenna 650 of transmitter 660. This approach detects channel-specific dispersive effects within the RF environment 630 and is inapplicable to noise-based channel estimation. The CSI may then be subsequently used to (a) calculate or (b) select from pre-calculated CFSK color tables.
Alternatively, the transceiver 610 may emit a signal from transmit antenna 664 and then derive CSI based upon the transmitted signal energy received through antenna 640.
Yet another alternative approach is to (a) calculate or (b) select from pre-calculated CFSK color tables based upon a command from an external or master node, which may or may not be aware of relevant channel conditions.
A method and system configured to provide a novel adaptation of an arbitrary phase spread spectrum waveform capable of supporting a variety of frequency selective spread modulations, incorporating optional amplitude shaping, and optionally enabling spreading bandwidth expansion and contraction, has been disclosed herein. Embodiments of each of the disclosed methods is exceedingly hardware efficient, making them practical additions to virtually any sequence-based spread spectrum communication system. Moreover, waveforms produced using the proposed modulation technique retain the constant envelope behavior of continuous phase modulated (CPM) signals, yet the proposed approach results in computationally efficient for receiver processing. That is, a receiver configured to effect CSFK demodulation may utilize despreader correlation processing similar to that used in processing a carrier shift keyed (CSK) or traditional sequence-based spread spectrum signal, as modified in accordance with the teachings herein to accommodate shaping of the frequency domain spectra of the transmitted spread spectrum signal.
In some configurations, the apparatus or system includes means for performing various functions as described herein. In one aspect, the aforementioned means may be a module including a processor or processors and associated memory in which embodiments of the invention reside, such as are shown in the preceding drawings and which are configured to perform the functions recited by the aforementioned means. This may be, for example, modules or apparatus residing in client devices, host server systems, and/or other network devices such as are shown and/or described herein. In another aspect, the aforementioned means may be a module or apparatus configured to perform the functions recited by the aforementioned means.
In one or more exemplary embodiments, the functions, methods and processes described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or encoded as one or more instructions or code on a non-transitory computer-readable medium. Computer-readable media includes computer storage media. Storage media may be any available non-transitory media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer.
As used herein, computer program products comprising computer-readable media including all forms of computer-readable medium except, to the extent that such media is deemed to be non-statutory, transitory propagating signals.
It is understood that the specific order or hierarchy of steps or stages in the processes and methods disclosed are examples of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the processes may be rearranged while remaining within the scope of the present disclosure. The accompanying method claims present elements of the various steps in a sample order, and are not meant to be limited to the specific order or hierarchy presented.
Those of skill in the art would understand that information and signals may be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.
Those of skill would further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.
The steps or stages of a method, process or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a user terminal.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.
The previous description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other aspects without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the aspects shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.
This application claims priority to, and the benefit of, U.S. Provisional Application No. 62/489,041, filed Apr. 24, 2017, entitled CHAOTIC SEQUENCE BASED FREQUENCY SHIFT KEYING, the disclosure of which is incorporated herein by reference in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 62489041 | Apr 2017 | US |
