Single-Input Single-Output (SISO) physical layer key exchange

Abstract

A processor coupled to the first communication device generates a first coded vector and a second coded vector and transmits them to the second communication device via a communication channel, which applies a channel transform to the coded vectors during transmission. A processor coupled to the second communication device receives the transformed signal, constructs a matrix based on the transformed signal, detects its effective channel, and identifies the left singular vector and the right singular vector of the effective channel. A precoding matrix is ​​selected from a codebook of unitary matrices based on the message, and a second coded vector is generated based on a second known vector, the precoding matrix, the complex conjugate of the left singular vector, and the right singular vector. The first codeword of the second coded vector and the second codeword of the second coded vector are sent to the first communication device for identification of the message.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to and is a continuation of U.S. non-provisional patent application No. 16 / 787,290, filed on February 11, 2020, entitled “SINGLE INPUT SINGLE OUTPUT (SISO) PHYSICAL LAYER KEY EXCHANGE,” the entire contents of which are incorporated herein by reference in their entirety for all purposes.

[0003] This application is related to the following applications: U.S. Non-Provisional Patent Application No. 15 / 351,428, filed on November 14, 2016, entitled “RELIABLE ORTHOGONAL SPREADING CODES IN WIRELESS COMMUNICATIONS” (now U.S. Patent No. 10,020,839), filed on July 1, 2019, entitled “SYSTEMS, METHODS AND APPARATUS FOR SECURE AND EFFICIENT WIRELESS COMMUNICATION OF SIGNALS USING AGENERALIZED APPROACH WITHIN UNITARY BRAID DIVISION MULTIPLEXING”, and U.S. Patent Application No. 16 / 459,245, filed on July 1, 2019, entitled “COMMUNICATION SYSTEM AND METHOD USING UNITARY BRAID DIVISIONAL MULTIPLEXING (UBDM) WITH PHYSICAL SER. 16 / 527,240, entitled "LAYERSECURITY," the disclosure of each of which is incorporated herein by reference in its entirety for all purposes.

[0004] Statement of Federal Government Interests

[0005] The U.S. Government holds a nonexclusive, irrevocable, royalty-free license to this invention, with the right to grant licenses for all U.S. Government purposes. Technical Field

[0006] The present disclosure relates to systems and methods for transmitting wireless signals for electronic communications, and in particular to increasing the data rate and reducing the computational complexity of wireless communications. Background Art

[0007] In multiple access communications, multiple user devices transmit signals to a receiver over a given communication channel. These signals are superimposed together to form a combined signal that propagates on that channel. The receiver then performs a separation operation on the combined signal to recover one or more individual signals from the combined signal. For example, each user device may be a cellular phone belonging to a different user, and the receiver may be a cellular tower. By separating the signals transmitted by different user devices, different user devices can share the same communication channel without interference.

[0008] The transmitter can transmit different symbols by changing the state of the carrier or subcarrier, such as by changing the amplitude, phase and / or frequency of the carrier. Each symbol can represent one or more bits. Each of these symbols can be mapped to a discrete value in the complex plane, thereby generating orthogonal amplitude modulation, or by assigning each symbol to a discrete frequency, thereby generating frequency shift keying. The symbols are then sampled at the Nyquist rate, which is at least twice the symbol transmission rate. The resulting signal is converted to analog by a digital-to-analog converter and then up-converted to the carrier frequency for transmission. When different user equipments send symbols simultaneously on the communication channel, the sinusoidal waves represented by those symbols are superimposed together to form a combined signal received at the receiver.

[0009] A known method of wireless signal communication is orthogonal frequency division multiplexing (OFDM), which is a method of encoding digital data on multiple carrier frequencies. OFDM methods have been adapted for signal communication that allows handling of harsh conditions of communication channels, such as attenuation, interference, and frequency selective fading. However, this method does not address the physical layer expectations for security of signal transmission. In addition, OFDM signals include signal amplitudes over a very large dynamic range, often involving transmitters that can handle high peak-to-average power ratios. Therefore, there is a need for improved systems, devices, and methods for secure, power-efficient methods of wireless communication of signals. Summary of the invention

[0010] In some embodiments, a processor coupled to a first communication device generates a first coded vector and a second coded vector and transmits them to a second communication device via a communication channel, which applies a channel transform to the coded vectors during transmission. A processor coupled to the second communication device receives the transformed signal, constructs a matrix based on the transformed signal, detects its effective channel, and identifies the left singular vector and the right singular vector of the effective channel. A precoding matrix is ​​selected from a codebook of unitary matrices based on the message, and a second coded vector is generated based on the complex conjugate of the second known vector, the precoding matrix, the left singular vector, and the right singular vector. The first codeword of the second coded vector and the second codeword of the second coded vector are sent to the first communication device for identification of the message.

[0011] In some embodiments, a communication method using UBDM or OFDM with physical layer security includes receiving, via a first communication device and at a first processor, a first symbol representing a first coded vector and a first signal for channel transformation. The method also includes receiving, via the first communication device and at the first processor, a second symbol representing the first coded vector and a second signal for channel transformation. The first processor detects a representation of an effective channel based on the first signal and the second signal. The first processor performs a singular value decomposition of the representation of the effective channel to identify a left singular vector of the representation of the effective channel and a right singular vector of the representation of the effective channel. The first processor selects a precoding matrix from a codebook of unitary matrices, the precoding matrix being associated with an index of a message for transmission. The first processor generates a second coded vector based on a second known vector, the precoding matrix, a complex conjugate of the left singular vector, and a right singular vector of the representation of the effective channel. The method also includes transmitting to a second communication device via a communication channel (1) a signal representing the first symbol of the second coded vector and (2) a signal representing the second symbol of the second coded vector for identifying the message at a second processor associated with the second communication device. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 is a schematic diagram of a secure and efficient Unitary Braid Divisional Multiplexing (UBDM) system according to some embodiments.

[0013] Figure 2 is a schematic diagram of a signal transmitter within a UBDM system according to some embodiments.

[0014] Figure 3 is a schematic diagram of a signal receiver within a UBDM system according to some embodiments.

[0015] Figure 4 is a schematic diagram of a communication system using UBDM or OFDM with physical layer security (PLS) with a single-input single-output (SISO) implementation in accordance with some embodiments.

[0016] Figure 5 is a flow chart illustrating a first method of performing UBDM or OFDM with PLS implemented with SISO according to some embodiments.

[0017] Figure 6 is a flow chart illustrating a second method of performing UBDM or OFDM with PLS implemented with SISO according to some embodiments.

[0018] Fig. 7A is a flow chart illustrating a method of operating a UBDM system according to an embodiment.

[0019] Figure 7B is a flow chart illustrating a method of operating a UBDM system according to an embodiment.

[0020] Fig. 8A FIG. 1 is a schematic diagram of signal processing at a signal transmitter of an OFDM system.

[0021] Figure 8B is a schematic diagram of signal processing at a signal transmitter of a UBDM system according to an embodiment.

[0022] Figure 8C is a schematic diagram of signal processing at a signal transmitter of a UBDM system according to an embodiment. DETAILED DESCRIPTION

[0023] The present disclosure describes a unitary weave division multiplexing (UBDM) system for modulation-based communication security, also referred to herein as a generalized UBDM (gUBDM) system, followed by a UBDM or OFDM system implementation including physical layer security (PLS) implemented via a single-input single-output (SISO) configuration. The PLS may be referred to as "enhanced MOPRO" and includes a modified version of a key exchange algorithm called MIMO-OFDM precoding with rotation (MOPRO).

[0024] In some embodiments, a communication method using unitary weave division multiplexing (UBDM) with PLS implemented with SISO includes receiving, via a first communication device and at a first processor, a first signal representing a first codeword and a channel transform. The method also includes receiving, via the first communication device and at the first processor, a second codeword representing the first codeword and a second signal representing the channel transform. Based on the first signal and the second signal, a representation of an effective channel is detected via the first processor. The first processor performs a singular value decomposition of the representation of the effective channel to identify a left singular vector of the representation of the effective channel and a right singular vector of the representation of the effective channel. The first processor selects a precoding matrix from a codebook of unitary matrices, the precoding matrix being associated with an index of a message for transmission. The first processor generates a second coded vector based on a second known vector, the precoding matrix, a complex conjugate of the left singular vector of the representation of the effective channel, and the right singular vector of the representation of the effective channel. The method also includes transmitting to a second communication device via a communication channel (1) a signal representing the first codeword of the second coded vector and (2) a signal representing the second codeword of the second coded vector for identification of the message at a second processor associated with the second communication device.

[0025] In some embodiments, a communication method using UBDM or OFDM with PLS implemented with SISO includes generating a first coded vector at a processor of a first communication device using a known vector and a unitary matrix. A first signal representing a first symbol of the first coded vector and a second signal representing a second symbol of the first coded vector are transmitted to a second communication device via a communication channel that applies a channel transform to the first signal and the second signal during transmission. A third signal representing the first symbol of the second coded vector and the channel transform, and a fourth signal representing the second symbol of the second coded vector and the channel transform are received at the processor and from the second communication device. The processor detects a representation of an effective channel based on the third signal and the fourth signal. The processor performs a singular value decomposition of the representation of the effective channel to identify a right singular vector of the representation of the effective channel. The method also includes querying a codebook of unitary matrices to identify messages associated with the third signal and the fourth signal based on the singular vectors and the unitary matrix of the representation of the effective channel.

[0026] In some embodiments described herein, a UBDM system with a SISO-implemented PLS includes a modified orthogonal frequency division multiplexing (OFDM) system. The modified OFDM system may include some components in common with an unmodified OFDM system, but also include a generalized version of the OFDM components (e.g., a subset of OFDM functionality). The UBDM system may be designed to implement modified OFDM steps during operation (e.g., in hardware and / or software executed by or stored in hardware) to perform pairing operations, including performing an inverse fast Fourier transform (iFFT) (or a fast Fourier transform FFT) on a signal at a signal transmitter to generate a transformed signal to be transmitted, and then performing a fast Fourier transform (FFT) (or an inverse Fourier transform iFFT) on the transformed signal at a receiver to recover the signal. The modification includes generalizing the iFFT / FFT performed by the transmitter to an arbitrary transform (represented by an arbitrary matrix, such as an arbitrary unitary matrix).

[0027] Embodiments of UBDM systems with SISO-implemented PLS, as described herein, and including embodiments with the above modifications of OFDM systems, can confer superior security and efficiency in signal transmission over wireless communication channels. Other benefits of embodiments of UBDM as described herein include the ability to use nonlinear transformations, and general implementations involving, as examples, equiangular tight frame (ETF) transformations or nearly equiangular tight frame (NETF) transformations. Standard OFDM does not allow generalization to ETF / NETF "overloads".

[0028] Generalization to arbitrary unitary implemented in a UBDM system as described herein can also have the effect of spreading the energy of each symbol or vector in the signal to be transmitted across different subcarriers. Spreading the energy of each symbol or vector in the signal to be transmitted can reduce the peak-to-average power ratio (PAPR) of the signal and provide a degree of spreading (and therefore interference suppression) comparable to systems such as direct sequence spread spectrum (DSSS) systems. Spreading the energy of each symbol or vector in the signal to be transmitted can also provide additional degrees of freedom in multiplexing. In other words, in addition to standard frequency division multiplexing and time division multiplexing, UBDM systems introduce code division multiplexing, which adds a powerful degree of freedom to multiplexing in signal transmission systems.

[0029] "Physical layer security" (PLS) refers to taking advantage of the physical properties of the communication channel between users of a communication system to exchange secret information. Although some of the foregoing UBDM implementations describe the application of security at the physical layer, strictly speaking, they are not combined with PLS, which involves exploiting the physical properties of a shared channel between two users. For example, in PLS, users generate secret keys for symmetric cryptography / security schemes (e.g., Advanced Encryption Standard (AES)) for secret information based on the physical properties of the communication channel. Unless the eavesdropper has a receiver close enough to one of the users to directly measure (or collect enough information to approximate) the physical properties of the communication channel, the eavesdropper will not be able to access the shared secret. According to the embodiments described below, PLS can be implemented in combination with UBDM (or generalized UBDM), OFDM, or any other communication system to enhance the security of communications.

[0030] As used herein, a "transmitter" (or "signal transmitter") refers to any collection of components used for transmission of a signal, including but not limited to any combination of one or more of the following: antennas, amplifiers, cables, digital-to-analog converters, filters, upconverters, processors (e.g., for reading bits and / or mapping bits to baseband), etc. Similarly, as used herein, a "receiver" (or "signal receiver") refers to any collection of components used for receiving a signal, including but not limited to any combination of one or more of the following: antennas, amplifiers, cables, analog-to-digital converters, filters, downconverters, processors, etc.

[0031] Sending and receiving signals in enhanced MOPRO implemented in SISO

[0032] Figure 11 is a schematic diagram of a secure and efficient unitary weave division multiplexing system 100, also referred to herein as a "UBDM system" or "system", according to an embodiment. UBDM 100 is configured to transmit and / or receive wireless electronic communications in a secure and efficient manner. UBDM system 100 includes a signal transmitter 101 and a signal receiver 103, as well as a communication network 106, such as Figure 1 As shown in . The UBDM system 100 optionally includes a signal transmitter 102 and a signal receiver 104. The UBDM system 100 is configured to process signals from the signal transmitter 101 and / or optionally from the signal transmitter 102, and transmit the signals to the signal receiver 103 and / or optionally to the signal receiver 104 through one or more communication channels defined via a communication network. Given a signal to be transmitted from the signal transmitter 101 and / or 102 to the signal receiver 103 and / or 104, the UBDM system 100 is configured so that the signal transmitter 101 and / or 102 can process the signal by applying an arbitrary transformation to generate a transformed signal to be transmitted to the signal receiver 103 and / or 104. The arbitrary transformation can be applied using one or more of hardware (e.g., a field programmable gate array) and / or software. The signal transmitter 101 and / or 102 also sends an indication of the applied arbitrary transformation to the signal receiver 103 and / or 104 (e.g., before transmitting the signal). Signal receivers 103 and / or 104 are configured to receive the transformed signal and an indication of any transformation applied by (one or more) signal transmitters, and apply the inverse of any transformation to recover the signal from the transformed signal. Although system 100 is shown as including two signal transmitters 101 and 102 and two signal receivers 103 and 104, similar UBDM systems may include any number of signal transmitters and / or signal receivers.

[0033] In some embodiments, the communication network 106 (also referred to as "network") can be any suitable communication network that includes one or more wired and / or wireless communication channels configured to transmit data, operating on public and / or private networks. Although not shown, in some embodiments, the signal transmitters 101, 102 and the signal receivers 103, 104 (or portions thereof) can be configured to operate within, for example, a data center (e.g., a cloud computing environment), a computer system, one or more server / host devices, etc. In some embodiments, the signal transmitters 101, 102 and the signal receivers 103, 104 can operate within various types of network environments that can include one or more devices and / or one or more server devices. For example, the network 106 can be or can include a private network, a virtual private network (VPN), a multi-protocol label switching (MPLS) circuit, the Internet, an intranet, a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), a globally interoperable microwave access network, or a wireless network. In some cases, communication network 106 may be a wireless network, such as, for example, a Wi-Fi or wireless local area network ("WLAN"), a wireless wide area network ("WWAN"), and / or a cellular network.

[0034] The communication network 106 may be or may include a wired network and / or a wireless network implemented using, for example, a gateway device, a bridge, a switch, etc. The wired network or the wireless network may use one or more communication channels, for example, (one or more) radio frequency (RF) communication channels, (one or more) extremely low frequency (ELF) communication channels, (one or more) ultra low frequency (ULF) communication channels, (one or more) low frequency (LF) communication channels, (one or more) intermediate frequency (MF) communication channels, (one or more) ultra high frequency (UHF) communication channels, (one or more) extremely high frequency (EHF) communication channels, (one or more) optical fiber communication channels, (one or more) electronic communication channels, (one or more) satellite communication channels, etc. The network 106 may include one or more network segments and / or may have portions based on various protocols such as the Internet Protocol (IP) and / or proprietary protocols. The communication network 106 may include at least a portion of the Internet. In some cases, the communication network 106 may include multiple networks or subnets operably coupled to each other by, for example, bridges, routers, switches, gateways, etc. (not shown).

[0035] Figure 2 is a schematic block diagram of an example signal transmitter 201 according to an embodiment, which signal transmitter 201 may be a UBDM system (such as the one described above with reference to Figure 1 The signal transmitter 201 may be similar in structure and function to the above-described UBDM system 100. Figure 1 1 and 102 of the system 100 shown and described in the specification. In some embodiments, the signal transmitter 201 may be or may include a processor configured to process instructions stored in a memory. The signal transmitter 201 may be a hardware-based computing device and / or a multimedia device, such as, for example, a server, a desktop computing device, a smart phone, a tablet computer, a wearable device, a laptop computer, etc. The signal transmitter 201 includes a processor 211, a memory 212 (e.g., including a data storage device), and a communication interface 213.

[0036] The processor 211 may be, for example, a hardware-based integrated circuit (IC) or any other suitable processing device configured to run and / or execute an instruction set or code. For example, the processor 211 may be a general-purpose processor, a central processing unit (CPU), an accelerated processing unit (APU), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic array (PLA), a complex programmable logic device (CPLD), a programmable logic controller (PLC), a graphics processing unit (GPU), a neural network processor (NNP), etc. The processor 211 is operably coupled to the memory 212 via a system bus (e.g., an address bus, a data bus, and / or a control bus, not shown).

[0037] The processor 211 may be configured to receive a signal to be transmitted and perform processing to transform the signal into a transformed signal by applying an arbitrary transform. In some embodiments, the processor 211 may apply an arbitrary transform defined as a unitary transform so that the transformed signal can be transmitted in a secure and efficient manner using a UBDM system.

[0038] Processor 211 may include a set of components including converter 214, arbitrary transformation selector 215, and arbitrary transformation applier 216. Processor 211 may receive a set of signals 221 and 222, perform a set of arbitrary transformations 231 and 232, and transmit a set of transformed signals 241 and 242.

[0039] In some embodiments, each of the converter 214, the arbitrary transformation selector 215, and the arbitrary transformation applicator 216 may be software stored in the memory 212 and executed by the processor 211. For example, each of the above-mentioned parts of the processor 211 may be a code that enables the processor 211 to execute the converter 214, the arbitrary transformation selector 215, and the arbitrary transformation applicator 216. The code may be stored in the memory 212 and / or a hardware-based device (such as, for example, an ASIC, an FPGA, a CPLD, a PLA, a PLC, etc.). In other embodiments, each of the converter 214, the arbitrary transformation selector 215, and the arbitrary transformation applicator 216 may be hardware configured to perform a corresponding function. In some embodiments, each component may be a combination of software and hardware. In some embodiments, one or more of the components of the processor 211 (e.g., the converter 214, the arbitrary transformation selector 215, the arbitrary transformation applicator 216) may be configured to operate based on one or more platforms (e.g., one or more similar or different platforms), and the platform may include one or more types of hardware, software, firmware, operating system, runtime library, etc. In some embodiments, the components of the signal transmitter may be configured to operate within a cluster of devices (e.g., a server farm). In such embodiments, the functionality and processing of the components of the signal transmitter 201 may be distributed to several devices in the cluster of devices. The signal transmitter 201 and the signal receiver (such as a server farm) may be configured to operate within a cluster of devices. Figure 3 The components of the signal receiver 301) shown and described in FIG. 3 may be or may include any type of hardware and / or software configured to process attributes.

[0040] Converter 214 may be configured to receive a signal to be transmitted and prepare the signal in a form that can be transformed by processor 211 using any transform. For example, in some embodiments, processor 211 may receive a parallel symbol set b n The converter 214 may be configured to convert the code element set b n Perform a parallel-to-serial computation (e.g., using shift registers) to convert the parallel symbol set b nConvert to a serial symbol set. In some other embodiments, converter 214 may include a configuration that performs serial-to-parallel calculations (e.g., using shift registers) on a serial symbol set to a parallel symbol set. In some embodiments, converter 214 may generate multiple vectors (e.g., representing a set of signals 221 and 221) based on a symbol set. In some implementations, converter 214 may receive a signal in the form of multiple input bits. Converter 214 may be configured to generate multiple symbols based on multiple input bits. Converter 214 may also be configured to generate multiple blocks based on multiple symbols, wherein each block from multiple blocks represents a vector from multiple vectors (e.g., representing a set of signals 221 and 222). Alternatively, converter 214 may also be configured to generate multiple blocks of multiple batches based on multiple symbols, wherein multiple blocks from each batch of multiple blocks of multiple batches represent vectors from multiple vectors (e.g., representing a set of signals 221 and 222).

[0041] The arbitrary transformation selector 215 can be configured to select an arbitrary transformation (e.g., arbitrary transformations 231 and 232) based at least in part on the signal to be transmitted or the plurality of vectors generated by the converter 214 to be applied to the plurality of vectors (e.g., a set representing the signals 221 and 221), so as to safely and efficiently transmit the vectors from the signal transmitter 201 to one or more receivers associated with the UBDM system. The arbitrary transformation (e.g., arbitrary transformations 231 and 232) can include one or any combination of nonlinear transformations, unitary transformations, ETF transformations, or NETF transformations. In some embodiments, the arbitrary transformation selector 215 can access a library of arbitrary transformations designed as unitary transformations (e.g., arbitrary transformations 231 and 232), from which an arbitrary transformation for transmitting a signal can be selected. The arbitrary transformation selector 215 can select an arbitrary transformation based on, for example, a transformation type and / or a criterion negotiated between two communication entities via a telecommunications handshake or otherwise input by a participant in the communication system. The criterion can include, for example, one or more of the following: a desired security level, a delay threshold, an error rate threshold, a minimum data rate, a maximum data rate, etc. It is worth noting that unitary transforms are the largest class of transforms that can be performed on symbol vectors that preserve the total power of the signal. If a non-unitary transform is used, then the inverse transform at the receiver will necessarily amplify the noise in some of the received symbols, whereas a unitary transform does not do this.

[0042] In some cases, the arbitrary transform selector 215 can be configured to select a transform that is not a unit matrix, a discrete Fourier matrix, or any other direct sum of Fourier matrices. For example, in some embodiments, the arbitrary transform selector 215 can have a library of unitary transforms and select a unitary transform U based on a set of guidelines and perform calculations to check whether U is a unit matrix, a discrete Fourier matrix, or any other direct sum of a set of Fourier matrices. If U is one of the above three categories, then in some embodiments, the arbitrary transform selector 215 can discard U and select another transform that can meet the guidelines that are not any of the above three categories. If the arbitrary transform selector 215 selects a transform U that is not a unit matrix, a discrete Fourier matrix, or any other direct sum of Fourier matrices, then it can assign U as an arbitrary transform A for use in an instance of a signal to be transmitted using a UBDM system according to that embodiment.

[0043] In some embodiments, the arbitrary transformation selector 215 may perform the selection based on a set of inputs received by the processor 211. In some embodiments, the arbitrary transformation selector 215 may perform the selection based on a set of parameters associated with the signal, a plurality of vectors, the nature of the signal transmission (e.g., security requirements, sensitivity of information content in the signal, the path of signal transmission, etc.). In some embodiments, the arbitrary transformation selector 215 may be configured to define and generate an arbitrary transformation according to a set of inputs received by the processor 211 (e.g., a set of user inputs received by the processor 211).

[0044] The arbitrary transformation applicator 216 can apply the selected arbitrary transformation to multiple vectors (e.g., vectors 221 and 222) to generate multiple transformed vectors (e.g., transformed vectors 241 and 242). In some embodiments, the multiple transformed vectors may have a total value substantially equal to the total value of the multiple vectors. In some embodiments, for example, the arbitrary transformation applicator 216 can be configured to perform matrix operations to apply the transformation matrix A to a set of vectors to generate transformed vectors. In some embodiments, the arbitrary transformation applicator 216 can be configured to perform any suitable number of processes (e.g., signal processing processes, suitable matrix operations) on the set of vectors before applying the arbitrary transformation. Multiple transformed vectors can then be sent to the signal transmitter antenna 217 and optionally sent to the signal transmitter antenna 218 included in the communicator 213 to be sent to one or more signal receivers associated with the signal receiver. Although shown as including two signal transmitter antennas 217 and 218, as described above, a similar signal transmitter may include and use a single transmitter antenna (e.g., signal transmitter antenna 217) according to some embodiments, which is configured to perform single-input single-output (SISO) operations. According to yet other embodiments, a similar signal transmitter may include any suitable higher number of signal transmitter antennas (i.e., more than two transmitter antennas). In some embodiments, signal transmitter 201 may include multiple antenna arrays configured to perform multiple-input multiple-output (MIMO) operations.

[0045] The memory 212 of the signal transmitter 201 may be, for example, a random access memory (RAM), a memory buffer, a hard drive, a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash drive, a secure digital (SD) memory card, an embedded multi-time programmable (MTP) memory, etc. The memory 212 may store, for example, one or more software modules and / or codes, which may include instructions for causing the processor 211 to perform one or more processes, functions, etc. (e.g., functions associated with the converter 214, the arbitrary transformation selector 215, and / or the arbitrary transformation applicator 216). In some embodiments, the memory 212 may include an expandable storage unit that can be incrementally added and used. In some embodiments, the memory 212 may be a portable memory (e.g., a flash drive, a portable hard disk, etc.) that can be operably coupled to the processor 211. In other cases, the memory may be remotely operably coupled to the signal transmitter 201. For example, a remote database server may be used as a memory and operably coupled to the signal transmitter 201.

[0046] The communication interface 213 may be a hardware device operably coupled to the processor 211 and the memory 212 and / or software stored in the memory 212 and executed by the processor 211. The communication interface 213 may include a signal transmitter antenna 217 and optionally a signal transmitter antenna 218. Figure 2 In addition to the transmitter antenna 217, a second transmitter antenna 218 is shown, but according to some embodiments, a signal transmitter similar to the signal transmitter 201 may have only a single transmitter antenna, or according to some other embodiments, any number of transmitter antennas. The communication interface 213 may be, for example, a network interface card (NIC), a Wi-Fi TM Modules, module and / or any other suitable wired and / or wireless communication device. In addition, the communication interface 213 may include a switch, a router, a hub and / or any other network device. The communicator 213 may be configured to connect the computing device 201 to a communication network (such as the one described above). Figure 1 In some cases, the communication network 213 may be configured to connect to a communication network such as the Internet, an intranet, a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), a World Interoperability for Microwave Access Network (WIMA), or the like via one or more communication channels. Networks based on optical fiber (or fiber optics), networks, virtual networks, and / or any combination thereof.

[0047] In some cases, communication interface 213 may facilitate communication via one or more communication channels over a communication network (eg, Figure 1 The communication interface 213 may be configured to receive and / or transmit a file or a collection of files to the communication network 106 shown and described above. In some cases, the received files may be processed by the processor 211 and / or stored in the memory 212, as described in further detail herein. In some cases, as previously described, the communication interface 213 may be configured to transmit the plurality of transformed vectors to at least one signal receiver antenna associated with at least one signal receiver connected to the communication network via the signal transmitter antenna 217. The communication interface 213 may also be configured to transmit and / or receive data associated with a library of any transformation system.

[0048] Figure 3 is a schematic block diagram of an example signal receiver 301 according to an embodiment, which may be a UBDM system (such as the one described above with reference to Figure 1 The signal receiver 301 may be similar in structure and function to the UBDM system 100 described above. Figure 11 and 10. The signal receiver 101 and signal transmitter 102 of the system 100 shown and described in the specification and the accompanying drawings. In some embodiments, the signal receiver 301 may be or may include a processor 311 configured to process instructions stored in a memory 312. The signal receiver 301 may be a hardware-based computing device and / or a multimedia device, such as, for example, a server, a desktop computing device, a smart phone, a tablet computer, a wearable device, a laptop computer, etc. The signal receiver 301 includes a processor 311, a memory 312, and a communication interface 313.

[0049] The processor 311 may be, for example, a hardware-based integrated circuit (IC) or any other suitable processing device configured to run and / or execute an instruction set or code. For example, the processor 311 may be a hardware-based integrated circuit (IC) or any other suitable processing device configured to run and / or execute a set of instructions or codes. For example, the processor 311 may be a general-purpose processor, a central processing unit (CPU), an accelerated processing unit (APU), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic array (PLA), a complex programmable logic device (CPLD), a programmable logic controller (PLC), a graphics processing unit (GPU), a neural network processor (NNP), etc. The processor 311 is operably coupled to the memory 312 via a system bus (e.g., an address bus, a data bus, and / or a control bus, not shown).

[0050] The processor 311 may be, for example, a hardware-based integrated circuit (IC) or any other suitable processing device configured to run and / or execute an instruction set or code. For example, the processor 311 may be a general-purpose processor, a central processing unit (CPU), an accelerated processing unit (APU), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic array (PLA), a complex programmable logic device (CPLD), a programmable logic controller (PLC), a graphics processing unit (GPU), a neural network processor (NNP), etc. The processor 311 is operably coupled to the memory 312 via a system bus (e.g., an address bus, a data bus, and / or a control bus, not shown).

[0051] The processor 311 may be configured to receive a signal to be transmitted and perform processing to transform the signal into a transformed signal by applying any transformation. The processor 311 may also or alternatively be configured to receive a signal transmitted via a communication network (e.g., Figure 1The processor 311 may be configured to transmit a transformed signal securely through one or more communication channels defined in the network 106 of the present invention, obtain information associated with an arbitrary transform used to generate the transformed signal, and process the transformed signal based on the information to recover the original signal (e.g., by applying the inverse of the arbitrary transform) so that the original signal can be received by the destination in a secure and efficient manner using the gUBDM system. In some embodiments, the processor 311 may apply an arbitrary transform defined as a unitary transform so that the transformed signal can be transmitted in a secure and efficient manner using the UBDM system.

[0052] Processor 311 may include a collection of components, including converter 314, arbitrary transformation identifier 315, and arbitrary transformation inverter 316. Processor 311 may include or access from memory 312 one or more transmitter antennas representing signals from a transmitter that is part of a UBDM system to which signal receiver 301 belongs (e.g., as described in reference Figure 2 The processor 311 may include or access a set of arbitrary transformations 331 and 332 identified in memory 312 based on information associated with the signal received from the signal transmitter, a set of inverse transformations 351 and 352 calculated based on the identified arbitrary transformations, and a plurality of vectors 321 and 322 representing a set of original signals.

[0053] Arbitrary transformation identifier 315 may be configured to receive information associated with a transformed signal (e.g., a transformed signal represented by transformed vectors 341 and 342) received via signal receiver antenna 317 and optionally via signal receiver antenna 318, the information including an indication of the identity of an arbitrary transformation used to generate the transformed signal. Arbitrary transformation identifier 315 is configured to identify an arbitrary transformation that may be used to recover an original signal (the original signal represented by plurality of vectors 321 and 322) from the transformed signal (e.g., transformed signals 341 and 342) based on the information.

[0054] The arbitrary transform invertor 316 generates the inverse of the identified arbitrary transform, also referred to as an inverse transform (e.g., inverse transforms 351 and 352), based on the identity of the arbitrary transform, which is configured to reverse the effect of the identified arbitrary transform to restore the original signal from the transformed signal. For example, in some embodiments, the arbitrary transform invertor 316 generates an inverse transform (A') 351, which is configured to be applied to a plurality of transformed vectors 341 and 342 representing the transformed signal received by the signal receiver 301, so that the inverse transform (A') 351 can reverse the effect of the arbitrary transform (A) 331 and restore a plurality of vectors 321 and 322 representing the original signal. In another example, in some embodiments, the arbitrary transform invertor 316 constructs a matrix and generates an inverse transform (A') based on the matrix, and the inverse transform (A') is configured to be applied to a plurality of transformed vectors 341 and 342 and restore a plurality of vectors 321 and 322.

[0055] Converter 314 may be configured to receive a plurality of vectors (eg, 321 and 322) representing the original signal and regenerate the original signal from the plurality of vectors. For example, in some embodiments, the processor may receive parallel codewords b n The converter 314 may be configured to convert the symbol set b n Perform (e.g., using a phase register) a serial-to-parallel computation to convert the serial symbol set b n Convert to a parallel symbol set that can be similar to the original signal. In one case, converter 314 may include a configuration (e.g., using a shift register) for performing parallel to serial calculations. In certain embodiments, converter 314 may receive a plurality of vectors (e.g., vectors 321 and 322) that recover and generate the original signal comprising a symbol set based on the vector. In certain embodiments, converter 314 may receive a plurality of vectors (e.g., vectors 321 and 322) that recover and generate multiple blocks of multiple batches based on the vectors recovered, and multiple blocks of each batch represent vectors in multiple vectors. Converter 314 may then regenerate multiple input bits based on multiple blocks of multiple batches, from which it may recover the original signal.

[0056] The memory 312 of the signal receiver 301 may be, for example, a random access memory (RAM), a memory buffer, a hard drive, a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash drive, a secure digital (SD) memory card, an embedded multi-time programmable (MTP) memory, etc. The memory 312 may store, for example, one or more software modules and / or codes, which may include instructions for causing the processor 311 to perform one or more processes, functions, etc. (e.g., functions associated with the converter 314, the arbitrary transformation identifier 315, and / or the arbitrary transformation inverter 316). In some embodiments, the memory 212 may include an expandable storage unit that can be added and used incrementally. In some embodiments, the memory 312 may be a portable memory (e.g., a flash drive, a portable hard disk, etc.) operably coupled to the processor 311. In other cases, the memory may be remotely coupled to the signal receiver 301. For example, a remote database server may be used as a memory and operably coupled to the signal receiver 301.

[0057] The communication interface 313 may be a hardware device operably coupled to the processor 311 and the memory 312 and / or software stored in the memory 312 and executed by the processor 311. The communication interface 313 may include a signal receiver antenna 317 and optionally a signal receiver antenna 318. Figure 3 In addition to the receiver antenna 317, a second receiver antenna 318 is shown, but according to some embodiments, a signal receiver similar to the signal receiver 301 may have only a single transmitter antenna, or according to some other embodiments, any number of transmitter antennas. The communication interface 313 may be, for example, a network interface card (NIC), a Wi-Fi TM Modules, module and / or any other suitable wired and / or wireless communication device. In addition, the communication interface 313 may include a switch, a router, a hub and / or any other network device. The communicator 213 may be configured to connect the computing device 301 to a communication network (such as the one described above). Figure 1 In some cases, the communication network 313 may be configured to connect to a communication network, such as the Internet, an intranet, a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), a World Interoperability for Microwave Access Network, or a network via one or more communication channels. Networks based on optical fiber (or fiber optics), networks, virtual networks, and / or any combination thereof.

[0058] In some cases, communication interface 313 may facilitate communication via a communication network (e.g., Figure 1The communication interface 313 may be configured to receive and / or transmit files and / or collections of files through one or more communication channels defined in the communication network 106 in the UBDM system 100 of the present invention. In some cases, the received files may be processed by the processor 311 and / or stored in the memory 312, as described in further detail herein. In some cases, as previously described, the communication interface 313 may be configured so that the signal receiver antenna 317 and optionally the signal receiver antenna 318 include one or more antennas tuned to receive a transformed signal of a specific predetermined center frequency within a predetermined bandwidth to receive a transformed signal safely and efficiently transmitted by one or more signal transmitter antennas associated with one or more signal transmitters connected to the communication network as part of the UBDM system. The communication interface 313 may also be configured to send and / or receive data associated with a library of any transformation system. In some embodiments, the signal receiver 301 may include multiple antenna arrays configured to perform multiple-input multiple-output (MIMO) operations.

[0059] Brief Introduction to Enhanced MOPRO Implemented by SISO

[0060] In an exemplary embodiment of the present disclosure, the first communication device receives an indication that a symbol b is transmitted using 4 subcarriers,

[0061]

[0062] After transmitting symbol b through a communication channel with a channel vector h, the channel vector h transforms symbol b into a transformed symbol. The transformed symbol received at the second communication device is the Hadamard product of symbol b and channel vector h. The second communication device receives the transformed symbol as a 4x1 matrix:

[0063]

[0064] The second communication device converts the transformed symbol (for example, using Figure 3 The converters 314 are shown and described as being arranged in a 2x2 matrix,

[0065]

[0066] The second communication device further performs matrix decomposition to represent the 2x2 matrix as a product of a 2x2 channel transformation matrix and a 2x2 symbol matrix.

[0067]

[0068] By doing so, the second communication device transforms a 4-component vector specifically designed for single-input single-output (SISO) operation into a 2x2 matrix while facilitating efficiency and physical layer security for MOPRO operation or enhanced MOPRO operation.

[0069] Enhanced MOPRO-MIMO

[0070] In one embodiment, MOPRO operation or enhanced MOPRO operation may be performed on a MIMO system. In one example, the MIMO system may be a 2x2 MIMO system used by users "Bob" and "Alice". This example will be performed for a single subcarrier. In a system with multiple subcarriers, the following process may be performed for each subcarrier. Alice initially selects an arbitrary unitary matrix G∈U(2), where U represents a unitary matrix. Alice then multiplies a publicly known / agreed training sequence B of 2 symbols b1 and b2 (in two separate symbols) by G to produce the encoded value for transmission to Bob:

[0071]

[0072] Alice then sends the encoded value to Bob. After passing through channel H, channel H has (where D is the diagonal and positive definite matrix of the channel singular values, B are the singular vectors on Bob's "side" of the channel (left singular values), and A are the singular vectors on Alice's "side" of the channel (right singular values)), Bob will receive:

[0073]

[0074] Bob knows the training values ​​in b (e.g., b1=1, b2=-1, etc.) and multiplies the received r by b. -1 Isolation Matrix In some embodiments, the training values ​​in b correspond to or are based on elements in one or more constellations of signals modulated by one or more digital modulation schemes. Examples of digital modulation schemes include, but are not limited to, binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), eight phase shift keying (8-PSK), and quadrature amplitude modulation (QAM) formats such as 16-QAM, 32-QAM, 64-QAM, etc.

[0075] When Bob performs a singular value decomposition on HG, he obtains Bob then responds to Alice with

[0076]

[0077] where ★ denotes complex conjugate, but without transpose, and F n is one of the elements of the public codebook that is a unitary matrix (Bob may choose this matrix, for example, as a way to encode the shared secret bits). It is desirable that Eve should not be able to determine which matrix F is being transmitted. n .

[0078] After transmitting t′ back to Alice, Alice receives r′, which is a version of t′ that has been distorted by the transpose of the channel (assuming channel reciprocity):

[0079]

[0080] Since Alice knows the (public) training sequence b, she can multiply this matrix by b –1 to remove it, thus isolating the matrix She can then perform a singular value decomposition (SVD) on this matrix to obtain:

[0081]

[0082] Since Alice knows G, she multiplies the right singular vector by G, leaving Then she will Multiplying by the transpose of the left singular vector leaves This left From this Alice can determine which matrix in the codebook this is, and recover the shared secret bits.

[0083] The foregoing is an example of how Enhanced MOPRO works. In conventional MOPRO, Bob does not include in his response to Alice , so Alice does not need to remove it. The MOPRO and enhanced MOPRO systems described in U.S. Patent Application No. 16 / 527,240 (incorporated herein by reference) use MIMO system operations as opposed to SISO systems, for example because if the 2x2 matrix is ​​reduced to a scalar, then SVD will no longer apply and the algorithm shown above will become infeasible. As explained herein, MOPRO and enhanced MOPRO can be performed using SISO systems, using the systems and methods described herein.

[0084] SISO-implemented MOPRO and enhanced MOPRO

[0085] In one embodiment, MOPRO operations or enhanced MOPRO operations may be performed on a single-input single-output (SISO) system. In one example, a SISO system may process a 2x2 matrix and perform MOPRO and / or enhanced MOPRO operations, but any matrix size may be used to implement the process. Alice (e.g., via Figure 2 The signal transmitter 201 shown and described starts from a publicly known training sequence of symbols b1 and b2, constructs an arbitrary unitary matrix G∈U(2), and calculates the product of the unitary matrix and the publicly known training sequence:

[0086]

[0087] All four components of the product of the unitary matrix G and the publicly known training sequence are transmitted to Bob via a communication channel (also referred to herein as a “channel”) (e.g., as described with respect to Figure 3 Thus, Alice splits the four components of Gb into two symbols and (two separate "bauds" are sent one after the other in a sequential manner),

[0088]

[0089] In each of the two symbols, each component is in a frequency interval (also referred to herein as a "subcarrier"). This means that after passing through the channel and applying the set of coefficients to the two symbols, Bob receives:

[0090]

[0091] From these two vectors, Bob constructs the following 2×2 matrix,

[0092]

[0093] Where the product Gb is used to obtain the penultimate equation. There are several other ways Alice and Bob can decompose the components. In some embodiments, Alice can permute the components in any way, and Bob in return can still construct a 2x2 matrix as described above.

[0094] At this point, the problem is almost identical to the MIMO version of MOPRO or enhanced MOPRO. The only difference is that the rank-2 property of this example is designed by splitting the multiple frequency subcarrier values ​​into a 2x2 matrix, rather than relying on multiple antennas to obtain a 2x2 matrix. However, mathematically, they are exactly the same problem. Therefore, Bob right-multiplies the matrix HGb by b -1To calculate HG, we then perform singular value decomposition (SVD) on the matrix HG. If the SVD of H is Then the SVD that Bob will obtain is:

[0095]

[0096] Bob then constructs the matrix t′ as:

[0097]

[0098] The meaning of each matrix is ​​the same as in the enhanced MOPRO example on a MIMO system above.

[0099] Based on the constructed t′ matrix, Bob constructs two symbols (corresponding to two separate bauds, sent one after the other) to transmit on the same frequency subcarrier used by Alice,

[0100]

[0101] because and are transmitted over the same frequency subcarriers, and assuming Bob responds quickly enough that the channel has not changed (or has not changed substantially), the channel will apply the expected set of channel coefficients, and Alice will receive:

[0102]

[0103] According to an embodiment, if Bob responds within 10-20 milliseconds for the local area network (LAN) protocol IEEE 802.11 or within 500 microseconds (e.g., within 250-500 microseconds) for the Long Term Evolution (LTE) 4G mobile telecommunications standard, then the channel can be considered static (i.e., substantially unchanged). A channel can be static for a period of time during which factors affecting or interfering with the channel do not change. Such factors can include, but are not limited to, weather conditions (e.g., humidity, fog, rain, etc.), the presence and characteristics of fixed objects, the presence and characteristics of moving objects, the presence and characteristics of terrain, and the stationarity of the transmitting and / or receiving equipment. When the channel is static, the correction applied to the received signal to remove the effects of that channel from the received signal (i.e., "equalizing" the channel) can remain constant.

[0104] Based on the above vectors, Alice then constructs a 2×2 matrix as:

[0105]

[0106] The matrix calculated in this SISO system operation example The matrix calculated above for the MIMO system operation example is Therefore, Alice follows the same process as for enhanced MOPRO operating in a MIMO system (i.e., remove b, take SVD, isolate F n and recover the shared secret bits). Thus, as described above, Alice and Bob can fully emulate the functionality of the enhanced MOPRO by operating the SISO system.

[0107] Although the examples given above show the implementation of the MOPRO or enhanced MOPRO operation of a 2×2 MIMO system by using a SISO system, there is no limitation on size, and the MOPRO or enhanced MOPRO operation of any n×n MIMO system can be implemented on a SISO system. In some cases, 2×3, 3×2, 3×3, 17×48 or any n×n MIMO system can be implemented. The larger the value of n in the n×n system implemented in SISO, the more subcarriers can be used. In one example, the MOPRO or enhanced MOPRO operation of a 3×3 MIMO system implemented in a SISO system can use a total of 9 subcarriers. In another example, the MOPRO or enhanced MOPRO operation of a 17×48 MIMO system implemented in a SISO system can use a total of 17×48=816 subcarriers.

[0108] In some embodiments, the SISO system set forth above may include additional physical security near Alice, making it difficult for Eve to approach Alice. Alternatively or additionally, the two intended communicating entities may respectively play the roles of Alice and Bob (as described above) at different times. For example, entity 1 may perform the steps outlined above for Alice, while entity 2 may perform the steps outlined above for Bob (resulting in secret bits originating from entity 2 and shared with entity 1). Entity 2 may then perform the steps outlined above for Alice, while entity 1 may perform the steps outlined above for Bob (resulting in secret bits originating from entity 1 and shared with entity 2). The entities may continue in this alternating manner, such that each entity produces approximately half of the total number of shared bits. In this case, if Eve is only near one of the entities, she can only recover half of the secret bits. If both entities produce enough bits, and the secret is (for example) a hash of two sets, then Eve has no hope of recovering the secret.

[0109] Although in the above example Alice and Bob decompose their encoded vectors into two separate 4-component symbols that appear to be adjacent subcarriers; doing so may not always be necessary. First, Alice and Bob can choose to use any 4 subcarriers. Using 4 subcarriers that are not close to each other may be desirable because doing so increases the chance of higher variance between the channel coefficients, thereby increasing the probability of obtaining a full-rank channel matrix with large singular values, which is desirable. For example, Alice and / or Bob can use subcarriers 1, 11, 21, and 31 as subcarriers for MOPRO exchange for a first SISO implementation. Alice and / or Bob can then use 2, 12, 22, and 32 simultaneously as MOPRO exchanges for a second SISO implementation in parallel with the MOPRO of the first SISO implementation. Alice and / or Bob can then use 3, 13, 23, and 33, etc.

[0110] Furthermore, in the above example, Alice and Bob both split their transmissions into two separate 4-component symbols; doing so may not always be necessary. In some cases, the subcarrier spacing may be chosen so that adjacent subcarriers have the same channel coefficients. In that case, all 8 components (e.g., from and ). In addition to the above example, instead of sending two consecutive 4-component transmissions in subcarriers 1, 11, 21, and 31, Alice (and Bob, in response) could place symbols in subcarriers 1, 11, 21, and 31. And the code element Place in 2, 12, 22 and 32.

[0111] When performing MOPRO operation with a SISO system, one difference compared to performing Enhanced MOPRO operation with a SISO system is that the matrix transmitted by Bob will not have Therefore, the term can be simply replaced by the unit term. Therefore, Bob transforms the matrix B ★ F n b is transmitted back to Alice. Alice then receives the matrix:

[0112] A ★ DF n b.

[0113] Alice can remove b, and SVD will immediately give her F n .

[0114] In any OFDM-like or UBDM-like system, the channel acts as a single complex coefficient at each subcarrier value, assuming proper cycling through the cyclic prefix. In other words, a symbol of (b1,b2,b3,b4,…) will become (h1b1,h2b2,h3b3,h4b4,…). i With h i+1 and h i-1 How much the difference is depends on the subcarrier spacing, which can be chosen or modified. In more mathematical terms, the channel will take the transmitted symbol and with the channel vector Perform a "Hadamard" product. The Hadamard product is expressed as and defined as:

[0115]

[0116] In some cases, a method of performing MOPRO and / or enhanced MOPRO using a SISO system includes: We start with some set of (for i in some set of indices) and apply some linear transformation to obtain the vector The collection of (where M i represents a set of linear operators). The method may also include converting the vector The components of A new collection of channels exist The Hadamard action on produces an output that the receiver can rearrange into the form Among them, H i is a matrix whose components depend in some way on the channel vector h.

[0117] Figure 4 is a schematic diagram of a PLS communication system using UBDM or OFDM with SISO-implemented physical layer security according to an embodiment, which is capable of performing the above-mentioned SISO-implemented MOPRO and enhanced MOPRO processes. Figure 4As shown in , the communication system 400 includes a first set 401 of communication devices and a second set 411 of communication devices, which are communicatively coupled to each other via a communication medium 440 (e.g., free space, a multipath wireless environment, etc.). The first set 401 of communication devices is communicatively coupled to a first processor 404, and the second set 411 of communication devices is communicatively coupled to a second processor 414. The first processor 404 is operably coupled to a memory 405 and the second processor 414 is operably coupled to a memory 415. Each of the first processor 404 and the second processor 414 is operably coupled to a storage repository storing a codebook of a unitary matrix 450 that can be publicly accessed. During operation of the PLS communication system 400, the processor 404 generates a first coded vector and a second coded vector and transmits the first coded vector and the second coded vector to the second set 411 of communication devices via a communication channel of the communication medium 440. The communication channel applies a channel transform to the first coded vector and the second coded vector during transmission, thereby generating a first transformed signal and a second transformed signal. The second processor 414 receives the first transformed signal and the second transformed signal, constructs a matrix from the first transformed signal and the second transformed signal, determines its effective channel representation / matrix, and identifies the left singular vector and the right singular vector of the effective channel. The second processor 414 selects a precoding matrix from the codebook of the unitary matrix 450 based on the message, and generates a third coded vector and a fourth coded vector based on the complex conjugate of the second known vector, the precoding matrix and the singular vector. The second processor 414 then sends the second coded vector to the first set 401 of the communication device to identify the message. Then, the first set 401 of the communication device can receive the third coded vector and the fourth coded vector from the second set 411 of the communication device. The processor 404 detects the representation of the effective channel based on the third coded vector and the fourth coded vector, and performs singular value decomposition on the representation of the effective channel to identify the singular vector of the representation of the effective channel. The processor 404 then performs a query on the codebook of the unitary matrix 450 to identify the message associated with the third coded vector and the fourth coded vector.

[0118] The methods and apparatus presented here represent many other possible methods and apparatus that cover other time and / or spectral dimensions besides that MOPRO and / or enhanced MOPRO can be performed using a SISO system. In some embodiments, the methods and apparatus that perform MOPRO and / or enhanced MOPRO using a SISO system can cover both time coherence and frequency / spectral coherence methods.

[0119] Figure 5 is a flow chart illustrating a first method 500 of performing UBDM or OFDM with a SISO-implemented PLS according to some embodiments. The method 500 may be, for example, Figure 4 The system 400 is implemented to perform the MOPRO and enhanced MOPRO processes of the SISO implementation described above. Figure 5 As shown in FIG. 5 , method 500 includes, at 502, communicating via a first communication device (e.g., from Figure 4 The communication device of the first set 401) and the first processor (eg, Figure 4 The method 500 also includes receiving, at 504, via the first communication device and at the first processor, a second symbol representing the first encoded vector and a channel-converted second signal.

[0120] The first processor detects a representation of an effective channel based on the first signal and the second signal at 506, and performs a singular value decomposition of the representation of the effective channel to identify a left singular vector of the representation of the effective channel and a right singular vector of the representation of the effective channel at 508. The first processor selects a precoding matrix from a codebook of unitary matrices (optionally, a publicly accessible codebook) at 510. The precoding matrix is ​​associated with an index of a message for transmission. The first processor generates a second coded vector based on a second known vector, the precoding matrix, a complex conjugate of the left singular vector, and the right singular vector of the representation of the effective channel at 512. The method 500 also includes transmitting the second coded vector to a second communication device (e.g., Figure 4 The method 500 may further include transmitting, to the second communication device 411, (1) a signal representing a first symbol of a second coded vector and (2) a signal representing a second symbol of the second coded vector for identification of the message at a second processor associated with the second communication device. The method 500 may also include transmitting, to the second communication device over the communication channel, a signal representing a plurality of additional coded vectors until the predetermined number of messages have been sent.

[0121] In some embodiments, generating the second coded vector includes multiplying the complex conjugate of the left singular vector by the precoding matrix to generate an intermediate matrix, and multiplying the intermediate matrix by the right singular vector of the representation of the effective channel to generate the second coded vector. Alternatively or additionally, the precoding matrix can be a first precoding matrix, the message can be a first message, and the index can be a first index, and the method 500 also includes selecting a second precoding matrix from a codebook of unitary matrices (the second precoding matrix is ​​associated with a second index of the second message for transmission), and generating a third coded vector based on the third known vector, the second precoding matrix, the complex conjugate of the left singular vector, and the right singular vector of the representation of the effective channel. The signal representing the third coded vector is then transmitted to the second communication device via the communication channel to identify the second message.

[0122] Figure 6600 is a flow chart illustrating a second method of performing UBDM or OFDM with a SISO-implemented PLS according to some embodiments. Figure 4 The system 400 is implemented to perform the MOPRO and enhanced MOPRO processes of the SISO implementation described above. Figure 6 As shown in FIG. 6 , method 600 includes, at 620, at a first communication device (eg, from Figure 4 The method 600 also includes, at 622, sending a first encoded vector to a second communication device (e.g., from a communication device of the first set 401 of communication devices) using the known vector and the unitary matrix. Figure 4 The method 600 further comprises transmitting, to the second communication device at 624, a second signal representing a second symbol of the first encoded vector and the channel transform to the second communication device and to the second communication device through the communication channel. The communication channel also applies a channel transform to the second signal during transmission. The processor receives from the second communication device: (1) a third signal representing the first symbol of the second encoded vector and the channel transform (at 626), and (2) a fourth signal representing the second symbol of the second encoded vector and the channel transform (at 628). The processor detects a representation of an effective channel based on the third signal and the fourth signal at 630, and performs a singular value decomposition of the representation of the effective channel at 632 to identify singular vectors of the representation of the effective channel. The method 600 further comprises querying a codebook of unitary matrices (optionally a publicly accessible codebook) at 634 to identify messages associated with the third signal and the fourth signal based on the singular vectors of the representation of the effective channel and the unitary matrix.

[0123] In some embodiments, the method 600 further comprises receiving, from the second communication device and at the processor via the communication channel, a plurality of additional signals representing a plurality of additional coded vectors from the second communication device until a predetermined number of messages have been received. Alternatively or additionally, the method 600 further comprises detecting, via the processor, a precoding matrix associated with an index of the message, the query of the codebook of unitary matrices being based on the precoding matrix.

[0124] Fig. 7A According to an embodiment, a UBDM system is used to utilize a first communication device (such as Figure 2 The signal transmitter 201 shown and described is a flow chart of a method 700A for transmitting a signal in a safe and efficient manner. Fig. 7AAs shown in , method 700A includes, at step 701A, generating a first coded vector using a first known vector and a unitary matrix via at least one processor operative to a first communication device. Method 700A also includes, at step 702A, transmitting a signal representing a first symbol of the first coded vector to a second communication device by applying a channel transform to the first symbol during transmission to generate a communication channel of the first transformed symbol. Method 700A also includes, at step 703A, transmitting a signal representing a second symbol of the first coded vector to a second communication device by applying a channel transform to the second symbol of the first coded vector during transmission to generate a communication channel of the second transformed symbol.

[0125] In some embodiments, the first communication device receives data representing the original signal to be transmitted in a secure and efficient manner. The data can also represent attributes associated with the signal, such as information related to the nature of the signal, the nature of the input bit, the size, the sensitivity of the information contained, security requirements, etc. In some cases, the signal transmitter can generate multiple code elements, wherein the code element is described as a pulse in a digital complex baseband signal. In some embodiments, the code element can be a waveform or state, and when it is transmitted through a communication channel defined in a communication network, the state or significant condition of the communication channel can be changed / modified and / or maintained, so that the state or condition lasts for a period of time. In some cases, the first communication device can decompose the data into multiple code elements, which can be modified and / or transmitted in parallel using a SISO transmission system and a MIMO transmission system, as further described below. In some cases, the signal transmitter can use a converter (e.g., converter 214) to convert parallel data into serial data. In some other cases, the signal transmitter can use a converter to convert serial data into parallel data. In some embodiments, generating multiple code elements based on data can be via using bit-to-code element mapping.

[0126] In some embodiments, the first communication device generates a plurality of symbols associated with the serial signal and decomposes the plurality of symbols into a plurality of batches of blocks, each batch of blocks representing a vector of a plurality of vectors, which are configured to be serially encoded and / or transmitted using a SISO transmission system as described herein. In some cases, the signal transmitter may use a converter (e.g., Figure 2 The converter 214) converts multiple parallel code elements into multiple serial blocks.

[0127] In some embodiments, the first communication device selects an arbitrary transform configured to be applied to the vector to generate a plurality of encoded vectors based at least in part on the plurality of vectors. For example, the signal transmitter may access a library of known arbitrary transforms including unitary transforms, equiangular tight frame (ETF) transforms, and near-equiangular tight frame (NETF) transforms. The signal transmitter may use an arbitrary transform selector (e.g., regarding Figure 2 The arbitrary transformation selector 215 shown and described above is used to select an arbitrary transformation to be applied to multiple vectors, such as a unitary transformation, to generate multiple encoded vectors. In some cases, the arbitrary transformation can select an equiangular tight frame (ETF) transformation, or in some other cases, the arbitrary transformation selector can select a nearly equiangular tight frame (NETF) transformation. In some embodiments, the arbitrary transformation selector can be configured to make the selected arbitrary transformation based on a matrix that is not a unit matrix or a discrete Fourier matrix. In some embodiments, the arbitrary transformation selector can be configured to make the selected arbitrary transformation based on a matrix that is not a direct sum of discrete Fourier matrices. The first communication device applies an arbitrary transformation to each vector in the multiple vectors to generate multiple encoded vectors. In some cases, applying an arbitrary transformation can make the multiple encoded vectors have a total value substantially equal to the total value of the multiple vectors.

[0128] In some embodiments, the first communications device transmits a communication channel to a second communications device (such as a communication channel associated with a first symbol) by applying a channel transformation to the first symbol during transmission to produce a first transformed symbol. Figure 3 The signal receiver 301 shown and described above transmits (e.g., at 702A) a signal representing a first symbol of a first coded vector of a plurality of coded vectors. In some cases, the first communication device transmits the signal representing the first symbol of the first coded vector to at least one transmitter antenna for transmitting the signal representing the first coded vector from the at least one antenna to a second communication device. In some cases, the plurality of coded vectors may be configured to be transmitted via at least one transmitter antenna associated with the first communication device (e.g., associated with the first communication device). Figure 2 The signal transmitter antenna 217 associated with the signal transmitter 201 shown and described is serially transmitted through at least one communication channel so that the serially transmitted first encoded vector can be received by at least one receiver associated with the UBDM system being used. For example, the at least one receiver may include at least one antenna, and the at least one receiver is associated with the second communication device (e.g., the signal receiver 301), and the at least one transmitter antenna may be associated with the first communication device (e.g., the signal transmitter 201), wherein the first communication device and the second communication device are configured to perform single-input single-output (MIMO) operations.

[0129] In some embodiments, the first communications device transmits a communication channel to the second communications device (e.g., with respect to a second symbol) by applying a channel transformation to the second symbol during transmission to produce a second transformed symbol. Figure 3 The signal receiver 301 shown and described above transmits (e.g., at 703A) a signal representing a second symbol of the first coded vector. In some cases, the first communication device transmits the signal representing the second symbol of the first coded vector to at least one transmitter antenna for transmitting the signal representing the first coded vector from the at least one antenna to the second communication device. In some cases, the plurality of coded vectors may be configured to be transmitted via at least one transmitter antenna associated with the first communication device (e.g., associated with the first communication device). Figure 2 The signal transmitter antenna 217 associated with the signal transmitter 201 shown and described is serially transmitted through at least one communication channel so that the serially transmitted first encoded vector can be received by at least one receiver associated with the UBDM system being used. For example, the at least one receiver may include at least one antenna, and the at least one receiver is associated with the second communication device (e.g., the signal receiver 301), and the at least one transmitter antenna may be associated with the first communication device (e.g., the signal transmitter 201), wherein the first communication device and the second communication device are configured to perform SISO operations.

[0130] In some embodiments, the signal includes a set of transformed symbols associated with the first coded vector, and the first communication device (e.g., signal transmitter 201) can place the set of transformed symbols on (one or more) communication channels (e.g., via signal transmitter antenna 217) at a fixed and known symbol rate. The second communication device (e.g., signal receiver 301) can perform the task of detecting the sequence of transformed symbols to reconstruct the first coded vector.

[0131] In some embodiments, the first communication device may be configured to transmit a signal representing the first encoded vector to a plurality of transmitters via a physical layer associated with an open system interconnection model (OSI). The OSI model is a conceptual model that characterizes and standardizes the communication functions of a telecommunication or computing system, regardless of its underlying internal structure and technology, with the goal of achieving interoperability of different communication systems using standard communication protocols. The OSI model uses information exchanged via a communication channel of a communication network to be partitioned into abstract layers (e.g., seven layers), each layer including a specific type of information.

[0132] For example, a layer may include a signal transmitter and a physical transmission medium (e.g., such as Figure 1The physical layer for transmitting and receiving unstructured raw data between wireless communication channels in a communication network such as the communication network 106 shown and described. It is configured to convert the data included in the transmitted signal into electrical, radio or optical signals. Layer specifications define characteristics such as voltage levels, timing of voltage changes, physical data rates, maximum transmission distances, modulation schemes, channel access methods, and physical connectors. This includes the layout of pins for wireless devices, voltages, line impedances, cable specifications, signal timing, and frequencies. Bit rate control is done at the physical layer and transmission modes can be defined as simplex, half-duplex, and full-duplex. The components of the physical layer can be described by network topology. The communication channel used to transmit signals can have specifications for the physical layer.

[0133] In some cases, the first arbitrary transform is used to generate a first coded vector and the second arbitrary transform is used to generate a second coded vector. Providing a signal representing the first arbitrary transform and / or the second arbitrary transform may include providing a first signal representing the first arbitrary transform and providing a second signal representing the second arbitrary transform. In some embodiments, transmitting the first transformed signal and providing the first signal representing the first arbitrary transform may be to a first receiver associated with a first receiver, and transmitting the second transformed signal generated using the second arbitrary transform and providing the second signal representing the second arbitrary transform may be to a second receiver antenna associated with a second receiver different from the first receiver. In some cases, the first and second signals representing the first arbitrary transform and the second arbitrary transform may be broadcast together to a wide audience including first and second signal receivers. In some cases, the first signal representing the arbitrary transform may be widely broadcast but the second signal representing the arbitrary transform may not be widely broadcast, so that the first signal receiver is able to recover the first coded vector but the second receiver cannot recover the second coded vector until the second signal representing the second arbitrary transform is provided or broadcast.

[0134] In order to generate the largest set of mutually orthogonal spreading codes, a unitary matrix A∈U(N) is chosen. If the nth column (or row, as long as there is consistency) of A is expressed as Then the N codes are n∈[1,...,N]. If a device wants to transmit data on all N codes, then it will be able to obtain N code symbols b n , multiplying each symbol by each component of its spreading code and then adding the resulting vectors together. The transmitted vector yes:

[0135]

[0136] where b n It's a code element.

[0137] The transmitter sends symbol b n ∈C (which is usually a complex number (floating point, double precision, etc.)) and This is true for all N codewords b n Repeat. Therefore, there are N symbols, each of which multiplies the N components of the code. This makes the complexity O(N 2 ), which is prohibitive for wideband applications and is large compared to the complexity of OFDM which has a complexity of O(N log N).

[0138] It is worth noting that for multiple access applications where each user is assigned a subset of codes, the multiple access application only needs to do O(N) work, which is better than OFDM. This makes DSSS implementation a suitable option for multiple access applications.

[0139] The complexity of UBDM is obtained to be approximately O(N log N) to match the OFDM reinterpretation. The baud rate of the transmission is

[0140]

[0141] This can be interpreted (up to normalization) as the discrete Fourier transform of the symbol:

[0142]

[0143] Figure 7B The diagram describes the Fig. 7A 700A is a flow chart of a method 700B that continues the method 700A of the present invention, which uses a UBDM system to receive a first set of signals in a secure and efficient manner, retrieve information from the first set of signals, and use a second communication device (such as a second communication device) to receive a first set of signals in a secure and efficient manner. Figure 3 The method 700B may be implemented by a processor associated with a second communication device (eg, the signal receiver 301). Figure 7BAs shown in , method 700B includes, at step 701B, receiving a first transformed signal including a first transformed codeword at a second communication device. Method 700B also includes, at step 702B, receiving a second transformed signal including a second transformed codeword. Method 700B also includes, at step 703B, constructing a matrix based on the first transformed signal and the second transformed signal. Method 700B also includes, at step 704B, detecting a representation of an effective channel based on the matrix, the effective channel being associated with a communication channel. Method 700B also includes, at step 705B, performing a singular value decomposition of the representation of the effective channel to identify singular vectors of the representation of the effective channel. Method 700B also includes, at step 706B, selecting a precoding matrix from a codebook of unitary matrices based on a message for transmission, the precoding matrix being associated with an index of a message for transmission. Method 700B also includes, at step 707B, generating a second coded vector based on a second known vector, a precoding matrix, and a complex conjugate of a singular vector. The method 700B also includes, at step 708B, transmitting (1) a signal representing the first symbol of the second encoded vector and (2) a signal representing the second symbol of the second encoded vector to the first communication device via a communication channel for identification of the message. The method 700B is explained in more detail below.

[0144] In some embodiments, the second communication device receives (e.g., at 701B) a first transformed signal including a first transformed symbol. The second communication device may include at least one receiver antenna (e.g., Figure 3 In some cases, the second communication device receives a first transformed signal representing a first symbol of a first coded vector from at least one receiver antenna for receiving a signal representing the first coded vector from at least one antenna from the first communication device. In some cases, the plurality of coded vectors may be configured to be transmitted via at least one receiver antenna associated with the second communication device (e.g., associated with the first communication device). Figure 3 The signal receiver antenna 317 associated with the signal receiver 301 shown and described is received in series through at least one communication channel. For example, at least one receiver may include at least one antenna, and at least one receiver may be associated with a second communication device (e.g., the signal receiver 301), and at least one transmitter antenna may be associated with a first communication device (e.g., the signal transmitter 201), wherein the first communication device and the second communication device are configured to perform SISO operations.

[0145] In some embodiments, the second communication device receives (e.g., at 702B) a second transformed signal including a second transformed symbol. In some cases, the second communication device receives a second transformed signal representing a second symbol of a first encoded vector from at least one receiver antenna for receiving a signal representing a first encoded vector from at least one antenna from the first communication device. In some cases, a plurality of encoded vectors may be configured to be received serially via at least one receiver antenna associated with the second communication device and through at least one communication channel. For example, at least one receiver may include at least one antenna, and at least one receiver may be associated with a second communication device (e.g., signal receiver 301), and at least one transmitter antenna may be associated with a first communication device (e.g., signal transmitter 201), wherein the first communication device and the second communication device are configured to perform SISO operations.

[0146] In some embodiments, the second communication device constructs (e.g., at 703B) a matrix based on the first transformed symbol of the first transformed signal and the second transformed symbol of the second transformed signal. In some cases, the second communication device constructs the matrix by arranging the elements of the first transformed symbol and the second transformed symbol to a matrix having at least two rows and two columns. The second communication device decomposes the matrix into at least a symbol matrix and a communication channel matrix. At 404B, the second communication device detects a representation of the effective channel based on the matrix and the effective channel associated with the communication channel.

[0147] In some embodiments, the second communications device performs a singular value decomposition of the representation of the effective channel (e.g., at 705B) to identify singular vectors of the representation of the effective channel. In one example, the singular value decomposition can be a factorization of a real or complex matrix, such as, for example, a factorization of the representation of the effective channel. At 706B, the second communications device selects a precoding matrix from a codebook of unitary matrices based on the message for transmission, the precoding matrix being associated with an index of the message for transmission. The precoding matrix can be selected from a codebook of unitary matrices that may or may not be publicly available.

[0148] In some embodiments, the second communication device generates a second coded vector based on the second known vector, the precoding matrix, and the complex conjugate of the singular vector (e.g., at 707B). At 708B, the second communication device transmits (1) a signal representing a first symbol of the second coded vector and (2) a signal representing a second symbol of the second coded vector to the first communication device via a communication channel for message identification. The communication channel may have a channel vector h that transforms the coded vector into a transformed symbol of the second coded vector.

[0149] In some embodiments, a UBDM system (e.g., UBDM system 100) may be partially similar in structure and / or function to an orthogonal frequency division multiplexing (OFDM) system in some aspects. For example, an example pipeline of OFDM system 800A may include: Fig. 8A The set of operations presented in , where the vector b can be a code element set b n .

[0150] Compared to the OFDM system 800A described above, the operations performed by the UBDM system 800B described herein (e.g., the UBDM system 100) are Figure 8B As shown in Figure 8B As shown in FIG. 8 , UBDM 800B may include an additional operator (e.g., linear operator) “A” between S / P block 802B and iFFT block. In use, according to Figure 8B In an associated example embodiment, UBDM 800B operates so that symbol b n The signal is received by the signal transmitter and first passes through a serial to parallel block (e.g., a converter similar to converter 214 of signal transmitter 201) to generate a set of transformed vectors. The set of transformed vectors then undergoes a linear transformation A to generate a set of transformed vectors. For example, the transformation can be performed by an arbitrary transformation applicator 803B similar to arbitrary transformation applicator 216, and the linear transformation A is selected by an arbitrary transformation selector similar to arbitrary transformation selector 215. In some embodiments, the transformed vector is then passed through an iFFT block to generate a second transformed vector, and the resulting second transformed vector can be transmitted to one or more receivers in the UBDM system.

[0151] In some other embodiments, the iFFT block may be skipped and the transformed vector generated by the arbitrary transform applicator may be transmitted to one or more receivers in the UBDM system. Expressed in another way,

[0152]

[0153] (in is a discrete Fourier matrix). In some embodiments, as described herein, A can be unitary by design, and it is known that is unitary. Due to the property of unitary matrices as groups, the product will also be unitary. Therefore, since A can be arbitrarily unitary, it is not necessary to include an iFFT matrix, and according to some embodiments, a UBDM system can be configured by replacing the iFFT block with an arbitrary unitary A, such as Figure 8C As shown in Figure 8COperations in a UBDM system 800C including an arbitrary transformation applicator 803C are shown according to an embodiment.

[0154] According to the above description, it can be used with OFDM systems (for example, Fig. 8A A signal transmitter and a signal receiver that operate with the OFDM system 800A) described herein can be easily adapted for use with the UBDM system described herein, where the iFFT operation is replaced at the transmitter with an arbitrary transform operation using A, and an FFT with a linear operation A′ is used at the signal receiver to invert the transform. Other details of the OFDM system can be retained.

[0155] Some embodiments described herein relate to methods. It should be understood that such methods can be computer-implemented methods (e.g., instructions stored in a memory and executed on a processor). In the case where the above method indicates that certain events occur in a certain order, the ordering of certain events can be modified. In addition, certain events can be repeatedly and concurrently executed in parallel processes where possible, as well as sequentially executed as described above. In addition, some embodiments can omit one or more of the described events.

[0156] All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and / or ordinary meanings of the defined terms.

[0157] Examples of computer code include, but are not limited to, microcode or microinstructions, machine instructions (such as those generated by a compiler), code for generating web services, and files containing higher-level instructions executed by a computer using an interpreter. For example, embodiments may be implemented using Python, Java, JavaScript, C++, and / or other programming languages ​​and development tools. Additional examples of computer code include, but are not limited to, control signals, encrypted code, and compressed code.

[0158] The drawings are primarily for illustrative purposes and are not intended to limit the scope of the subject matter described herein. The drawings are not necessarily drawn to scale; in some cases, various aspects of the subject matter disclosed herein may be exaggerated or enlarged in the drawings to facilitate understanding of different features. In the drawings, like reference numerals generally refer to like features (e.g., functionally similar and / or structurally similar elements).

[0159] The actions performed as part of the disclosed (one or more) methods may be ordered in any suitable manner. Thus, embodiments may be constructed that perform processes or steps in an order different from that shown (which may include performing some steps or processes simultaneously), even if shown as sequential actions in illustrative embodiments. In other words, it should be understood that such features may not necessarily be limited to a specific order of execution, but may be executed in a manner consistent with the present disclosure in a serial, asynchronous, concurrent, parallel, simultaneous, synchronous, etc., with any number of threads, processes, services, servers, etc., etc. As such, some of these features may be contradictory because they cannot exist simultaneously in a single embodiment. Similarly, some features apply to one aspect of the innovation but not to other aspects.

[0160] Where a range of values ​​is provided, it is understood that each intervening value, to the tenth of the unit of the lower limit, between the upper and lower limits of that range, and any other stated or intermediate value in that stated range are encompassed within the disclosure unless the context clearly dictates otherwise. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges, which are also encompassed within the disclosure, subject to any explicitly excluded limits in the stated ranges. Where the stated range includes one or two limits, ranges excluding one or both of those included limits are also encompassed within the disclosure.

[0161] As used herein in the specification and the examples, the phrase "and / or" should be understood to refer to "either or both" of the elements so combined, i.e., elements present in combination in some cases and elements present separately in other cases. Multiple elements listed with "and / or" should be understood in the same manner, i.e., "one or more" of the elements so connected. In addition to the elements specifically identified by the "and / or" clause, other elements may optionally be present, whether related or unrelated to those specifically identified elements. Thus, as a non-limiting example, when used in conjunction with open language such as "comprising", a reference to "A and / or B" may refer to only A (optionally including elements other than B) in one embodiment; to only B (optionally including elements other than A) in another embodiment; to both A and B (optionally including other elements) in yet another embodiment; and so on.

[0162] As used herein in the specification and the embodiments, "or" should be understood to have the same meaning as "and / or" as defined above. For example, when the items in the list are separated, "or" or "and / or" should be interpreted as inclusive, that is, including at least one of multiple elements or element lists, but also including more than one, and (optionally) additional unlisted items. Only the terms that are clearly indicated in the opposite direction, such as "only one" or "just one", or when used in the embodiments, "consisting of..." will refer to only including one element in multiple elements or element lists. In general, the term "or" as used herein should be interpreted as indicating exclusive substitution (that is, "one or the other, but not both") only when the signature has an exclusive term (such as "any one", "one of them", "only one of them" or "just one of them"). When used in the embodiments, "consisting essentially of..." should have the common meaning used in the field of patent law.

[0163] As used in the specification and embodiments herein, the phrase "at least one" refers to a list of one or more elements and should be understood to refer to at least one element selected from one or more elements in the list of elements, but does not necessarily include at least one of each element specifically listed in the list of elements, and does not exclude any combination of elements in the list of elements. This definition also allows that elements other than the elements specifically identified in the list of elements to which the phrase "at least one" refers may optionally be present, whether related to or unrelated to those specifically identified elements. 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") may refer to at least one, optionally including more than one A, without B (and optionally including elements other than B) in one embodiment; may refer to at least one, optionally including more than one B, without A (and optionally including elements other than A) in another embodiment; may refer to at least one, optionally including more than one B, without A (and optionally including elements other than A) in yet another embodiment; may refer 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); and so on.

[0164] In the examples and the above description, all transitional phrases, such as "includes," "comprising," "carrying," "having," "containing," "involving," "maintaining," "consisting of," etc., should be understood as open-ended, i.e., meaning including but not limited to. As described in Section 2111.03 of the U.S. Patent Office Manual of Patent Examining Procedures, only the transitional phrases "consisting of" and "consisting essentially of" should be closed or semi-closed transitional phrases, respectively.

Claims

1. A system for single-input single-output SISO, comprising: a first communication device comprising a first antenna; a second communication device including a second antenna; At least one processor operably coupled to a first communication device, the at least one processor for the first communication device being configured to: generating a first coded vector based on an arbitrary unitary matrix and a known training sequence, transmitting a signal representing the first symbol of the first coded vector to a second communication device via a first antenna at a first time by applying a channel transform to a first symbol of the first coded vector during transmission to generate a communication channel of a first transformed symbol, and transmitting a signal representing a second symbol of the first coded vector to a second communication device via the first antenna at a second time by applying a channel transform to the second symbol of the first coded vector during transmission to produce a communication channel for a second transformed symbol; as well as at least one processor operably coupled to a second communication device, the at least one processor for the second communication device being configured to: receiving via a second antenna a first transformed signal including first transformed symbols, receiving via a second antenna a second transformed signal including second transformed symbols, constructing a matrix based on the first transformed signal and the second transformed signal, detecting a representation of an effective channel based on the matrix, the effective channel being associated with the communication channel, performing a singular value decomposition of the representation of the effective channel to identify singular vectors of the representation of the effective channel, selecting a precoding matrix based on a message for transmission, the precoding matrix being associated with an index of the message for transmission, generating a second coded vector based on the precoding matrix and the singular vectors, and (1) a signal representing a first symbol of the second encoded vector and (2) a signal representing a second symbol of the second encoded vector are transmitted to the first communication device via the second antenna over the communication channel for identification of the message.

2. The system of claim 1 , wherein the at least one processor operably coupled to the second communication device is configured to generate the second encoded vector by: multiplying the complex conjugate of the singular vector by the precoding matrix to produce an intermediate matrix; and The intermediate matrix is ​​multiplied by the training values ​​to produce a second encoded vector.

3. The system of claim 1, wherein the at least one processor for the second communication device is configured to select the precoding matrix from a codebook of unitary matrices.

4. The system of claim 1, wherein the precoding matrix is ​​a first precoding matrix, the message is a first message, and the index is a first index, the at least one processor operably coupled to the second communication device is further configured to: selecting a second precoding matrix, the second precoding matrix being associated with a second index of a second message for transmission, Producing a third encoded vector, and (1) a signal representing a first symbol of the third encoded vector and (2) a signal representing a second symbol of the third encoded vector are transmitted to the first communication device via the communication channel for identification of the second message.

5. The system of claim 1, wherein the at least one processor operably coupled to the second communication device is further configured to transmit a signal representing a plurality of additional encoded vectors to the first communication device over the communication channel until a predetermined number of messages have been sent.

6. A system for single-input single-output (SISO), comprising: a first communication device comprising a first antenna; a second communication device including a second antenna; At least one processor operably coupled to a first communication device, the at least one processor for the first communication device being configured to: generating a first coded vector based on an arbitrary unitary matrix and a known training sequence, transmitting a signal representing a first symbol of the first coded vector to a second communication device via a first antenna at a first time over a communication channel, the communication channel applying a channel transform to the first symbol during transmission, and transmitting a signal representing a second symbol of the first coded vector to a second communication device at a second time via a communication channel via a first antenna, the communication channel applying a channel transform to the second symbol during transmission; as well as at least one processor operably coupled to a second communication device, the at least one processor for the second communication device being configured to: receiving a first transformed signal via a second antenna, the first transformed signal comprising a version of the first symbol that has been transformed by channel transformation, receiving a second transformed signal via a second antenna, the second transformed signal comprising a version of the second symbol that has been transformed by channel transformation, constructing a matrix based on the first transformed signal and the second transformed signal, detecting a representation of an effective channel based on the matrix, the effective channel being associated with the communication channel, performing a singular value decomposition of the representation of the effective channel to identify left singular vectors of the representation of the effective channel and right singular vectors of the representation of the effective channel, selecting a precoding matrix based on a message for transmission, the precoding matrix being associated with an index of the message for transmission, generating a second coded vector based on the complex conjugate of the left singular vector of the representation of the effective channel and the right singular vector of the representation of the effective channel, and (1) a signal representing a first symbol of the second encoded vector and (2) a signal representing a second symbol of the second encoded vector are transmitted to the first communication device via the second antenna over the communication channel for identification of the message.

7. The system of claim 6, wherein the at least one processor operably coupled to the second communication device is configured to generate the second encoded vector by: multiplying the complex conjugate of the left singular vector by the precoding matrix to produce an intermediate matrix; and The intermediate matrix is ​​multiplied by the right singular vector of the representation of the effective channel to produce a second encoded vector.

8. The system of claim 6, wherein the at least one processor for the second communication device is configured to select the precoding matrix from a codebook of unitary matrices.

9. The system of claim 6, wherein the precoding matrix is ​​a first precoding matrix, the message is a first message, and the index is a first index, the at least one processor operably coupled to the second communication device is further configured to: selecting a second precoding matrix, the second precoding matrix being associated with a second index of a second message for transmission, Producing a third encoded vector, and (1) a signal representing a first symbol of the third encoded vector and (2) a signal representing a second symbol of the third encoded vector are transmitted to the first communication device via the communication channel for identification of the second message.

10. The system of claim 6, wherein the at least one processor operably coupled to the second communication device is further configured to transmit a signal representing a plurality of additional encoded vectors to the first communication device over the communication channel until a predetermined number of messages have been sent.

11. The system of claim 6, wherein: The at least one processor operably coupled to the first communication device is further configured to: receiving a third transformed signal, the third transformed signal comprising a version of the first symbol of the second encoded vector that has been transformed by a channel transform; and receiving a fourth transformed signal, the fourth transformed signal comprising a version of the second symbol of the second encoded vector that has been transformed by the channel transform, The identifying of the message includes removing a representation of a right singular vector of a representation of an effective channel from each of the third transformed signal and the fourth transformed signal.

12. A method for single-input single-output (SISO), comprising: receiving, at a first processor via a first communication device, a first symbol representing a first coded vector and a channel transformed first signal at a first time, wherein the first coded vector is generated based on an arbitrary unitary matrix and a known training sequence; receiving, at the first processor via the first communication device, a second symbol representing the first encoded vector and a channel transformed second signal at a second time; detecting, via the first processor, an indication of a valid channel based on the first signal and the second signal; performing, via the first processor, a singular value decomposition of the representation of the effective channel to identify left singular vectors of the representation of the effective channel and right singular vectors of the representation of the effective channel; selecting, via the first processor, a precoding matrix associated with an index of a message for transmission; generating, via the first processor, a second encoded vector based on a complex conjugate of a left singular vector of a representation of an effective channel and a right singular vector of a representation of an effective channel; as well as (1) a signal representing a first symbol of a second encoded vector and (2) a signal representing a second symbol of the second encoded vector are transmitted to a second communication device via a communication channel for recognition of the message at a second processor associated with the second communication device.

13. The method of claim 12, wherein generating a second encoded vector comprises: multiplying the complex conjugate of the left singular vector by the precoding matrix to produce an intermediate matrix; as well as The intermediate matrix is ​​multiplied by the right singular vector of the representation of the effective channel to produce a second encoded vector.

14. The method of claim 12, wherein the precoding matrix is ​​selected from a codebook of unitary matrices.

15. The method of claim 12, wherein the precoding matrix is ​​a first precoding matrix, the message is a first message, and the index is a first index, the method further comprising: selecting a second precoding matrix, the second precoding matrix being associated with a second index of a second message for transmission, Producing a third encoded vector, and A signal representing the third encoded vector is transmitted to the second communication device via the communication channel for identification of the second message.

16. The method of claim 12, further comprising: A signal representing a plurality of additional encoded vectors is transmitted to the second communication device over the communication channel until a predetermined number of messages have been sent.

17. A method for single-input single-output (SISO), comprising: At a processor of the first communication device, generating a first encoded vector based on an arbitrary unitary matrix and a known training sequence; transmitting a first signal representing a first symbol of a first coded vector to a second communication device at a first time via a single antenna of the first communication device over a communication channel, the communication channel applying a channel transform to the first signal during transmission; transmitting a second signal representing a second symbol of the first encoded vector to a second communication device at a second time via the single antenna over a communication channel, the communication channel applying a channel transform to the second signal during transmission; receiving, at the processor, from a second communication device via the single antenna, a first symbol representing a second encoded vector and a channel transformed third signal; receiving, at the processor, from a second communication device via the single antenna, a second symbol representing a second encoded vector and a channel transformed fourth signal; detecting, via the processor, an indication of a valid channel based on the third signal and the fourth signal; performing, via the processor, a singular value decomposition of the representation of the effective channel to identify singular vectors of the representation of the effective channel; and Messages associated with the third signal and the fourth signal are identified based on singular vectors representing the effective channel.

18. The method of claim 17, wherein the message is identified based on a codebook of a unitary matrix.

19. The method of claim 17, further comprising: A plurality of additional signals representing a plurality of additional encoded vectors from the second communication device are received at the processor from the second communication device via the communication channel until a predetermined number of messages have been received.

20. The method of claim 17, further comprising: detecting, via the processor, a precoding matrix associated with an index of the message, Identifying the message is based on the precoding matrix.

21. A non-transitory processor-readable medium storing instructions that, when executed by a processor, cause the processor to perform the following operations: receiving, via a communication channel, a first transformed signal comprising first transformed symbols of a first coded vector at a first time, wherein the first coded vector is generated based on an arbitrary unitary matrix and a known training sequence, receiving a second transformed signal including second transformed symbols of the first encoded vector at a second time via the communication channel, constructing a matrix based on the first transformed signal and the second transformed signal, detecting a representation of an effective channel based on the matrix, the effective channel being associated with the communication channel, performing a singular value decomposition of the representation of the effective channel to identify singular vectors of the representation of the effective channel, generating a second coded vector based on a precoding matrix and the singular vectors, the precoding matrix being associated with an index of a message for transmission, and (1) a signal representing a first symbol of the second encoded vector and (2) a signal representing a second symbol of the second encoded vector are transmitted to a communication device via a communication channel for identification of the message.

22. The non-transitory processor-readable medium of claim 21, wherein the instructions to cause the processor to generate the second encoded vector include instructions to: multiplying the complex conjugate of the singular vector by the precoding matrix to produce an intermediate matrix; and The intermediate matrix is ​​multiplied by the training values ​​to produce a second encoded vector.

23. The non-transitory processor-readable medium of claim 21 further storing instructions for causing the processor to: select a precoding matrix from a codebook of publicly accessible unitary matrices based on the message.

24. The non-transitory processor-readable medium of claim 21, wherein the precoding matrix is ​​a first precoding matrix, the message is a first message, and the index is a first index, the non-transitory processor-readable medium further storing instructions for causing the processor to: Selecting a first precoding matrix from a codebook of unitary matrices, selecting a second precoding matrix from a codebook of unitary matrices, the second precoding matrix being associated with a second index of a second message for transmission, generating a third coded vector based on the second precoding matrix, and The method causes (1) a signal representing a first symbol of a third encoded vector and (2) a signal representing a second symbol of the third encoded vector to be transmitted to the communication device via a communication channel for identification of a second message.

25. The non-transitory processor-readable medium of claim 21 further storing instructions for causing the processor to transmit a signal representing a plurality of additional encoded vectors to the communication device over a communication channel until a predetermined number of messages have been sent.

26. A non-transitory processor-readable medium storing instructions that, when executed by a processor, cause the processor to: receiving a first transformed signal at a first time via a communication channel, the first transformed signal comprising a version of a first symbol of a first coded vector that has been transformed by a channel transform associated with the communication channel, wherein the first coded vector is generated based on an arbitrary unitary matrix and a known training sequence, receiving a second transformed signal at a second time, the second transformed signal comprising a version of the second symbol of the first encoded vector that has been transformed by the channel transform, constructing a matrix based on the first transformed signal and the second transformed signal, detecting a representation of an effective channel based on the matrix, the effective channel being associated with the communication channel, performing a singular value decomposition of the representation of the effective channel to identify left singular vectors of the representation of the effective channel and right singular vectors of the representation of the effective channel, generating a second coded vector based on the left singular vector of the representation of the effective channel and the right singular vector of the representation of the effective channel, and (1) a signal representing a first symbol of the second encoded vector and (2) a signal representing a second symbol of the second encoded vector are transmitted to a communication device via a communication channel for message identification.

27. The non-transitory processor-readable medium of claim 26, wherein the instructions to cause the processor to generate the second encoded vector include instructions to: multiplying the complex conjugate of the left singular vector of the representation of the effective channel by the precoding matrix to produce an intermediate matrix; and The intermediate matrix is ​​multiplied by the right singular vector of the representation of the effective channel to produce a second encoded vector.

28. The non-transitory processor-readable medium of claim 26, further storing instructions for causing the processor to select a precoding matrix from a codebook of publicly accessible unitary matrices based on the message.

29. The non-transitory processor-readable medium of claim 26, wherein the message is a first message, the non-transitory processor-readable medium further storing instructions for causing the processor to: selecting a first precoding matrix from a codebook of unitary matrices that is publicly accessible, selecting a second precoding matrix, the second precoding matrix being associated with a second index of a second message for transmission, generating a third coded vector based on the second precoding matrix, and The method causes (1) a signal representing a first symbol of a third encoded vector and (2) a signal representing a second symbol of the third encoded vector to be transmitted to the communication device via a communication channel for identification of a second message.

30. The non-transitory processor-readable medium of claim 26, further storing instructions for causing the processor to cause a signal representing a plurality of additional encoded vectors to be transmitted to the communication device over a communication channel until a predetermined number of messages have been sent.

31. The non-transitory processor-readable medium of claim 26, further storing instructions for causing the processor to: receiving a third transformed signal, the third transformed signal comprising a version of the first symbol of the second encoded vector that has been transformed by a channel transform; and receiving a fourth transformed signal, the fourth transformed signal comprising a version of the second symbol of the second encoded vector that has been transformed by the channel transform, The identifying of the message includes removing a representation of a right singular vector of a representation of an effective channel from each of the third transformed signal and the fourth transformed signal.

32. A non-transitory processor-readable medium storing instructions that, when executed by a first processor, cause the first processor to perform the following operations: Receiving, via a single antenna of a first communication device, a first symbol representing a first coded vector and a channel-transformed first signal at a first time, wherein the first coded vector is generated based on an arbitrary unitary matrix and a known training sequence; receiving, via the single antenna of the first communication device, a second symbol representing the first encoded vector and a channel transformed second signal at a second time; detecting an indication of a valid channel based on the first signal and the second signal; performing a singular value decomposition of the representation of the effective channel to identify left singular vectors of the representation of the effective channel and right singular vectors of the representation of the effective channel; generating a second coded vector based on (i) a complex conjugate of a left singular vector of a representation of the effective channel and (ii) a right singular vector of a representation of the effective channel; as well as Causes transmission of (1) a signal representing a first symbol of a second encoded vector and (2) a signal representing a second symbol of the second encoded vector to a second communication device via a communication channel for identification of a message at a second processor associated with the communication device.

33. The non-transitory processor-readable medium of claim 32, wherein the instructions to cause the processor to generate the second encoded vector include instructions to: multiplying the complex conjugate of the left singular vector of the representation of the effective channel by the precoding matrix to produce an intermediate matrix; and The intermediate matrix is ​​multiplied by the right singular vector of the representation of the effective channel to produce a second encoded vector.

34. The non-transitory processor-readable medium of claim 32, further storing instructions for causing the processor to select a precoding matrix from a codebook of publicly accessible unitary matrices.

35. The non-transitory processor-readable medium of claim 32, wherein the message is a first message, the non-transitory processor-readable medium further storing instructions for causing the processor to: selecting a first precoding matrix from a codebook of publicly accessible unitary matrices based on the message, selecting a second precoding matrix, the second precoding matrix being associated with a second index of a second message for transmission, Producing a third encoded vector, and A signal representing the third encoded vector is caused to be transmitted to the communication device via the communication channel for identification of the second message.

36. The non-transitory processor-readable medium of claim 32 further storing instructions for causing the processor to cause a signal representing a plurality of additional encoded vectors to be transmitted to a communication device over a communication channel until a predetermined number of messages have been sent.

37. A non-transitory processor-readable medium storing instructions that, when executed by a processor, cause the processor to: Generate a first encoded vector based on an arbitrary unitary matrix and a known training sequence; causing a first signal representing a first symbol of a first encoded vector to be transmitted to a communication device at a first time via a single antenna over a communication channel, the communication channel applying a channel transform to the first signal during transmission; causing a second signal representing a second symbol of the first encoded vector to be transmitted to the communication device at a second time via the single antenna over a communication channel, the communication channel applying a channel transform to the second signal during transmission; receiving from the communication device a first symbol representing a second encoded vector and a channel transformed third signal; receiving from the communication device a second symbol representing a second encoded vector and a channel transformed fourth signal; detecting an indication of a valid channel based on the third signal and the fourth signal; identifying singular vectors representing the effective channel; and Messages associated with the third signal and the fourth signal are identified based on singular vectors representing the effective channel.

38. The non-transitory processor-readable medium of claim 37, wherein the instructions to cause the processor to identify the message include instructions to identify the message based on a codebook of publicly accessible unitary matrices.

39. The non-transitory processor-readable medium of claim 37 further stores instructions for causing the processor to perform the following operations: receiving multiple additional signals representing multiple additional encoded vectors from the communication device via the communication channel until a predetermined number of messages have been received.

40. The non-transitory processor-readable medium of claim 37 further storing instructions for causing the processor to: identifying a precoding matrix associated with an index of the message, The instructions that cause the processor to identify the message include instructions for identifying the message based on the precoding matrix.

Images