WO2023180933A1 - Downlink channel covariance matrix estimation via two-dimensional spatial resampling in frequency division duplex systems - Google Patents

Abstract

A method, system and apparatus for downlink channel covariance matrix estimation by way of two-dimensional spatial resampling in frequency division duplex (FDD) systems are disclosed. According to one aspect, a method in a network node includes determining a downlink covariance matrix based at least in part on a discrete time Fourier transform (DTFT) of entries of an uplink covariance matrix, the DTFT being implemented numerically as a multiplication of a transformation matrix and the uplink covariance matrix, the transformation matrix having entries that depend on a ratio of an uplink frequency and a downlink frequency and a geometry of an antenna array of the network node. The method also includes applying the downlink covariance matrix to determine downlink signals.

Description

DOWNLINK CHANNEL COVARIANCE MATRIX ESTIMATION VIA TWO- DIMENSIONAL SPATIAL RESAMPLING IN FREQUENCY DIVISION DUPLEX SYSTEMS

FIELD

The present disclosure relates to wireless communications, and in particular, to downlink channel covariance matrix estimation by way of two-dimensional spatial resampling in frequency division duplex (FDD) systems.

BACKGROUND

The Third Generation Partnership Project (3 GPP) has developed and is developing standards for Fourth Generation (4G) (also referred to as Long Term Evolution (LTE)) and Fifth Generation (5G) (also referred to as New Radio (NR)) wireless communication systems. Such systems provide, among other features, broadband communication between network nodes, such as base stations, and mobile wireless devices (WD), as well as communication between network nodes and between WDs. Sixth Generation (6G) wireless communication systems are also under development.

Accurate channel state information (CSI) enables efficient utilization of the available radio resources in massive Multiple-Input Multiple-Output (MIMO) systems. For Time Division Duplex (TDD) systems, the uplink (UL) and downlink (DL) channels share the same frequency band; hence, DL CSI may be obtained from UL CSI due to channel reciprocity. However, for Frequency Division Duplex (FDD) systems, channel reciprocity does not hold due to the gap between the UL and DL frequency bands. In FDD systems, the channel spatial covariance matrix plays a crucial role in CSI acquisition. Since the coherence time of the channel spatial covariance matrix is longer than the channel coherence time, the training overhead may be significantly reduced.

Moreover, since the propagation directions are frequency invariant for the UL and DL bands, the angular power spectrum (APS), i.e., the signal power distribution in the angular domain, is frequency invariant for the UL and DL bands. The frequency invariance of the APS is exploited in several proposed methods to estimate the DL spatial covariance matrix from an observation of the UL spatial covariance matrix. The main idea of these methods is to estimate the UL covariance matrix, then using this matrix: either explicitly estimate the APS and use it to compute an estimate of the DL covariance matrix or apply some transformation to the UL covariance matrix estimate to get the DL covariance matrix, where the APS frequency invariance assumption is implicitly preserved in the applied transformation. A1though these methods are based on the same assumption, they have different accuracy and complexity.

Downlink covariance matrix estimation has been proposed for onedimensional arrays in where spatial resampling of the uplink covariance matrix using a one-dimensional Sine function was utilized to estimate the downlink covariance matrix from a subset of the elements of the uplink covariance matrix. The proposed scheme was shown to have superior performance to earlier approaches. Furthermore, only the first row and column of the uplink covariance matrix is used to compute the downlink covariance matrix using a matrix-vector multiplication, and hence, the complexity of the algorithm was shown to be smaller than some known methods.

Legacy solutions for FDD systems rely on using the covariance matrix estimated from uplink measurements without any frequency correction. This may lead to significant performance degradation when the duplex gap between uplink and downlink transmission bands is large, e.g., for LTE band 4, the uplink band is 1710-1755 MHz while the downlink band is 2110-2155 MHz, i.e., the duplex gap is 400 MHz.

Some known frequency correction methods for covariance matrices have high complexity. For example, one algorithm explicitly estimates the APS samples by solving a complex optimization problem and then estimates the downlink covariance from the estimated APS. The total complexity of the algorithm may be shown to be of where M is the number of base station antennas and g » M

is the number of samples in the APS estimate. Another known scheme uses a truncated Fourier series expansion to represent the APS and obtains the downlink covariance matrix using a matrix multiplication operation that multiples the vectorized uplink covariance matrix by a transformation matrix. The complexity of the scheme is dominated by this matrix multiplication and is of

One proposed method utilizes a Fourier series expansion of the APS where only the first row and column of the uplink covariance matrix are used to compute the downlink covariance matrix. The complexity of the algorithm is of

However, the algorithm is limited to one-dimensional uniform linear arrays and cannot be directly used for practical two-dimensional arrays that are commonly used in Massive Multiple Input Multiple Output (MIMO) systems.

SUMMARY

Some embodiments advantageously provide methods and network nodes for downlink channel covariance matrix estimation by way of two-dimensional spatial resampling in frequency division duplex (FDD) systems.

Some embodiments disclosed herein are applicable to massive MIMO systems with users communicating with a network node (base station) operating in FDD mode. In FDD systems, unlike time division duplex (TDD) systems, frequency separation between uplink and downlink results in lack of channel reciprocity and subsequently different uplink/downlink channel covariance matrices. For these systems, a method is disclosed to approximate a downlink covariance matrix using only uplink covariance samples. In some embodiments, methods disclosed herein are applicable to two-dimensional antenna arrays.

Some embodiments include methods to implicitly approximate the APS by obtaining a different form of the integral that computes the uplink covariance matrix from the APS. An intermediate function of the APS is derived which may be approximated as the discrete time Fourier transform (DTFT) of a subset of the uplink covariance matrix entries. The accuracy of the approximation depends on the number of antennas at the array, i.e., a higher number of array antennas in massive MIMO yields better APS approximation. The APS approximation is used to obtain the DL covariance matrix, yielding the Whittaker-Shannon interpolation in which entries of the downlink covariance matrix may be expressed as a linear combination of their uplink counterparts.

Furthermore, some embodiments may be implemented as a linear transformation which maps the UL covariance to its DL counterpart, which reduces the complexity. First, the transformation matrix is constant, and its elements only depend on the UL/DL carrier frequencies and the geometry of the antenna array. Hence, it may be computed in advance of operation and saved. Second, the elements of the transformation matrix are Sinc-function samples in which the elements of the transformation matrices are integrals which may be computed numerically.

A downlink covariance matrix estimation technique is disclosed for two- dimensional antenna arrays that implicitly estimates an intermediate function of the APS which may be approximated as the DTFT of a subset of the uplink covariance matrix entries. The APS intermediate function approximation is used to obtain the DL covariance matrix. This yields the Whittaker-Shannon interpolation in which entries of the downlink covariance matrix may be expressed as a linear combination of their uplink counterparts, where the linear coefficients may be obtained from the Sine function based on the array geometry and uplink-downlink frequency ratio.

Some embodiments provide a low-complexity implementation of an algorithm that uses the first row and column of a Toeplitz version of the uplink covariance matrix to estimate the downlink covariance matrix using linear operations implemented in matrix multiplication form, where the linear combination coefficients may be obtained using the Whittaker-Shannon interpolation technique.

In some embodiments, the downlink covariance matrix is determined based on uplink channel estimates in FDD systems with low computational complexity.

Significant performance improvement in received downlink signal to interference plus noise ratio (SINR) is shown through simulations and comparison to a baseline legacy method where the uplink covariance matrix is used for downlink precoding.

According to one aspect, a network node configured to communicate with a processing circuitry. The processing circuitry is configured to determine a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of a first uplink covariance matrix. The DTFT is implemented numerically as a multiplication of a transformation matrix and the first uplink covariance matrix, entries of the transformation matrix depending on a ratio of an uplink frequency and a downlink frequency and a geometry of the antenna array. The processing circuitry is also configured to apply the downlink covariance matrix to determine downlink signals.

According to this aspect, in some embodiments, the transformation matrix entries are samples of Sine functions. In some embodiments, the downlink covariance matrix is determined based at least in part on only one row and one column of the first uplink covariance matrix. In some embodiments, the processing circuitry is further configured to determine the first uplink covariance matrix based at least in part on projections of samples of a second uplink covariance matrix to cones of a set of Toeplitz matrices, the second uplink covariance matrix being determined based at least in part on received signal measurements. In some embodiments, the projections are determined by numerically solving a convex optimization problem. In some embodiments, the convex optimization problem is based at least in part on a Frobenius norm of a difference between a Toeplitz matrix of the set of Toeplitz matrices and the second uplink covariance matrix. In some embodiments, the Toeplitz matrix is positive semi-definite. In some embodiments, the transformation matrix is determined in advance of receiving uplink transmissions from the WD. In some embodiments, the DTFT approximates an angular power spectrum of entries of the first uplink covariance matrix. In some embodiments, the downlink covariance matrix is determined based at least in part on the approximation of the angular power spectrum.

According to another aspect, a method in a network node having an antenna array, the network node configured to communicate with a wireless device, WD, is provided. The method includes determining a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of a first uplink covariance matrix, where the DTFT is implemented numerically as a multiplication of a transformation matrix and the first uplink covariance matrix, entries of the transformation matrix depending on a ratio of an uplink frequency and a downlink frequency and a geometry of the antenna array. The method also includes applying the downlink covariance matrix to determine downlink signals.

According to this aspect, In some embodiments, the method also includes determining the first uplink covariance matrix based at least in part on projections of samples of a second uplink covariance matrix to cones of a set of Toeplitz matrices, the second uplink covariance matrix being determined based at least in part on received signal measurements. In some embodiments, the projections are determined by numerically solving a convex optimization problem. In some embodiments, the convex optimization problem is based at least in part on a Frobenius norm of a difference between a Toeplitz matrix of the set of Toeplitz matrices and the second uplink covariance matrix. In some embodiments, the Toeplitz matrix is positive semi- definite. In some embodiments, the transformation matrix is determined in advance of receiving uplink transmissions from the WD. In some embodiments, the DTFT approximates an angular power spectrum of entries of the first uplink covariance matrix. In some embodiments, the downlink covariance matrix is determined based at least in part on the approximation of the angular power spectrum.

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 schematic diagram of an example network architecture illustrating a communication system connected via an intermediate network to a host computer according to the principles in the present disclosure;

FIG. 2 is a block diagram of a host computer communicating via a network node with a wireless device over an at least partially wireless connection according to some embodiments of the present disclosure;

FIG. 3 is a flowchart illustrating example methods implemented in a communication system including a host computer, a network node and a wireless device for executing a client application at a wireless device according to some embodiments of the present disclosure;

FIG. 4 is a flowchart illustrating example methods implemented in a communication system including a host computer, a network node and a wireless device for receiving user data at a wireless device according to some embodiments of the present disclosure;

FIG. 5 is a flowchart illustrating example methods implemented in a communication system including a host computer, a network node and a wireless device for receiving user data from the wireless device at a host computer according to some embodiments of the present disclosure;

FIG. 6 is a flowchart illustrating example methods implemented in a communication system including a host computer, a network node and a wireless device for receiving user data at a host computer according to some embodiments of the present disclosure; FIG. 7 is a flowchart of an example process in a network node for downlink channel covariance matrix estimation by way of two-dimensional spatial resampling in frequency division duplex (FDD) systems;

FIG. 8 is a graph of relative loss in a received signal to interference plus noise ratio (SINR) as evaluated versus the ratio of downlink frequency to uplink frequency; and

FIG. 9 is a block diagram of an example process for determining a downlink covariance matrix from noisy uplink signals according to some embodiments of the present disclosure.

DETAILED DESCRIPTION

Before describing in detail example embodiments, it is noted that the embodiments reside primarily in combinations of apparatus components and processing steps related to downlink channel covariance matrix estimation by way of two-dimensional spatial resampling in frequency division duplex (FDD) systems. 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. Like numbers refer to like elements throughout the description.

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 may 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), integrated access and backhaul (IAB) node, relay 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 may 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 (loT) device, or a Narrowband loT (NB-IOT) device, etc.

Also, in some embodiments the generic term “radio network node” is used. It may 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), IAB node, 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), 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, may 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.

Some embodiments provide downlink channel covariance matrix estimation by way of two-dimensional spatial resampling in frequency division duplex (FDD) systems.

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 16a, 16b, 16c (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 18a, 18b, 18c (referred to collectively as coverage areas 18). Each network node 16a, 16b, 16c is connectable to the core network 14 over a wired or wireless connection 20. A first wireless device (WD) 22a located in coverage area 18a is configured to wirelessly connect to, or be paged by, the corresponding network node 16a. A second WD 22b in coverage area 18b is wirelessly connectable to the corresponding network node 16b. While a plurality of WDs 22a, 22b (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 may 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 may 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 may be in communication with an eNB for LTE/E-UTRAN and a gNB for NR/NG-RAN.

The communication system 10 may itself be connected to a host computer 24, which may be embodied in the hardware and/or software of a standalone server, a cloud-implemented server, a distributed server or as processing resources in a server farm. The host computer 24 may be under the ownership or control of a service provider, or may be operated by the service provider or on behalf of the service provider. The connections 26, 28 between the communication system 10 and the host computer 24 may extend directly from the core network 14 to the host computer 24 or may extend via an optional intermediate network 30. The intermediate network 30 may be one of, or a combination of more than one of, a public, private or hosted network. The intermediate network 30, if any, may be a backbone network or the Internet. In some embodiments, the intermediate network 30 may comprise two or more sub-networks (not shown).

The communication system of FIG. 1 as a whole enables connectivity between one of the connected WDs 22a, 22b and the host computer 24. The connectivity may be described as an over-the-top (OTT) connection. The host computer 24 and the connected WDs 22a, 22b are configured to communicate data and/or signaling via the OTT connection, using the access network 12, the core network 14, any intermediate network 30 and possible further infrastructure (not shown) as intermediaries. The OTT connection may be transparent in the sense that at least some of the participating communication devices through which the OTT connection passes are unaware of routing of uplink and downlink communications. For example, a network node 16 may not or need not be informed about the past routing of an incoming downlink communication with data originating from a host computer 24 to be forwarded (e.g., handed over) to a connected WD 22a. Similarly, the network node 16 need not be aware of the future routing of an outgoing uplink communication originating from the WD 22a towards the host computer 24.

A network node 16 is configured to include a covariance unit 32 which is configured to determine a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of an uplink covariance matrix, the DTFT being implemented numerically as a multiplication of a transformation matrix and the uplink covariance matrix, the transformation matrix having entries that depend on a ratio of an uplink frequency and a downlink frequency and a geometry of an antenna array of the network node

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. In a communication system 10, a host computer 24 comprises hardware (HW) 38 including a communication interface 40 configured to set up and maintain a wired or wireless connection with an interface of a different communication device of the communication system 10. The host computer 24 further comprises processing circuitry 42, which may have storage and/or processing capabilities. The processing circuitry 42 may include a processor 44 and memory 46. In particular, in addition to or instead of a processor, such as a central processing unit, and memory, the processing circuitry 42 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 44 may be configured to access (e.g., write to and/or read from) memory 46, 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).

Processing circuitry 42 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 host computer 24. Processor 44 corresponds to one or more processors 44 for performing host computer 24 functions described herein. The host computer 24 includes memory 46 that is configured to store data, programmatic software code and/or other information described herein. In some embodiments, the software 48 and/or the host application 50 may include instructions that, when executed by the processor 44 and/or processing circuitry 42, causes the processor 44 and/or processing circuitry 42 to perform the processes described herein with respect to host computer 24. The instructions may be software associated with the host computer 24.

The software 48 may be executable by the processing circuitry 42. The software 48 includes a host application 50. The host application 50 may be operable to provide a service to a remote user, such as a WD 22 connecting via an OTT connection 52 terminating at the WD 22 and the host computer 24. In providing the service to the remote user, the host application 50 may provide user data which is transmitted using the OTT connection 52. The “user data” may be data and information described herein as implementing the described functionality. In one embodiment, the host computer 24 may be configured for providing control and functionality to a service provider and may be operated by the service provider or on behalf of the service provider. The processing circuitry 42 of the host computer 24 may enable the host computer 24 to observe, monitor, control, transmit to and/or receive from the network node 16 and or the wireless device 22.

The communication system 10 further includes a network node 16 provided in a communication system 10 and including hardware 58 enabling it to communicate with the host computer 24 and with the WD 22. The hardware 58 may include a communication interface 60 for setting up and maintaining a wired or wireless connection with an interface of a different communication device of the communication system 10, as well as a radio interface 62 for setting up and maintaining at least a wireless connection 64 with a WD 22 located in a coverage area 18 served by the network node 16. 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 communication interface 60 may be configured to facilitate a connection 66 to the host computer 24. The connection 66 may be direct or it may pass through a core network 14 of the communication system 10 and/or through one or more intermediate networks 30 outside the communication system 10.

In the embodiment shown, the hardware 58 of the network node 16 further includes processing circuitry 68. The processing circuitry 68 may include a processor 70 and a memory 72. In particular, in addition to or instead of a processor, such as a central processing unit, and memory, the processing circuitry 68 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 70 may be configured to access (e.g., write to and/or read from) the memory 72, 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 74 stored internally in, for example, memory 72, 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 74 may be executable by the processing circuitry 68. The processing circuitry 68 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 70 corresponds to one or more processors 70 for performing network node 16 functions described herein. The memory 72 is configured to store data, programmatic software code and/or other information described herein. In some embodiments, the software 74 may include instructions that, when executed by the processor 70 and/or processing circuitry 68, causes the processor 70 and/or processing circuitry 68 to perform the processes described herein with respect to network node 16. For example, processing circuitry 68 of the network node 16 may include the covariance unit 32 which is configured to determine a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of an uplink covariance matrix, the DTFT being implemented numerically as a multiplication of a transformation matrix and the uplink covariance matrix, the transformation matrix having entries that depend on a ratio of an uplink frequency and a downlink frequency and a geometry of an antenna array of the network node.

The communication system 10 further includes the WD 22 already referred to. The WD 22 may have hardware 80 that may include a radio interface 82 configured to set up and maintain a wireless connection 64 with a network node 16 serving a coverage area 18 in which the WD 22 is currently located. The radio interface 82 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 80 of the WD 22 further includes processing circuitry 84. The processing circuitry 84 may include a processor 86 and memory 88. In particular, in addition to or instead of a processor, such as a central processing unit, and memory, the processing circuitry 84 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 86 may be configured to access (e.g., write to and/or read from) memory 88, 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 90, which is stored in, for example, memory 88 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 90 may be executable by the processing circuitry 84. The software 90 may include a client application 92. The client application 92 may be operable to provide a service to a human or non-human user via the WD 22, with the support of the host computer 24. In the host computer 24, an executing host application 50 may communicate with the executing client application 92 via the OTT connection 52 terminating at the WD 22 and the host computer 24. In providing the service to the user, the client application 92 may receive request data from the host application 50 and provide user data in response to the request data. The OTT connection 52 may transfer both the request data and the user data. The client application 92 may interact with the user to generate the user data that it provides.

The processing circuitry 84 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 86 corresponds to one or more processors 86 for performing WD 22 functions described herein. The WD 22 includes memory 88 that is configured to store data, programmatic software code and/or other information described herein. In some embodiments, the software 90 and/or the client application 92 may include instructions that, when executed by the processor 86 and/or processing circuitry 84, causes the processor 86 and/or processing circuitry 84 to perform the processes described herein with respect to WD 22.

In some embodiments, the inner workings of the network node 16, WD 22, and host computer 24 may be as shown in FIG. 2 and independently, the surrounding network topology may be that of FIG. 1.

In FIG. 2, the OTT connection 52 has been drawn abstractly to illustrate the communication between the host computer 24 and the wireless device 22 via the network node 16, without explicit reference to any intermediary devices and the precise routing of messages via these devices. Network infrastructure may determine the routing, which it may be configured to hide from the WD 22 or from the service provider operating the host computer 24, or both. While the OTT connection 52 is active, the network infrastructure may further take decisions by which it dynamically changes the routing (e.g., on the basis of load balancing consideration or reconfiguration of the network).

The wireless connection 64 between the WD 22 and the network node 16 is in accordance with the teachings of the embodiments described throughout this disclosure. One or more of the various embodiments improve the performance of OTT services provided to the WD 22 using the OTT connection 52, in which the wireless connection 64 may form the last segment. 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. There may further be an optional network functionality for reconfiguring the OTT connection 52 between the host computer 24 and WD 22, in response to variations in the measurement results. The measurement procedure and/or the network functionality for reconfiguring the OTT connection 52 may be implemented in the software 48 of the host computer 24 or in the software 90 of the WD 22, or both. In embodiments, sensors (not shown) may be deployed in or in association with communication devices through which the OTT connection 52 passes; the sensors may participate in the measurement procedure by supplying values of the monitored quantities exemplified above, or supplying values of other physical quantities from which software 48, 90 may compute or estimate the monitored quantities. The reconfiguring of the OTT connection 52 may include message format, retransmission settings, preferred routing etc.; the reconfiguring need not affect the network node 16, and it may be unknown or imperceptible to the network node 16. Some such procedures and functionalities may be known and practiced in the art. In certain embodiments, measurements may involve proprietary WD signaling facilitating the host computer’s 24 measurements of throughput, propagation times, latency and the like. In some embodiments, the measurements may be implemented in that the software 48, 90 causes messages to be transmitted, in particular empty or ‘dummy’ messages, using the OTT connection 52 while it monitors propagation times, errors, etc.

Thus, in some embodiments, the host computer 24 includes processing circuitry 42 configured to provide user data and a communication interface 40 that is configured to forward the user data to a cellular network for transmission to the WD 22. In some embodiments, the cellular network also includes the network node 16 with a radio interface 62. In some embodiments, the network node 16 is configured to, and/or the network node’s 16 processing circuitry 68 is configured to perform the functions and/or methods described herein for preparing/initiating/maintaining/ supporting/ending a transmission to the WD 22, and/or preparing/terminating/ maintaining/supporting/ending in receipt of a transmission from the WD 22. In some embodiments, the host computer 24 includes processing circuitry 42 and a communication interface 40 that is configured to a communication interface 40 configured to receive user data originating from a transmission from a WD 22 to a network node 16. In some embodiments, the WD 22 is configured to, and/or comprises a radio interface 82 and/or processing circuitry 84 configured to perform the functions and/or methods described herein for preparing/initiating/maintaining/ supporting/ending a transmission to the network node 16, and/or preparing/ terminating/maintaining/supporting/ending in receipt of a transmission from the network node 16.

Although FIGS. 1 and 2 show various “units” such as covariance 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. Further, the execution of the functions of the covariance unit 32 may be distributed among a plurality of processors, including processor 44 of host computer 24.

FIG. 3 is a flowchart illustrating an example method implemented in a communication system, such as, for example, the communication system of FIGS. 1 and 2, in accordance with one embodiment. The communication system may include a host computer 24, a network node 16 and a WD 22, which may be those described with reference to FIG. 2. In a first step of the method, the host computer 24 provides user data (Block S100). In an optional substep of the first step, the host computer 24 provides the user data by executing a host application, such as, for example, the host application 50 (Block S102). In a second step, the host computer 24 initiates a transmission carrying the user data to the WD 22 (Block S104). In an optional third step, the network node 16 transmits to the WD 22 the user data which was carried in the transmission that the host computer 24 initiated, in accordance with the teachings of the embodiments described throughout this disclosure (Block S106). In an optional fourth step, the WD 22 executes a client application, such as, for example, the client application 92, associated with the host application 50 executed by the host computer 24 (Block s 108).

FIG. 4 is a flowchart illustrating an example method implemented in a communication system, such as, for example, the communication system of FIG. 1, in accordance with one embodiment. The communication system may include a host computer 24, a network node 16 and a WD 22, which may be those described with reference to FIGS. 1 and 2. In a first step of the method, the host computer 24 provides user data (Block SI 10). In an optional substep (not shown) the host computer 24 provides the user data by executing a host application, such as, for example, the host application 50. In a second step, the host computer 24 initiates a transmission carrying the user data to the WD 22 (Block S 112). The transmission may pass via the network node 16, in accordance with the teachings of the embodiments described throughout this disclosure. In an optional third step, the WD 22 receives the user data carried in the transmission (Block S 114).

FIG. 5 is a flowchart illustrating an example method implemented in a communication system, such as, for example, the communication system of FIG. 1, in accordance with one embodiment. The communication system may include a host computer 24, a network node 16 and a WD 22, which may be those described with reference to FIGS. 1 and 2. In an optional first step of the method, the WD 22 receives input data provided by the host computer 24 (Block SI 16). In an optional substep of the first step, the WD 22 executes the client application 92, which provides the user data in reaction to the received input data provided by the host computer 24 (Block SI 18). Additionally or alternatively, in an optional second step, the WD 22 provides user data (Block S120). In an optional substep of the second step, the WD provides the user data by executing a client application, such as, for example, client application 92 (Block S122). In providing the user data, the executed client application 92 may further consider user input received from the user. Regardless of the specific manner in which the user data was provided, the WD 22 may initiate, in an optional third substep, transmission of the user data to the host computer 24 (Block S124). In a fourth step of the method, the host computer 24 receives the user data transmitted from the WD 22, in accordance with the teachings of the embodiments described throughout this disclosure (Block S126).

FIG. 6 is a flowchart illustrating an example method implemented in a communication system, such as, for example, the communication system of FIG. 1, in accordance with one embodiment. The communication system may include a host computer 24, a network node 16 and a WD 22, which may be those described with reference to FIGS. 1 and 2. In an optional first step of the method, in accordance with the teachings of the embodiments described throughout this disclosure, the network node 16 receives user data from the WD 22 (Block S128). In an optional second step, the network node 16 initiates transmission of the received user data to the host computer 24 (Block S130). In a third step, the host computer 24 receives the user data carried in the transmission initiated by the network node 16 (Block S132).

FIG. 7 is a flowchart of an example process in a network node 16 for downlink channel covariance matrix estimation by way of two-dimensional spatial resampling in frequency division duplex (FDD) systems. 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 68 (including the covariance unit 32), processor 70, radio interface 62 and/or communication interface 60. Network node 16 such as via processing circuitry 68 and/or processor 70 and/or radio interface 62 and/or communication interface 60 is configured to determine a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of a first uplink covariance matrix, the DTFT being implemented numerically as a multiplication of a transformation matrix and the first uplink covariance matrix, entries of the transformation matrix depending on a ratio of an uplink frequency and a downlink frequency and a geometry of an antenna array of the network node (Block S134). The process also includes applying the downlink covariance matrix to determine downlink signals (Block S136).

In some embodiments, entries of the transformation matrix include samples of Sine functions. In some embodiments, the downlink covariance matrix is determined based at least in part on only one row and one column of the uplink covariance matrix. In some embodiments, the transformation matrix is determined in advance of receiving uplink transmissions from the WD. In some embodiments, the process also includes determining a sample matrix that minimizes a Frobenius norm of a difference between the sample matrix and an uplink signal covariance matrix determined from received signal measurements. In some embodiments, elements of the transformation matrix are factors of terms in a sum of products, the terms including terms of the uplink covariance matrix. In some embodiments, the terms in the sum implicitly include an approximation of an angular power spectrum, APS, associated with the antenna array. In some embodiments, the method also includes determining the first uplink covariance matrix based at least in part on projections of samples of a second uplink covariance matrix to cones of a set of Toeplitz matrices, the second uplink covariance matrix being determined based at least in part on received signal measurements. In some embodiments, the projections are determined by numerically solving a convex optimization problem. In some embodiments, the convex optimization problem is based at least in part on a Frobenius norm of a difference between a Toeplitz matrix of the set of Toeplitz matrices and the second uplink covariance matrix. In some embodiments, the Toeplitz matrix is positive semi-definite. In some embodiments, the transformation matrix is determined in advance of receiving uplink transmissions from the WD. In some embodiments, the DTFT approximates an angular power spectrum of entries of the first uplink covariance matrix. In some embodiments, the downlink covariance matrix is determined based at least in part on the approximation of the angular power spectrum.

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 downlink channel covariance matrix estimation by way of two-dimensional spatial resampling in frequency division duplex (FDD) systems.

Consider a MIMO channel between a network node and a single antenna wireless device (WD) 22. It is assumed that the network node 16 is equipped with an M × N -antenna uniform rectangular array (URA) in the yz plane. The N antennas of each row are L_y-equidistant and M antennas of each column are L_z -equidistant. The system employs FDD access in which the uplink transmission (from WD 22 to network node 16) occurs over the frequency interval

while the downlink transmission occurs on the frequency interva where f_u

and f_d are the frequencies of the uplink and downlink carriers, respectively, and w_u and w_d are the bandwidths of the uplink and downlink carriers, respectively. Consider a narrow-band transmission, i.e., In this case, the

entire uplink and downlink frequency intervals may be each seen as a single frequency, f_u and f_d, respectively. θ Consider, a wide sense stationary (WSS) uncorrelated scattering channel model in which the channel vectors evolve in time according to a WSS process. In this model, samples of time-variant channel vector h(t) at intervals of channel coherence time T_c, i.e., h[n] = h(nT_c), constitute a zero-mean WSS circularly symmetric Gaussian process that is white in the time domain and correlated in the spatial domain.

For this URA, the uplink and downlink steering vectors are given by:

where (. )^T denotes vector transpose, is the steering vector

corresponding to the n-th column of antennas in the URA and is given by:

Considering a right-handed Cartesian coordinate system, the antenna at the n- the column and m-th row of the URA has coordinates

and its corresponding entry in the steering vector is

given by:

where 0 ∈ [-π, π] is the azimuth angle of arrival and φ 6 [-π/2, π/2] is elevation angle of arrival. Using the URA steering vector, the (p, q)-th element of the uplink and downlink spatial covariance matrices is given by:

where p = (p₁ — 1)M + q₁, q = (p₂ — 1)M + q₂.

Since the channel covariance matrix R⁽ⁱ⁾ , i ∈ {ul, dl} contains a weighted summation of matrices with the structure A⁽ⁱ⁾ = a⁽ⁱ⁾a⁽ⁱ⁾

∈ c^NM×NM, i ∈ {ul, dl} where denotes vector transpose, the covariance matrix R® will have the same properties as A⁽ⁱ⁾. Using the URA steering vectors a⁽ⁱ⁾, it may be shown that A⁽ⁱ⁾ has the following structure:

Furthermore, it may be shown that each block is

given by:

Using the last two equations, it may be shown that:

• , the diagonal blocks of A⁽ⁱ⁾ are

equal;

• that is, the blocks parallel to main

diagonal blocks are equal;

• Each diagonal block is positive semi-definite,

Hermitian and Toeplitz with 1 on the diagonal;

• Off-diagonal blocks are only Toeplitz and

• Therefore, A⁽ⁱ⁾ is block Hermitian (subsequently Hermitian) and block Toeplitz.

Since R⁽ⁱ⁾ contains covariance matrix R⁽ⁱ⁾ also holds these properties.

Therefore, in a URA system, the uplink and downlink covariance matrices may be expressed as:

Wherein is Toeplitz and Hermitian while

are only Toeplitz. Therefore, the first row and first column of each first

column-block, i.e., is considered.

Downlink Channel Covariance Matrix Approximation

Using the discrete-time Fourier transform (DTFT), a method to approximate the downlink covariance matrix R^(dl) for a URA is provided. A direct transform from the uplink covariance matrix to its downlink counterpart is also provided. The pq-th entry of R^(ul) and R^(dl) may be considered as a 2-dimensional Inverse Discrete Time Fourier transform of the APS, ρ(θ, Φ ). So, the DTFT of R^(ul) leads to an approximation of ρ(θ, Φ ) that may be used to get an estimate of R^(dl).

Approximation of APS

In this section, an implicit approximation of the APS by obtaining a different form of the integral that computes the uplink covariance matrix is provided. Due to the properties of R^(ul) and R^(dl) highlighted in the previous subsection, only the elements of the first row and the first column of the submatrices included in the first block-column of R^(ul) are used. Using the expression for the steering vectors of a URA, it may be shown that the pq-th entry of R^(ul) may be written as:

where

To get the second equation above, the following substitution:

is used in the transition from the second equation to the third one. Also, the following change of variables is used: y = sin(θ) cos(Φ) , z = sin(Φ), and

To move from the third equation to the fourth one, the following substitution is used:

and to get the fifth equation from the fourth equation, the following substitutions are used:

Similarly, it may be shown that:

The definition of ρ₅(u, v) depends on the values of γ_y and γ_z . More precisely, the following four cases are considered:

Comparing the equation defining r with the DTFT pair, it may be seen

that ρ₅(u, v) may be interpreted as DTFT of uplink covariance matrix entries; therefore, an approximation of ρ₅(u, v) may be obtained from:

The accuracy of this approximation depends on the number of antennas in the URA. A higher number of antennas provides more accurate approximation.

An approximation of Downlink Channel Covariance Matrix

The approximation of the APS may be used to obtain downlink covariance entries. Substituting for ρ₅(u, v) into r

yields:

In particular, let contain the first-row and first-column

entries of the n-th block of the first block-column of the downlink covariance matrix, R^(dl), and let

contain the first-row and first-column entries of all first block-column of the estimated R^(ul). An approximation of is

given by:

It may be seen that Ψ and Φ _n depend only on the frequency ratio, and

may be computed offline in advance of operation.

Uplink Channel Covariance Matrix Sample Computation

So far, it has been assumed that the uplink channel covariance matrix is available. In practice, uplink covariance matrix samples may be computed at the network node 16 by a limited number of noisy uplink channel vectors. More precisely, transmitting pilots at the WD 22, the noisy channel vector received at the network node 16 during the 1-th coherence time is given by y_l = h_l + n_l, wherein h_l is the channel vector and is Gaussian noise vector with zero mean and covariance matrix Let L denote the number of available samples of y_l. Using 1 = 1, ... , L, the covariance matrix sample may be computed by:

given is Hermitian but not necessarily Toeplitz.

To overcome this potential drawback, the computed uplink covariance matrix sample may be projected to the cone of Toeplitz positive semi-definite matrices by using the following convex optimization problem:

wherein T₊ denotes the set of positive semi-definite Toeplitz M X M matrices and denotes the Frobenius norm of a matrix. This projected uplink covariance

may be used in the disclosed method instead of actual R^(ul).

Note that the above optimization problem may be efficiently solved where the constraint X E T₊ corresponds to a set of linear constraints on the elements of X. Numerical Simulations

In this section, the performance of the arrangements disclosed herein is compared with the performance of a legacy method in which there is no downlink covariance matrix estimation, and the noisy uplink covariance matrix is used directly as the estimated downlink covariance matrix. The performance of the methods will be compared at a signal to noise ratio (SNR) of 35 dB.

FIG. 8 is a graph of an example of relative loss in a received signal to interference plus noise ratio (SINR) as evaluated versus the ratio of downlink frequency to uplink frequency The performance metric used in the simulations is the relative loss in the downlink received signal to interference plus noise ratio (SINR) ratio which is given by:

where v is the principal eigenvector of the downlink covariance matrix of the tested scheme, R_d is the actual downlink covariance matrix (not the estimated one) and λ_{d ,max} is the largest eigenvalue of the actual downlink covariance matrix. More precisely, the metric shows the relative loss in the received SINR at the user using a precoder composed of the principal eigenvector of the estimated downlink covariance matrix and the received SINR using the principal eigenvector of the exact downlink covariance matrix.

In some embodiments, it may be assumed that a noisy version of uplink channel covariance matrix is available at the network node 16. In particular, the network node 16 has access to uplink covariance samples through noisy channel estimates. To obtain a noisy channel vector at network node 16, the APS is used to generate the actual uplink covariance matrix R_u and then the actual channel vector is computed as

wherein η_l is a Gaussian random vector with zero mean and identity covariance matrix. Afterwards, a noisy version of h_l is assumed to be available at the network node 16 and used for computing the estimated uplink covariance matrix.

FIG. 9 is a block diagram of one example of determining a downlink covariance matrix from channel estimates. The functional blocks 94-102 in FIG. 9 may, for example, be implemented by the covariance unit 32 of the processing circuitry 68. A first uplink covariance matrix is determined by a first covariance matrix determination unit 94. A Toeplitz matrix determination unit 96 determines a Toeplitz covariance matrix based on the uplink covariance matrix determined by the first covariance matrix determination unit 94. An extraction unit 98 extracts a first row and column of a first block-column to construct an intermediate covariance matrix. This matrix is pre- and post-multiplied in downlink covariance vector unit 100 to determine covariance vectors. Downlink covariance matrix unit 102 constructs the downlink covariance matrix from the covariance vectors.

Some embodiments may include one or more of the following:

Embodiment A1. A network node configured to communicate with a wireless device (WD), the network node configured to, and/or comprising a radio interface and/or comprising processing circuitry configured: determine a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of an uplink covariance matrix, the DTFT being implemented numerically as a multiplication of a transformation matrix and the uplink covariance matrix, the transformation matrix having entries that depend on a ratio of an uplink frequency and a downlink frequency and a geometry of an antenna array of the network node; and apply the downlink covariance matrix to determine downlink signals.

Embodiment A2. The network node of Embodiment A1, wherein entries of the transformation matrix include samples of Sine functions.

Embodiment A3. The network node of any of Embodiments A1 and A2, wherein the downlink covariance matrix is determined based at least in part on only one row and one column of the uplink covariance matrix.

Embodiment A4. The network node of any of Embodiments A1 -A3, wherein the transformation matrix is determined in advance of receiving uplink transmissions from the WD.

Embodiment A5. The network node of any of Embodiments A1-A4, wherein the network node, radio interface and/or processing circuitry are further configured to determine the uplink covariance matrix based at least in part on determining a sample matrix that minimizes a Frobenius norm of a difference between the sample matrix and an uplink signal covariance matrix determined from received signal measurements.

Embodiment A6. The network node of any of Embodiments A1-A5, wherein elements of the transformation matrix are factors of terms in a sum of products, the terms including terms of the uplink covariance matrix.

Embodiment A7. The network node of Embodiment A6, wherein the terms in the sum implicitly include an approximation of an angular power spectrum, APS, associated with the antenna array.

Embodiment B1. A method implemented in a network node, the method comprising: determining a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of an uplink covariance matrix, the DTFT being implemented numerically as a multiplication of a transformation matrix and the uplink covariance matrix, the transformation matrix having entries that depend on a ratio of an uplink frequency and a downlink frequency and a geometry of an antenna array of the network node; and applying the downlink covariance matrix to determine downlink signals.

Embodiment B2. The method of Embodiment B1, wherein entries of the transformation matrix include samples of Sine functions.

Embodiment B3. The method of any of Embodiments B1 and B2, wherein the downlink covariance matrix is determined based at least in part on only one row and one column of the uplink covariance matrix.

Embodiment B4. The method of any of Embodiments B1-B3, wherein the transformation matrix is determined in advance of receiving uplink transmissions from the WD.

Embodiment B5. The method of any of Embodiments B1-B4, further comprising determining a sample matrix that minimizes a Frobenius norm of a difference between the sample matrix and an uplink signal covariance matrix determined from received signal measurements.

Embodiment B6. The method of any of Embodiments B1-B5, wherein elements of the transformation matrix are factors of terms in a sum of products, the terms including terms of the uplink covariance matrix.

Embodiment B7. The method of Embodiment B6, wherein the terms in the sum implicitly include an approximation of an angular power spectrum, APS, associated with the antenna array. As will be appreciated by one of skill in the art, the concepts described herein may be embodied as a method, data processing system, computer program product and/or computer storage media storing an executable computer program. 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.” Any process, step, action and/or functionality described herein may be performed by, and/or associated to, a corresponding module, which may be implemented in software and/or firmware and/or hardware. 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 may 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, may be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer (to thereby create a special 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 may 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 Python, 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's computer, partly on the user's computer, as a stand-alone software package, partly on the user'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'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 may 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.

Abbreviations that may be used in the preceding description include:

Abbreviation Explanation AoA Angle of Arrival

APS Angular Power Spectrum

BS Base Station

CSI Channel State Information

DL Downlink

FDD Frequency Division Duplex

MIMO Multiple-Input Multiple-Output

SU Single User

TDD Time Division Duplex

UL Uplink

ULA Uniform Linear Array

WD Wireless Device

WSS Wide Sense Stationary

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.

Claims

What is claimed is:

1. A network node (16) configured to communicate with a wireless device, WD (22), the network node (16) comprising: an antenna array (63); and processing circuitry (68) configured to: determine a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of a first uplink covariance matrix, the DTFT being implemented numerically as a multiplication of a transformation matrix and the first uplink covariance matrix, entries of the transformation matrix depending on a ratio of an uplink frequency and a downlink frequency and a geometry of the antenna array (63); and apply the downlink covariance matrix to determine downlink signals.

2. The network node (16) of Claim 1, wherein the transformation matrix entries are samples of Sine functions.

3. The network node (16) of any of Claims 1 and 2, wherein the downlink covariance matrix is determined based at least in part on only one row and one column of the first uplink covariance matrix.

4. The network node (16) of any of Claims 1-3, wherein the processing circuitry (68) is further configured to determine the first uplink covariance matrix based at least in part on projections of samples of a second uplink covariance matrix to cones of a set of Toeplitz matrices, the second uplink covariance matrix being determined based at least in part on received signal measurements.

5. The network node (16) of Claim 4, wherein the projections are determined by numerically solving a convex optimization problem.

6. The network node (16) of Claim 5, wherein the convex optimization problem is based at least in part on a Frobenius norm of a difference between a Toeplitz matrix of the set of Toeplitz matrices and the second uplink covariance matrix.

7. The network node (16) of Claim 6, wherein the Toeplitz matrix is positive semi-definite.

8. The network node (16) of any of Claims 1-7, wherein the transformation matrix is determined in advance of receiving uplink transmissions from the WD (22).

9. The network node (16) of any of Claims 1-8, wherein the DTFT approximates an angular power spectrum of entries of the first uplink covariance matrix.

10. The network node (16) of Claim 9, wherein the downlink covariance matrix is determined based at least in part on the approximation of the angular power spectrum.

11. A method in a network node (16) having an antenna array (63), the network node (16) configured to communicate with a wireless device, WD (22), the method comprising: determining (S134) a downlink covariance matrix based at least in part on a discrete time Fourier transform, DTFT, of entries of a first uplink covariance matrix, the DTFT being implemented numerically as a multiplication of a transformation matrix and the first uplink covariance matrix, entries of the transformation matrix depending on a ratio of an uplink frequency and a downlink frequency and a geometry of the antenna array (63); and applying (S136) the downlink covariance matrix to determine downlink signals.

12. The method of Claim 11, wherein the transformation matrix entries are samples of Sine functions.

13. The method of any of Claims 11 and 12, wherein the downlink covariance matrix is determined based at least in part on only one row and one column of the first uplink covariance matrix.

14. The method of any of Claims 11-13, further comprising determining the first uplink covariance matrix based at least in part on projections of samples of a second uplink covariance matrix to cones of a set of Toeplitz matrices, the second uplink covariance matrix being determined based at least in part on received signal measurements.

15. The method of Claim 14, wherein the projections are determined by numerically solving a convex optimization problem.

16. The method of Claim 15, wherein the convex optimization problem is based at least in part on a Frobenius norm of a difference between a Toeplitz matrix of the set of Toeplitz matrices and the second uplink covariance matrix.

17. The method of Claim 16, wherein the Toeplitz matrix is positive semi- definite.

18. The method of any of Claims 11-17, wherein the transformation matrix is determined in advance of receiving uplink transmissions from the WD (22).

19. The method of any of Claims 11-18, wherein the DTFT approximates an angular power spectrum of entries of the first uplink covariance matrix.

20. The method of Claim 19, wherein the downlink covariance matrix is determined based at least in part on the approximation of the angular power spectrum.