Patent Publication Number: US-2022224423-A1

Title: Distortion detection with multiple antennas

Description:
TECHNICAL FIELD 
     Wireless communication and in particular, to distortion detection with multiple antennas. 
     BACKGROUND 
     Passive Inter-Modulation (PIM) is an important concern for cellular operators as more downlink channels are being transmitted from the cellular radio sites. As used herein, PIM refers to interference generated by two or more carrier frequencies being exposed to non-linear mixing. The resulting signal will contain additional, unwanted frequencies or intermodulation products. As the “Passive” portion of the name implies, this non-linear mixing does not involve active devices and is frequently caused by the metallic materials and workmanship of the interconnects and other passive components in the system. Thus, one example of PIM sources includes imperfect metal connections. To add to the challenge, the newly added radio channels belong to a rising number of radio bands which increases the odds of having PIM that desensitizes the uplink receivers. 
     A growing number of cellular operators now require that the presence of PIM in the uplink channels be reported by radio equipment so that PIM mitigation measures can then be taken. 
     Some PIM-detection (PIM-D) techniques have been reported in the literature. For example, one approach suggests measuring the noise floor in the uplink channels during transmission time intervals (TTIs) where no uplink (UL) traffic is scheduled and in the guard bands of the uplink channels when uplink traffic is present. However, this approach can miss some PIM occurrences during the site operation since 1) PIM may not be present during the uplink TTIs where no traffic is scheduled and 2) PIM may not appear in the UL channel guard bands. Another approach introduces a method where the signal envelope for each of the downlink (DL) carriers is correlated with the uplink signal envelope. However, in this approach, the PIM problems involving DL carriers that are external to the radio, such as the ones that are transmitted by the same operator in another radio band with different equipment, may go unnoticed. In addition, the PIM levels may be so low with respect to the UL noise floor that the envelope correlation may not detect any anomaly. 
     In another approach, a non-linear model of the PIM is generated from the transmitted DL signals. The PIM model is then correlated with the uplink channels. This approach has at least the following drawbacks.
         This technique does not scale well when the number of DL antennas involved in creating the PIM increases as in massive-multiple-input-multiple-output (massive MIMO) systems. The number of non-linear terms that are required to create the PIM model increases exponentially with the number of DL antennas.   The PIM model must be tailored to suit a specific carrier configuration with non-linear terms that match the intermodulation band which creates the PIM problem. Therefore, the PIM model must be adjusted for every carrier configuration. This makes the solution hard to scale to various deployment scenarios.   The PIM model must be tuned to the exact frequency offset with respect to the UL channel. In the situation where there are multiple victim UL channels, each of them requires the PIM model to be tuned to a different frequency offset and may also require a different PIM model.   The non-linear order of the model must closely match that of the PIM, which may fluctuate over time.   Oversampling is needed when generating the PIM model to avoid aliasing, which increases the implementation cost.       

     SUMMARY 
     Some embodiments advantageously provide a method and system for distortion detection with multiple antennas. 
     There may be two time durations where 1) the UL power due to wireless device (WD) traffic, interference and noise is not expected to vary, and 2) a DL covariance matrix is expected to vary. The DL covariance matrix change could be due to a change in power (e.g., physical resource block (PRB) loading in 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE)), or a change in the precoder. In LTE, these two time durations could correspond to two symbols in the same transmission time interval (TTI). The DL variation could be due to the absence/presence of cell specific reference signals (CRS) in certain symbols, or the difference between the control symbols and the data symbols. The change in the UL covariance matrix is determined. The spatial structure of the matrix that represents the change in UL corresponds to the spatial structure of the PIM signal. In other words, the decomposition of this matrix will result in vectors, where each vector corresponds to the channel between the PIM source(s) and the base station antenna ports. 
     Some advantages of some embodiments may include one or more of the following: 
     1. Does not require modelling the non-linear behavior of the PIM source; 
     2. Does not require knowledge of the DL signals for all embodiments; 
     3. Detects PIM external to the antenna; 
     4. Works in the presence of WD traffic, WD interference and noise; and 
     5. Can provide spatial information about PIM source(s). 
     According to one aspect, a method in a network node for determining passive intermodulation, PIM, characteristics at the network node is provided. The method includes capturing signals from each of at least one antenna port at a first time and a second time. The method also includes determining a first covariance matrix based on signals captured at the first time. Further, the method includes determining a second covariance matrix based on signals captured at the second time. Yet further, the method includes determining a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time. 
     According to this aspect, in some embodiments, the method further includes decomposing, at least in part, the difference matrix to generate eigenvectors and eigenvalues, the eigenvectors representing a PIM subspace, each eigenvalue corresponding to a change in PIM in a direction indicated by a corresponding eigenvector. In some embodiments, the difference matrix has submatrices and the decomposing is of at least a portion of the difference matrix. In some embodiments, the portion of the difference matrix to be decomposed is determined by a comparison of elements of the difference matrix to at least one threshold. In some embodiments, the method includes averaging a plurality of difference covariance matrices. In some embodiments, of the difference matrices are weighted, at least one of the weights being based at least in part on diagonal elements of the difference covariance matrix. In some embodiments, a measurement of a signal of the signals is prescreened to determine whether the measurement is used to determine the difference covariance matrix. In some embodiments, the prescreening is based on whether a sum of diagonal elements of the difference matrix exceeds a first threshold. In some embodiments, the prescreening is based on whether a difference between a sum of diagonal elements of the first covariance matrix and a sum of diagonal elements of the second covariance matrix exceeds a second threshold. In some embodiments, the prescreening is based on whether a sum of diagonal elements of the first and second covariance matrices does not exceed a third threshold. 
     According to another aspect, an apparatus is configured to determine passive intermodulation, PIM, characteristics at the network node. The apparatus includes processing circuitry configured to capture signals from each of at least one antenna port at a first time and a second time. The processing circuitry is further configured to determine a first covariance matrix based on signals captured at the first time. The processing circuitry is configured to determine a second covariance matrix based on signals captured at the second time. The processing circuitry is further configured to determine a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time. 
     According to this aspect, in some embodiments, the processing circuitry  48  is further configured to decompose, at least in part, the difference matrix to generate eigenvectors and eigenvalues, the eigenvectors representing a PIM subspace, each eigenvalue corresponding to a change in PIM in a direction indicated by a corresponding eigenvector. In some embodiments, the difference matrix has submatrices and decomposing is of at least a portion of the difference matrix. In some embodiments, the portion of the difference matrix to be decomposed is determined by a comparison of elements of the difference matrix to at least one threshold. the processing circuitry is further configured to average a plurality of difference matrices. averages of the difference matrices are weighted, at least one of the weights being based at least in part on diagonal elements of the difference covariance matrix. a measurement of a signal of the signals is prescreened to determine whether the measurement is used to determine the difference matrix. the prescreening is based on whether a sum of diagonal elements of the difference matrix exceeds a first threshold. the prescreening is based on whether a difference between a sum of diagonal elements of the first covariance matrix and a sum of diagonal elements of the second covariance matrix exceeds a second threshold. In some embodiments, the prescreening is based on whether a sum of diagonal elements of the first and second covariance matrices does not exceed a third threshold. 
     According to yet another aspect, a method in a network node for determining passive intermodulation, PIM, characteristics at the network node is provided. The method includes capturing signals from each of at least one antenna port at a first time and a second time, an antenna port being one of a physical antenna port and a logical antenna port. The method also includes determining a first covariance matrix based on signals captured at the first time. The method also includes determining a second covariance matrix based on signals captured at the second time, the first and second covariance matrices comprising correlation terms, each correlation term being based at least in part on an expected value of a product of signals received from two antenna ports. The method further includes determining a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time. The method further includes decomposing at least part of the difference matrix to generate eigenvectors and eigenvalues, the eigenvectors representing a PIM subspace, each eigenvalue corresponding to a change in PIM in a direction indicated by a corresponding eigenvector. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete understanding of the present embodiments, and the attendant advantages and features thereof, will be more readily understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein: 
         FIG. 1  is a block diagram of a wireless communication network; 
         FIG. 2  is a block diagram of a network node and a wireless device (WD); 
         FIG. 3  is a flowchart of an exemplary process for PIM characterization; 
         FIG. 4  is a flowchart of an alternative exemplary process for PIM characterization; 
         FIG. 5  is a flowchart of a process for PIM characterization using logical antenna port mapping; 
         FIG. 6  is a flowchart of a process for PIM characterization using a downlink metric; and 
         FIG. 7  is a flowchart of a process for PIM characterization based on antenna groups. 
     
    
    
     DETAILED DESCRIPTION 
     Before describing in detail exemplary embodiments, it is noted that the embodiments reside primarily in combinations of apparatus components and processing steps related to distortion detection with multiple antennas. Accordingly, components have been represented where appropriate by conventional symbols in the drawings, showing only those specific details that are pertinent to understanding the embodiments so as not to obscure the disclosure with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein. 
     As used herein, relational terms, such as “first” and “second,” “top” and “bottom,” and the like, may be used solely to distinguish one entity or element from another entity or element without necessarily requiring or implying any physical or logical relationship or order between such entities or elements. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the concepts described herein. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes” and/or “including” when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     In embodiments described herein, the joining term, “in communication with” and the like, may be used to indicate electrical or data communication, which may be accomplished by physical contact, induction, electromagnetic radiation, radio signaling, infrared signaling or optical signaling, for example. One having ordinary skill in the art will appreciate that multiple components may interoperate, and modifications and variations are possible of achieving the electrical and data communication. 
     In some embodiments described herein, the term “coupled,” “connected,” and the like, may be used herein to indicate a connection, although not necessarily directly, and may include wired and/or wireless connections. 
     The term “network node” used herein can be any kind of network node comprised in a radio network which may further comprise any of base station (BS), radio base station, base transceiver station (BTS), base station controller (BSC), radio network controller (RNC), g Node B (gNB), evolved Node B (eNB or eNodeB), Node B, multi-standard radio (MSR) radio node such as MSR BS, multi-cell/multicast coordination entity (MCE), relay node, integrated access and backhaul (IAB) node, donor node controlling relay, radio access point (AP), transmission points, transmission nodes, Remote Radio Unit (RRU) Remote Radio Head (RRH), a core network node (e.g., mobile management entity (MME), self-organizing network (SON) node, a coordinating node, positioning node, MDT node, etc.), an external node (e.g., 3rd party node, a node external to the current network), nodes in distributed antenna system (DAS), a spectrum access system (SAS) node, an element management system (EMS), etc. The network node may also comprise test equipment. The term “radio node” used herein may be used to also denote a wireless device (WD) such as a wireless device (WD) or a radio network node. 
     In some embodiments, the non-limiting terms wireless device (WD) or a user equipment (UE) are used interchangeably. The WD herein can be any type of wireless device capable of communicating with a network node or another WD over radio signals, such as wireless device (WD). The WD may also be a radio communication device, target device, device to device (D2D) WD, machine type WD or WD capable of machine to machine communication (M2M), low-cost and/or low-complexity WD, a sensor equipped with WD, Tablet, mobile terminals, smart phone, laptop embedded equipped (LEE), laptop mounted equipment (LME), USB dongles, Customer Premises Equipment (CPE), an Internet of Things (IoT) device, or a Narrowband IoT (NB-IOT) device etc. 
     Also, in some embodiments the generic term “radio network node” is used. It can be any kind of a radio network node which may comprise any of base station, radio base station, base transceiver station, base station controller, network controller, RNC, evolved Node B (eNB), Node B, gNB, Multi-cell/multicast Coordination Entity (MCE), relay node, access point, radio access point, Remote Radio Unit (RRU) Remote Radio Head (RRH). 
     Note that although terminology from one particular wireless system, such as, for example, 3GPP LTE and/or New Radio (NR) (also known as “5G”), may be used in this disclosure, this should not be seen as limiting the scope of the disclosure to only the aforementioned system. Other wireless systems, including without limitation Wide Band Code Division Multiple Access (WCDMA), Worldwide Interoperability for Microwave Access (WiMax), Ultra Mobile Broadband (UMB) and Global System for Mobile Communications (GSM), may also benefit from exploiting the ideas covered within this disclosure. 
     Note further, that functions described herein as being performed by a wireless device or a network node may be distributed over a plurality of wireless devices and/or network nodes. In other words, it is contemplated that the functions of the network node and wireless device described herein are not limited to performance by a single physical device and, in fact, can be distributed among several physical devices. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     A method in a network node and an apparatus for determining passive intermodulation (PIM) characteristics at the network node are provided. According to one aspect, a method may include capturing signals from each of at least one antenna port at a first time and a second time. The method includes determining a first covariance matrix based on signals captured at the first time. The method also includes determining a second covariance matrix based on signals captured at the second time. The method further includes determining a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time. As used herein, the term “time,” e.g., first time and second time, can refer to an instantaneous point in time or a time interval. 
     Referring now to the drawing figures, in which like elements are referred to by like reference numerals, there is shown in  FIG. 1  a schematic diagram of a communication system  10 , according to an embodiment, such as a 3GPP-type cellular network that may support standards such as LTE and/or NR (5G), which comprises an access network  12 , such as a radio access network, and a core network  14 . The access network  12  comprises a plurality of network nodes  16   a ,  16   b ,  16   c  (referred to collectively as network nodes  16 ), such as NBs, eNBs, gNBs or other types of wireless access points, each defining a corresponding coverage area  18   a ,  18   b ,  18   c  (referred to collectively as coverage areas  18 ). Each network node  16   a ,  16   b ,  16   c  is connectable to the core network  14  over a wired or wireless connection  20 . A first wireless device (WD)  22   a  located in coverage area  18   a  is configured to wirelessly connect to, or be paged by, the corresponding network node  16   c . A second WD  22   b  in coverage area  18   b  is wirelessly connectable to the corresponding network node  16   a . While a plurality of WDs  22   a ,  22   b  (collectively referred to as wireless devices  22 ) are illustrated in this example, the disclosed embodiments are equally applicable to a situation where a sole WD is in the coverage area or where a sole WD is connecting to the corresponding network node  16 . Note that although only two WDs  22  and three network nodes  16  are shown for convenience, the communication system may include many more WDs  22  and network nodes  16 . 
     Also, it is contemplated that a WD  22  can be in simultaneous communication and/or configured to separately communicate with more than one network node  16  and more than one type of network node  16 . For example, a WD  22  can have dual connectivity with a network node  16  that supports LTE and the same or a different network node  16  that supports NR. As an example, WD  22  can be in communication with an eNB for LTE/E-UTRAN and a gNB for NR/NG-RAN. 
     A network node  16  is configured to include a PIM unit  32  which is configured to determine a difference matrix, the difference matrix being based on a difference between first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time. 
     Example implementations, in accordance with an embodiment, of the WD  22 , network node  16  and host computer  24  discussed in the preceding paragraphs will now be described with reference to  FIG. 2 . 
     The communication system  10  includes a network node  16  provided in a communication system  10  and including hardware  38  enabling it to communicate with the WD  22 . The hardware  38  may include a radio interface  42  for setting up and maintaining at least a wireless connection  46  with a WD  22  located in a coverage area  18  served by the network node  16 . The radio interface  42  may be formed as or may include, for example, one or more RF transmitters, one or more RF receivers, and/or one or more RF transceivers. 
     In the embodiment shown, the hardware  38  of the network node  16  further includes processing circuitry  48 . The processing circuitry  48  may include a processor  50  and a memory  52 . In particular, in addition to or instead of a processor, such as a central processing unit, and memory, the processing circuitry  48  may comprise integrated circuitry for processing and/or control, e.g., one or more processors and/or processor cores and/or FPGAs (Field Programmable Gate Array) and/or ASICs (Application Specific Integrated Circuitry) adapted to execute instructions. The processor  50  may be configured to access (e.g., write to and/or read from) the memory  52 , which may comprise any kind of volatile and/or nonvolatile memory, e.g., cache and/or buffer memory and/or RAM (Random Access Memory) and/or ROM (Read-Only Memory) and/or optical memory and/or EPROM (Erasable Programmable Read-Only Memory). 
     Thus, the network node  16  further has software  44  stored internally in, for example, memory  52 , or stored in external memory (e.g., database, storage array, network storage device, etc.) accessible by the network node  16  via an external connection. The software  44  may be executable by the processing circuitry  48 . The processing circuitry  48  may be configured to control any of the methods and/or processes described herein and/or to cause such methods, and/or processes to be performed, e.g., by network node  16 . Processor  50  corresponds to one or more processors  50  for performing network node  16  functions described herein. The memory  52  is configured to store data, programmatic software code and/or other information described herein. In some embodiments, the software  44  may include instructions that, when executed by the processor  50  and/or processing circuitry  48 , causes the processor  50  and/or processing circuitry  48  to perform the processes described herein with respect to network node  16 . For example, processing circuitry  48  of the network node  16  may include PIM unit  32  configured to process a difference matrix corresponding to PIM changes over time. 
     The communication system  10  further includes the WD  22  already referred to. The WD  22  may have hardware  60  that may include a radio interface  62  configured to set up and maintain a wireless connection  46  with a network node  16  serving a coverage area  18  in which the WD  22  is currently located. The radio interface  62  may be formed as or may include, for example, one or more RF transmitters, one or more RF receivers, and/or one or more RF transceivers. 
     The hardware  60  of the WD  22  further includes processing circuitry  64 . The processing circuitry  64  may include a processor  66  and memory  68 . In particular, in addition to or instead of a processor, such as a central processing unit, and memory, the processing circuitry  64  may comprise integrated circuitry for processing and/or control, e.g., one or more processors and/or processor cores and/or FPGAs (Field Programmable Gate Array) and/or ASICs (Application Specific Integrated Circuitry) adapted to execute instructions. The processor  66  may be configured to access (e.g., write to and/or read from) memory  68 , which may comprise any kind of volatile and/or nonvolatile memory, e.g., cache and/or buffer memory and/or RAM (Random Access Memory) and/or ROM (Read-Only Memory) and/or optical memory and/or EPROM (Erasable Programmable Read-Only Memory). 
     Thus, the WD  22  may further comprise software  70 , which is stored in, for example, memory  68  at the WD  22 , or stored in external memory (e.g., database, storage array, network storage device, etc.) accessible by the WD  22 . The software  70  may be executable by the processing circuitry  64 . The software  70  may include a client application  72 . The client application  72  may be operable to provide a service to a human or non-human user via the WD  22 . 
     The processing circuitry  64  may be configured to control any of the methods and/or processes described herein and/or to cause such methods, and/or processes to be performed, e.g., by WD  22 . The processor  66  corresponds to one or more processors  66  for performing WD  22  functions described herein. The WD  22  includes memory  68  that is configured to store data, programmatic software code and/or other information described herein. In some embodiments, the software  70  and/or the client application  72  may include instructions that, when executed by the processor  66  and/or processing circuitry  64 , causes the processor  66  and/or processing circuitry  64  to perform the processes described herein with respect to WD  22 . 
     In some embodiments, the inner workings of the network node  16  and WD  22  may be as shown in  FIG. 2  and independently, the surrounding network topology may be that of  FIG. 1 . 
     The wireless connection  46  between the WD  22  and the network node  16  is in accordance with the teachings of the embodiments described throughout this disclosure. More precisely, the teachings of some of these embodiments may improve the data rate, latency, and/or power consumption and thereby provide benefits such as reduced user waiting time, relaxed restriction on file size, better responsiveness, extended battery lifetime, etc. In some embodiments, a measurement procedure may be provided for the purpose of monitoring data rate, latency and other factors on which the one or more embodiments improve. 
     Although  FIGS. 1 and 2  show various “units” such as PIM unit  32  as being within a respective processor, it is contemplated that these units may be implemented such that a portion of the unit is stored in a corresponding memory within the processing circuitry. In other words, the units may be implemented in hardware or in a combination of hardware and software within the processing circuitry. 
       FIG. 3  is a flowchart of an exemplary process in a network node  16  for determining PIM characteristics at the network node  16 . One or more blocks described herein may be performed by one or more elements of network node  16  such as by one or more of processing circuitry  48  (including the PIM unit  32 ), processor  50 , and/or radio interface  42 . Network node  16  such as via processing circuitry  48  and/or processor  50  and/or radio interface  62  is configured to capture signals from each of at least one antenna port at a first time and a second time (Block S 100 ). The process also includes determining a first covariance matrix based on signals captured at the first time and also includes determining a second covariance matrix based on signals captured at the second time (Block S 102 ). The process further includes determining a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time (Block S 104 ). 
       FIG. 4  is a flowchart of an alternative exemplary process that may be performed by the processing circuitry  48 , and more particularly with the aid of the PIM unit  32 , according to some embodiments of the present disclosure. The process includes capturing signals from each of at least one antenna port at a first time and a second time, an antenna port being one of a physical antenna port and a logical antenna port (Block S 106 ). The process includes determining a first covariance matrix based on signals captured at the first time (Block S 108 ). The process also includes determining a second covariance matrix based on signals captured at the second time, the first and second covariance matrices comprising correlation terms, each correlation term being based at least in part on an expected value of a product of signals received from two antenna ports (Block S 110 ). The process further includes determining a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time (Block S 112 ). The process also includes decomposing at least part of the difference matrix to generate eigenvectors and eigenvalues, the eigenvectors representing a PIM subspace, each eigenvalue corresponding to a change in PIM in a direction indicated by a corresponding eigenvector (Block S 114 ). 
     Having described the general process flow of arrangements of the disclosure and having provided examples of hardware and software arrangements for implementing the processes and functions of the disclosure, the sections below provide details and examples of arrangements for distortion detection with multiple antennas. 
     In some embodiments, with reference to  FIG. 5 , the following steps may be performed by, for example, processing circuitry  48 , including PIM unit  32  in some embodiments, and/or by other processing circuitry separate from the network node  16 .
         1. Make at least 1 UL measurement (Block S 116 ), where each UL measurement includes:
           a. Capturing the raw data (commonly referred to as IQ data) during 2 time periods from 1 or more antenna ports (simultaneous captures across the antenna ports). These can be from physical antenna ports, or logical ports (physical antenna ports can be mapped to logical antenna ports with a matrix transform—see right side of  FIG. 5 , Block S 117 ).
               The time domain signals for each antenna port (r i ) are shown below in the presence of multiple interferers r int , multiple WD&#39;s carrying desired WD  22  traffic r ue , and PIM from potentially multiple PIM sources r pim . The channel between each of these signal sources and antenna port i may be denoted by h src,i  (src=int, WD  22  or pim). The interference term here also includes noise.   
               
               

     
       
         
           
             
               
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                     b. Between the 2 time periods the covariance matrix should change for the DL (requirement #1). A change in the DL transmit covariance matrix can result in a change in the DL transmit power hitting a PIM source. In one embodiment, the DL transmit covariance matrix can be measured across multiple time periods to find the two time periods with a sufficient difference. In another embodiment, the DL transmit covariance may not be measured as it is expected to vary between specific time periods in a wireless physical layer protocol. One example would be between symbols with and without CRS in LTE within the same TTI. 
                     c. Between the two time periods (Block S 120 ), the UL covariance matrix may be expected not to change for the components of the UL transmit covariance that are due to WD UL traffic, WD interference and noise (requirement #2). For this to be true the scheduled UL TTI&#39;s in a network should not start or stop between the start time of the 1 st  time period and the stop time of the 2 nd  time period.
                   The UL covariance values between each pair of antennas are the elements of the UL covariance matrix. (See Block S 118 ). The expression below corresponds to the covariance between the received signals in antenna ports i and j for a single time period.   
                 
                   
                 
               
             
           
         
       
    
     
       
         
           
             
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                         It is typical for E[r i ]=0. The remainder of this disclosure will use this typical value—although this is not necessary for all embodiments. In other words, embodiments described herein may be extended to non-zero E[r i ]. 
                       
                     
                     d. Any change in the UL covariance matrix between two time periods may be assumed to be due to a changing level of PIM—which changes due to the change in the DL covariance matrix.
                   For each i, j pair in the UL covariance matrix there will be the correlation terms for the first and the second time intervals. The difference of the result for the two intervals removes the interference and WD  22  traffic contributions to the UL covariance. The channels are assumed to remain static between the two durations.   During the first time period the covariance terms are:   
                 
                   
                 
               
             
           
         
       
    
     
       
         
           
             
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                         During the second time period the correlation terms are: 
                       
                     
                   
                 
               
             
           
         
       
    
     
       
         
           
             
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                         The difference between the covariance terms between the first and the second time periods is: 
                       
                     
                   
                 
               
             
           
         
       
    
     
       
         
           
             
               
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                         (Block S 122 ) It may be assumed that channels do not vary between the two intervals, which may correspond to some OFDM symbols. The UL interference power and desired WD  22  power do not vary between the first and the second symbols: |r int,1st | 2 =|r int,2nd | 2  and |r int,1st | 2 =|r int,2nd | 2 , which may be based on requirement #2. 
                         The following signals are assumed to be independent: 
                          Interferers are independent of other interferers: r int  with other r int ; 
                          Desired WD  22  traffic may be independent of other desired WD  22  traffic; 
                          All interferers are independent of desired WD  22  traffic; 
                          All interferers are independent of the PIM signals; and 
                          All desired WD  22  traffic may be independent of the PIM signals. 
                         The difference between the covariance terms (Block S 122 ) between the first and second time periods becomes independent of the interference and desired WD  22  traffic in the UL: 
                       
                     
                   
                 
               
             
           
         
       
    
     
       
         
           
             
               
                 
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             2. It is noted that the beamforming weights that maximize the PIM power in the receiver are very close to the solution that maximizes the difference in PIM power between the two time periods. There can be a scaling coefficient that differs between the two beamforming solutions.
           In other words, the dominant vectors from the decomposition of the difference-covariance matrix (which is defined below) will represent the weighting coefficients that maximize the PIM signal (i.e., are the conjugate of the channel from the PIM source to the receive branches).
               a. The beamforming weights are sufficient to describe the spatial properties of the PIM source. An example of a spatial property may be where an external PIM source is located relatively close to one of the antennas. Another example is when antenna branches have an in-line PIM source. Another would be where the PIM signal is picked up by multiple antenna ports with unique relative phase and amplitude offsets between the ports.   b. For each UL measurement, the change in UL covariance may be calculated between the two time periods. This change is denoted by difference-covariance.
                   i. The difference-covariance may be used to isolate PIM from the other signals in the UL (WD, interference and noise). This may be done without knowledge of the other signals in the UL.    The following equation may be used to isolate PIM from UL interference and WD traffic. It corresponds to the difference between the covariance matrices (R Δpim ) during the first and the second time periods. This difference-covariance matrix is:   
                   
               
         
           
         
       
    
     
       
         
           
             
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             3. In one embodiment there is a decomposition (Block S 124 ) of each difference-covariance matrix. An example would be an eigen-based decomposition. The eigenvectors would represent the PIM-subspace in the UL. The eigenvalues would correspond to the change in PIM in the direction of the corresponding eigenvector across the two time periods.
           a. In some embodiments, only a portion of the difference-covariance matrix may be decomposed. The elements of the difference-covariance may be used to determine which sub-matrix should be decomposed.
               i. A threshold could be applied to the elements of a difference-covariance matrix to determine which elements should be included in each subset.   
               
         
             4. In another embodiment the difference-covariance matrices are averaged together. One example would be a weighted average, where the weights are calculated from the diagonal elements of the corresponding difference-covariance matrix.
           a. The weighted difference-covariance matrix can then be decomposed as discussed in 3.   
         
             5. The difference covariance matrix may not always be decomposable. In this case, it may be sufficient just to use the values of the difference-covariance matrix (or averaged version) to determine which branches are impacted by PIM, and to make some determination about whether the PIM is in-line or external. 
             6. A full decomposition of the difference-covariance matrix (or averaged difference-covariance matrix) may not be required if only some of the dominant directions are desired to be known. An example is the power method, which is an iterative technique used to find the dominant eigenvector. The dominant eigenvector would be useful when the PIM spatial properties can be mostly represented by a single vector (instead of a matrix). 
             7. Measurements can be prescreened to determine whether they should be used or discarded. Some examples of the prescreening are:
           a. The sum of the diagonal of the difference-covariance matrix must exceed a first threshold;   b. The difference of the sum of the diagonal of the DL covariance matrix between the first and the second time periods should exceed a 2 nd  threshold. Since this prescreening may be used on the DL, it could alternatively be used to trigger an UL measurement; and   c. The sum of the diagonal of both of the first and the second UL covariance matrices should not exceed a 3 rd  threshold.   
         
             8. Each calculation of the difference-covariance matrix can be used on its own. However, it may be advantageous to combine multiple results to improve the accuracy of the solutions.
           a. Multiple difference-covariance matrix results could be combined to improve the accuracy. This is a repeat of step  4   a.      b. Multiple spatial decomposition results could be combined to improve the accuracy:
               i. After several spatial decomposition results are available—they could be compared to determine the spatial decomposition that is most consistent across multiple measurements. A weighting of the results could apply here as the PIM to ‘other-signal’ ratio could be different for each measurement.   
               
         
             9. Although methods have been described for detecting PIM, these methods may also detect non-linear behavior from other sources of distortion. Other sources could include power amplifier distortion leaking into the receiver, or components in the receiver. 
             10. The output of this function, that is, the non-linear distortion detection algorithm for multiple antennas, could be:
           a. Spatial decomposition of the PIM source(s). This output may be useful do identify the location of the PIM source, or be used as an input to additional antenna port combining functions.
               i. This decomposition can be the full decomposition of the difference covariance matrix. Alternatively, it could just provide the dominant spatial vectors of the decomposition.   ii. The spatial decomposition could be provided considering all antenna ports together. Alternatively, the decomposition could be provided on each subset of the antenna ports (denoted by antenna groups).   
               b. Identification of which antenna ports have PIM present. The diagonal of the difference covariance matrix could provide a measure of the PIM on each antenna port. This information could be passed to other functions that are related to PIM management (e.g., detect, report, mitigate PIM, etc.).   c. Identify which antenna ports belong in a subset. The suitability for antenna ports to be within the same antenna group can be based on the non-diagonal terms of the difference correlation matrix. This could then be used to reduce the complexity of the algorithm in further runs.
               i. As a non-limiting example of one state of one embodiment, if the absolute value of the difference covariance matrix is as follows, it may be concluded that ports  1  and  2  have been hit by the same PIM source and that ports  2  and  3  are substantially PIM free:   
               
         
           
         
       
    
     
       
         
           
             
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             11. The spatial properties may be determined by taking the difference between two covariance matrices. There are other covariance comparison techniques that can be used to determine the spatial properties of a non-stationary process in a stationary process.
           a. One example would be to project the covariance matrix of the first time period onto the covariance matrix of the second time period to estimate the spatial properties of the signal that has unchanging 2nd order statistics between the two time intervals. The spatial representation of these signals could then be removed from the covariance matrix of the second time period. This should leave one with an estimate of the spatial representation of the signal that had changing 2nd order statistics between the two time intervals.   
         
           
         
       
    
       FIG. 6  shows an embodiment where the two time periods are chosen from a set of time periods that is greater than 2. The measured data (Block S 126 ) (DL and/or UL) can be used to choose the two time periods, by ensuring that the DL (or UL) power variation exceeds a certain threshold between the two symbols. The predetermined trigger (Block S 128 ) may still be used to ensure that the set of time periods captured is not expected to have a variation in UL power due to desired WD  22  traffic and interference. Optionally, a downlink metric such as covariance or power may be calculated (Block S 130 ), which serves as a basis for choosing the first and the second intervals (Block S 132 ). Then, UL covariance matrices are obtained from the captured data (Block S 134 ). To do this, there may be a waiting period between the first and the second time intervals (Block S 136 ). The difference between the UL covariance matrices is calculated (Block S 138 ) and processed (Block S 140 ). Note that the trigger for data capture (Block S 128 ) may be predetermined and may be based on physical layer characteristics. Note also that if DL capture is available prior to uplink captures, then it could also be used as input to UL data capture (to only capture first and second symbols). The result of the step of choosing first and second time intervals (Block S 132 ) may be input to step S 136 , in the event it is desirable to calculate the UL covariance for all time periods. 
       FIG. 7  shows an example embodiment where the processing by the processing circuitry  48  is performed for subsets of the antenna ports (where each subset is an antenna group). Note that some or all of this processing and the processing described below may be performed by the PIM unit  32  of processor  50 . In other words, in some embodiments, the processor  50  may be configured, such as by software, firmware, etc., to in all or part, perform the functions herein ascribed to the PIM unit  32 . The new function could be input to any of the vertically stacked blocks. It may reduce the processing of all the following blocks where data/processing is split into subsets. A function that identifies antenna groups (Block S 142 ) may be based on the difference matrix discussed above or based on information from some other PIM related function that is running, such as PIM detection, PIM mitigation, etc. In Step S 144 , the UL covariance based on captured data is calculated for each antenna group. To do this, there may be a waiting period between first and the second time intervals (Block S 146 ). The difference between the UL covariance matrices is calculated for each antenna group (Block S 148 ) and processed for each antenna group (Block S 150 ). The processing of each antenna group (Block S 150 ) may include matrix decomposition to determine the spatial properties of PIM sources for each antenna group. The processing may include identifying which antenna ports are impacted by the PIM for each antenna group. These ports may be ordered from most impacted to least impacted. The processing may include identifying and/or refining the antenna groups. 
     Note that the capture of data from which the covariance matrices are obtained may be captured near an antenna. The remaining steps of the methods described herein may be performed away from the antenna and away from the network node as desired or needed. For example, the difference covariance matrix calculation and decomposition can be remote from the antennas. As another example, the decomposition could be moved to another location away from the antennas. In this example, the difference covariance matrices can be sent from near the antennas to the remote location. 
     Thus, appropriate time periods are chosen such that the only variation in power across the 2 UL periods is due to a change in PIM power—which is due to a change in the amount of power hitting the PIM source. The change in UL covariance matrix between the time periods is determined, and the properties of this ‘difference’ matrix are used to identify the spatial properties of the PIM source(s). 
     According to one aspect, a method in a network node  16  for determining passive intermodulation, PIM, characteristics at the network node  16  is provided. The method includes capturing signals from each of at least one antenna port at a first time and a second time. The method also includes determining a first covariance matrix based on signals captured at the first time. Further, the method includes determining a second covariance matrix based on signals captured at the second time. Yet further, the method includes determining a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time. 
     According to this aspect, in some embodiments, the method further includes decomposing, at least in part, the difference matrix to generate eigenvectors and eigenvalues, the eigenvectors representing a PIM subspace, each eigenvalue corresponding to a change in PIM in a direction indicated by a corresponding eigenvector. In some embodiments, the difference matrix has submatrices and the decomposing is of at least a portion of the difference matrix. In some embodiments, the portion of the difference matrix to be decomposed is determined by a comparison of elements of the difference matrix to at least one threshold. In some embodiments, the method includes averaging a plurality of difference covariance matrices. In some embodiments, of the difference matrices are weighted, at least one of the weights being based at least in part on diagonal elements of the difference covariance matrix. In some embodiments, a measurement of a signal of the signals is prescreened to determine whether the measurement is used to determine the difference covariance matrix. In some embodiments, the prescreening is based on whether a sum of diagonal elements of the difference matrix exceeds a first threshold. In some embodiments, the prescreening is based on whether a difference between a sum of diagonal elements of the first covariance matrix and a sum of diagonal elements of the second covariance matrix exceeds a second threshold. In some embodiments, the prescreening is based on whether a sum of diagonal elements of the first and second covariance matrices does not exceed a third threshold. 
     According to another aspect, an apparatus is configured to determine passive intermodulation, PIM, characteristics at the network node  16 . The apparatus includes processing circuitry  48  configured to capture signals from each of at least one antenna port at a first time and a second time. The processing circuitry  48  is further configured to determine a first covariance matrix based on signals captured at the first time. The processing circuitry  48  is configured to determine a second covariance matrix based on signals captured at the second time. The processing circuitry  48  is further configured to determine a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time. 
     According to this aspect, in some embodiments, the processing circuitry  48  is further configured to decompose, at least in part, the difference matrix to generate eigenvectors and eigenvalues, the eigenvectors representing a PIM subspace, each eigenvalue corresponding to a change in PIM in a direction indicated by a corresponding eigenvector. In some embodiments, the difference matrix has submatrices and decomposing is of at least a portion of the difference matrix. In some embodiments, the portion of the difference matrix to be decomposed is determined by a comparison of elements of the difference matrix to at least one threshold. the processing circuitry is further configured to average a plurality of difference matrices. averages of the difference matrices are weighted, at least one of the weights being based at least in part on diagonal elements of the difference covariance matrix. a measurement of a signal of the signals is prescreened to determine whether the measurement is used to determine the difference matrix. the prescreening is based on whether a sum of diagonal elements of the difference matrix exceeds a first threshold. the prescreening is based on whether a difference between a sum of diagonal elements of the first covariance matrix and a sum of diagonal elements of the second covariance matrix exceeds a second threshold. In some embodiments, the prescreening is based on whether a sum of diagonal elements of the first and second covariance matrices does not exceed a third threshold. 
     According to yet another aspect, a method in a network node  16  for determining passive intermodulation, PIM, characteristics at the network node  16  is provided. The method includes capturing signals from each of at least one antenna port at a first time and a second time, an antenna port being one of a physical antenna port and a logical antenna port. The method also includes determining a first covariance matrix based on signals captured at the first time. The method also includes determining a second covariance matrix based on signals captured at the second time, the first and second covariance matrices comprising correlation terms, each correlation term being based at least in part on an expected value of a product of signals received from two antenna ports. The method further includes determining a difference matrix, the difference matrix being based on a difference between the first and second covariance matrices, the difference matrix corresponding to changes in PIM between the first time and the second time. The method further includes decomposing at least part of the difference matrix to generate eigenvectors and eigenvalues, the eigenvectors representing a PIM subspace, each eigenvalue corresponding to a change in PIM in a direction indicated by a corresponding eigenvector. 
     As will be appreciated by one of skill in the art, the concepts described herein may be embodied as a method, data processing system, and/or computer program product. Accordingly, the concepts described herein may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects all generally referred to herein as a “circuit” or “module.” Furthermore, the disclosure may take the form of a computer program product on a tangible computer usable storage medium having computer program code embodied in the medium that can be executed by a computer. Any suitable tangible computer readable medium may be utilized including hard disks, CD-ROMs, electronic storage devices, optical storage devices, or magnetic storage devices. 
     Some embodiments are described herein with reference to flowchart illustrations and/or block diagrams of methods, systems and computer program products. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     These computer program instructions may also be stored in a computer readable memory or storage medium that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instruction means which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. It is to be understood that the functions/acts noted in the blocks may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Although some of the diagrams include arrows on communication paths to show a primary direction of communication, it is to be understood that communication may occur in the opposite direction to the depicted arrows. 
     Computer program code for carrying out operations of the concepts described herein may be written in an object oriented programming language such as Java® or C++. However, the computer program code for carrying out operations of the disclosure may also be written in conventional procedural programming languages, such as the “C” programming language. The program code may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer. In the latter scenario, the remote computer may be connected to the user&#39;s computer through a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). 
     Many different embodiments have been disclosed herein, in connection with the above description and the drawings. It will be understood that it would be unduly repetitious and obfuscating to literally describe and illustrate every combination and subcombination of these embodiments. Accordingly, all embodiments can be combined in any way and/or combination, and the present specification, including the drawings, shall be construed to constitute a complete written description of all combinations and subcombinations of the embodiments described herein, and of the manner and process of making and using them, and shall support claims to any such combination or subcombination. 
     It will be appreciated by persons skilled in the art that the embodiments described herein are not limited to what has been particularly shown and described herein above. In addition, unless mention was made above to the contrary, it should be noted that all of the accompanying drawings are not to scale. A variety of modifications and variations are possible in light of the above teachings without departing from the scope of the following claims.