PATENT DOCUMENT

Publication Number: US-10756774-B2
Application Number: US-201816224658-A
Country: US
Kind Code: B2

Title: Nonlinear interference cancellation

Abstract:
The representative embodiments discussed in the present disclosure relate to techniques in which a transmitter may operate in an uplink multiple-input, multiple-output (MIMO) mode of operation. More specifically, in some embodiments, the transmitter may concurrently transmit a first and a second signal within the same frequency band via a first and second antenna, respectively. Further, in some embodiments, the transmitter may include circuitry and/or logic to offset nonlinear interference present in the transmitted signals as a result of antenna coupling between the first and second antenna and a nonlinear element (e.g., a power amplifier) within the transmitter.

Claims:
What is claimed is: 
     
       1. A transmitter configured to concurrently transmit a first transmission signal via a first antenna and a second transmission signal via a second antenna, comprising:
 a first multiple-input, multiple-output (MIMO) transmitter communicatively coupled to the first antenna, wherein the first MIMO transmitter is configured to prepare an expected first signal for transmission via the first antenna and to transmit the first transmission signal at the first antenna based at least in part on the expected first signal; 
 a second multiple-input, multiple-output (MIMO) transmitter communicatively coupled to the second antenna, wherein the second MIMO transmitter is configured to prepare an expected second signal for transmission via the second antenna and to transmit the second transmission signal at the second antenna based at least in part on the expected second signal, wherein the expected second signal is in the same frequency band as the expected first signal; and 
 multiple-input, multiple-output intermodulation distortion (MIMO IMD) cancellation circuitry communicatively coupled to the first MIMO transmitter and the second MIMO transmitter, wherein the MIMO IMD cancellation circuitry is configured to: 
 receive the expected first signal from the first MIMO transmitter; 
 receive the expected second signal from the second MIMO transmitter; 
 determine a first set of cross-modulation products based at least in part on the expected first signal, the expected second signal, and a first set of weight factors; and 
 inject the inverse of the first set of cross-modulation products into the expected first signal at the first MIMO transmitter. 
 
     
     
       2. The transmitter of  claim 1 , wherein the transmitter is configured to operate in an uplink multiple-input, multiple-output (UL-MIMO) mode to concurrently transmit the first transmission signal and the second transmission signal. 
     
     
       3. The transmitter of  claim 1 , wherein the transmitter is configured to support data communication over a 5th generation (5G) cellular network, a long term evolution (LTE) cellular network, or a combination thereof. 
     
     
       4. The transmitter of  claim 1 , wherein the first MIMO transmitter comprises a nonlinear circuit element, and wherein, the first transmission signal comprises the expected first signal and nonlinear interference produced by the nonlinear circuit element. 
     
     
       5. The transmitter of  claim 4 , wherein the nonlinear circuit element comprises a power amplifier. 
     
     
       6. The transmitter of  claim 1 , wherein the MIMO IMD cancellation circuitry is configured to:
 receive the first transmission signal from the first MIMO transmitter; 
 compare the first transmission signal with the expected first signal; and 
 determine the first set of weight factors based at least in part on the comparison of the expected first signal and the first transmission signal. 
 
     
     
       7. The transmitter of  claim 6 , wherein receiving the first transmission signal comprises receiving a discrete time representation of the first transmission signal sampled at twice a Nyquist rate of a bandwidth of a channel implemented to carry the first transmission signal, the second transmission signal, or both. 
     
     
       8. The transmitter of  claim 1 , wherein the MIMO IMD cancellation circuitry is configured to predict the first set of cross-modulation products based at least in part on a Volterra model. 
     
     
       9. The transmitter of  claim 1 , wherein the MIMO IMD cancellation circuitry is configured to:
 determine a second set of weight factors based in part on the second transmission signal and the expected second signal; 
 determine a second set of cross-modulation products based at least in part on the expected first signal, the expected second signal, and the second set of weight factors; and 
 inject the inverse of the second set of cross-modulation products into the expected second signal at the second MIMO transmitter. 
 
     
     
       10. The transmitter of  claim 1 , wherein the first set of cross-modulation products comprise at least third order cross-modulation products of a cross-modulation of the expected first signal cross with the expected second signal. 
     
     
       11. The transmitter of  claim 1 , wherein the first MIMO transmitter comprises:
 digital transmitter circuitry configured to identify the expected first signal; 
 digital pre-distortion and envelope tracking circuitry communicatively coupled to the digital transmitter circuitry and configured to:
 receive a feedback signal from digital signal processing circuitry of the first MIMO transmitter; and 
 modify the expected first signal to offset distortion introduced by a power amplifier of the first MIMO transmitter in the first transmission signal based at least in part on the feedback signal and to produce an updated first signal; 
 a digital-to-analog converter (DAC) configured to convert the updated first signal from a digital signal to an analog signal to generate a first analog signal; and 
 envelope tracking circuitry configured to regulate power supplied to the power amplifier based at least in part on an envelope of the expected first signal, wherein the power amplifier is configured to amplify the first analog signal based at least in part on the regulated power to produce the first transmission signal. 
 
 
     
     
       12. The transmitter of  claim 1 , wherein the first MIMO transmitter comprises a feedback receiver path communicatively coupled to the MIMO IMD cancellation block and configured to route the first transmission signal to the MIMO cancellation block, wherein the feedback receiver path comprises:
 an analog-to-digital converter (ADC) configured to convert the first transmission signal from an analog signal to a digital signal. 
 
     
     
       13. A method of operating a transmitter in an uplink multiple-input, multiple-output (UL-MIMO) mode, comprising:
 receiving, at multiple-input, multiple-output intermodulation distortion (MIMO IMD) cancellation circuitry communicatively coupled to a first MIMO transmitter of the transmitter, an expected first signal, wherein the first MIMO transmitter is configured to prepare the expected first signal for transmission at a first antenna of the transmitter; 
 receiving, at the MIMO IMD cancellation circuitry, an expected second signal from a second MIMO transmitter of the transmitter communicatively coupled to the MIMO IMD cancellation circuitry, wherein the second MIMO transmitter is configured to prepare the expected second signal for transmission at a second antenna of the transmitter, wherein the expected second signal is in the same frequency band as the expected first signal; 
 determining, using the MIMO IMD cancellation circuitry, a first set of cross-modulation products based at least in part on the expected first signal, the expected second signal, and a first set of weight factors; 
 injecting the inverse of the first set of cross-modulation products into the expected first signal at the first MIMO transmitter to produce an updated first signal; and 
 transmitting, at the first antenna, a first transmission signal based in part on the updated first signal. 
 
     
     
       14. The method of  claim 13 , comprising determining, using the MIMO IMD cancellation circuitry, the first set of weight factors, wherein determining the first set of weight factors comprises:
 capturing, at a feedback receiver path of the first MIMO transmitter, the first transmission signal; 
 comparing, using the MIMO IMD cancellation circuitry, the captured first transmission signal with the expected first signal; and 
 determining the first set of weight factors based at least in part on the comparison. 
 
     
     
       15. The method of  claim 14 , comprising determining the first set of weight factors with a regular periodicity. 
     
     
       16. The method of  claim 14 , comprising determining the first set of weight factors in response to a change in frequency and/or power supplied to the transmitter. 
     
     
       17. The method of  claim 14 , comprising determining, using the MIMO IMD cancellation circuitry, the first set of weight factors, wherein determining the first set of weight factors comprises:
 retrieving the first set of weight factors from non-transitory memory, wherein the non-transitory memory is initialized with the first set of weight factors, and, wherein, the first set of weight factors comprise at least one non-zero weight factor. 
 
     
     
       18. A method of operating a multiple-input, multiple-output intermodulation distortion (MIMO IMD) cancellation circuitry of a transmitter operating in an uplink multiple-input, multiple-output (UL-MIMO) mode, comprising:
 receiving, at first input circuitry of the MIMO IMD cancellation block, a first transmission signal captured at a first feedback receiver path of a first MIMO transmitter of the transmitter, wherein the first input circuitry is communicatively coupled to the first MIMO transmitter; 
 receiving, at second input circuitry of the MIMO IMD cancellation circuitry, an expected first signal from the first MIMO transmitter, wherein the second input circuitry is communicatively coupled to the first MIMO transmitter, and, wherein the first MIMO transmitter is configured to prepare the expected first signal for transmission at a first antenna of the transmitter; 
 receiving, at third input circuitry of the MIMO IMD cancellation circuitry, an expected second signal from a second MIMO transmitter of the transmitter, wherein the third input circuitry is communicatively coupled to the second MIMO transmitter, and, wherein the second MIMO transmitter is configured to prepare the expected second signal for transmission at a second antenna of the transmitter; 
 comparing, using training circuitry of the MIMO cancellation circuitry, the first transmission signal with the expected first signal; 
 determining, using the training circuitry, a first set of weight factors based at least in part on the comparison of the first transmission signal and the expected first signal; 
 scaling, using mixing product calculation and scaling circuitry of the MIMO IMD cancellation circuitry, a first set of cross-modulation products based at least in part on the first set of weight factors to produce a first set of scaled cross-modulation products, wherein the mixing product calculation and scaling circuitry is configured to determine the first set of cross-modulation products based at least in part on the first expected signal and the second expected signal; and 
 outputting, using mixing product calculation and scaling circuitry of the MIMO IMD cancellation circuitry, the inverse of the first set of scaled cross-modulation products to the first MIMO transmitter. 
 
     
     
       19. The method of  claim 18 , wherein receiving the expected first signal comprises sampling the expected first signal in discrete time to produce a sampled first signal, wherein receiving the expected second signal comprises sampling the expected second signal in discrete time to produce a sampled second signal, and, wherein the mixing product calculation and scaling circuitry is configured to determine the first set of cross-modulation products based at least in part on the first sampled signal and the second sampled signal delayed by one or more samples. 
     
     
       20. The method of  claim 18 , comprising:
 receiving, at fourth input circuitry of the MIMO IMD cancellation block, a second transmission signal captured at a second feedback receiver path of the second MIMO, wherein the fourth input circuitry is communicatively coupled to the second MIMO transmitter; 
 comparing, using training circuitry of the MIMO cancellation circuitry, the second transmission signal with the expected second signal; 
 determining, using the training circuitry, a second set of weight factors based at least in part on the comparison of the second transmission signal and the expected second signal; 
 scaling, using the mixing product calculation and scaling circuitry of the MIMO IMD cancellation circuitry, a second set of cross-modulation products based at least in part on the second set of weight factors to produce a second set of scaled cross-modulation products, wherein the mixing product calculation and scaling circuitry is configured to determine the second set of cross-modulation products based at least in part on the first expected signal and the second expected signal; and 
 outputting, using mixing product calculation and scaling circuitry of the MIMO IMD cancellation circuitry, the inverse of the second set of scaled cross-modulation products to the second MIMO transmitter.

Description:
BACKGROUND 
     The present disclosure relates generally to cellular and wireless devices and, more particularly, to cellular and wireless devices having a transceiver capable of reducing nonlinear interference (e.g., cross-modulation products) present in signals transmitted using an uplink multiple-input, multiple-output (UL-MIMO) mode of operation. 
     This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present disclosure, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. 
     Transceivers are commonly included in various electronic devices, and particularly, portable electronic devices such as, for example, phones (e.g., mobile and cellular phones, cordless phones, personal assistance devices), computers (e.g., laptops, tablet computers), internet connectivity routers (e.g., Wi-Fi routers or modems), radios, televisions, or any of various other stationary or handheld devices. Certain types of transceivers, known as wireless transceivers, may be used to generate wireless signals to be transmitted by way of an antenna in the transceiver. Moreover, certain transceivers include multiple antennas such that each antenna may concurrently transmit a respective signal within the same frequency band over a wireless channel (e.g., air). However, concurrently transmitting signals from antennas that are proximate to one another (e.g., within the same transceiver) may introduce distortion, such as nonlinear interference, into the transmitted signals. 
     SUMMARY 
     A summary of certain embodiments disclosed herein is set forth below. It should be understood that these aspects are presented merely to provide the reader with a brief summary of these certain embodiments and that these aspects are not intended to limit the scope of this disclosure. Indeed, this disclosure may encompass a variety of aspects that may not be set forth below. 
     As described in greater detail below, the transceiver may include multiple antennas to operate in an uplink multiple-input, multiple output (UL-MIMO) (e.g., spatial multiplexing) mode. As such, two or more of the antennas may concurrently transmit a respective data signal within the same frequency band. However, because the antennas are transmitting within the same frequency band concurrently, the antennas may become coupled. For instance, a first antenna of a first transmitter within the transceiver may transmit a first signal while simultaneously receiving a second signal transmitted by a second antenna of a second transmitter of the transceiver. Similarly, the second antenna may receive the first signal while transmitting the second signal. Accordingly, nonlinear elements of the transceiver, such as a power amplifier, may cross-modulate the signal transmitted at the first antenna with signals received from proximate, coupled antennas (e.g., the second antenna). As a result, the first antenna may transmit the first signal with nonlinear interference (e.g., cross-modulation products and/or intermodulation distortion), and the second antenna may transmit the second signal with nonlinear interference, which may degrade certain performance characteristics, such as the adjacent channel leakage ratio (ACLR) and/or the error vector magnitude (EVM) of the transceiver. 
     Accordingly, to limit the distortion caused by the cross-modulation of signals, the transceiver may include circuitry and/or logic, such as a multiple-input, multiple output intermodulation (MIMO IMD) cancellation block, implemented to estimate cross-modulation products present in a transmitted signal. The MIMO IMD cancellation block may estimate the cross-modulation products based in part on the signals expected to be transmitted by the transceiver before distortion is introduced by nonlinear interference (e.g., expected signals) and the signals transmitted by the transceiver (e.g., transmission signals), which may include nonlinear interference. In some embodiments, for example, the MIMO IMD cancellation block may estimate the cross-modulation products and scale the estimated cross-modulation products using a set of weight factors based in part on a model, such as a Volterra model. Further, the transceiver may inject the inverse of the estimated cross-modulation products into the expected signals to offset the nonlinear interference predicted to be present in the transmission signals. 
     Accordingly, the representative embodiments discussed in the present disclosure relate to techniques in which nonlinear interference resulting from antenna coupling may be reduced in transmitted signals. More specifically, in some embodiments, the nonlinear interference may be predicted based on expected signals, transmission signals, and a set of weight factors. The expected signals may then be modified based on the prediction to offset the nonlinear interference. Further, in some embodiments, a method to determine the set of weight factors based in part on one or more of the expected signals and one or more of the transmission signals may be employed regularly and/or based in part on certain conditions of the transceiver and/or an electronic device such that the efficacy of the predictions may be improved. 
     Various refinements of the features noted above may exist in relation to various aspects of the present disclosure. Further features may also be incorporated in these various aspects as well. These refinements and additional features may exist individually or in any combination. For instance, various features discussed below in relation to one or more of the illustrated embodiments may be incorporated into any of the above-described aspects of the present disclosure alone or in any combination. The brief summary presented above is intended only to familiarize the reader with certain aspects and contexts of embodiments of the present disclosure without limitation to the claimed subject matter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various aspects of this disclosure may be better understood upon reading the following detailed description and upon reference to the drawings in which: 
         FIG. 1  is a schematic block diagram of an electronic device including a transceiver, in accordance with an embodiment; 
         FIG. 2  is a perspective view of a notebook computer representing an embodiment of the electronic device of  FIG. 1 ; 
         FIG. 3  is a front view of a hand-held device representing another embodiment of the electronic device of  FIG. 1 ; 
         FIG. 4  is a front view of another hand-held device representing another embodiment of the electronic device of  FIG. 1 ; 
         FIG. 5  is a front view of a desktop computer representing another embodiment of the electronic device of  FIG. 1 ; 
         FIG. 6  is a front view and side view of a wearable electronic device representing another embodiment of the electronic device of  FIG. 1 ; 
         FIG. 7  is a schematic block diagram of an embodiment of a transmitter of the transceiver that may exhibit non-linear interference, in accordance with an embodiment; 
         FIG. 8  is schematic block diagram of a transmitter including a multiple-input, multiple-output intermodulation distortion (MIMO IMD) cancellation block, in accordance with an embodiment; 
         FIG. 9  is a schematic block diagram of the MIMO IMD cancellation block of  FIG. 8 , in accordance with an embodiment; 
         FIG. 10  is a block diagram of a method for operating the transmitter of  FIG. 8  in an UL-MIMO mode, in accordance with an embodiment; and 
         FIG. 11  is a block diagram of a method for calculating a set of weight factors used to scale cross-modulation products predicted according to the method of  FIG. 10 , in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     One or more specific embodiments of the present disclosure will be described below. These described embodiments are only examples of the presently disclosed techniques. Additionally, in an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
     When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Additionally, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. 
     With the foregoing in mind, a general description of suitable electronic devices that may employ a transceiver capable of reducing nonlinear interference present in signals transmitted in an uplink multiple-input, multiple-output (UL-MIMO) mode of operation will be provided below. Turning first to  FIG. 1 , an electronic device  10  according to an embodiment of the present disclosure may include, among other things, one or more processor(s)  12 , memory  14 , nonvolatile storage  16 , a display  18 , input structures  22 , an input/output (I/O) interface  24 , a network interface  26 , a transceiver  28 , and a power source  29 . The various functional blocks shown in  FIG. 1  may include hardware elements (including circuitry), software elements (including computer code stored on a computer-readable medium) or a combination of both hardware and software elements. It should be noted that  FIG. 1  is merely one example of a particular implementation and is intended to illustrate the types of components that may be present in the electronic device  10 . 
     By way of example, the electronic device  10  may represent a block diagram of the notebook computer depicted in  FIG. 2 , the handheld device depicted in  FIG. 3 , the handheld device depicted in  FIG. 4 , the desktop computer depicted in  FIG. 5 , the wearable electronic device depicted in  FIG. 6 , or similar devices. It should be noted that the processor(s)  12  and other related items in  FIG. 1  may be generally referred to herein as “data processing circuitry.” Such data processing circuitry may be embodied wholly or in part as software, firmware, hardware, or any combination thereof. Furthermore, the data processing circuitry may be a single contained processing module or may be incorporated wholly or partially within any of the other elements within the electronic device  10 . 
     In the electronic device  10  of  FIG. 1 , the processor(s)  12  may be operably coupled with the memory  14  and the nonvolatile storage  16  to perform various algorithms. Such programs or instructions executed by the processor(s)  12  may be stored in any suitable article of manufacture that includes one or more tangible, computer-readable media at least collectively storing the instructions or routines, such as the memory  14  and the nonvolatile storage  16 . The memory  14  and the nonvolatile storage  16  may include any suitable articles of manufacture for storing data and executable instructions, such as random-access memory, read-only memory, rewritable flash memory, hard drives, and optical discs. Also, programs (e.g., an operating system) encoded on such a computer program product may also include instructions that may be executed by the processor(s)  12  to enable the electronic device  10  to provide various functionalities. 
     In certain embodiments, the display  18  may be a liquid crystal display (LCD), which may allow users to view images generated on the electronic device  10 . In some embodiments, the display  18  may include a touch screen, which may allow users to interact with a user interface of the electronic device  10 . Furthermore, it should be appreciated that, in some embodiments, the display  18  may include one or more organic light emitting diode (OLED) displays, or some combination of LCD panels and OLED panels. 
     The input structures  22  of the electronic device  10  may enable a user to interact with the electronic device  10  (e.g., pressing a button to increase or decrease a volume level). The I/O interface  24  may enable the electronic device  10  to interface with various other electronic devices, as may the network interface  26 . The network interface  26  may include, for example, one or more interfaces for a personal area network (PAN), such as a Bluetooth network, for a local area network (LAN) or wireless local area network (WLAN), such as an 802.11x Wi-Fi network, and/or for a wide area network (WAN), such as a 3 rd  generation (3G) cellular network, 4th generation (4G) cellular network, 5 th  generation (5G) cellular network, long term evolution (LTE) cellular network, long term evolution enhanced license assisted access (LTE-eLAA) cellular network, or long term evolution advanced (LTE-A) cellular network. The network interface  26  may also include one or more interfaces for, for example, broadband fixed wireless access networks (WiMAX), mobile broadband Wireless networks (mobile WiMAX), asynchronous digital subscriber lines (e.g., ADSL, VDSL), digital video broadcasting-terrestrial (DVB-T) and its extension DVB Handheld (DVB-H), ultra-wideband (UWB), alternating current (AC) power lines, and so forth. 
     In certain embodiments, to allow the electronic device  10  to communicate over the aforementioned wireless networks (e.g., Wi-Fi, WiMAX, mobile WiMAX, 4G, 5G, LTE, and so forth), the electronic device  10  may include a transceiver  28 . The transceiver  28  may include any circuitry that may be useful in both wirelessly receiving and wirelessly transmitting signals (e.g., data signals). Indeed, in some embodiments, as will be further appreciated, the transceiver  28  may include a transmitter and a receiver combined into a single unit, or, in other embodiments, the transceiver  28  may include a transmitter separate from the receiver. For example, the transceiver  28  may transmit and receive OFDM signals (e.g., OFDM data symbols) to support data communication in wireless applications such as, for example, PAN networks (e.g., Bluetooth), WLAN networks (e.g., 802.11x Wi-Fi), WAN networks (e.g., 3G, 4G, 5G, and LTE, LTE-eLAA, and LTE-A cellular networks), WiMAX networks, mobile WiMAX networks, ADSL and VDSL networks, DVB-T and DVB-H networks, UWB networks, and so forth. Further, as described in greater detail below, the transceiver  28  may include two or more antennas, which may each transmit and/or receive data. Accordingly, in some embodiments, the transceiver  28  may use the two or more antennas to operate in an uplink multiple-input, multiple output (UL-MIMO) (e.g., spatial multiplexing) mode of operation. As such, the transceiver  28  may concurrently transmit multiple data signals within the same frequency band, which may increase the bit rate of data transmitted by the transceiver  28 . Moreover, using UL-MIMO, the transceiver  28  may support data communication in certain wireless applications, such as a 5G and/or LTE network. As further illustrated, the electronic device  10  may include a power source  29 . The power source  29  may include any suitable source of power, such as a rechargeable lithium polymer (Li-poly) battery and/or an alternating current (AC) power converter. 
     In certain embodiments, the electronic device  10  may take the form of a computer, a portable electronic device, a wearable electronic device, or other type of electronic device. Such computers may include computers that are generally portable (such as laptop, notebook, and tablet computers) as well as computers that are generally used in one place (such as conventional desktop computers, workstations and/or servers). In certain embodiments, the electronic device  10  in the form of a computer may be a model of a MacBook®, MacBook® Pro, MacBook Air®, iMac®, Mac® mini, or Mac Pro® available from Apple Inc. By way of example, the electronic device  10 , taking the form of a notebook computer  10 A, is illustrated in  FIG. 2  in accordance with one embodiment of the present disclosure. The depicted computer  10 A may include a housing or enclosure  36 , a display  18 , input structures  22 , and ports of an I/O interface  24 . In one embodiment, the input structures  22  (such as a keyboard and/or touchpad) may be used to interact with the computer  10 A, such as to start, control, or operate a GUI or applications running on computer  10 A. For example, a keyboard and/or touchpad may allow a user to navigate a user interface or application interface displayed on display  18 . 
       FIG. 3  depicts a front view of a handheld device  10 B, which represents one embodiment of the electronic device  10 . The handheld device  10 B may represent, for example, a portable phone, a media player, a personal data organizer, a handheld game platform, or any combination of such devices. By way of example, the handheld device  10 B may be a model of an iPhone® available from Apple Inc. of Cupertino, Calif. The handheld device  10 B may include an enclosure  36  to protect interior components from physical damage and to shield them from electromagnetic interference. The enclosure  36  may surround the display  18 . The I/O interfaces  24  may open through the enclosure  36  and may include, for example, an I/O port for a hard wired connection for charging and/or content manipulation using a standard connector and protocol, such as the Lightning connector provided by Apple Inc., a universal serial bus (USB), or other similar connector and protocol. 
     Input structures  22 , in combination with the display  18 , may allow a user to control the handheld device  10 B. For example, the input structures  22  may activate or deactivate the handheld device  10 B, navigate user interface to a home screen, a user-configurable application screen, and/or activate a voice-recognition feature of the handheld device  10 B. Other input structures  22  may provide volume control or may toggle between vibrate and ring modes. The input structures  22  may also include a microphone that may obtain a user&#39;s voice for various voice-related features, and a speaker that may enable audio playback and/or certain phone capabilities. The input structures  22  may also include a headphone input that may provide a connection to external speakers and/or headphones. 
       FIG. 4  depicts a front view of another handheld device  10 C, which represents another embodiment of the electronic device  10 . The handheld device  10 C may represent, for example, a tablet computer, or one of various portable computing devices. By way of example, the handheld device  10 C may be a tablet-sized embodiment of the electronic device  10 , which may be, for example, a model of an iPad® available from Apple Inc. of Cupertino, Calif. 
     Turning to  FIG. 5 , a computer  10 D may represent another embodiment of the electronic device  10  of  FIG. 1 . The computer  10 D may be any computer, such as a desktop computer, a server, or a notebook computer, but may also be a standalone media player or video gaming machine. By way of example, the computer  10 D may be an iMac®, a MacBook®, or other similar device by Apple Inc. It should be noted that the computer  10 D may also represent a personal computer (PC) by another manufacturer. A similar enclosure  36  may be provided to protect and enclose internal components of the computer  10 D such as the display  18 . In certain embodiments, a user of the computer  10 D may interact with the computer  10 D using various peripheral input devices, such as the keyboard  22 A or mouse  22 B (e.g., input structures  22 ), which may connect to the computer  10 D. 
     Similarly,  FIG. 6  depicts a wearable electronic device  10 E representing another embodiment of the electronic device  10  of  FIG. 1  that may be configured to operate using the techniques described herein. By way of example, the wearable electronic device  10 E, which may include a wristband  43 , may be an Apple Watch® by Apple Inc. However, in other embodiments, the wearable electronic device  10 E may include any wearable electronic device such as, for example, a wearable exercise monitoring device (e.g., pedometer, accelerometer, heart rate monitor), or other device by another manufacturer. The display  18  of the wearable electronic device  10 E may include a touch screen display  18  (e.g., LCD, OLED display, active-matrix organic light emitting diode (AMOLED) display, and so forth), as well as input structures  22 , which may allow users to interact with a user interface of the wearable electronic device  10 E. 
     As previously noted above, each embodiment (e.g., notebook computer  10 A, handheld device  10 B, handheld device  10 C, computer  10 D, and wearable electronic device  10 E) of the electronic device  10  may include a transceiver  28 . With the foregoing in mind,  FIG. 7  depicts a schematic block diagram of an embodiment of a transmitter  50  within the transceiver  28 , which may be disposed within a modem (not shown) of the electronic device  10 . In the illustrated embodiment, the transmitter  50  is separate from the receiver within the transceiver  28 , but in some embodiments, the transceiver  28  may include a transmitter  50  and a receiver combined into a single unit. Further, the various functional blocks shown in  FIG. 7  may include hardware elements (including circuitry), software elements (including computer code stored on a computer-readable medium) or a combination of both hardware and software elements. It should also be noted that  FIG. 7  is merely one example of a particular implementation and is intended to illustrate the types of components that may be present in the transmitter  50 . As such, functional blocks may be added or omitted, and their arrangement within the transmitter  50  may be modified. 
     To facilitate uplink multiple-input, multiple-output (UL-MIMO) (e.g., spatial multiplexing) techniques for data transmission, the transmitter  50  may include a number of multiple-input, multiple-output (MIMO) transmitters  52  (e.g.,  52 A,  52 B). More specifically, the transmitter  50  may include a number of MIMO transmitters  52  that are each implemented to concurrently transmit a respective data signal within the same frequency band via a respective antenna  54 . For example, a first MIMO transmitter  52 A may be implemented to wirelessly transmit a first data signal via a first antenna  54 A, while a second MIMO transmitter  52 B may be implemented to wirelessly transmit a second data signal in the same frequency band as the first data signal via a second antenna  54 B. 
     As illustrated, each MIMO transmitter  52  (e.g.,  52 A,  52 B) may include logic and/or circuitry suitable to prepare the respective data signals for transmission. For example, the MIMO transmitters  52  may include digital transmitter circuitry  56  implemented to receive and/or identify a digital signal to be wirelessly transmitted. Further, the MIMO transmitters  52  may include a digital pre-distortion (DPD) and envelope tracking (ET) engine  58 . The DPD and ET engine  58  may apply a gain to the signal identified by the digital transmitter circuitry  56 . The DPD and ET engine  58 , as well as other suitable gain control elements (e.g., gain control element  60 ) in the MIMO transmitters  52 , may apply gain to the signal so that the amplitude of an output signal of the DPD and ET engine  58  is within a suitable operating range of the circuitry that may receive the output signal of the gain control element  60  as an input. More specifically, the DPD and ET engine  58  may apply distortion to the signal to offset distortion (e.g., gain and/or phase distortion) that the power amplifier  64  may introduce. That is, for example, the DPD and ET engine  58  may introduce distortion intended to have the opposite effect on the signal compared to the distortion (e.g., gain and/or phase distortion) the power amplifier  64  may introduce, as described in greater detail below. 
     A digital-to-analog converter (DAC)  62  may convert the output of the DPD and ET engine  58  and/or the gain control element  60  from a digital signal to an analog signal to prepare the signal for transmission across an analog channel (e.g., air). The power amplifier  64  may receive the output of the DAC  62  and may amplify the analog signal for transmission across a channel. Additionally or alternatively, while not illustrated, a mixer may receive the output of the DAC  62  as an input and adjust (e.g., shift) the frequency of the analog signal to a suitable frequency for the channel the analog signal will be transmitted on. The mixer may additionally or alternatively perform frequency modulation (FM) or amplitude modulation (AM) to modify the frequency or amplitude of the analog signal, respectively. The output of the mixer may then feed into an input of the power amplifier  64  for amplification suitable for signal transmission across a channel. 
     Further, in some embodiments, to control the power supplied to the power amplifier  64 , which may control the amplification applied to the signal output by the MIMO transmitters  52 , each of the MIMO transmitters  52  may contain an envelope tracker  66 . The envelope tracker  66  may include suitable logic and/or circuitry, such as a dynamic voltage and/or current supply, to regulate the power supplied to the power amplifier  64  based at least in part on one or more characteristics (e.g., amplitude, envelope, and/or the like) of the signal identified at the digital transmitter circuitry  56  and/or the signal output by the DPD and ET engine  58 . Accordingly, in some embodiments, the DPD and ET engine  58  may provide information related to the one or more characteristics of a signal to the envelope tracker  66 , and the envelope tracker  66  may control the amplification applied at the power amplifier  64  to the signal based in part on the received information. 
     As further illustrated, the MIMO transmitters  52  may each include a feedback receiver path  68 . The MIMO transmitters  52  may use the feedback receiver path  68  to capture information related to the signal transmitted at the antenna  54 . Accordingly, the load  70  (e.g., impedance) applied to the transmission path  72  and/or the feedback receiver path  68  may be selected to receive data at the feedback receiver path  68  while minimizing the reflected power and/or maximizing the forward power of the transmission path  72 . As such, in some embodiments, the load  70  applied to the transmission path  72  and/or the feedback receiver path  68  may be relatively low (e.g., 50 ohms). 
     In some embodiments, the feedback receiver path  68  may include a switch  74 , which may route the signal output by the power amplifier  64  to the feedback receiver path  68  and/or the transmission path  72  (e.g., the antenna  54 ). Moreover, the feedback receiver path  68  may include an analog-to-digital converter (ADC)  76 . The ADC  76  may convert the signal routed by the switch  74  to the feedback receiver path  68  from an analog signal suitable to be output over an analog channel (e.g., air) at the antenna  54  to a digital signal. A gain control element  60  may then adjust the gain of the digital signal so that the digital signal may be processed by digital signal processing (DSP) circuitry  78 . The DSP circuitry  78  may include logic and/or circuitry suitable to determine the distortion (e.g., gain and/or phase distortion) introduced by the power amplifier  64  such that the DPD and ET engine  58  may offset this distortion, as discussed above. 
     While the DSP circuitry  78 , the feedback receiver path  68 , and/or the DPD and ET engine  58  may mitigate distortion (e.g., gain and/or phase distortion) caused by the power amplifier  64  in the signals transmitted by the antenna  54 , the signals may be susceptible to several types of noise and/or distortion. More specifically, because each of the first MIMO transmitter  52 A and the second MIMO transmitter  52 B may concurrently transmit a respective signal in the same frequency band, the transmitted signals may include intermodulation products (e.g., cross-modulation products and/or nonlinear interference). For instance, the antennas  54  of the MIMO transmitters  52 , which may be disposed proximate to one another in the electronic device  10 , may become coupled together. As such, while the first antenna  54 A is transmitting the first signal, the first antenna  54 A may receive the second signal transmitted by the second MIMO transmitter  52 B. Moreover, while the second antenna  54 B is transmitting the second signal, the second antenna  54 B may receive the first signal transmitted by the first MIMO transmitter  52 A. In the first MIMO transmitter  52 A, the second signal may propagate to the power amplifier  64 . The power amplifier  64  may have finite reverse intermodulation distortion, which may mix the second signal (e.g., a coupled signal) and the input signal received from the DAC  62  (e.g., the signal to be transmitted at the first antenna  54 A). Accordingly, the power amplifier  64  may cross-modulate the second signal (e.g., the coupled signal) and the input signal received from the DAC  62 , which may result in a transmitted signal having intermodulation products and may degrade the adjacent channel leakage ratio (ACLR) and the error vector magnitude (EVM) of the first MIMO transmitter  52 A and/or the transmitter  50 . Further, at the second MIMO transmitter  52 B, the first signal may propagate to the power amplifier  64 , where the first signal and the input signal received from the DAC  62  may become cross-modulated. As such, the adjacent channel leakage ratio (ACLR) and the error vector magnitude (EVM) of the second MIMO transmitter  52 B may also degrade as a result of antenna coupling with the first antenna  54 A. 
     It may be appreciated that while cross-modulation of signals resulting from antenna coupling is described herein as occurring at the power amplifier  64 , any suitable nonlinear element (e.g., circuitry) in the MIMO transmitters  52  may cross-modulate the signals. Moreover, the performance degradation (e.g., ACLR and/or EVM degradation) of the MIMO transmitters  52  resulting from the cross-modulation may be exacerbated by certain modes of the power amplifier  64  and/or additional nonlinear elements. For instance, in a cellular system, the power amplifier  64  may operate in an envelope tracking (ET) mode. In ET mode, the power amplifier  64  may apply nonlinear gain to input signals, as the power amplifier  64  may operate in constant compression (e.g., gain compression). On the other hand, in other modes of operation, the power amplifier  64  may apply more linear gain to the input signals. As a result, the effects of the cross-modulation may be more apparent (e.g., the performance degradation may increase) in an electronic device  10  with a power amplifier  64  operating in ET mode than in an electronic device  10  with a power amplifier  64  operation in another mode of operation. Moreover, while the cross-modulated signals are described as being concurrently transmitted, it may be appreciated that a delay may exist between the start of the transmission of the first signal and the start of the transmission of the second signal or vice versa and/or that a delay may exist between the end of the transmission of the first signal and the end of the transmission of the second signal or vice versa. 
     Accordingly, in some embodiments, to limit distortion caused by the intermodulation products and/or cross-modulation described herein, the transmitter  50  may include a multiple-input, multiple-output intermodulation distortion (MIMO IMD) cancellation block  90 , as shown in  FIG. 8 . The MIMO IMD cancellation block  90  may include circuitry and/or logic to determine the mixing products (e.g., the cross-mixing and/or intermodulation products) in each of a first transmission signal transmitted at the first antenna MA and a second transmission signal transmitted at the second antenna MB. Accordingly, the MIMO IMD cancellation block  90  may receive the first transmission signal received at the feedback receiver path  68  of the first MIMO transmitter  52 A and may receive the second transmission signal received at the feedback receiver path  68  of the second MIMO transmitter  52 B. Further, the MIMO IMD cancellation block  90  may receive the first signal expected to be output at the antenna MA (e.g., an expected first signal) from the first MIMO transmitter  52 A if mixing products resulting from a respective coupled signal were not present and may receive the second signal expected to be output at the antenna MB (e.g., an expected second signal) from the second MIMO transmitter  52 B if mixing products from a respective coupled signal were not present. Based on the first transmission signal, the second transmission signal, the expected first signal, and the expected second signal, the MIMO IMD cancellation block may determine the mixing products present in each of the first transmission signal (e.g., a distorted version of the expected first signal) and the second transmission signal (e.g., a distorted version of the expected second signal), as described in greater detail below. Moreover, the MIMO IMD cancellation block  90  may provide the inverse of the identified mixing products in the first transmission signal to the first MIMO transmitter  52 A and may provide the inverse of the identified mixing products in the second transmission signal to the second MIMO transmitter  52 B. As such, the MIMO transmitters  52  may cancel the respective mixing products from the expected signals (e.g., the expected first signal, the expected second signal) to offset the distortion later included in the transmission signals (e.g., the first transmission signal, the second transmission signal) due to cross-modulation. Moreover, in some embodiments, the transmitter  50  may meet and/or exceed the standards of the 3rd Generation Partnership Project (3GPP), such as a certain ACLR and/or EVM, by using the MIMO IMD cancellation block  90  during UL-MIMO, which may facilitate use of a 5G and/or LTE network. 
     Turning now to  FIG. 9 , a more detailed embodiment of the MIMO IMD cancellation block  90  is shown. In some embodiments, the MIMO IMD cancellation block  90  may determine the mixing-products present in a signal transmitted by the first MIMO transmitter  52 A using a simplified Volterra model (e.g., a Volterra series). Generally, using the simplified Volterra model, the MIMO IMD cancellation block  90  may determine a set of weight factors (e.g., coefficients) and may determine the mixing products that may result from an expected signal (e.g., a signal to be transmitted at the first antenna MA) and an expected coupled signal (e.g., a signal expected to be transmitted at the second antenna MB) based on the set of weight factors, the expected signal, and the expected coupled signal. The mixing products may then be cancelled from an expected signal before the expected signal is transmitted to offset the distortion resulting from the mixing products. Accordingly, as illustrated, the MIMO IMD cancellation block  90  may include a training engine  92 , which may be used to calculate the set of weight factors, and a mixing product calculation and scaling block  94 , which may be used to calculate the mixing products. 
     For simplicity, portions of the first MIMO transmitter  52 A and the second MIMO transmitter  52 B are omitted and certain functional blocks (e.g., gain control element  60 , DAC  62 , envelope tracker  66 , power amplifier  64 ) are represented by a transceiver and radio-frequency (RF) front-end block  96  in the illustrated embodiment. However, it may be appreciated that the MIMO transmitters  52  may include each of the components described herein and/or illustrated in  FIG. 8 . Further, the components of the transmitter  50  described herein (e.g., digital transmitter circuitry  56 , DPD and ET engine  58 , gain control element  60 , DAC  62 , power amplifier  64 , envelope tracker  66 , and/or the like) may remain unchanged (e.g., may operate the same) in  FIGS. 8 and 9 , even with the addition of the MIMO IMD cancellation block  90 . Moreover, the MIMO IMD cancellation block  90  may be communicatively coupled via input and/or output circuitry (e.g., wiring and/or interconnects) to the first MIMO transmitter  52 A and/or the second MIMO transmitter  52 B at the digital transmitter circuitry  56 , at an adder of the digital transmitter circuitry  56 , at the feedback receiver path  68 , at the DSP circuitry  78 , and/or the like, as illustrated in  FIGS. 8 and 9 . Thus, embodiments described herein are intended to be illustrative and not limiting. 
     In the illustrated embodiment, x 1 (n) represents the expected first signal of the first MIMO transmitter  52 A (e.g., the expected signal), and x 2  (n) represents the expected second signal of the second MIMO transmitter  52 B, which represents an expected coupled signal relative to the expected first signal. Further, y c1 (n) represents the mixing products (e.g., interference) predicted to be present in the first transmission signal (b 1 (n)) transmitted at the first antenna  54 A as a result of antenna coupling with the second antenna  54 B. Additionally, y c2 (n) represents the mixing products (e.g., interference) predicted to be present in the second transmission signal (b 2 (n)) transmitted at the second antenna  54 B as a result of antenna coupling with the first antenna  54 A. The second transmission signal (b 2 (n)) may additionally represent a coupled transmission relative to the first transmission signal (b 1 (n)). Accordingly, y 1 (n) represents an updated (e.g., modified) first signal, which may include the inverse of the mixing products (−y c1 (n)) injected into the expected first signal, and y 2 (n) represents an updated (e.g., modified) second signal, which may include the inverse of the mixing products (−y c2 (n)) injected into the expected second signal. Further, H 1  may represent a first set of weight factors, which may correspond to mixing product scaling factors for the mixing products predicted to be present in the first transmission signal, and H 2  may represent a second set of weight factors, which may correspond to mixing product scaling factors for the mixing products predicted to be present in the second transmission signal. 
     In some embodiments, the mixing product calculation and scaling block  94  may estimate and/or predict the mixing products resulting from third order nonlinearity based in part on the equation:
 
 y   3c ( n )= h   3,1   |x   1 ( n )| 2   x   2 ( n )+ h   3,2   x   1   2 ( n ) x   2   * ( n )+ h   3,3   x   1   * ( n ) x   2   2 ( n )+ h   3,4   x   1 ( n )| x   2 ( n )| 2 ,
 
where, as illustrated in  FIG. 9 , x 1 (n) represents the expected first signal of the first MIMO transmitter  52 A (e.g., the expected signal), x 2  (n) represents the expected second signal of the second MIMO transmitter  52 B (e.g., the expected coupled signal), y 3c (n) represents the mixing products resulting from third order nonlinearity of the expected signal and the expected coupled signal, * represents the conjugate function, and h i,j  represents the set (e.g., vector) of weight factors, where i corresponds to the harmonic order and j corresponds to the coefficient order of each weight factor. Further, the first expected signal (x 1 (n)) and/or the expected coupled signal (x 2 (n)) may represent narrowband modulated signals represented by complex envelope notation in discrete time. In some embodiments, for example, the first expected signal (x 1 (n)) and/or the expected coupled signal (x 2  (n)) may be sampled by the MIMO IMD cancellation block  90  and/or the transmitter  50  at a rate twice the Nyquist rate or greater of the channel bandwidth and/or of the signals (e.g., the first expected signal, the expected coupled signal, the transmission signals, and/or the like) to be represented in discrete time. In such embodiments, the respective harmonics of the signals in the evolved universal terrestrial radio access (E-UTRA) ACLR1 (e.g., LTE) zone may be captured.
 
     In some embodiments, the expected coupled signal (x 2 (n)) may be much weaker than the expected signal (x 1 (n)). More specifically, the coupled transmission signal (b 2  (n)) may be much weaker than the first transmission signal (b 1 (n)) at the first antenna MA. Accordingly, the weights h 3,3  and h 3,4  may be neglected to simplify the equation. Moreover, in practice, the expected coupled signal (x 2 (n)) may be delayed and filtered before it reaches a nonlinear element (e.g., the power amplifier  64 ) in the transmitter  50 . Accordingly, a memory term (m) may be introduced to terms involving the expected coupled signal (x 2  (n)), and in some embodiments, the memory term (m) may be ignored for the expected signal (x 1 (n)) for simplicity. As such, the equation to determine the mixing products may be re-expressed as: 
                   y     3   ⁢   c       ⁡     (   n   )       ≅           ∑   M       m   =   0       ⁢         h     1   ,   1       ⁡     (   m   )       ⁢       x   2     ⁡     (   n   )           +         h     3   ,   1       ⁡     (   m   )       ⁢              x   1     ⁡     (   n   )            2     ⁢       x   2     ⁡     (     n   -   m     )         +         h     3   ,   2       ⁡     (   m   )       ⁢       x   1   2     ⁡     (   n   )       ⁢       x   2   *     ⁡     (     n   -   m     )             ,         
where M represents the memory depth. In some embodiments, the memory depth may be set based in part on the length of the delay in the expected coupled signal (x 2  (n)), which may be estimated based in part on the structure of the second MIMO transmitter  52 B and/or determined experimentally. Additionally or alternatively, the memory depth may be set to capture a certain number of samples of the expected coupled signal (x 2  (n)).
 
     Further, in some embodiments, a linear coupled transmission signal (b 2  (n)) term (e.g., a second order term) may be present at the output of the first MIMO transmitter  52 A. Accordingly, the total interference (mixing products) to be reduced and/or cancelled may be estimated by the equation: 
                   y     c   ⁢   1       ⁡     (   n   )       ≅           ∑     M   -   1         m   =   0       ⁢         h     1   ,   1       ⁡     (   m   )       ⁢       x   2     ⁡     (     n   -   m     )           +         h     3   ,   1       ⁡     (   m   )       ⁢              x   1     ⁡     (   n   )            2     ⁢       x   2     ⁡     (     n   -   m     )         +         h     3   ,   2       ⁡     (   m   )       ⁢       x   1   2     ⁡     (   n   )       ⁢       x   2   *     ⁡     (     n   -   m     )             ,         
where the inverse of the total interference signal (−y c1 (n)) may be output from the mixing product calculation and scaling block  94  such that adding the expected signal with the output of the mixing product calculation and scaling block  94  may offset (e.g., reduce) distortion introduced by cross-modulation during transmission of the first transmission signal (b 1 (n)). Accordingly, the updated signal (y 1 (n)) output by the DPD and ET engine  58  may represent the expected first signal with the inverse of the total interference signal injected and adjusted with digital pre-distortion to offset distortion of the power amplifier  64 , as discussed above. Further, the power amplifier  64  may amplify the updated signal (y 1 (n)) to produce the first transmission signal (b 1 (n)), which may include cross-modulation products resulting from the second transmission signal (b 2  (n)) (e.g., a coupled transmission signal) and may be output by the first antenna  54 A.
 
     The total interference signal (y c1 (n)) may also be expressed as the product of a vector, H (e.g., H 1 , H 2 ), which may include the set of weight factors, h i,j (m), and a basis function (Φ). For instance, the total interference signal (y c1 (n)) may be expressed as:
 
 y   c1 ( n )= H·Φ,  
 
where H 1  may be represented by the 3M×1 vector,
 
[h 1,1 (1),h 1,1 (2), . . . h 1,1 (M),h 3,1 (1), . . . h 3,1 (M),h 3,2 (1), . . . h 3,2 (M)] T , and the basis function (Φ) corresponding to the first transmission signal, may be represented by the 1×3M vector, [x 2 (n),x 2 (n−1), . . . , x 2 (n−M), +|x 1 (n)| 2 x 2 (n), . . . , |x 1 (n)| 2 x 2 (n−M), x 1   2 (n)x 2 *( n ), . . . , x 1   2 (n)x 2 *(n−M)]. Accordingly, the MIMO IMD cancellation block  90  may determine the basis function (Φ) based on the expected signal (x 1 (n)) and the expected coupled signal (x 2 (n)) received from the first MIMO transmitter  52 A and the second MIMO transmitter  52 B, respectively. Further, in some embodiments, the training engine  92  may calculate the set of weight factors (H) based in part on the first transmission signal (b 1 (n)) transmitted at the first MIMO transmitter  52 A and captured on the feedback receiver path  68 . For instance, the set of weight factors (H) may be determined from the equation:
 
 A·H=e   1 ,
 
where A represents a matrix:
 
               A   =     [           Φ   ⁡     (   1   )                 Φ   ⁡     (   2   )               ⋮             Φ   ⁡     (   N   )             ]       ,         
where N represents a certain number (e.g., 2000), and e 1  represents the error function:
 
 e   1 ( n )= b   1 ( n )− x   1 ( n ).
 
Accordingly, the training engine  92  may solve for the set of weight factors (H) using a normalized least mean squares and/or a recursive least square algorithm. Moreover, in some embodiments, the training engine  92  may calculate the set of weight factors with a regular periodicity (e.g., every millisecond (ms), every 5 ms, every 10 ms, and/or the like) and/or in response to certain conditions (e.g., a change in frequency, power, and/or the like) in the transmitter  50  and/or the electronic device  10 , as described in greater detail below. Accordingly, the training engine  92  and/or the MIMO IMD cancellation block  90  may store the most recently calculated set of weight factors in a storage location, such as memory  14 , nonvolatile storage  16 , and/or a look up table (LUT), and may update the stored values of the set of weight factors after subsequent calculations of the set of weight factors. In such embodiments, the mixing product calculation and scaling block  94  may receive and/or retrieve the set of weight factors from the storage location. Further, in some embodiments, the storage location may be initialized (e.g., calibrated) with an initial set of weight factors, which the MIMO and IMD cancellation block  90  may use to adjust an initial expected first signal when a first transmission signal is not available (e.g., captured) and/or has not been transmitted at the first antenna MA yet. To facilitate a more rapid convergence of the error function below a certain threshold, which may approach zero (e.g., no error), the initial set of weight factors may include one or more non-zero weight factors.
 
     For simplicity, equations described above with reference to  FIG. 9  are described in the context of the first MIMO transmitter  52 A. For example, the expected second signal (x 2 (n)) is described herein as an expected coupled signal relative to the expected first signal. Moreover, the predicted mixing products (y c1 (n)) are determined to be injected into the first expected signal (x 1 (n)). However, it may be appreciated that the first expected signal (x 1 (n)) may be described as an expected coupled signal with respect to the second expected signal (x 2 (n)). Accordingly, the techniques described herein may be applied to predict and cancel the cross-modulation products in the second MIMO transmitter  52 B. Moreover, in embodiments with additional transmission signals transmitted concurrently with the first and second transmission signals (e.g., additional antennas  54 ), the techniques may be extended to include the cross-modulation and/or distortion contributed by the additional transmission signals. Additionally or alternatively, the techniques may be extended to include higher order cross-modulation product harmonics and/or may rely on an alternative model. Thus, embodiments described herein are intended to be illustrative and not limiting. 
     Turning now to  FIG. 10 , a flow chart of a method  150  for operating the transmitter  50  in an UL-MIMO mode while minimizing the presence of mixing products in signal transmissions is shown, in accordance with embodiments described herein. Although the description of the method  150  is described in a particular order, which represents a particular embodiment, it should be noted that the method  150  may be performed in any suitable order, and steps may be added or omitted. 
     To initiate the method  150 , the transmitter  50  may prepare expected signals for transmission (process block  152 ). More specifically, the transmitter  50  may prepare a respective expected signal at each of the MIMO transmitters  52  included in the transmitter  50  for simultaneous transmission in the same frequency band. For example, the first MIMO transmitter  52 A may determine and/or receive the first expected signal (x 1 (n)) using the digital transmitter circuitry  56 . Further, the second MIMO transmitter  52 B may determine and/or receive the second expected signal (x 2 (n)) in the same frequency band as the first expected signal using the digital transmitter circuitry  56 . 
     The transmitter  50  may additionally calculate (e.g., predict) the cross-modulation products that may be introduced to the expected signals (e.g., the first expected signal, the second expected signal) during transmission (process block  154 ). For example, as discussed above, the MIMO IMD cancellation block  90  of the transmitter may calculate (e.g., estimate) the mixing products for each of the expected signals based in part on the expected signals and their respective expected coupled signals. For instance, in the example described with reference to  FIG. 9 , to calculate the mixing products of the expected first signal, the MIMO IMD cancellation block  90  may use the expected first signal and the second expected signal (e.g., an expected coupled signal relative to the expected first signal). Moreover, in other embodiments, the MIMO IMD cancellation block  90  may use the expected first signal and any suitable number of expected coupled signals, which may each correspond to an expected signal to be simultaneously transmitted along with the expected first signal at another MIMO transmitter  52  proximate to the first MIMO transmitter  52 A (e.g., within the transmitter  50  and/or within the electronic device  10 ). Further, in some embodiments, the MIMO IMD cancellation block  90  may predict the mixing products using a simplified Volterra model. 
     The transmitter  50  may also weight (e.g., scale) each cross-modulation product and calculate the inverse of the result (process block  156 ). As described in greater detail below, the transmitter  50  may determine a set of weight factors (e.g., coefficients) to scale the cross-modulation products according to their respective contribution to the distortion of the transmission signal using the MIMO IMD cancellation block  90 . In some embodiments, for example, the training engine  92  of the MIMO IMD cancellation block may calculate the set of weight factors (H 1 ) based in part on the signal transmitted by the first MIMO transmitter  52 A (e.g., the first transmission signal), which may include intermodulation product distortion. Further, the training engine  92  of the MIMO IMD cancellation block may calculate the set of weight factors (H 2 ) based in part on the signal transmitted by the second MIMO transmitter  52 B (e.g., the second transmission signal), which may also include intermodulation product distortion. As discussed in greater detail below, the transmitter  50  may determine the set of weight factors with a certain periodicity and/or in response to a certain event and/or device condition. 
     Moreover, the transmitter  50  may calculate the inverse of the scaled cross-modulation products (e.g., −y c1 (n), −y c2 (n)) such that the inverse of the scaled cross-modulation products may be injected to the respective expected signals (process block  158 ). Accordingly, the MIMO transmitters  52  may receive respective inverse scaled cross-modulation products from the MIMO IMD cancellation block  90 . The MIMO transmitters  52  may then add the respective inverse of the scaled cross-modulation products to a respective expected signal to cancel the respective scaled cross-modulation products from the respective expected signal. As such, in other embodiments, the MIMO transmitters  52  may receive the respective scaled cross-modulation products from the MIMO IMD cancellation block  90  and may subtract these from a respective expected signal. In some cases, the MIMO transmitters  52  may perform additional signal adjustments (e.g., at the DPD and ET engine  58 ) to produce a respective updated signal (e.g., (y 1 (n)), (y 2 (n))) to be transmitted. 
     The transmitter  50  may then transmit signals (process block  160 ). In some embodiments, the updated signal (e.g., (y 1 (n), (y 2 (n))) may be modified (e.g., distorted) by cross-modulation products at the power amplifier  64  of the respective MIMO transmitter  52  (e.g.,  52 A,  52 B). Accordingly, the transmitter  50  may transmit a first transmission signal (b 1 (n)) at the first antenna  54 A via the first MIMO transmitter  52 A. Further, the transmitter  50  may transmit a second transmission signal (b 2  (n)) at the second antenna  54 B via the second MIMO transmitter  52 B. In some embodiments, because the transmitter  50  the respective predicted inverse of the cross-modulation products were injected into the respective expected signals, the distortion introduced in the transmission signals due to cross-modulation products may be reduced. For instance, in some embodiments, the error between an expected signal and the corresponding transmission signal may be minimized compared to a transmission signal prepared from the expected signal using other techniques. 
     It may be appreciated that the transmitter  50  may perform the method  150  in real-time. That is, for example, the transmitter  50  may continue to calculate updated cross-modulation products as additional expected signals are prepared for transmission and may continue to inject the inverse of the scaled updated cross-modulation products into the additional expected signals. Accordingly, the method  150  and/or a portion of the method  150  may be repeated any suitable number of instances. However, in some embodiments, the transmitter  50  may be implemented to perform the method  150  when operating in an UL-MIMO mode. 
     Turning now to  FIG. 11 , a flow chart of a method  200  for calculating (e.g., training) the set of weight factors (H) used to scale the cross-modulation products, as described above with reference to process block  156 , is illustrated. The method  200  may be used with a regular periodicity (e.g., every millisecond (ms), every 5 ms, every 10 ms, and/or the like) and/or in response to certain conditions (e.g., a result of the error function, a change in frequency, power, and/or the like) in the transmitter  50  and/or the electronic device  10 . Further, although the description of the method  200  is described in a particular order, which represents a particular embodiment, it should be noted that the method  200  may be performed in any suitable order, and steps may be added or omitted. 
     To initiate the method  200 , the transmitter  50  may capture the signals transmitted at the antennas  54  (e.g., the transmission signals) (process block  202 ). More specifically, the feedback receiver paths  68  of each of the MIMO transmitters  52  may route the respective transmission signals to the MIMO IMD cancellation block  90 . Accordingly, for the embodiment illustrated in  FIG. 9 , the training engine  92  of the MIMO cancellation block  90  may receive the first transmission signal (b 1 (n)) from the feedback receiver path  68  of the first MIMO transmitter  52 A and may receive the second transmission signal (b 2 (n)) from the feedback receiver path  68  of the second MIMO transmitter  52 B. 
     The MIMO cancellation block  90  of the transmitter  50  may then compare the captured signals (e.g., the transmission signals) with corresponding expected signals (process block  204 ). For example, the training engine  92  may determine the difference between an expected signal and the resulting transmission signal, which may correspond to the error signal (e) (e.g., error function), as described above. Using this comparison, the transmitter  50  may then determine the set of weight factors corresponding to the cross-modulation product terms for each expected signal (process block  206 ). In some embodiments, for example, the MIMO IMD cancellation block  90  may determine the set of weight factors based in part on both the cross-modulation product terms and the comparison (e.g., the error signal). As described above, the determined set of weight factors may then be used to scale predicted cross-modulation products. 
     Further, in some embodiments, the method  200  may be repeated any suitable number of instances. For example, in some embodiments, the method  200  may be repeated at regular intervals (e.g., every millisecond (ms), every 5 ms, every 10 ms, and/or the like). Moreover, the interval may be selected to minimize an impact on the power consumption of the electronic device  10  and/or to minimize the intermodulation products present in a signal transmitted by the transmitter  50 . For example, in some embodiments, a smaller interval may reduce the intermodulation products present in the transmitted signal (e.g., reduce the result of the error function), as the set of weight factors may be determined more regularly. However, the smaller interval may increase the power consumption of the electronic device, as the calculations involved in the method  200  are performed more frequently. Accordingly, the method  200  may additionally or alternatively be performed based in part on a certain event and/or device condition (e.g., frequency, power, and/or the like). For example, in some embodiments, the transmitter  50  may perform the method  200  during a high-power mode of the electronic device  10  and may not update the set of weight factors during a lower-power mode of the electronic device  10 . 
     The specific embodiments described above have been shown by way of example, and it should be understood that these embodiments may be susceptible to various modifications and alternative forms. It should be further understood that the claims are not intended to be limited to the particular forms disclosed, but rather to cover all modifications, equivalents, and alternatives falling within the spirit and scope of this disclosure. 
     The techniques presented and claimed herein are referenced and applied to material objects and concrete examples of a practical nature that demonstrably improve the present technical field and, as such, are not abstract, intangible or purely theoretical. Further, if any claims appended to the end of this specification contain one or more elements designated as “means for [perform]ing [a function] . . . ” or “step for [perform]ing [a function] . . . ”, it is intended that such elements are to be interpreted under 35 U.S.C. 112(f). However, for any claims containing elements designated in any other manner, it is intended that such elements are not to be interpreted under 35 U.S.C. 112(f).

Metadata:
Filing Date: 20181218
Publication Date: 20200825
Grant Date: 20200825
Priority Date: 20181218
Inventors: SARKAS, IOANNIS
WAGNER, ELMAR
Assignee: APPLE INC
CPC Classifications: [{"code": "H04B7/0413", "inventive": true, "first": false, "tree": "[]"}, {"code": "H04B1/0475", "inventive": true, "first": true, "tree": "[]"}, {"code": "H04B7/0426", "inventive": true, "first": false, "tree": "[]"}, {"code": "H04B1/525", "inventive": true, "first": true, "tree": "[]"}, {"code": "H04B1/0475", "inventive": true, "first": false, "tree": "[]"}, {"code": "H04B7/0417", "inventive": true, "first": false, "tree": "[]"}, {"code": "H04B1/0475", "inventive": true, "first": false, "tree": "[]"}, {"code": "H04B7/0417", "inventive": true, "first": false, "tree": "[]"}, {"code": "H04B1/525", "inventive": true, "first": true, "tree": "[]"}, {"code": "H04B7/0426", "inventive": true, "first": false, "tree": "[]"}]
Family ID: 71073073