Patent Publication Number: US-9887864-B1

Title: Methods, devices and systems of heterogeneous time-reversal paradigm enabling direct connectivity in internet of things

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of, and claims priority to, U.S. patent application Ser. No. 15/200,429, filed on Jul. 1, 2016, which is a continuation of U.S. patent application Ser. No. 14/943,648, filed on Nov. 17, 2015, now U.S. Pat. No. 9,402,245, issued on Jul. 26, 2016, which is a continuation of U.S. patent application Ser. No. 14/202,651, filed on Mar. 10, 2014 now U.S. Pat. No. 9,226,304, issued on Dec. 29, 2015. This application claims priority to U.S. provisional application 62/219,315, filed on Sep. 16, 2015, the entire contents of which are herein incorporated by reference. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to heterogeneous time-reversal paradigm to enable direct connectivity in the Internet of things. 
     BACKGROUND 
     Ubiquitous RFID tags, sensors, actuators, mobile phones etc. cut across many areas of modern-day living, which offers the ability to measure, infer and understand the environmental indicators. The proliferation of these devices creates the term “Internet of Things” (IoT), wherein these devices blend seamlessly with the environment around us, and the information is shared across the whole platform. The notion “Internet of Things” dates back to 1999 when first proposed by Kevin Ashton. Even though logistic is the originally considered application, in the past decade, the coverage of Internet of Things has been extended to a wide range of applications including healthcare, utilities, transport etc. Due to its high impact on several aspects of everyday life and behavior of the potential users, Internet of Things is listed as one of the six “disruptive civil technologies” by the US National Intelligence Council. 
     Considering the massive number of devices and various application scenarios in Internet of Things, the devices within Internet of Things are highly heterogeneous. From the perspective of communication, one of the significant heterogeneity is the bandwidth heterogeneity and thus the corresponding radio-frequency front end. To address the bandwidth heterogeneity, various communication standards such as ZigBee, Bluetooth and Wi-Fi are adopted simultaneously in the current Internet of Things platform, which leads to a wild growth of co-located wireless communication standards. When multiple wireless communication standards are operated in the same geographical environment, the devices often suffer from harmful interference. Furthermore, the communication between devices with different communication standards is only possible by gateway nodes, resulting in the fragmentation of the whole network, hampering the objects interoperability and slowing down the development of a unified reference model for Internet of Things. 
     To enable the connectivity between devices with various bandwidths, some existing works build middlewares to hide the technical details of different communication standards from the application layer. Service Oriented Device Architecture (SODA) is proposed as a promising approach to integrate Service Oriented Architecture (SOA) principles into the Internet of Things. An effective SOA-based integration of Internet of Things is illustrated in enterprise service. Business Process Execution Language (BPEL) has been widely used as the process language in the middleware. However, these technologies used to realize middleware architectures are often not suitable for resource-constrained scenario due to their complexity. 
     SUMMARY 
     In general, in one aspect, a more effective approach of connecting devices with different bandwidths to a network is provided. By integrating the multirate signal processing into time-reversal technique, the proposed system is capable of supporting these heterogeneous devices with a single set of radio frequency front-end, and therefore it is a unified framework for connecting devices of heterogeneous bandwidths. The increase of complexity in the proposed system lies in the digital processing at the base station, instead of at the devices&#39; end, which can be handled with more powerful digital signal processor. Meanwhile, the complexity of the devices stays low and therefore satisfies the low complexity and scalability requirement of Internet of Things. Since there is no middleware in the proposed scheme and the additional physical layer complexity is concentrated at the base station, the proposed heterogeneous time-reversal system better satisfies the low-complexity and energy-efficiency requirement for the devices compared with the middleware approach. 
     The method includes providing base stations that are connected to a network, and at each of the base stations, receiving probe signals from terminal devices with heterogeneous bandwidths that intend to communicate with the base station. The heterogeneous devices are grouped into different device types based on distinct spectrum occupation. For each of the terminal devices belonging to various device types that intends to communicate with the base station, the base station calculates a signature waveform based on a time-reversed waveform of a channel response signal derived from the corresponding probe signal and device bandwidth. For each of the terminal devices that the base station intends to transmit downlink data, the base station determines a downlink transmit signal for the terminal device based on the downlink data, the corresponding signature waveform and device types based on the spectrum occupation. The base station transmits the downlink signals to the terminal devices with heterogeneous bandwidths. Each base station has a broadcast region such that terminal devices within the broadcast region can communicate with the base station, several base stations are positioned at locations such that they have overlapping broadcast regions, several terminal devices are located within the overlapped broadcast regions, the base stations transmit the downlink signals using a same frequency band, and some downlink signals transmitted by base stations having overlapping broadcast regions also overlap in time. 
     Implementations of the method may include one or more of the following features. Each base station can receive each probe signal from the corresponding terminal device through multiple wireless transmission paths, and the corresponding signature waveform is dependent on the multiple wireless transmission paths and device types. Determining a downlink transmit signal for the terminal device, based on the downlink data, the corresponding signature waveform and device type, can include performing a convolution of the corresponding signature waveform and the downlink data or a modified version of the downlink data and corresponding multirate signal processing based on device type to produce the downlink transmit signal. The method can include simultaneously communicate with devices of heterogeneous bandwidths using a single radio frequency front-end. The method can include, when the number of terminal devices exceeds a maximum number of terminal devices that can be supported by existing base stations, adding another base station to communicate with the additional devices beyond the maximum number of terminal devices without modifying the frequency band used by the existing base stations for transmitting the downlink signals, in which the added base station and the existing base stations share the same frequency band for transmitting the downlink signals. The method can include, at each base station receiving a combined signal that includes uplink signals from multiple terminal devices of heterogeneous bandwidths, and determining the uplink signal from each terminal device based on the combined signal, device type and the corresponding signature waveform for the terminal device. Different terminal devices within the same device type can transmit uplink signals to the same base station using the same frequency band. Different types of terminal devices can transmit uplink signals to the same base station using their specific frequency band. These uplink signals overlap in time. Different terminal devices can transmit uplink signals to different base stations using the same frequency band, and several uplink signals can overlap in time. Transmitting the downlink signals to the terminal devices can include generating a combined downlink signal that combines the downlink signals, and transmitting the combined downlink signal to the terminal devices through multiple wireless propagation paths. The base stations can be located within at least one of a common room, a common floor of a building, a common building, a common vehicle, or a common city block. Each base station can transmit each downlink signal to a particular terminal device through multiple wireless transmission paths, and the signature waveform associated with the particular terminal device is configured such that portions of the downlink signal propagating through the multiple wireless transmission paths interfere constructively at the location of the particular terminal device so that the signal strength at the location of the particular terminal device is stronger than at other locations. The signal strength at the location of the particular terminal device can be at least 3 dB stronger than at other locations more than a half of a wavelength away. The terminal devices can include at least one of environment sensors, utility meters, electrical appliances, lighting devices, audio-video devices, cameras, phones, climate control systems, power generators, timing devices, plant care devices, clothing, food containers, beacons, components in assembly lines, vehicles, or robots. 
     In general, in another aspect, a heterogeneous wireless system is provided. The system includes a base station having a first frequency shifter to shift a frequency of a first downlink signal to produce a first frequency-shifted downlink signal having a first center frequency; a second frequency shifter to shift a frequency of a second downlink signal to produce a second frequency-shifted downlink signal having a second center frequency that is different from the first center frequency; an adder to combine the first and second frequency-shifted downlink signals to produce a combined downlink signal; and a radio frequency (RF) module to convert the combined downlink signal to a combined RF signal that includes information about the first downlink signal and the second downlink signal. 
     In general, in another aspect, an apparatus for implementing a heterogeneous wireless system is provided. The apparatus includes a first frequency shifter to shift a frequency of a first digital downlink signal to produce a first frequency-shifted digital signal, the first digital downlink signal intended for a first terminal device; a second frequency shifter to shift a frequency of a second digital downlink signal to produce a second frequency-shifted digital signal, the second digital downlink signal intended for a second terminal device; an adder to combine the first and second frequency-shifted digital signals to produce a combined digital signal; a digital-to-analog converter to convert the combined digital signal to a combined analog signal; and a radio frequency (RF) module to convert the combined baseband signal to a combined RF signal that has a first component derived from the first digital downlink signal and a second component derived from the second digital downlink signal, the first component having a first center frequency substantially the same as a first carrier frequency associated with the first terminal device, the second component having a second center frequency substantially the same as a second carrier frequency associated with the second terminal device. 
     In general, in another aspect, a heterogeneous wireless system is provided. The system includes a data processor configured to: combine data signals intended for a first group of multiple devices of a first type to generate a first combined signal, shift a frequency of the first combined signal to generate a first frequency-shifted combined signal having a first center frequency, combine data signals intended for a second group of multiple devices of a second type to generate a second combined signal, shift a frequency of the second combined signal to generate a second frequency-shifted combined signal having a second center frequency, and combine the first frequency-shifted combined signal and the second frequency-shifted combined signal to generate a composite downlink signal. The system includes a radio frequency module configured to generate a radio frequency downlink signal based on the composite downlink signal. 
     In general, in another aspect, a heterogeneous wireless system is provided. The system includes a base station having: a data processor configured to generate a composite downlink signal that includes signal components derived from data signals intended to be transmitted to devices having different frequency spectrum requirements, in which the process of generating the composite downlink signal includes: embedding location-specific signature waveforms in the signal components to enable different portions of a signal transmitted by the base station to converge at different devices that are intended to receive the respective portions, the location-specific signature waveforms each being associated with a location of a respective one of the devices, modifying a spectral distribution of the signal components based on information about a frequency spectrum associated with the base station and information about frequency spectrums associated with the devices, and combining the signal components to generate the composite downlink signal. 
     In general, in another aspect, a heterogeneous wireless system is provided. The system includes a base station having: a data processor configured to receive a composite uplink signal that includes components derived from a first uplink signal sent from a first device and a second uplink signal sent from a second device; modify a frequency distribution of a processed version of the composite uplink signal by an amount that is dependent on a spectral characteristic associated with the first device to generate a first frequency-shifted uplink signal; estimate first uplink data symbols sent from the first device based on the first frequency-shifted uplink signal and a first location-specific signature waveform that is associated with a location of the first device; modify a frequency distribution of a processed version of the composite uplink signal by an amount that is dependent on a spectral characteristic associated with the second device to generate a second frequency-shifted uplink signal; and estimate second uplink data symbols sent from the second device based on the second frequency-shifted uplink signal and a second location-specific signature waveform that is associated with a location of the second device. 
     In general, in another aspect, a heterogeneous wireless system is provided. The system includes a base station having: a data processor configured to process a composite uplink signal that includes signal components derived from data signals sent from devices having different spectral characteristics, in which the processing of the composite uplink signal includes: making one or more copies of the composite uplink signal; modifying spectral distributions of the composite uplink signal and the one or more copies of the composite uplink signal to generate frequency-shifted composite uplink signals; and estimating data symbols sent from the devices based on the frequency-shifted composite uplink signals and location-specific signature waveforms that are associated with locations of the devices. 
     In general, in another aspect, a method for operating a heterogeneous wireless system is provided. The method includes: at a base station, shifting a frequency of a first downlink signal to produce a first frequency-shifted downlink signal having a first center frequency; shifting a frequency of a second downlink signal to produce a second frequency-shifted downlink signal having a second center frequency that is different from the first center frequency; combining the first and second frequency-shifted downlink signals to produce a combined downlink signal; converting the combined downlink signal to a combined RF signal; and transmitting the combined RF signal, in which the combined RF signal includes information about the first downlink signal and the second downlink signal. 
     In general, in another aspect, a method for operating a heterogeneous wireless system is provided. The method includes: generating a first downlink signal based on data symbols to be transmitted to a first device and a location specific signature waveform that is associated with a location of the first device; generating a second downlink signal based on data symbols to be transmitted to a second device and a location specific signature waveform that is associated with a location of the second device; generating a combined downlink signal that includes a first component and a second component, the first component having a version of the first downlink signal shifted to a first carrier frequency associated with the first device, the second component having a version of the second downlink signal shifted to a second carrier frequency associated with the second device, the second carrier frequency being different from the first carrier frequency; and transmitting the combined downlink signal. 
     In general, in another aspect, a method for operating a heterogeneous wireless system is provided. The method includes: combining data signals intended for a first group of multiple devices of a first type to generate a first combined signal; shifting a frequency of the first combined signal to generate a first frequency-shifted combined signal having a first center frequency; combining data signals intended for a second group of multiple devices of a second type to generate a second combined signal; shifting a frequency of the second combined signal to generate a second frequency-shifted combined signal having a second center frequency; combining the first frequency-shifted combined signal and the second frequency-shifted combined signal to generate a composite downlink signal; generating a radio frequency downlink signal based on the composite downlink signal; and transmitting the radio frequency downlink signal. 
     In general, in another aspect, a method for operating a heterogeneous wireless system is provided. The method includes: receiving a composite uplink signal that includes components derived from a first uplink signal sent from a first device and a second uplink signal sent from a second device; modifying a frequency distribution of the composite uplink signal by an amount that is dependent on a spectral characteristic associated with the first device to generate a first frequency-shifted uplink signal; estimating first uplink data symbols sent from the first device based on the first frequency-shifted uplink signal and a first location-specific signature waveform that is associated with a location of the first device; modifying a frequency distribution of the composite uplink signal by an amount that is dependent on a spectral characteristic associated with the second device to generate a second frequency-shifted uplink signal; and estimating second uplink data symbols sent from the second device based on the second frequency-shifted uplink signal and a second location-specific signature waveform that is associated with a location of the second device. 
     In general, in another aspect, a heterogeneous time-reversal wireless system is provided to simultaneously communicate with multiple terminal devices with heterogeneous frequency bandwidths and spectrum allocations. 
     In general, in another aspect, a method of connecting devices to a network is provided. The method includes providing a first base station and a second base station to a network. The method includes at the first base station configured to communicate with devices located within a first broadcast region, receiving probe signals from a first group of terminal devices located within the first broadcast region, and calculating signature waveforms for the first group of terminal devices based on time-reversed waveforms of channel response signals derived from the received probe signals. The base station determines downlink signals for the first group of terminal devices based on the corresponding signature waveforms, each downlink signal intended to be sent to one of the first group of terminal devices, different downlink signals intended to be sent to different ones of the first group of terminal devices. The base station transmits the downlink signals to the first group of terminal devices. The method includes at the second base station configured to communicate with devices located within a second broadcast region, receiving probe signals from a second group of terminal devices located within the second broadcast region, and calculating signature waveforms for the second group of terminal devices based on time-reversed waveforms of channel response signals derived from the received probe signals. The second base station determines downlink signals for the second group of terminal devices based on the corresponding signature waveforms, each downlink signal intended to be sent to one of the second group of terminal devices, different downlink signals intended to be sent to different ones of the second group of terminal devices. The second base station transmits the downlink signals to the second group of terminal devices. The first broadcast region overlaps the second broadcast region, at least one of the terminal devices is located within the overlapped broadcast region, the first and second base stations transmit the downlink signals using the same frequency band, and the downlink signals transmitted by the first and second base stations overlap in time. 
     Implementations of the method may include one or more of the following features. The first and second base stations can be located within at least one of a common room, a common floor of a building, a common building, a common vehicle, or a common city block. Each base station can receive each probe signal from the corresponding terminal device through multiple wireless transmission paths, and the corresponding signature waveform is dependent on the multiple wireless transmission paths and device type. Determining a downlink transmit signal for the terminal device based on the downlink data, device type and the corresponding signature waveform can include performing a convolution of the corresponding signature waveform and the downlink data or a modified version of the downlink data to produce the downlink transmit signal. The method can include at each base station receiving a combined signal that includes uplink signals from multiple terminal devices of heterogeneous bandwidths, and determining the uplink signal from each terminal device based on the combined signal, device type and the corresponding signature waveform for the terminal device. Different terminal devices can transmit uplink signals to the same base station using the device type specific frequency band, and several uplink signals can overlap in time. Different terminal devices can transmit uplink signals to different base stations using the device type specific frequency band, and several uplink signals can overlap in time. Transmitting the downlink signals to the first group of terminal devices can include generating a combined downlink signal that combines the downlink signals, and transmitting the combined downlink signal to the first group of terminal devices through multiple wireless propagation paths. The first base station can transmit each downlink signal to a particular terminal device through multiple wireless transmission paths, and the signature waveform associated with the particular terminal device can be configured such that portions of the downlink signal propagating through the multiple wireless transmission paths interfere constructively at the location of the particular terminal device so that the signal strength at the location of the particular terminal device is stronger than at other locations. The signal strength at the location of the particular terminal device can be at least 3 dB stronger than at other locations more than a half of a wavelength away. The terminal devices can include at least one of environment sensors, utility meters, electrical appliances, lighting devices, audio-video devices, cameras, phones, climate control systems, power generators, timing devices, plant care devices, clothing, food containers, beacons, components in assembly lines, vehicles, or robots. 
     In general, in another aspect, a system for connecting multiple devices to a network is provided. The system includes base stations in which each base station has a network port for connecting to a network, and an input module to receive probe signals from terminal devices with heterogeneous bandwidths that intend to communicate with the base station. The base station includes a data processor to, for each of the terminal devices with heterogeneous bandwidths that intends to communicate with the base station, calculate a signature waveform based on a time-reversed waveform of a channel response signal derived from the corresponding probe signal on the device type specific frequency band. For each of the terminal devices that the base station intends to transmit downlink data, the data processor determines a downlink transmit signal for the terminal device based on the downlink data, device type and the corresponding signature waveform. The system includes an output module to transmit the downlink signals to the terminal devices. Each base station has a broadcast region such that terminal devices within the broadcast region can communicate with the base station, several base stations are positioned at locations such that they have overlapping broadcast regions, and the base stations are configured to transmit the downlink signals using a common frequency band. 
     Implementations of the system may include one or more of the following features. The data processor can determine a downlink transmit signal for the terminal device based on the downlink data, device type and the corresponding signature waveform by performing a convolution of the corresponding signature waveform and the downlink data or a modified version of the downlink data and going through the device type specific multirate signal processing to produce the downlink transmit signal. At each base station, the input device can receive a combined signal that includes uplink signals from multiple terminal devices belonging to same or different device types, and the data processor can determine the uplink signal from each terminal device based on the combined signal, device type and the corresponding signature waveform for the terminal device. The data processor can generate a combined downlink signal that combines the downlink signals, and the output module can transmit the combined downlink signal to the terminal devices through multiple wireless propagation paths. Each base station can transmit each downlink signal to a particular terminal device through multiple wireless transmission paths, and the signature waveform associated with the particular terminal device can be configured such that portions of the downlink signal propagating through the multiple wireless transmission paths interfere constructively at the location of the particular terminal device so that the signal strength at the location of the particular terminal device is stronger than at other locations. The signal strength at the location of the particular terminal device can be at least 3 dB stronger than at other locations more than a half of a wavelength away. The base station can be part of at least one of an environment sensors hub, a utility meter hub, an electrical appliance, a lighting device, an audio-video device, cameras, a phone, a climate control system, a power generator, a timing device, a plant care device, a wearable device hub, a food container hub, a beacon hub, a component in an assembly line, a vehicle, or a robot. 
     Other aspects include other combinations of the features recited above and other features, expressed as methods, apparatus, systems, program products, and in other ways. 
     Advantages of the aspects and implementations may include one or more of the following. Time-reversal systems can have low power consumption, good interference reduction, provide better battery life, and support multiple concurrent active users. The proposed heterogeneous time-reversal system can directly connect devices with heterogeneous bandwidths, which is a unified framework compared with middleware approach. The asymmetric architecture of heterogeneous time-reversal systems can reduce the computational complexity and thus the cost of the terminal devices, the total number of which is typically very large for the Internet of Things. The removal of middleware in the proposed system better satisfies the low-complexity and energy-efficiency of Internet of Things. The unique location-specific signatures in heterogeneous time-reversal systems can provide physical-layer security and enhance the privacy and security of customers in the Internet of Things. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1A  is a diagram showing an exemplary environment for operating a time-reversal system. 
         FIG. 1B  is a graph of an exemplary recorded channel response waveform. 
         FIG. 1C  is a graph of an exemplary time-reversed waveform generated by reversing the waveform of  FIG. 1B  with respect to time. 
         FIG. 2  is a diagram showing an exemplary environment for operating a time-reversal system having multiple receivers. 
         FIG. 3  is a graph showing an exemplary heterogeneous time-reversal system for the Internet of Things. 
         FIG. 4  is a diagram showing the channel probing phase of an exemplary homogeneous time-reversal system. 
         FIG. 5  is a diagram showing the downlink transmission phase of a conventional homogeneous time reversal system. 
         FIG. 6  is a diagram showing the uplink transmission phase of a conventional homogeneous time reversal system. 
         FIG. 7  is a graph of an exemplary spectrum allocation of devices with heterogeneous bandwidth. 
         FIG. 8  is a graph of the channel probing phase of a type i device. 
         FIG. 9  is a diagram of an exemplary time-reversal division multiple access downlink system with heterogeneous devices. 
         FIG. 10  is a diagram of an exemplary time-reversal division multiple access uplink system with heterogeneous devices. 
         FIG. 11  is a graph showing the bit-error-rate performance of three devices in an exemplary heterogeneous time-reversal system. 
         FIG. 12A  is a graph showing the improved bit-error-rate with Time Division Multiple Access in the heterogeneous time-reversal system with no channel coding for high-definition audio device. 
         FIG. 12B  is a graph showing the improved bit-error-rate with Time Division Multiple Access in the heterogeneous time-reversal system with smaller rate backoff for high-definition audio device. 
         FIG. 13  is a graph showing the improved bit-error-rate with Spectrum Allocation in the heterogeneous time-reversal system. 
         FIG. 14  is a graph showing the spectrum allocation of an exemplary Smart Home application. 
         FIG. 15  is a graph showing the bit-error-rate of devices in Smart Homes application using heterogeneous time-reversal communication. 
     
    
    
     DETAILED DESCRIPTION 
     Overview of Time-Reversal Wireless System 
     The following provides an overview of a time-reversal wireless system. Referring to  FIG. 1A , a time-reversal system can be used in an environment having structures or objects that may cause one or more reflections of wireless signals. For example, a venue  102  may have a first room  104  and a second room  106 . When a first device  108  in the first room  104  transmits a signal to a second device  110  in the second room  106 , the signal can propagate in several directions and reach the second device  110  by traveling through several propagation paths, e.g.,  112 ,  114 , and  116 . The signal traveling through multiple propagation paths is referred to as a multipath signal. As the signal travel through the propagation paths, the signal may become distorted. The multipath signal received by the second device  110  can be quite different from the signal transmitted by the first device  108 . 
     For example, referring to  FIG. 1B , when the first device  108  sends a pulse signal, the signal received by the second device  110  may have a waveform  120 . The waveform  120  is referred to as the channel impulse response (CIR) signal. 
     Referring to  FIG. 1C , a time-reversed waveform  130  can be generated by reversing the waveform  120  with respect to time. If the second device  110  sends a signal having the waveform  130 , the signal will propagation in various directions, including through propagation paths  112 ,  114 , and  116  (in reverse direction relative to the propagation direction of the impulse signal), and reach the first device  108 . The multipath signal received at the first device  108  may form an impulse signal that is similar to the impulse signal previously sent from the first device  108  to the second device  110 . 
     The waveforms  120  and  130  shown in  FIGS. 1B and 1C  are merely examples. The waveforms in time-reversal systems can vary depending on, e.g., the environment and the information or data being transmitted. In addition, the initial signal sent from the first device  108  can be any sort of signal, of which an impulse is just one example. The initial signal can be any waveform. 
     When the second device  110  intends to transmit a data stream to the first device  108 , the second device  110  may use a normalized time-reversed conjugate of the signal received from the device  108  as a basic transmission waveform. The second device  110  may encode the data stream on the basic waveform and transmit the signal through the wireless channel. The signal received at the device  108  may be described as the convolution of the transmitted signal and the channel impulse response, plus additive white Gaussian noise. Because the transmitted signal has been designed based on a time reversed version of the channel impulse response, the first device  108  may only need to perform a simple adjustment to the received signal and down-sample it to recover the data stream transmitted by the second device  110 . 
     In some examples a transmitting device or base station or access point may send signals to two or more receiving devices at the same time. The transmitted signals travel through multiple propagation paths to each receiver. Because the receivers are positioned at different locations, the multipath signals travel through different propagation paths to reach the receivers. By carefully constructing the waveform of the signal sent from the transmitter, it is possible to allow each receiver to receive data intended for the receiver with sufficient high quality. 
     Referring to  FIG. 2 , the first device  108  may communicate with the second device  110  and a third device  140 . The second device  110  may send a probe signal that travels through propagation paths  112 ,  114 , and  116  to the first device  108 . The probe signal can be, e.g., a pulse signal, a signal that has a predetermined waveform, or a signal that includes symbols. The first device  108  may record the received waveform representing the channel response for a first multipath channel. The third device  140  may send a probe signal that travels through propagation paths  142 ,  144 , and  146  to the first device  108 . The first device  108  may record the received waveform representing the channel response for the second multipath channel. 
     The first device  108  constructs a downlink signal based on a first time-reversed multipath channel response, a second time-reversed multipath channel response, a first data stream intended for the second device  110 , and a second data stream intended for the third device  140 . The first device  108  may transmit the downlink signal so that a first portion of the downlink signal travels through propagation paths  112 ,  114 , and  116  to reach the second device  110 . A second portion of the downlink signal may travel through propagation paths  142 ,  144 , and  146  to reach the third device  140 . The first signal portion received at the second device  110  may form a first data stream. The second signal portion received at the third device  140  may form a second data stream. 
     In the example of  FIG. 2 , the first device  108  transmits two data streams simultaneously to the second device  110  and the third device  140 . Using the same principle, the second device  110  can receive channel impulse response signals from the first device  108  and the third device  140 , and then transmit two data streams simultaneously to the first device  108  and the third device  140  using waveforms that are determined according to time-reversed channel impulse response signals. The third device  140  can also receive channel impulse response signals from the first device  108  and the second device  110 , and then transmit two data streams simultaneously to the first device  108  and the second device  110  using waveforms that are determined according to time-reversed channel impulse response signals. In general, when there are three or more devices, each device can transmit two or more data streams simultaneously to two or more other devices. 
     Heterogeneous Time-Reversal Wireless System 
     A big challenge of indoor communication and indoor Internet of Things applications is the presence of many multi-paths with similar path lengths. While multipath fading may be known to cause problems in communication and may often be suppressed by rake receivers or equalizers, time reversal machine (TRM) technology recognizes hidden values of multi-paths and seeks to capture and exploit the inherent structures of the multi-paths to achieve high communication capacity, low power consumption, good battery life, collision-free multiple access, low cost terminal devices, heterogeneous terminal devices, indoor positioning, life detection, scalability, privacy and security, etc. A high sampling frequency may be used to capture the useful details of the multi-paths. The following are some of the advantages that may be achieved by the TRM system. 
     High communication capacity: The TRM system supports spatial division multiple access supporting high throughput for each TRM device (e.g., Internet of Things devices, smart phones, smart devices). The TRM system achieves high signal-to-noise ratio due to its inherent nature to fully harvest energy from the surrounding environment by exploiting the multi-path propagation to recollect all the signal energy that could be collected as the ideal RAKE receiver. The achievable rate can be very high when the bandwidth is sufficiently wide. 
     Good battery life: Many TRM devices (e.g., Internet of Things devices, smart phones, smart devices) may be powered by small batteries. The TRM devices may need to be designed to have low power consumption and use wireless communication techniques that have low computational complexity. The TRM system uses physics instead of electronics to perform channel equalization and thus supports low power consumption and low computational complexity. The TRM system has a potential of over an order of magnitude of power consumption reduction and interference alleviation, which means that the TRM system can provide better battery life and support multiple concurrent active users. 
     Collision-free multiple access: The TRM system allows many active TRM devices to connect to the Internet and transmit/receive data concurrently without collision with other TRM devices. The TRM system uses low-interference wireless technologies to reduce the interference among and within devices or things. 
     Low cost terminal devices: The TRM system is designed so that most of the processing for signal communication is performed at the base station, thus allowing the terminal TRM devices (e.g., handsets, smart devices, Internet of Things devices), to be simple with low cost, low power consumption and good battery life. The terminal TRM devices only need to perform simple processing and thus can use low cost processors. In some examples, by using an asymmetric TRM architecture, only a simple one-tap detection is needed. 
     Heterogeneous terminal devices: The TRM system can support a high level of heterogeneity among the TRM devices connected to the Internet. For example, TRM devices that have different functionality, technology, and application fields can communicate with one another. The wireless technology used by the TRM system can support heterogeneous terminal devices with different quality-of-service (QoS) options, such as bit rate, adjustment of waveform and back-off factor. Conventional technologies (e.g., ZigBee, Z-Wave, Bluetooth, and WiFi) may not simultaneously support a high level of heterogeneity among terminal devices and support a wide range of density of terminal devices. 
     Secure communication: The TRM system provides added security by using spatial division multiple access. Only the intended TRM device at a particular location can receive the intended information. The unique location-specific signature in the TRM system can provide additional physical-layer security and thus can enhance the privacy and security of customers. 
     Indoor positioning: The TRM system exploits the details of the multi-paths so that each TRM device can determine the current location of the individual receiver. 
     Life detection: The TRM system exploits the changes of the details of the multi-paths and allows TRM devices to detect movements of living things in the environment, e.g., breathing of humans in the environment. 
     Scalability: The system supports a wide range of density of TRM devices (e.g., Internet of Things devices, smart phones, smart devices) and uses wireless technology that is highly scalable to provide satisfactory quality of service for low to high density areas. 
     Privacy and security: The TRM system allows each TRM device (e.g., Internet of Things device, smart device, smart phone) to have a unique identification, and ensures privacy and the security of the customers. 
     The broadband wireless channels used by the time reversal communication may be a set of wireless channels (e.g., Wi-Fi channels with 20 or 40 MHz bandwidth, Zigbee, BlueTooth, Z-Wave), mobile communication channels (e.g., 3G/4G/5G/6G, WiMax), etc. Multiple antennas may be used in the transmitter and receiver. Multiple narrow-band channels may be combined to achieve a large effective bandwidth. 
     This disclosure provides a heterogeneous time-reversal wireless communication system for implementing the Internet of Things. Referring to  FIG. 3 , in some implementations, a time-reversal wireless communication system  300  includes time-reversal base stations  302  that communicate with many things, objects, or devices, such as smart sensors  304 , smart home appliances  306 , healthcare devices  308 , entertainment devices  310 , and security devices  312 , etc. For example, the smart home appliance  306  may have embedded sensors that can communicate with base stations. 
     The following describes an example of a time-reversal communication system assuming all devices share the same frequency and bandwidth. The channel impulse response between two transceivers is modeled as
 
 h ( t )=Σ v=1   V   h   v δ( t−τ   v ),  (1)
 
where h v  is the complex channel gain of the v-th path of the channel impulse response, τ v  is the corresponding path delay, and V is the total number of the underlying multi-paths (assuming infinite system bandwidth and time resolution). Without loss of generality, we assume that τ 1 =0 in the following discussion, i.e., the signal at the first path arrives at time t=0, and as a result, the delay spread of the multi-path channel τ C  is given by τ C =τ V −τ 1 =τ V .
 
     Considering a communication system with a limited bandwidth, pulse shaping filters can be deployed to limit the effective bandwidth of transmission. In some examples, raised-cosine filter can be used as a pulse shaping filter that reduces the inter-symbol-interference (ISI). Generally, the raised-cosine filter is splitted into two root-raised-cosine filters RRC B,f     s   [n] and deployed at each side of the transceivers, where B is the available bandwidth and f s  is the sample rate of the system. In some examples, based on the Nyquist rate, an α-times oversampling (i.e., f s =αB) is implemented to counter the sampling frequency offset (SFO). 
     Channel Probing Phase 
     Referring to  FIG. 4 , channel probing is performed when an access point (AP)  320  communicates with a terminal device  322  using time-reversal communication technology. In general, time-reversal communication includes a channel probing phase followed by a data transmission phase. Prior to the access point&#39;s time-reversal transmission of data, in the channel probing phase, the terminal device  322  upsamples an impulse signal  324  by α using an upsampling unit  326 , filters the upsampled signal by using α root-raise-cosine (RRC) filter RRC B,f     s      328 , where B is the bandwidth and f s =αB is the sample rate. One of the purposes of increasing the bit rate is that by oversampling, we can obtain the correct sample when there exists sample frequency offset between the transmitter and the receiver in the data transmission phase. Since the oversampling is one of the steps in the data transmission phase, to estimate the channel correctly, we also include oversampling and downsampling in the channel probing phase. The value of a can be chosen by the user. For example, a can be chosen to be equal to 4, but can also be other values. The root-raised-cosine filter can perform pulse shaping to limit the bandwidth. In the heterogeneous time-reversal system, different types of devices use different bandwidths, so the bandwidths of the root-raised-cosine filters for the different types of devices are also different. 
     The filtered signal is converted to an analog baseband signal by a digital-to-analog converter (DAC)  330 . The baseband signal is modulated to a high carrier frequency by a voltage-controlled oscillator (VCO)  332 , then put through a bandpass filter  334  and amplified by a power amplifier  336  to produce a radio frequency (RF) signal. The RF signal is broadcasted by an antenna  338 . The broadcast signal passes through a multipath channel  340  having a profile h, in which noise n′ is added to the signal. The broadcast signal is captured by an antenna  342  at the access point  320 . The captured signal is amplified by a low-noise amplifier (LNA)  344 , filtered by a bandpass filter  346 , and converted to the analog baseband signal using a voltage-controlled oscillator  348 . The baseband signal is sampled by an analog-to-digital converter (ADC)  350  with a sample rate f s =αB to produce a digital signal. The digital signal is filtered by a root-raised-cosine filter RRC B,f     s      352  and downsampled by a factor α by a downsampling unit  354 . Because an impulse signal was transmitted by the terminal device  322 , the downsampled signal is treated as a channel estimate ĥ  356 . 
     The root-raised-cosine filter  328  is a digital filter, and the root-raised-cosine filter  352  is an analog filter, they both have the same bandwidth. The bandpass filter  334  defines the frequency band used by the terminal device  322 . Thus, if the terminal device  322  includes a bandpass filter  334  having a passband from frequency f1 to frequency f2, we say that the terminal device  322  uses or is associated with the frequency band f1 to f2. In the example of  FIG. 4 , the passband of the bandpass filter  334  in the terminal device  322  is the same as the passband of the bandpass filter  346  in the access point  320 . 
     The access point  320  can also be a base station or a transceiver that communicates with multiple other devices using the communication techniques described here. 
     With a sampling rate f s =αB, the discrete channel impulse response can be written as
 
   h [n]=Σ   v=1   V   h   v   δ[nT   s −τ v ],  (2)
 
where T S =1/(αB). Assume perfect channel estimation (noise and interference are ignored in the channel probing phase), the equivalent channel impulse response between two root-raised-cosine filters  328 ,  352  in  FIG. 4  is written as
 
{tilde over ( h )}=( RRC   B,f     s     * h *RRC   B,f     s   ).  (3)
 
Based on the polyphase identity, the equivalent channel impulse response (between the expander and decimator) for the system with bandwidth B can be represented as
 
{circumflex over ( h )}=( RRC   B,f     s     * h *RRC   B,f     s   ) [α] ,  (4)
 
where (•) [α]  represents α-times decimation. From equation (4), one can see that those paths represented in equation (2), whose time differences are within the main lobe of raised-cosine filter, are mixed together for the system with a limited bandwidth B.
 
     In  FIG. 4 , the upsampling unit  326  and the root-raised-cosine filter  328  of the terminal device  322  can be implemented using, e.g., a digital signal processor, a field programmable gate array (FPGA), or discrete components. Similarly, the root-raised-cosine filter  352  and the downsampling unit  354  of the access point  320  can be implemented using, e.g., a digital signal processor, a field programmable gate array (FPGA), or discrete components. 
     Data Transmission Phase 
     Upon acquiring the equivalent channel impulse response ĥ, different designs of signature waveforms (e.g., basic time-reversal signature, zero forcing (ZF) signature, and minimum mean square equalizer (MMSE) signature) can be implemented at the access point side. Assuming the basic time-reversal signature is considered, the access point time-reverses (and conjugates, when complex-valued) the equivalent channel impulse response ĥ, and uses the normalized time-reversal waveform as the basic time-reversal signature g, i.e., 
                       g   ⁡     [   n   ]       =           h   ^     *     ⁡     [     L   -   1   -   n     ]              h   ^              ,           (   5   )               
where L is the number of taps in ĥ.
 
     A diagram of the procedures of time-reversal data transmission is shown in  FIG. 5 . The diagram can also represent the modules used in the time-reversal data transmission. There is a sequence of information symbols X[k]  360  to be transmitted to the terminal device  322 . To match the symbol rate with the system chip rate 1/B, the symbols  360  are upsampled by backoff factor D using an upsampling unit  362 . The upsampled symbols are filtered by the signature waveform g at unit  364 , the signature embedded symbols are upsampled by a at an upsampling unit  366 , and filtered by a root-raised-cosine filter RRC B,αB    368 . The filtered digital signal is converted to an analog baseband signal by a DAC  370 . The baseband signal is modulated to a high carrier frequency by the voltage-controlled oscillator  348 , put through the bandpass filter  346  and amplified by a power amplifier  372  to produce an RF signal. The RF signal is broadcasted by the antenna  342 . The broadcast signal passes through a multipath channel  386  having a profile h, in which the signal is corrupted with additive noise n. The broadcast signal is captured by the terminal device antenna  338 , amplified by a low noise amplifier  374 , filtered by the bandpass filter  334 , and carried to baseband signal by the voltage-controlled oscillator  332  to produce an analog baseband signal. The analog baseband signal is converted to a digital signal by an ADC  376  having a sampling rate f s =αB to produce a digital signal that is filtered by a root-raised-cosine filter  378  and downsampled by a factor α using downsampling unit  380  and downsampled by a factor D using downsampling unit  382  to produce a downsampled signal Y[k]  384 , which can be used to estimate the transmitted information symbol X[k]  360 . 
     Referring again to  FIG. 5 , after a rate backoff factor D is introduced to match the symbol rate with chip rate by inserting (D−1) zeros between two symbols, i.e., 
                       X     [   D   ]       ⁡     [   k   ]       =     (             X   ⁡     [     k   /   D     ]       ,               if   ⁢           ⁢     (     k   ⁢           ⁢   mod   ⁢           ⁢   D     )       =   0     ,               0   ,               if   ⁢           ⁢     (     k   ⁢           ⁢   mod   ⁢           ⁢   D     )       ≠   0     ,                     (   6   )               
where (•) [D]  denotes the D-times interpolation, the signature embedded symbols before the α-times expander can be written as
 
 S[k ]=( X   [D]   *g )[ k].   (7)
 
Based on the previous derivation in the channel probing phase, the system components between the expander and decimator in  FIG. 4  can be replaced by ĥ. Therefore, the signal received at the terminal device side before the decimator with rate D is the convolution of S[k] and ĥ, plus additive white Gaussian noise (AWGN) ñ[k] with zero-mean and variance σ N   2 , i.e.,
 
 Y   [D]   [k ]=( S*ĥ )[ k]+ñ[k].   (8)
 
Then, terminal device  322  decimates the symbols with backoff factor D in order to detect the information symbols {X[k]}, i.e.,
 
                       Y   ⁡     [   k   ]       =           p   u       ⁢       (       h   ^     *   g     )     ⁡     [     L   -   1     ]       ⁢     X   ⁡     [     k   -       L   -   1     D       ]         +         p   u       ⁢       ∑       l   =   0     ,     l   ≠       (     L   -   1     )     /   D             (       2   ⁢   L     -   2     )     /   D       ⁢         (       h   ^     *   g     )     ⁡     [   Dl   ]       ⁢     X   ⁡     [     k   -   l     ]             +     n   ⁡     [   k   ]           ,           (   9   )               
where n[k] ñ[Dk] and p u  stands for the power amplifier.
 
     Benefiting from temporal focusing, the power of (ĥ*g) achieves its maximum at (L−1) for 
               X   ⁡     [     k   -       L   -   1     D       ]       ,         
i.e.,
 
                       (       h   ^     *   g     )     ⁡     [     L   -   1     ]       =           ∑     l   =   0       L   -   1       ⁢         h   ^     ⁡     [   l   ]       ⁢         h   ^     *     ⁡     [   l   ]                  h   ^            =            h   ^          .               (   10   )               
Consequently, the resulting signal-to-interference-plus-noise ratio (SINR) is obtained as
 
                     SINR   =         p   u     ⁢            h   ^          2             p   u     ⁢       ∑       l   =   0     ,     l   ≠       (     L   -   1     )     /   D             (       2   ⁢   L     -   2     )     /   D       ⁢              (       h   ^     *   g     )     ⁡     [   Dl   ]            2         +     σ   N   2           ,           (   11   )               
assuming that each information symbol X [k] has unit power.
 
     Regarding the uplink, the previously designed signature waveform g serves as the equalizer at the access point side as shown in  FIG. 6 . Similar to the signal flow in the downlink, the access point  320  can detect the information symbol based on the temporal focusing of (ĥ*g) in the uplink. Such a scheme of both downlink and uplink is defined as the asymmetric architecture, which provides the asymmetric complexity distribution between the access point  320  and the terminal device  322 . The asymmetric complexity distribution between access points (or base stations) and terminal devices is described in U.S. patent application Ser. No. 13/969,271, filed on Aug. 16, 2013, titled “Time-Reversal Wireless Systems Having Asymmetric Architecture,” herein incorporated by reference in its entirety. 
     Note that the homogeneous time-reversal system can be extended to multi-user scenario, which exploits the spatial degrees of freedom in the environment and uses the multipath profile associated with each user&#39;s location as a location-specific signature for the user. A time-reversal division multiple access system in which a base station transmits downlink data to multiple terminal users is described in U.S. Pat. No. 9,226,304, the entire contents of which are incorporated by reference. A multi-user time-reversal system in which the RF signals transmitted to or from different terminal devices have the same (or substantially the same) center frequency and bandwidth is referred to as a homogeneous time-reversal system. In a homogeneous time-reversal system, different users can adopt different rate backoff factors to accommodate the different QoS requirements for various applications in the Internet of Things. In the homogeneous time-reversal system, all devices in the system share the same bandwidth and thus the same sampling rate, which increases not only the hardware cost but also computation burden for the low-end terminal devices. 
     The following describes a heterogeneous time-reversal system that supports the heterogenous QoS required by diverse applications, as well as heterogeneous hardware capabilities (such as bandwidth, sampling rate, computational power, and storage capacity, etc.). 
     Heterogeneous Time-Reversal System for Internet of Things 
     Referring to  FIG. 7 , in a heterogeneous time-reversal system, N types of terminal devices with distinct spectrum allocation and bandwidths are supported simultaneously by a single access point.  FIG. 7  is a graph  390  showing that different types of terminal devices can have different carrier frequencies (f c     i   ) and bandwidths (B i ). In this example, a type 1 device can use a frequency band from frequency f 1a  to frequency f 1b , in which the carrier frequency is (f 1a +f 1b )/2. A type 2 device can use a frequency band from frequency f 2a  to frequency f 2b , in which the carrier frequency is (f 2a +f 2b )/2. In general, a type i device can use a spectral band from frequency f 1a  to frequency f 1b , in which the carrier frequency is (f 1a +f 1b )/2. Different types of devices can use frequency bands that either overlap or not overlap. In the example of  FIG. 7 , type 1 devices and type 2 devices use different frequency bands that do not overlap. For example, f2a can be equal to or greater than f1b. Type 3 devices and type 4 devices can use different frequency bands that do not overlap. For example, f4a can be equal to or greater than f3b. In the example of  FIG. 7 , type 3 and type 4 devices can use frequency bands that overlap the frequency band used by the type 1 devices. Type 5 to type N devices can use frequency bands that overlap the frequency band used by the type 2 devices. The frequency band allocation shown in  FIG. 7  is just an example, other ways of allocating frequency bands to various devices can also be used. 
     In order to support the heterogeneous terminal devices, there are several modifications at both access point and terminal device sides of the homogeneous time-reversal system. As stated before, heterogeneous terminal devices of different types have distinct center frequencies (f c     i   &#39;s) and bandwidths (B i &#39;s). First of all, the radio-frequency (RF) components of different types have to be distinct. Specifically, the oscillation frequency of the voltage-controlled oscillator at type i terminal device is set to f c     i    and the bandwidth of analog bandpass filter is B i . Then, the ADC deployed for type i terminal devices has the sampling rate of f s     i   =αB i  based on the previous discussion. Furthermore, various root-raised-cosine filters for different types are required, i.e.,  . In order to support heterogeneous terminal devices simultaneously, the bandwidth of the access point, denoted as B AP , is the aggregated bandwidth of all heterogeneous terminal devices. Even though more complicated digital signal processing is implemented at the access point to handle different data streams for various types, only one set of RF components is needed at the access point side. The digital signal processing includes frequency shift, rate convertor and root-raised-cosine filter. More specifically, a frequency shift component exp jω     i     n  is implemented for each type of terminal devices to support multiple carrier frequencies. The parameter ω i  is determined based on the difference between the center frequency of type i device f c     i    and the center frequency of the access point f c     AP   , and n is the time index. A distinct sample rate convertor (expander or decimator) with rate αB AP /B i  is deployed for each type i terminal device to enable the multirate processing. The root-raised-cosine filter RRC B     i     ,αB     AP    for type i terminal device is utilized to limit the effective bandwidth of signals for the heterogeneous terminal devices. 
       FIG. 8  is a diagraph of the channel probing phase of a type i terminal device. Compared with the diagram in  FIG. 4 , there are some differences. At a terminal device  400 , prior to the data transmission phase, an impulse signal  324  is upsampled by α using an upsampling unit  326 , filtered by a root-raised-cosine filter RRC B     i     ,αB     i   [n]  402 , converted to an analog signal by the DAC  330 , and transmitted out after going through the RF components at the terminal device side. The transmitted signal propagates to an access point  406  through a multipath channel  404  represented by h i (t). The signal captured by the access point  406  is amplified by a low-noise amplifier (LNA)  344 , filtered by a bandpass filter  346 , and converted in frequency using a voltage-controlled oscillator  348  to generate a baseband signal. The access point  406  samples the received signal with a higher sample rate f s =αB AP  using the ADC  350 , shifts the signal to baseband (based on the difference between f c     i    and f c     AP   ) using the frequency shift component  408 , filters the signal through the other matched root-raised-cosine filter RRC B     i     ,αB     AP   [n]  410 , downsamples the waveform by αB AP /B i  using the downsampling unit  412 , and finally records the downsampled waveform as ĥ i , which can represent a channel estimate  414 . With a sample rate f s =αB AP , the discrete channel impulse response can be written as
 
   h     i   [n]=h   i ( nT   s ),  (12)
 
where T s =1/(αB AP ).
 
     Since the digital-to-analog convertor (DAC)  330  serves as an interpolator, the transmitted signal of the terminal device shown in  FIG. 8  is mathematically equivalent to that generated through the following process: upsampled by αB AP /B i , filtered by RRC B     i     ,αB     AP   [n], and converted to analog signal by the DAC. Therefore, similarly the equivalent channel impulse response for the type i terminal device with bandwidth B i  can be expressed as
 
 ĥ   i =√{square root over (β i )}( RRC   B     i     ,αB     AP     * h     i   *RRC   B     i     ,αB     AP   ) [αβ     i     ] ,  (13)
 
where β i =B AP /B i  and √{square root over (β i )} is used to compensate the power difference between RRC B     i     ,αB     i   [n] and RRC B     i     ,αB     AP   [n].
 
     Even though the channel probing by a single type of device is discussed above, the same principle can be applied to multi-type terminal devices by deploying different digital processing (, e.g., frequency shift, root-raised-cosine filtering and downsampling with type-specific factor) for multi-type devices in parallel. In other words, the access point can support heterogeneous terminal devices with one single set of RF components but more complicated digital processing. 
     In some implementations, system information (e.g., bandwidth and carrier frequency of the terminal device) can be transmitted from the terminal devices to the access point using one or more control channels, e.g., one or more pilot channels. When performing channel probing, the access point  406  can configure the frequency shifter  408 , the root-raised-cosine filter  410 , and the downsampling unit  412  with the appropriate parameters based on the system information provided by the terminal devices. 
     Data Transmission Phase 
     Suppose N types of terminal devices are communicating with the access point simultaneously, where the number of terminal devices in type i is denoted as M i . Upon acquiring the equivalent channel impulse responses, the signature waveform g i,j  is determined for the j th  terminal device in the type i with various existing design methods. Here, we use the basic time-reversal signature design as an example, 
                         g     i   ,   j       ⁡     [   n   ]       =           h   ^       i   ,   j     *     ⁡     [     L   -   1   -   n     ]                h   ^       i   ,   j                ,           (   14   )               
where ĥ i,j  is defined in (13).
 
     First, the downlink data transmission from an access point  440  to heterogeneous terminal devices  442  in a heterogeneous system  420  is considered. Referring to  FIG. 9 , let {X i,j [k]}  422  be the sequence of information symbols transmitted to the j th  terminal device of type i. Similar to the case in the homogeneous time-reversal system, a rate backoff factor D i,j    424  is introduced to adjust the symbol rate, i.e., the symbol rate for the j th  terminal device of type i is (B i /D i,j ). Then, the signature g i,j    426  is embedded into the terminal device-specific data stream X i,j   [D     i,j     ]  and the signature embedded symbols of the same type i are merged together (e.g., using an adder  428 ) as S i , e.g.,
 
 S   i =Σ j=1   M     i   ( X   i,j   [D     i,j     ]   *g   i,j ).  (15)
 
Later, the merged symbols S i  go through the type-specific digital signal processing, i.e., upsampled with factor αB AP /B i  using an upsampling unit  430 , filtered by a root-raised-cosine filter RRC B     i     ,αB     AP      432  and carried to the type-specific digital frequency with frequency shift exp(−jω i n) using a frequency shifter  434 . The processed data streams of N types are mixed together (e.g., using an adder  436 ) to generate a composite downlink signal  452 . The composite downlink signal  452  passes through one set of RF components  438  at the access point  440 , and is broadcasted to all the heterogeneous terminal devices.
 
     Regarding the receiver (i.e., terminal device) side, here we use the j th  terminal device of type i as an example. The broadcast signal propagates to the terminal device through a multipath channel  444  having a profile h i,j (t). Because of the spatial-temporal focusing effect, the downlink signal that has been processed with the signature waveform g i,Mi  converges at the Mi-th terminal device of type i. The composite downlink signal broadcast from the access point  440  travels through different multipaths to reach different terminal devices  442 . After the downlink signal is received at the terminal device, the signal passes through an analog bandpass filter  446  having a center frequency at f c     i    and a bandwidth B i . Note that the filtered signal includes not only the intended signal but also interferences, e.g., inter-user inference (IUI) from other terminal devices within the same type and the inter-type-interference (ITI) from other terminal devices of the other types (whose spectrum overlaps with type i). Because of the spatial-temporal focusing effect, the interferences are suppressed due to the unique multipath profile. Afterwards, the signal is carried to baseband and sampled with a sample rate f s     i   =αB i  (e.g., using an analog-to-digital converter  448 ), which is much smaller than that at the access point for the low-end terminal devices. The sampled signal goes through a raised-root-cosine filter RRC B     i     ,αB     i      450  and the rate matching decimator to generate symbols {Y i,j [k]}, from which {X i,j [k]} can be determined. 
       FIG. 10  is a diagram of the system architecture for uplink transmission of data from the terminal devices  442  to the access point  440  of the heterogeneous system  420 . The figure shows that the heterogeneous time-reversal system  420  has an asymmetric architecture. As will be described in more detail below, the access point  440  handles more complicated signal and data processing, while the data processing at the terminal devices  442  is simpler. This allows lower-cost data processors to be used at the terminal devices. 
     The following describes the processing of uplink signals that is performed at the terminal devices  442 . Let X i,j    462  be the information symbols transmitted to the j th  terminal device of type i. A rate backoff factor D i,j    464  is introduced to adjust the symbol rate, and the signal is upsampled by α using an upsampling unit  466 . The upsampled signal is filtered by a root-raised-cosine filter RRC B     i     ,αB     i      468 , in which B 1  is the frequency bandwidth used by the terminal device. The filtered signal is converted to an analog baseband signal using a digital-to-analog converter  470 . The baseband signal is modulated to a high carrier frequency by a voltage-controlled oscillator  332 , and put through a bandpass filter  472  having a center frequency f ci  and a bandwidth B i . The filtered signal is amplified by a power amplifier  336  to produce a radio frequency (RF) signal. The RF signal is broadcasted by an antenna  338 . 
     The signal from the j th  terminal device of type i passes a multipath channel having a profile h i,j . Noise is added to the uplink signal as the uplink signal passes the multipath channel. The uplink signals from all of the terminal devices  442 , after passing the respective multipath channels, are received at the antenna  342  of the access point  440 . The signal received by the antenna  342  is an aggregate of the uplink signals transmitted from the terminal devices through the various multipath channels, and is referred to as a composite uplink signal. 
     The following describes the processing of the composite uplink signal that is performed at the access point  440 . Similar to the homogeneous time-reversal system, in the heterogeneous time-reversal system  420 , the precoding signatures g i,j &#39;s in the downlink can serve as the equalizers in the uplink. After converting the signal into digital domain through a single set of RF components at the access point  440 , multiple parallel digital processing (e.g., frequency shift, root-raised-cosine filtering, and rate conversion) are performed to support N types of terminal devices  442  simultaneously. 
     In some implementations, the composite uplink signal received at the antenna  342  is amplified by a low-noise amplifier  344 , and filtered by a bandpass filter  474  having a center frequency f cAP  and a bandwidth B AP . The pass band of the bandpass filter  474  spans a frequency range that encompasses the pass bands of the bandpass filters  472  of the terminal devices  442 . The filtered signal is converted to the analog baseband signal using a VCO  348 . The baseband signal is sampled by an analog-to-digital converter (ADC)  476  with a sample rate f s =αB AP  to produce a digital signal  484 . 
     In some implementations, the digital signal  484  is divided into N parallel data streams for the N types of terminal devices. For example, one of the data stream is associated with the i-th type of device, and the digital signal  484  is carried to the type-specific digital frequency with frequency shift exp(jω i n) using a frequency shifter  478 . The digital signal is then filtered by a raised-root-cosine filter RRC B     i     ,αB     AP      480  and downsampled by a factor αB AP /B i  using a downsampling unit  482  to produce a digital signal  486 . 
     In some implementations, the digital signal  486  is divided into M 1  parallel data streams that are associated with the M i  terminal devices of type i. For example, one of the data streams is associated with the j-th terminal device of type i. The signature waveform g i,j  used to process the downlink signal for the j-th terminal device of type i can also serve as the equalizer for processing the uplink signal from the j-th terminal device of type i. In this example, the signature waveform g i,j    488  is applied to the digital signal  486 , and the resulting signal is downsampled by a factor of D i,j  using a downsampling unit  490  to produce a downsampled signal Y i,j    492 , which can be used to estimate the transmitted information symbols X i,j    462 . 
     The access point  440  may include detection modules that perform interference cancellation and detection that cancels the inter-symbol interference and the inter-user interference to determine the user uplink data X ij . For example, an inter-symbol interference and inter-user interference cancellation technique is described in U.S. application Ser. No. 13/969,320, titled “Multiuser Time-Reversal Division Multiple Access Uplink system With Parallel Interference Cancellation,” filed on Aug. 6, 2013, the contents of which are incorporated by reference in their entirety. 
     Compared with the homogeneous time-reversal system, the heterogeneous time-reversal system  420  maintains the capability to support different QoS through not only varying the backoff factor D i,j  but also providing the flexibility for terminal devices to select various bandwidths (B i &#39;s). More importantly, the heterogeneous time-reversal system architecture further promotes the benefit of the asymmetric complexity. In the heterogeneous time-reversal system  420 , the complexity is even more concentrated at the access point side, as compared to that of the homogeneous time-reversal system. In some implementations, regarding the access point, a single set of RF components is used. Even though more complicated parallel digital signal processing is needed at the access point, it can be satisfied with more powerful digital signal processing (DSP) unit at an affordable cost and complexity. Regarding the heterogeneous terminal devices, the ADC sample rate is reduced significantly for those devices with smaller bandwidths, which lowers the cost of hardware significantly for the low-end terminal devices. In addition, the lower sample rate decreases the computational burden. 
     In some implementations, the transmitted waveforms can be designed based on given design criteria such as system performance, quality of service constraints, or fairness among users. The amplitude and phase of each tap of the waveform can be adjusted based on the channel information, such that after convolving with the channel, the received signal at the receiver retains most of the intended signal strength and rejects or suppresses the interference as much as possible. Techniques for waveform design are described in U.S. patent application Ser. No. 13/706,342, titled “Waveform Design for Time-Reversal Systems,” filed on Dec. 5, 2012, the contents of which are incorporated by reference in their entirety. 
     Performance Analysis of a Heterogeneous Time-Reversal System 
     The heterogeneous time-reversal system is analyzed under the general scenario, where N types of terminal devices are supported in the system and the number of type i terminal device is M i . The spectrum usage of the different types of devices is shown in  FIG. 7 . 
     Let {X i,j [k]} denote the information symbols for the j th  terminal device in type i, and D i,j  and g i,j  are the backoff factor and the embedded signature for the symbols {X i,j [k]}, respectively. The terminal devices in type i suffer from inter-type-interference from type k terminal devices, where k∈T i  and T i  denotes the set of types of devices whose spectrum is overlapped with type i devices. In other words, the data streams of type k devices, where k∉T i , cause no interference to type i terminal devices. 
     Regarding the channel impulse response, we denote  h   i,j  as the discrete channel impulse response from the access point to the j th  terminal device in type i with sample rate f s =αB AP . Let ĥ i     m     ,k     n    be the equivalent channel impulse response for the data stream of the m th  terminal device in type i between the access point to the n th  terminal device in type k. Similar to equation (13), the equivalent channel impulse response for data streams can be derived as 
                       h   ^         i   m     ,     k   n         =     (                 β   i       ⁢       (       RRC       B   i     ,     α   ⁢           ⁢     B   AP           *       h   _       i   ,   n       *     RRC       B   i     ,     α   ⁢           ⁢     B   AP             )       [     αβ   ⁢           ⁢   i     ]         ,             i   =   k     ,                   (       RRC       B   i     ,     α   ⁢           ⁢     B   AP           *       h   _       k   ,   n       *     RRC       B   k     ,     α   ⁢           ⁢     B   k           [     β   k     ]         )       [   α   ]       ,             i   ≠   k     ,                     (   16   )               
where β i =B AP /B i . From equation (16), the length of the equivalent channel impulse response solely depends on the types of data stream and the receiving terminal device. Once the channel impulse responses are estimated, various signature design methods can be deployed. For example, the basic time-reversal signature of the j th  terminal device of a type i device can be written as:
 
                       g     i   ,   j       ⁡     [   n   ]       =             h   ^         i   j     ,     i   j       *     ⁡     [     L   -   1   -   n     ]                h   ^         i   j     ,     i   j                .             (   17   )               
Thus, the received symbols at the j th  terminal device Y i,j  of type i can be expressed as
 
     
       
         
           
             
               
                 
                   
                     
                       
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     In equation (18), the first term is the intended signal, the second and third terms represent the inter-symbol interference (ISI) and the inter-user interference within the same type, and the inter-type-interference from overlapped types (k∈T i ) is expressed as the fourth term. Based on equation (18), the SINR for the j th  terminal device in type i within the general heterogeneous time-reversal system can be calculated correspondingly similar to equation (11). 
     Time Division Multiple Access and Spectrum Allocation 
     We first consider three devices in the heterogeneous time-reversal system, whose features are listed in Table 1. According to the table, the bit rates of the high-definition (HD) video and the high-definition audio are around 18 Mbits/s and 4 Mbits/s. The bandwidth of the access point is assumed to be 150 MHz to support simultaneous data transmission to these 3 devices. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Device  
                 Bandwidth 
                 Backoff 
                   
                 Coding 
                 Waveform 
               
               
                 Name 
                 (MHz) 
                 Factor 
                 Modulation 
                 Rate 
                 Design 
               
               
                   
               
             
            
               
                 HD Video 1 
                 150  
                  8 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                 HD Audio 1 
                 50 
                 12 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                 HD Audio 2 
                 50 
                 12 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                   
               
            
           
         
       
     
     We first consider the case that three devices are categorized into two types, where Type 1 includes the high-definition video device and Type 2 includes two high-definition audio devices. Referring to  FIG. 11 , a graph  500  shows the bit error rate (BER) performance of three devices under such a scenario. It can be inferred from the figure that the bit error rate performance of the two high-definition audio devices (represented by curves  502  and  504 , which in this example overlap each other) is much worse compared with the bit error rate of high-definition video (represented by curve  506 ). The reason for this result is that the suppression of inter-user interference in the time-reversal system heavily depends on the number of resolved independent multipaths, which increases with the bandwidth. Since the bandwidth of two high-definition audio is much narrower, the inter-user interference from the other devices becomes more severe with the basic time-reversal signature. In order to tackle the inter-user interference for the devices with a narrower bandwidth, along with the time-reversal technology, other techniques can also be used in the heterogeneous time-reversal system. 
     We first consider applying time division multiple access (TDMA) to the heterogeneous time-reversal system. In this example, the access point supports one high-definition audio at a time. To maintain the same QoS requirement in terms of bit rate, either adjusting the coding rate or decreasing the backoff factor is adopted in the system. Referring to  FIGS. 12A and 12B , graphs  510  and  520  show the improved bit error rate performance of three devices with TDMA. In  FIG. 12A , the graph  510  show results in which the channel coding is removed. In  FIG. 12B , the graph  520  shows the results in which the backoff rate is decreased to maintain the same bit rate for the high-definition audio. Compared with the bit error rate in  FIG. 11 , the bit error rate performance shown in  FIGS. 12A and 12B  is improved significantly with the TDMA. Moreover, a comparison of graphs  510  and  520  indicate that decreasing the backoff factor to maintain the bit rate is a better strategy for the devices with narrow bandwidths. In some implementations, additional waveform design techniques can be implemented in the heterogeneous time-reversal system to achieve even better performance. 
     Even though a narrow bandwidth decreases the number of resolved independent multipaths thus resulting in severer inter-user interference, a narrow bandwidth on the other hand provides more flexibility for spectrum allocation. Therefore, another way to improve the bit error rate performance in the example of  FIG. 11  is to arrange the spectrum allocation smartly to remove unnecessary interference. For example, the three devices in Table 1 can be categorized into three distinct types, where two high-definition audio devices are allocated into two spectrally non-overlapped types. Referring to  FIG. 13 , a graph  530  shows the improved bit error rate performance with the spectrum allocation described above. 
     Heterogeneous Time-Reversal System Case Study: Smart Homes 
     We choose Smart Homes as an example of the Internet of Things application to test the bit error rate performance with the heterogeneous time-reversal paradigm. Instrumenting buildings with the Internet of Things technologies will help in not only reducing resources (electricity, water) consumption but also in improving the satisfaction level of humans. Typically, the high-definition video and high-definition audio are employed in the Smart Homes for both the security monitoring and entertainment. Moreover, smart sensors are used in the Smart Homes to both monitor resource consumptions as well as to proactively detect the users&#39; need. Therefore, in the following simulation, we assume one high-definition video, one high-definition audio and five smart sensors in the Smart Homes are supported by the heterogeneous time-reversal paradigm. The specific features of these devices are listed in Table 2, the spectrum allocation is shown in  FIG. 14 , and the corresponding bit error rate performance is shown in a graph  540  in  FIG. 15 . The results show good bit error rate performance for all types of devices. Note the saturation of the bit error rate for the high-definition video is due to the dominant inter-user interference with the basic time-reversal signature. In addition, the slight difference in the bit error rate for the smart sensors comes from the frequency-selectivity of the channel. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Device 
                 Bandwidth 
                 Backoff 
                   
                 Coding 
                 Waveform 
               
               
                 Name 
                 (MHz) 
                 Factor 
                 Modulation 
                 Rate 
                 Design 
               
               
                   
               
             
            
               
                 HD Video 1 
                 150  
                  8 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                 HD Audio 1 
                 50 
                 12 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                 Smart Sensor 1 
                 10 
                 10 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                 Smart Sensor 2 
                 10 
                 10 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                 Smart Sensor 3 
                 10 
                 10 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                 Smart Sensor 4 
                 10 
                 10 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                 Smart Sensor 5 
                 10 
                 10 
                 QPSK 
                 ½ 
                 Basic TR 
               
               
                   
               
            
           
         
       
     
     In some implementations, the access point  302 ,  320 ,  406 , or  440  can be part of a mobile or stationary device. For example, the access point can be implemented as part of a sensor module, a controller, a mobile phone, a laptop computer, a desktop computer, a modem, a router, or an electronic appliance that communicates wirelessly with multiple other devices. For example, a mobile phone or a laptop computer may communicate simultaneously with the smart sensors  304 , the smart home appliances  306 , the healthcare devices  308 , the entertainment devices  310 , the security devices  312 , printers, thermometers, lighting control systems, and other devices using the techniques described above. 
     The access point can include one or more processors and one or more computer-readable mediums (e.g., RAM, ROM, SDRAM, hard disk, optical disk, and flash memory). The one or more processors can perform various calculations described above. The calculations can also be implemented using application-specific integrated circuits (ASICs). The term “computer-readable medium” refers to a medium that participates in providing instructions to a processor for execution, including without limitation, non-volatile media (e.g., optical or magnetic disks), and volatile media (e.g., memory) and transmission media. Transmission media includes, without limitation, coaxial cables, copper wire and fiber optics. 
     The features described above can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result. A computer program can be written in any form of programming language (e.g., C, Java, Perl, Python), including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, a browser-based web application, or other unit suitable for use in a computing environment. 
     Suitable processors for the execution of a program of instructions include, e.g., both general and special purpose microprocessors, digital signal processors, and the sole processor or one of multiple processors or cores, of any kind of computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memories for storing instructions and data. Generally, a computer will also include, or be operatively coupled to communicate with, one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits).
         While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination.   Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.       

     Thus, particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous. 
     Other embodiments are within the scope of the following claims. For example, the devices that communicate with the base station can be different from those shown in  FIG. 3 , and can include many more objects. In the time-reversal wireless communication system, a transmitter and a receiver need to obtain information about the overall system, e.g., information about the communication channel and information about time synchronization. In some implementations, such information is obtained in a channel probing (CP) phase and a data transmission (DT) phase of a time-reversal communication system. In the channel probing phase, the transmitter acquires channel information to realize the focusing effects, while in the data transmission phase, the receiver acquires timing information to synchronize and sample relevant signals. The process of obtaining channel information in the channel probing phase and obtaining synchronization in the data transmission phase is referred to as time-reversal handshaking. Techniques for time-reversal handshaking is described in U.S. Pat. No. 9,313,020, titled “Handshaking Protocol For Time-Reversal System,” the contents of which are incorporated by reference in their entirety.