Total radiated power for uplink MIMO with non-aligned transmit polarizations

Abstract

Various aspects of the present disclosure relate to uplink MIMO total radiated power. A test equipment receives (1102), from a first antenna of a UE, a first transmission and determines (1104) a first radiated power measurement for each of two orthogonal polarizations based on a radiated power of the first transmission. The test equipment receives (1106), from a second antenna of the UE, a second transmission and determines (1108) a second radiated power measurement for each of two orthogonal polarizations based on a radiated power of the second transmission. The test equipment determines (1110) a radiated power of a multi-antenna transmission based at least in part on a multi- antenna precoder, the first radiated power measurement, and the second radiated power measurement.

Description

TOTAL RADIATED POWER FOR UPLINK MIMO WITH NON- ALIGNED TRANSMIT POLARIZATIONS TECHNICAL FIELD

[0001] The present disclosure relates to wireless communications, and more specifically to total radiated power (TRP) for an uplink (UL) MIMO with non-aligned transmit polarizations. BACKGROUND

[0002] A wireless communications system may include one or multiple network communication devices, which may be known as a network equipment (NE), supporting wireless communications for one or multiple user communication devices, which may be otherwise known as user equipment (UE), or other suitable terminology. The wireless communications system may support wireless communications with one or multiple user communication devices by utilizing resources of the wireless communication system (e.g., time resources (e.g., symbols, slots, subframes, frames, or the like) or frequency resources (e.g., subcarriers, carriers, or the like). Additionally, the wireless communications system may support wireless communications across various radio access technologies including third generation (3G) radio access technology, fourth generation (4G) radio access technology, fifth generation (5G) radio access technology, among other suitable radio access technologies beyond 5G (e.g., 5G-Advanced (5G-A), sixth generation (6G), etc.). SUMMARY

[0003] An article “a” before an element is unrestricted and understood to refer to “at least one” of those elements or “one or more” of those elements. The terms “a,” “at least one,” “one or more,” and “at least one of one or more” may be interchangeable. As used herein, including in the claims, “or” as used in a list of items (e.g., a list of items prefaced by a phrase such as “at least one of” or “one or more of” or “one or both of) indicates an inclusive list such that, for example, a list of at least one of A, B, or C means A or B or C or AB or AC or BC or ABC (i.e., A and B and C). Also, as used herein, the phrase “based on” shall not be construed as a reference to a closed set of conditions. For example, an example step that is described as “based on condition A” may be based on both acondition A and a condition B without departing from the scope of the present disclosure. In other words, as used herein, the phrase “based on” shall be construed in the same manner as the phrase “based at least in part on.” Further, as used herein, including in the claims, a “set” may include one or more elements.

[0004] A test equipment for wireless communication is described. In some examples, the test equipment may implement, or may be implemented by, an NE. The test equipment may be configured to, capable of, or operable to receive, from a first antenna of a UE, a first transmission; determine a first radiated power measurement for each of two orthogonal polarizations based on a measured radiated power of the first transmission; receive, from a second antenna of the UE, a second transmission; determine a second radiated power measurement for each of the two orthogonal polarizations based on a measured radiated power of the second transmission; and determine a radiated power(e.g., ^^^, ^^ for an azimuth ^ and elevation ^) of a multi-antenna transmission based atleast in part on a multi-antenna precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission, and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

[0005] A processor for wireless communication is described. The processor may be configured to, capable of, or operable to receive, at a test equipment and from a first antenna of a UE, a first transmission; determine a first radiated power measurement for each of two orthogonal polarizations based on a measured radiated power of the first transmission; receive, at the test equipment and from a second antenna of the UE, a second transmission; determine a second radiated power measurement for each of the two orthogonal polarizations based on a measured radiated power of the second transmission;and determine a radiated power (e.g., ^^^, ^^ for an azimuth ^ and elevation ^) of amulti-antenna transmission based at least in part on a multi-antenna precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission, and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

[0006] A method performed or performable by a test equipment for wireless communication is described. The method may include receiving, from a first antenna of a UE, a first transmission; determining a first radiated power measurement for each of twoorthogonal polarizations based on a measured radiated power of the first transmission; receive, from a second antenna of the UE, a second transmission; determining a second radiated power measurement for each of the two orthogonal polarizations based on a measured radiated power of the second transmission; and determining a radiated power(e.g., ^^^, ^^ for an azimuth ^ and elevation ^) of a multi-antenna transmission based atleast in part on the precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission, and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

[0007] A UE for wireless communication is described. The UE may be configured to, capable of, or operable to receive, from a test equipment, an instruction to use a multi- antenna precoder for a multi-antenna transmission, wherein the test equipment determinesa radiated power for an azimuth and an elevation (e.g., ^^^, ^^ for an azimuth ^ andelevation ^) relative to the UE based at least in part on the multi-antenna precoder and radiated power measurements of separate transmissions from individual antennas of the UE; transmit from a first antenna, to the test equipment according to the a first single- antenna precoder for transmission from the first antenna, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment; and transmit from a second antenna, to the test equipment according to a second single-antenna precoder for transmission from the second antenna, a second transmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment.

[0008] A processor for wireless communication is described. The processor may be configured to, capable of, or operable to receive, from a test equipment, an instruction to use a multi-antenna precoder for a multi-antenna transmission, wherein the test equipmentdetermines a radiated power for an azimuth and an elevation (e.g., ^^^, ^^ for an azimuth^ and elevation ^) relative to the UE based at least in part on the multi-antenna precoderand radiated power measurements of separate transmissions from individual antennas of the UE; transmit from a first antenna, to the test equipment according to the a first single- antenna precoder for transmission from the first antenna, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment; and transmit from a second antenna, to the test equipment according to a second single-antenna precoder for transmission from the second antenna, a secondtransmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment.

[0009] A method performed or performable by a UE for wireless communication is described. The method may include receiving, from a test equipment, an instruction to use a multi-antenna precoder for a multi-antenna transmission, wherein the test equipmentdetermines a radiated power for an azimuth and an elevation (e.g., ^^^, ^^ for an azimuth^ and elevation ^) relative to the UE based at least in part on the multi-antenna precoderand radiated power measurements of separate transmissions from individual antennas of the UE; transmitting from a first antenna, to the test equipment according to the a first single-antenna precoder for transmission from the first antenna, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment; and transmitting from a second antenna, to the test equipment according to a second single-antenna precoder for transmission from the second antenna, a second transmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 illustrates an example of a wireless communications system in accordance with aspects of the present disclosure.

[0011] Figure 2 illustrates an example of a transmitter diagram with two transmit antennas, in accordance with aspects of the present disclosure.

[0012] Figure 3 illustrates an example of distribution of loss due to phase alignment error with the coherent, two antenna port precoders, in accordance with aspects of the present disclosure.

[0013] Figure 4 illustrates an example of a transmitter diagram with four transmit antennas, in accordance with aspects of the present disclosure.

[0014] Figure 5 illustrates an example of a distribution of loss due to phase alignment error with the coherent, four antenna port precoders, in accordance with aspects of the present disclosure.

[0015] Figure 6 illustrates an example of a procedure to determine the TRP of a UE, in accordance with aspects of the present disclosure.

[0016] Figure 7 illustrates an example of a UE in accordance with aspects of the present disclosure.

[0017] Figure 8 illustrates an example of a processor in accordance with aspects of the present disclosure.

[0018] Figure 9 illustrates an example of an NE in accordance with aspects of the present disclosure.

[0019] Figure 10 illustrates a flowchart of a method performed by a UE in accordance with aspects of the present disclosure.

[0020] Figure 11 illustrates a flowchart of a method performed by a test equipment in accordance with aspects of the present disclosure. DETAILED DESCRIPTION

[0021] A wireless communications system includes communication devices, such as UEs, that transmit and receive wireless communications as signaling over the FR1 and FR2 frequency ranges. The frequency ranges in Third Generation Partnership Project (3GPP) include designated FR1 and FR2 frequency ranges, such as for transmitting and / or receiving radio signals at frequencies lower than 6 GHz (e.g., FR1), or higher than 6 GHz (e.g., FR2 or millimeter wave (mmWave)).

[0022] For an operability requirement, the UEs have to meet transmission power requirements to confirm how a UE will likely perform when used in the wireless communications system. The testing can include evaluating a UE transmitting with at least a minimum uplink radiated power requirement for operability in the wireless communications system, which is determined as TRP. The TRP represents the combined power emitted by a device antenna, or an antenna array, when transmitting a signal, and TRP encompasses both direction and radiation efficiency of the device antenna or antenna array.

[0023] The issue of how to measure TRP for a communication device, such as a UE that supports coherent uplink multiple-input multiple-output (MIMO) (e.g., single-layer MIMO transmission), is more complex than simply measuring TRP for a single-antenna device. A UE may include at least two transmit antennas, which support transmit diversity and / or MIMO. A MIMO system may be implemented with two or moretransmitters and receivers to simultaneously transmit and receive wireless communications using multiple antennas, such as at a UE, to improve uplink transmission performance. By utilizing multiple antennas (e.g., of an antenna array), a UE can simultaneously transmit communications on different spatial paths for improved coverage and reliability, as well as for higher throughput. For a UE that has two antennas, and for single layer transmission, a codebook designed to match specific antenna configurations for two antenna transmission can be used to control the relative phase of the two antennas using the precoder to co-phase (e.g., align the signal phases) at a signal receiver.

[0024] For a UE that has two antennas, current proposed methods for measuring TRP include a first method, in which for each azimuth and elevation, the radiated power is measured for each antenna separately. The power for the two antennas is summed, and the power is integrated over a sphere to estimate the total radiated power. The current proposed methods for measuring TRP also include a second method, in which for each azimuth and elevation, the radiated power is measured for each of the precoders. For a given azimuth and elevation, the radiated power is taken as the maximum over the set of precoders, and the power is integrated over the sphere to estimate the total radiated power.

[0025] However, neither of these two methods fully establish the ability to accurately measure TRP for a device that supports coherent uplink MIMO. In the first proposed method, the radiated power is underestimated given that the transmissions from the two antennas can be at least partially co-phased using single-layer uplink MIMO with the best precoder. In implementations, the best precoder is selected based on the precoder that supports the highest signal-to-noise ratio (SNR) or the highest signal-to-interference ratio (SIR) at the gNB.

[0026] However, there is an unknown phase offset between the two transmit paths. In a best case scenario, the power with co-phasing of the two antennas can be as much as 3dB greater than the sum of the per-antenna powers. It should also be noted that summing the transmitter powers can also overestimate the radiated power, such as if the transmitter power adds out of phase. In the worst case scenario, the signals from the two transmit antennas can completely cancel. Accordingly, the first proposed method relies on too many assumptions about the signal response at the gNB and the SNR of the receivedsignals, and introduces parameters that may overestimate or underestimate the radiated power.

[0027] In the second proposed method, a concern is that the gNB precoder selection may not always be optimal given that precoder selection is based on noisy measurements. As a result, the precoder selection is proposed to be emulated in the test. However, realistic emulation of precoder selection will require an assumption of the distance between the gNB and the UE in order to determine the signal-to-noise ratios of the channel estimates used to select the precoder. In the case of extreme distance, or in the case that one of the antennas does not have significant gain in the direction of the gNB, there is no benefit in transmitting from the second antenna, and therefore the best precoder is a single antenna precoder.

[0028] Additionally, the current definition of phase coherence provides for variation of the relative phase of the signals at the transmit antennas over time. Typically, the relative phase between the two antennas and the relative gain between the two antennas can vary from a last sounding reference signal (SRS) transmission, and the relative phase between the antennas is unspecified and unknown.

[0029] Aspects of the disclosure are directed to uplink MIMO TRP. In some embodiments, to evaluate the performance of the precoders used for uplink transmission, the radiated power is averaged over the distribution of the random phase offset. Alternatively, the performance of the precoders can be evaluated for the worst-case phase offset. Notably, neither of these approaches can be implemented via measurement during a radiated test, given there is not a current technique to measure or control the phase between the device antennas. However, as detailed in the described techniques, the average and worst-case performance of the precoders over the phase can be evaluated analytically using the per-antenna power measurements.

[0030] Aspects of the present disclosure are described in the context of a wireless communications system.

[0031] Figure 1 illustrates an example of a wireless communications system 100 in accordance with aspects of the present disclosure. The wireless communications system 100 may include one or more NE 102, one or more UE 104, and a core network (CN) 106. The wireless communications system 100 may support various radio accesstechnologies. In some implementations, the wireless communications system 100 may be a 4G network, such as a Long-Term Evolution (LTE) network or an LTE-Advanced (LTE-A) network. In some other implementations, the wireless communications system 100 may be a New Radio (NR) network, such as a 5G network, a 5G-Advanced (5G-A) network, or a 5G ultrawideband (5G-UWB) network.

[0032] In other implementations, the wireless communications system 100 may be a combination of a 4G network and a 5G network, or other suitable radio access technology (RAT) including Institute of Electrical and Electronics Engineers (IEEE) 802.11 (Wi-Fi), IEEE 802.16 (WiMAX), IEEE 802.20. The wireless communications system 100 may support radio access technologies beyond 5G, for example, 6G. Additionally, the wireless communications system 100 may support technologies, such as time division multiple access (TDMA), frequency division multiple access (FDMA), or code division multiple access (CDMA), etc.

[0033] The one or more NE 102 may be dispersed throughout a geographic region to form the wireless communications system 100. One or more of the NE 102 described herein may be or include or may be referred to as a network node, a base station, a network element, a network function, a network entity, a radio access network (RAN), a NodeB, an eNodeB (eNB), a next-generation NodeB (gNB), or other suitable terminology. An NE 102 and a UE 104 may communicate via a communication link, which may be a wireless or wired connection. For example, an NE 102 and a UE 104 may perform wireless communication (e.g., receive signaling, transmit signaling) over a Uu interface.

[0034] An NE 102 may provide a geographic coverage area for which the NE 102 may support services for one or more UEs 104 within the geographic coverage area. For example, an NE 102 and a UE 104 may support wireless communication of signals related to services (e.g., voice, video, packet data, messaging, broadcast, etc.) according to one or multiple radio access technologies. In some implementations, an NE 102 may be moveable, for example, a satellite associated with a non-terrestrial network (NTN). In some implementations, different geographic coverage areas associated with the same or different radio access technologies may overlap, but the different geographic coverage areas may be associated with different NE 102.

[0035] The one or more UE 104 may be dispersed throughout a geographic region of the wireless communications system 100. A UE 104 may include or may be referred to as a remote unit, a mobile device, a wireless device, a remote device, a subscriber device, a transmitter device, a receiver device, or some other suitable terminology. In some implementations, the UE 104 may be referred to as a unit, a station, a terminal, or a client, among other examples. Additionally, or alternatively, the UE 104 may be referred to as an internet-of-things (IoT) device, an internet-of-everything (IoE) device, or machine- type communication (MTC) device, among other examples.

[0036] A UE 104 may be able to support wireless communication directly with other UEs 104 over a communication link. For example, a UE 104 may support wireless communication directly with another UE 104 over a device-to-device (D2D) communication link. In some implementations, such as vehicle-to-vehicle (V2V) deployments, vehicle-to-everything (V2X) deployments, or cellular-V2X deployments, the communication link may be referred to as a sidelink. For example, a UE 104 may support wireless communication directly with another UE 104 over a PC5 interface.

[0037] An NE 102 may support communications with the CN 106, or with another NE 102, or both. For example, an NE 102 may interface with other NE 102 or the CN 106 through one or more backhaul links (e.g., S1, N2, N3, or network interface). In some implementations, the NE 102 may communicate with each other directly. In some other implementations, the NE 102 may communicate with each other or indirectly (e.g., via the CN 106). In some implementations, one or more NE 102 may include subcomponents, such as an access network entity, which may be an example of an access node controller (ANC). An ANC may communicate with the one or more UEs 104 through one or more other access network transmission entities, which may be referred to as a radio heads, smart radio heads, or transmission-reception points.

[0038] The CN 106 may support user authentication, access authorization, tracking, connectivity, and other access, routing, or mobility functions. The CN 106 may be an evolved packet core (EPC), or a 5G core (5GC), which may include a control plane entity that manages access and mobility (e.g., a mobility management entity (MME), an access and mobility management functions (AMF)) and a user plane entity that routes packets or interconnects to external networks (e.g., a serving gateway (S-GW), a Packet Data Network (PDN) gateway (P-GW), or a user plane function (UPF)). In someimplementations, the control plane entity may manage non-access stratum (NAS) functions, such as mobility, authentication, and bearer management (e.g., data bearers, signal bearers, etc.) for the one or more UEs 104 served by the one or more NE 102 associated with the CN 106.

[0039] The CN 106 may communicate with a packet data network over one or more backhaul links (e.g., via an S1, N2, N3, or another network interface). The packet data network may include an application server. In some implementations, one or more UEs 104 may communicate with the application server. A UE 104 may establish a session (e.g., a protocol data unit (PDU) session, or a PDN connection, or the like) with the CN 106 via an NE 102. The CN 106 may route traffic (e.g., control information, data, and the like) between the UE 104 and the application server using the established session (e.g., the established PDU session). The PDU session may be an example of a logical connection between the UE 104 and the CN 106 (e.g., one or more network functions of the CN 106).

[0040] In the wireless communications system 100, the NEs 102 and the UEs 104 may use resources of the wireless communications system 100 (e.g., time resources (e.g., symbols, slots, subframes, frames, or the like) or frequency resources (e.g., subcarriers, carriers)) to perform various operations (e.g., wireless communications). In some implementations, the NEs 102 and the UEs 104 may support different resource structures. For example, the NEs 102 and the UEs 104 may support different frame structures. In some implementations, such as in 4G, the NEs 102 and the UEs 104 may support a single frame structure. In some other implementations, such as in 5G and among other suitable radio access technologies, the NEs 102 and the UEs 104 may support various frame structures (i.e., multiple frame structures). The NEs 102 and the UEs 104 may support various frame structures based on one or more numerologies.

[0041] One or more numerologies may be supported in the wireless communications system 100, and a numerology may include a subcarrier spacing and a cyclic prefix. A first numerology (e.g., ^=0) may be associated with a first subcarrier spacing (e.g., 15kHz) and a normal cyclic prefix. In some implementations, the first numerology (e.g.,^=0) associated with the first subcarrier spacing (e.g., 15 kHz) may utilize one slot persubframe. A second numerology (e.g., ^=1) may be associated with a second subcarrier spacing (e.g., 30 kHz) and a normal cyclic prefix. A third numerology (e.g., ^=2) may beassociated with a third subcarrier spacing (e.g., 60 kHz) and a normal cyclic prefix or an extended cyclic prefix. A fourth numerology (e.g., ^=3) may be associated with a fourthsubcarrier spacing (e.g., 120 kHz) and a normal cyclic prefix. A fifth numerology (e.g.,^=4) may be associated with a fifth subcarrier spacing (e.g., 240 kHz) and a normalcyclic prefix.

[0042] A time interval of a resource (e.g., a communication resource) may be organized according to frames (also referred to as radio frames). Each frame may have a duration, for example, a 10 millisecond (ms) duration. In some implementations, each frame may include multiple subframes. For example, each frame may include 10 subframes, and each subframe may have a duration, for example, a 1 ms duration. In some implementations, each frame may have the same duration. In some implementations, each subframe of a frame may have the same duration.

[0043] Additionally, or alternatively, a time interval of a resource (e.g., a communication resource) may be organized according to slots. For example, a subframe may include a number (e.g., quantity) of slots. The number of slots in each subframe may also depend on the one or more numerologies supported in the wireless communicationssystem 100. For instance, the first, second, third, fourth, and fifth numerologies (i.e., ^=0,^=1, ^=2, ^=3, ^=4) associated with respective subcarrier spacings of 15 kHz, 30 kHz,60 kHz, 120 kHz, and 240 kHz may utilize a single slot per subframe, two slots per subframe, four slots per subframe, eight slots per subframe, and 16 slots per subframe, respectively.

[0044] Each slot may include a number (e.g., quantity) of symbols (e.g., orthogonal frequency domain multiplexing (OFDM) symbols). In some implementations, the number (e.g., quantity) of slots for a subframe may depend on a numerology. For a normal cyclic prefix, a slot may include 14 symbols. For an extended cyclic prefix (e.g., applicable for 60 kHz subcarrier spacing), a slot may include 12 symbols. The relationship between the number of symbols per slot, the number of slots per subframe, and the number of slots per frame for a normal cyclic prefix and an extended cyclic prefix may depend on a numerology. It should be understood that reference to a first numerology (e.g., ^=0) associated with a first subcarrier spacing (e.g., 15 kHz) may be used interchangeably between subframes and slots.

[0045] In the wireless communications system 100, an electromagnetic (EM) spectrum may be split, based on frequency or wavelength, into various classes, frequency bands, frequency channels, etc. By way of example, the wireless communications system 100 may support one or multiple operating frequency bands, such as frequency range designations FR1 (410 MHz – 7.125 GHz), FR2 (24.25 GHz – 52.6 GHz), FR3 (7.125 GHz – 24.25 GHz), FR4 (52.6 GHz – 114.25 GHz), FR4a or FR4-1 (52.6 GHz – 71 GHz), and FR5 (114.25 GHz – 300 GHz). In some implementations, the NEs 102 and the UEs 104 may perform wireless communications over one or more of the operating frequency bands. In some implementations, FR1 may be used by the NEs 102 and the UEs 104, among other equipment or devices for cellular communications traffic (e.g., control information, data). In some implementations, FR2 may be used by the NEs 102 and the UEs 104, among other equipment or devices for short-range, high data rate capabilities.

[0046] FR1 may be associated with one or multiple numerologies (e.g., at least three numerologies). For example, FR1 may be associated with a first numerology (e.g., ^=0), which includes 15 kHz subcarrier spacing; a second numerology (e.g., ^=1), which includes 30 kHz subcarrier spacing; and a third numerology (e.g., ^=2), which includes 60 kHz subcarrier spacing. FR2 may be associated with one or multiple numerologies (e.g., at least 2 numerologies). For example, FR2 may be associated with a third numerology (e.g., ^=2), which includes 60 kHz subcarrier spacing; and a fourth numerology (e.g., ^=3), which includes 120 kHz subcarrier spacing.

[0047] In the wireless communications system 100, a UE 104 (e.g., a representative of a particular model of UEs) has testing requirements to confirm how the UE performs in a radiated environment. A communication device, such as a UE 104 operating in the FR2 frequency range (also referred to as a FR2 device) has uplink, transmit radiated power requirements for operability in the wireless communications system 100. Conventional device testing is typically performed as conductive tests on a device, at least in part because radiated tests can be time consuming and costly.

[0048] According to implementations, one or more of the UEs 104 and a test equipment are operable to implement various aspects of the techniques described with reference to the present disclosure. For example, a UE 104 can transmit separate transmissions from individual antennas of the UE, and the test equipment receives theseparate transmissions and can measure each separate transmission for radiated power. In certain embodiments, the test equipment may be implemented by a NE 102 and / or a function in the CN 106. In other embodiments, the test equipment may be a standalone apparatus used to evaluate one or more UEs 104.

[0049] The issue of how to measure TRP for a MIMO communication device, such as a UE that supports coherent uplink MIMO, is more complex than simply measuring TRP for a single-antenna device. A MIMO system may be implemented with two or more transmitters and receivers to simultaneously transmit and receive wireless communications using multiple antennas, to improve uplink transmission performance. By utilizing multiple antennas (e.g., of an antenna array), a UE can simultaneously transmit communications on different spatial paths for improved coverage and reliability, as well as for higher throughput.

[0050] To meet the power class, it is generally necessary to transmit on all of the antennas. This can be done using transparent transmit diversity, or alternatively using single-layer uplink MIMO. There is a problem, however, in that the relative phase between the transmit antennas is unspecified and unknown.

[0051] For single-layer MIMO transmission, a codebook designed to match specific antenna configurations for two antenna transmission can be used to control the relative phase of the two antennas using the precoder to co-phase (e.g., align the signal phases) at a signal receiver. Note that when the signals are co-phased, the actual received power can be 3 dB greater than the sum of the per-antenna power measurements.

[0052] In aspects of the described techniques, the total radiated power (TRP) isdetermined or calculated (e.g., by test equipment) as the integral of the radiated power^^^, ^^ over the unit sphere given by equation (1):TRP = 1 ^^ ^^ ^ ^^ ^ ^^ ^^ .

[0053] finite set of directionsgiven by ^^^^ , ^^^: ^ = 1, ^^, then the total radiated power can be expressed as equation(2):1for an appropriate weighting function # that depends on the set of directions^^^^ , ^^^: ^ = 1, ^^ . In some implementations, the weighting function #^^^ , ^^^corresponds to the area on the unit sphere closer to ^^^ , ^^^ than to any other direction inthe set ^^^$, ^$^: % ≠ ^^.

[0054] For a UE that has two antennas, prior proposed techniques for measuring TRPinclude separately measuring the radiated power ^^^, ^^ for each antenna, for eachazimuth ^ and elevation ^. The measured powers for the two antennas are summed, andthe radiated power ^^^, ^^ is integrated over a sphere to estimate the TRP.

[0055] The prior proposed methods for measuring TRP also include a second technique whereby, the UE cycles through all of the coherent single-layer precoders for two antennas and the gNB (e.g., test equipment) measures (i.e., for each of the single-layer precoders) the maximum radiated power ^^^, ^^ for each azimuth ^ and elevation^. The radiated power is taken as the maximum over the set of precoders, and the power^^^, ^^ is integrated over the sphere to estimate the TRP.

[0056] However, neither of these two prior proposed techniques fully establish the ability to accurately measure the TRP for a communication device (e.g., UE) that supports coherent uplink MIMO. In the first prior proposed technique, the radiated power is underestimated given that the transmissions from the two antennas can be at least partially co-phased using single-layer uplink MIMO with the best precoder. In implementations, the best precoder is selected based on the precoder that supports the highest SNR or the highest SIR at the gNB.

[0057] However, there is an unknown, random phase offset between the transmit paths of a single-layer MIMO signal. In a best case scenario, the power with co-phasing of the two antennas can be as much as 3 dB greater than the sum of the per-antenna powers. It should also be noted that summing the transmitter powers can also overestimate the radiated power, such as if the transmitter power adds out of phase. In the worst case scenario, the signals from the two transmit antennas can completely cancel. Accordingly, the first prior proposed technique relies on too many assumptions about the signal response at the gNB and the SNR of the received signals, and introduces parameters that may overestimate or underestimate the radiated power.

[0058] In the second prior proposed technique, a concern is that the gNB precoder selection may not always be optimal given that precoder selection is based on noisy measurements. While it has been proposed that the precoder selection be emulated in the test, the realistic emulation of precoder selection will require an assumption of the distance between the gNB and the UE in order to determine the signal-to-noise ratios of the channel estimates used to select the precoder. In the case of extreme distance, or in the case that one of the antennas does not have significant gain in the direction of the gNB, there is no benefit in transmitting from the second antenna, and therefore the best precoder is a single antenna precoder.

[0059] Additionally, the current definition of phase coherence provides for variation of the relative phase of the signals at the transmit antennas over time. The requirement for coherent uplink MIMO defines the maximum allowable change in the relative power and relative phase measured between two antenna connectors in any slot within the specified time window from the relative gain and relative phase measured using the most recent SRS transmission on the same two antenna connectors, for the purpose of uplink transmission (codebook or non-codebook usage).

[0060] As indicated in Table 1 below, the relative phase between the two antennas and the relative gain between the two antennas can vary by as much as 40 degrees and 4 dB, respectively, in a time interval of 20 msec from a last SRS transmission, and the relative phase between the antennas is unspecified and unknown. These requirements apply when the UL transmission power at each antenna connector is larger than 0 dBm for SRS transmission and for the duration of time window. Difference of relative phase error Difference of relative power error Time window 40 degrees 4 dB 20 msec Table 1: Maximum Allowable Difference of Relative Phase and Power

[0061] Accordingly, the relative gain difference between the two antennas is also unspecified and unknown. Therefore, due to the random phase offset between the antennas, the power measured in a particular direction using the best precoder becomes a random variable that depends on the value of the random phase offset.

[0062] Figure 2 depicts an exemplary model of a transmitter 200 with two transmit antennas, in accordance with aspects of the present disclosure. For the purposes ofmeasuring TRP, it may be assumed that both antennas are transmitting at full power. For this reason, minimal variation of the transmit power is assumed on the two antennas.

[0063] Precoders W0 and W1 are applied to the transmitter 200. Additionally, there is a random phase offset between the two antennas, represented by the quantity e(). It can be noted that while the relative phase change is limited, there is no requirement on the relative phase offset so that this phase is unknown and can be any value θ. In other words, the value of θ is not constant, but changes over time.

[0064] Accordingly, it is unknown how quickly the value of θ changes, and the operators and manufacturers have no control over the value and rate of change of θ. The phase θ could be changing slowly (i.e., up to the 40 degrees over a 20 msec interval) or could be changing at some other rate. Accordingly, the testing cannot account for the random phase offset just by measuring over a period of time because the period of time over which to take a measurement is unknown.

[0065] Table 2 defines the precoding matrix W for a single-layer transmission using two antenna ports for transmit precoding matrix index (TPMI) values 0-5. The precoders W0, W1in Figure 2 correspond to [1, 0], [1, -j], etc. in the precoding matrix W. TPMI W (ordered from left to right in increasing order of TPMI index) Index 0– 5 1 1 1 1 1 1 / 10 / 00 / 10 / 1 0 21 1 – –34 2−34√2 0 √2 1 √2 1 √2 −1 √2 √2Table 2: Precoding Matrix W for Single-Layer Transmission using Two Antenna Ports with Transform Precoding Enabled

[0066] In general, the relative phase between the two transmit antennas can be modeled as a uniform random variable in the interval [0, 2^). Due to the random phase offset, the precoders indexed 2 through 5 in Table 2, above, become the coherentprecoders listed in Table 3, where the second weight 5"of each precoder is multiplied bye().TPMIW ^ordered from left to right in increasing order of TPMI index^ Index2 – 5 1 1 1 / 1 0 / 1 1 1 1() ()0 23 e()4 2 ()4√2 1 e √2 −1 e √2 √2 −3 eTable 3: Coherent Precoders

[0067] While the coherence requirement limits the rate of change of θ to 40 degrees every 20 msec, the rate of change can be much slower. Since this phase offset is unspecified and its value and its rate of change are unknown, it would be difficult to ensure that the effect of the random phase offset is properly captured by measurement.

[0068] Due to the random phase offsets between the two transmit antennas, the powerP^φ, ϕ^ transmitted in a particular azimuth ^ and elevation ^ using the best precoder is arandom variable with a distribution depending on the distribution of the random phase offset θ between the two transmit antennas.

[0069] To evaluate the performance of the precoders, the radiated power can be averaged over the distribution of the phase θ. Alternatively, the performance of the precoders can be evaluated for the worst-case phase θ. However, neither of these approaches can be implemented via measurement as there is no way to measure or control the phase offset between the antennas in a radiated test. But the average and worst-case performance of the precoders over the phase θ can be evaluated analytically using the per antenna power measurements.

[0070] A third proposed technique addresses the fact that the power for a given precoder in any direction is a random variable which depends on the random phase offsets between the transmit antennas. In this technique, it was proposed that the TRP could be computed analytically using the per-antenna power measurements (when transmitting separately) using one of three approaches: 1) The average power over phase for each elevation ^ and azimuth ^; 2) The minimum power over phase for each elevation ^ and azimuth ^; or 3) The maximum power over phase for each elevation ^ and azimuth ^.

[0071] This third technique implicitly assumes that the polarization of the two transmit antennas is aligned. However, this is not a valid assumption. Accordingly, the present disclosure proposed solutions for the analytical evaluation of TRP for the case that the polarizations are not aligned. In this case, the average transmit power, minimum transmit power, and maximum transmit power can be defined in terms of the per-antennapower measurements where the transmit power on each of two orthogonal receive polarizations is measured and recorded separately.

[0072] It is generally the case that the test equipment measures the power received from the UE on two orthogonal polarizations. The orientation of the orthogonal polarizations of the test equipment relative to the UE can be arbitrarily defined.

[0073] Embodiments of a first solution describe techniques for determining TRP metrics for UL MIMO with non-aligned transmit polarizations and random phase offsets for a UE with two transmit antennas.

[0074] Let ^","^^, ^^ and ^",^^^, ^^ denote the power received by the test equipmentfrom the first UE transmit antenna on the first and second polarizations for elevation ^and azimuth ^. Similarly, let ^^,"^^, ^^ and ^^,^^^, ^^ denote the power received by thetest equipment from the second UE transmit antenna on the first and second polarizations for elevation ^ and azimuth ^.

[0075] Let ^"^^, ^^ and ^^^^, ^^ denote the total power received by the testequipment from the first and second antennas for elevation ^ and azimuth ^ so that: ^"^^, ^^ = ^","^^, ^^ + ^",^^^, ^^, and^^^^, ^^ = ^^,"^^, ^^ + ^^,^^^, ^^ .

[0076] When suppressing the azimuth and elevation in the notation, the total power received by the test equipment becomes: ^" = ^"," + ^",^^^ = ^^," + ^^,^ .

[0077] To determine the power received both antennas transmit simultaneously with a particular precoder, the phases I"and I^and the phase offset J must be known. For example, with the use of thewith TPMI index 2 given by" M√^ K1 1 e() L , thepower of the received signal elevation ^ and azimuth ^ would be given by equation (4) (P (^ P ^ ^^^^, ^^ = NO^ Q + R"O^^"e ST)^N + NO^ ( PQ + R (^ PST)^N ,^N^where R" = ±1 and R^ = ±1 depend on the sign of the projection of the antenna patternonto the second polarization axis relative to the sign of its projection on to the first axis. The power of the received signal in equation (2) depends on I"and I^, and the relative phase offset J through the phase differenceI^ − I" + J.

[0078] Since the power of the received signal depends on the relative phase offset J, the optimal precoder will also depend on J. Since J is unspecified and unknown, the radiated power can be determined in one of two ways:

[0079] First, as the power of the best precoder for each J, averaged over J over the interval [0, 2^), denoted ^VWX,YVZ.

[0080] Second, as the power of the best precoder for each J, for the worst-case phaseJ over the interval [0, 2^), denoted ^Y[\,YVZ.

[0081] Because the first approach averages the power of the best precoder as a function of the relative phase J on the interval [0, 2^), the result is independent of theinitial phase difference I^ − I". For the second approach, let J]^ denote the phase thatresults in the minimum power for the best precoder when I^ − I" = 0. If I^ − I" ≠ 0,then the phase JY[\ − ^I^ − I"^ will yield the same powerthatproduced the minimum power for I^ − I" = 0. As a result, it can be assumed that I^ −I" = 0 for both approaches i) and ii).

[0082] Accordingly, the power of the best precoder for each J, averaged over J over the interval [0, 2^), would be given by equation (5):^VWX,YVZ1 ^^( ^ ^ ^= ^ m ^N ^ + ^ )N + + ()N − ()N1 ^^^VWX,YVZ =2^ ^ max`^" + ^^ + 2aO^","^^," + R"R^O^",^^^,^b cos J , ^" + ^^^1^^^VWX,YVZ = ^" + ^^ +2^ ^ max^e cos J , −e cos J, e sin J , −e sin J^ ^J^wheree= 2aO^","^^," + R"R^O^",^^^,^b .

[0085] This|e| ^^^VWX,YVZ = ^" + ^^ +2^ ^ max^cos J , − cos J, sin J , − sin J^ ^J^| | j mj oj nj= ^" + ^^ + g^^ hilkjk cos J ^J − iknjk cos J ^J − ikmjk sin J ^J + ijkk sin J ^Jp

[0086] ^"," = ^^," and ^",^ = ^^,^^from which it follows that^^^ ^ ^^ ^^

[0087] Conversely, if the polarizations of the two antennas are orthogonal, then R^ =−R" and for some angle t, we have^"," = ^" cos t and ^",^ = ^" sin tand ^^," = ^" sin t and ^^,^ = ^" cos t0^VWX,YVZ = ^" + ^^ ^orthogonal polarizations^

[0088] The maximum power over J over the set of precoders in (1) is given by ^YVZ,YVZ = m)ax max`^" + ^^ + 2aO^","^^," + R"R^O^",^^^,^b cos J , ^" + ^^by ^Y[\,YVZ = in max`^" + ^^ + 2aO^","^^," + R"R^O^",^^^,^b cos J , ^" + ^^= ^" + ^ √^^ + ^ |e|= ^" + ^^ + √2NO^","^^," + R"R^O^",^^^,^N

[0090] To of the two transmitantennas are allowed to be different, we have (without the elevation ^ and azimuth ^ suppressed)^VWX,YVZ^^, ^^ = ^"^^, ^^ + ^^^^, ^^4√2from thefirst UE transmit antenna on the first and second polarizations, and similarly, ^^,"^^, ^^and ^^,^^^, ^^ denote the power received by the test equipment from the second UEtransmit antenna on the first and second polarizations. Finally, we have ^"^^, ^^ = ^","^^, ^^ + ^",^^^, ^^^^^^, ^^ = ^^,"^^, ^^ + ^^,^^^, ^^ ,and R" ± 1 and R^ ± 1 depend on the sign of the projection of the antenna pattern onto thesecond polarization axis relative to the sign of its projection on to the first polarization axis.

[0091] For the case that the polarizations of the two transmit antennas are the sameand ^" = ^^ = ^, the power with exact phase alignment is 4 ^ while the power of thebest precoder for the worst-case relative phase J is given by 3.4 ^, which is a difference of 0.7 dB. The power of the best precoder averaged over the relative phase is approximately 3.8 P which is 0.2 dB less than the power for perfect phase alignment.

[0092] Figure 3 is a is a chart depicting a complementary cumulative distribution function (CCDF) 300 of the phase alignment error is shown for the case that thepolarizations of the two transmit antennas are the same and the power received from thetwo antennas transmitting separately is equal so that ^" = ^^, in accordance with aspectsof the present disclosure. The CCDF 300 shows the probability that a given phase alignment error exceeds a particular decibel (dB) value for the coherent, two antenna port precoders in Table 3 (i.e., with same polarization and equal power), in accordance with aspects of the present disclosure. The x-axis tracks the loss due to phase alignment error (in dB), while the y-axis tracks the probability that loss is exceeded.

[0093] From Figure 3, it can be observed that the power corresponding to the best precoder is quite insensitive to the phase offset J. Furthermore, it should be noted thatthe phase alignment loss is greatest when ^" = ^^ for the given azimuth and elevation,but will generally be significantly less.

[0094] In some embodiments, for single-layer uplink MIMO with two antennas, theradiated power ^^^, ^^ for elevation ^ and azimuth ^ can be defined as the averagepower of the best precoder given by ^VWX,YVZ^^, ^^ = ^"^^, ^^ + ^^^^, ^^4+ √2^ uv^","^^, ^^^^,"^^, ^^ + R"R^v^",^^^, ^^^^,^^^, ^^uwhere ^^,(^^,that is receivedby the test equipment on the j-th polarization, where 3 ∈ ^1,2^ and the polarizations areorthogonal with respect to each other. Here, R" = ±1 and R^ = ±1 for the first and secondtransmit antennas depend on the sign ofprojection of the antenna pattern onto the second polarization axis relative to the sign of its projection on to the first polarization axis.

[0095] Alternatively, for single-layer uplink MIMO with two antennas, the radiatedpower ^^^, ^^ for elevation ^ and azimuth ^ can be defined as the minimum power ofthe best precoder given by: ^Y[\,YVZ^^, ^^= ^"^^, ^^ + ^^^^, ^^where ^^,(^^,that is receivedby the test equipment on the j-th polarization, where 3 ∈ ^1,2^ and the polarizations areorthogonal with respect to each other. Here, R" = ±1 and R^ = ±1 for the first and secondtransmit antennas depend on the sign of the projection of the antenna pattern onto the second polarization axis relative to the sign its projection on to the first polarization axis.

[0096] Alternatively, for single-layer uplink MIMO with two antennas, the radiatedpower ^^^, ^^ for elevation ^ and azimuth ^ can be defined as the maximum power ofthe best precoder given by: ^YVZ,YVZ^^, ^^= ^"^^, ^^ + ^^^^, ^^where ^^,(^^,that is receivedby the test equipment on the j-th polarization, where 3 ∈ ^1,2^ and the polarizations areorthogonal with respect to each other. Here, R" = ±1 and R^ = ±1 for the first and secondtransmit antennas depend on the sign of projection of the antenna pattern onto thesecond polarization axis relative to the sign of its projection on to the first polarization axis.

[0097] Regardless of which alternative is used to define ^^^, ^^ as the radiatedpower in elevation ^ and azimuth ^, the total radiated power (TRP) is determined orcalculated (e.g., by test equipment) as the integral of the radiated power ^^^, ^^ over theunit sphere given by equation (1): 1^^ ^TRP = ^ ^ ^^^, ^^ sin ^ ^^ ^^ .

[0098] a finite set of directionsgiven by ^^^^ , ^^^: ^ = 1, ^^, then the total radiated power can be expressed as equation(2): 1= ^ ^^^^ ^^^ ^^^for an appropriateon the set of directions^^^^ , ^^^: ^ = 1, ^^ . In some implementation, the weighting function #^^^ , ^^^corresponds to the area on the unit sphere closer to ^^^ , ^^^ than to any other direction inthe set ^^^$, ^$^: % ≠ ^^.

[0099] Embodiments of a second solution describe techniques for determining TRP metrics for UL MIMO with non-aligned transmit polarizations and random phase offsets for a UE with two transmit antennas.

[0100] If the two-antenna coherent precoders are used are used to define TRP for devices with two transmit antennas, it seems reasonable to consider using the four- antenna coherent precoders to define TRP for devices with four transmit antennas.

[0101] As the number of UE transmit antennas increases from two to four, the number of single-layer coherent precoders increases from 4 to 16. As a result, the prior proposed techniques for measuring the power for all 16 precoders at each azimuth and elevation is still possible but may be significantly more time consuming.

[0102] Moreover, the second, third and fourth antennas each have a random phase offset with respect to the first antenna. Similarly, as in the case of two transmit antennas, the measurements of the prior proposed techniques will not address the randomness of the phase offsets between the antennas, but will instead only be a snapshot of these phase offsets at one point in time. As such, the TRP can be determined using a similar approach as used as for the case of two antennas, but it is significantly more complicated given that there are more precoders and also that there are now three random phase offsets rather than one.

[0103] Figure 4 depicts an exemplary model of a transmitter 400 with four transmit antennas, in accordance with aspects of the present disclosure. For the purposes of measuring TRP, it may be assumed that all four antennas are transmitting at full power. For this reason, minimal variation of the transmit power is assumed on the four antennas.

[0104] Precoders W0, W1, W2, and W3 are applied to the transmitter 400. Additionally,there is a random phase offset between the four antennas, represented by the quantitiese()Q , e()S, and e()n . It can be noted that while the relative phase change is limited,on the relative phase offsets so that these phases are unknown and can be any value θn. In other words, the value of θnis not constant, but changes over time.

[0105] Accordingly, it is unknown how quickly the value of θn changes, and the operators and manufacturers have no control over the value and rate of change of θn. The phase θn could be changing rapidly (i.e., up to the 40 degrees over a 20 msec interval) orcould be changing at some other rate. Accordingly, the testing cannot account for the random phase offset just by measuring over a period of time because the period of time over which to take a measurement is unknown.

[0106] Table 4 defines the precoding matrix W for a single-layer transmission using four antenna ports. The precoders W0, W1 in Figure 2 correspond to [1, 0, 0, 0], [1, -j, -j, 1], etc. in the precoding matrix W. TPMI W (ordered from left to right in increasing order of TPMI index) Index 0– 71 01 112 y 1 1010 1 100z2 y10z2 y01 11z2 y00z2 y01z2 y0−1 z 12 y013z2 y0−3 z0 0 0 1 0 0 0 08 – 15 001 1102y 10111110z2 y10z12 y10 z 12 y10z2 y11z12 {13 | 2 y1−1 z 1{−13|1−1 3 −3 −1 23 1 −316 – 23 1 1 1 111{311{311 1{3 | 131y−1 z 1 −1 1y−11 −12 1| 23|2 −1 2 {−3|2 1 { 3 | 2 −1z{−3 |1 −1 1 2 23 −3 −3 −1 324 – 27 1 1– – – – 11111{−3{−3{−3 1| −32 1|2 3|2 −1 2 {−3 |−3 −1 3 1Table 4: Precoding Matrix W for Single-Layer Transmission using Four Antenna Ports with Transform Precoding Enabled

[0107] Due to the random phase offsets, the precoders indexed 12 through 15 in Table 4, above, become the coherent precoders listed in Table 5, considering three randomphase offsets relative to the first antenna, modeled by J" , J^ , and J}.TPMI W (ordered from left to right in increasing order of TPMI index) Index 12 – 1511 12{e()Q ()Q1( 1)Q1( 1)Qe()S|12 {e3 e()S|2 {e−e()S|2 {e−e()S|−e()n 3 e()n e()n e()nTable 5: Coherent Precoders

[0108] In the same manner as with the two transmit antennas, the power can be measured for the four transmit antennas transmitting separately. Let ^", ^^, ^}, and ^~note the received power ^^^, ^^ for elevation ^ and azimuth ^ received from each of theantennas transmitting one at a time.

[0109] It can be noted that the single antenna power measurements already reflect the scaling factor of 1⁄ 2 corresponding to the precoders with TPMI indices 0, 1, 2, and 3, sothis scaling factor is not included in the expressions below. In the same manner as for two transmit antennas, ^YVZ,YVZ, ^VWX,YVZ, and ^Y[\,YVZcan be defined for the set of 16 coherent precoders in Table 6.3.1.5-2 [7] with TPMI indices 12-27.

[0110] Applying this same random phasing to all of the precoders, the average of the maximum power over the set of precoders can be expressed as: 1^^ ^^ ^^^VWX,YVZ = ^ ^ ^ "^ m^^a^x^^ ^N^^,"O^ ()"," + ^^,^O^^,"e Q + ^ ()^,}O^},"e Sindices 12-27 are in Table 6 below: i= 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 271-j-j1

[0111] In a manner similar to that used previously, ^},^^^, ^^ and ^~,^^^, ^^ denotethe power of the third and fourth transmit antennas received by the test equipment on the first and second polarizations for elevation ^ and azimuth ^, so that: ^}^^, ^^ = ^},"^^, ^^ + ^},^^^, ^^^~^^, ^^ = ^~,"^^, ^^ + ^~,^^^, ^^ .

[0112] Similarly, R} = ±1 and R~ = ±1 depend on the sign of the projection of theantenna pattern onto the second polarization axis relative to the sign of its projection on to the first polarization axis.

[0113] The squared term in the integrand of equation (3) can be expressed as: N^ ( ^^,"O^"," + ^^,^O^^,"e)Q + ^^,}O^},"e()S + ^^,~O^~,"e()nNn ^N

[0115] The average ^VWX,YVZ^^, ^^ can then be evaluated numerically as given inequation (7): 1^^ ^^ ^^^ = ^ ^ ^ ^ ^ ^ ()Q ^ ^ ()S= ^" + ^^ + ^} + ^~1^^ ^^ ^^Qbphase can be expressed as given in equation (8): ^Y[\,YVZ =)Q m ()Q ()S,)iSn,)n"^ m^^a^x^^ ^N^^,"O^"," + ^^,^O^^,"e + ^^,}O^},"e +N^

[0117] Finally, the maximum power of the best precoder over the set of precoders is given by equation (9): ()YVZ,YVZ ^,"O"," ^,^O ^," Q O^ e()S + ^ ()^,~O^ e n ^^ = max max ^N^ ^ + ^ ^ e + ^ N^_=Q maSx)n"^ m^^a^x^^`^ + ^ + ^ + ^ + 2 a ^ ^ + RR ^ ^ b ^^a ∗ !()Q) ,) , " ^ } ~ O"," ^," " ^O",^ ^,^ ^^,"^^,^ e bthat the maximum is achieved for ^ = 1, J" = J^ = 0, and J} = ^, in which case^ ^^YVZ,YVZ = NO^"," + O^^," + O^}," + O^~,"N + NO^",^ + O^^,^ + O^^,} + O^^,~Npolarization, the maximum power of the best precoder over the set of precoders is: ^^YVZ,YVZ = NO^"," + O^^," + O^}," + O^~,"N .

[0119] Finally,^, then ^YVZ,YVZ16 ^^.

[0120] The expressions in equations (7-9) can both be evaluated numerically. In the special case in which the polarizations of all four transmit antennas are aligned and ^" = ^^ = ^} = ^~ = ^,we have ^^YVZ,YVZ = 16 ^ ,^ X,YVZ = 12 ^VW .7 ^ , and^ = 8 ^Y[\,YVZ ^ .

[0121] From the above, it can be observed that depending on the state of the random phase offsets between the antennas, the power of the best precoder can vary by 3 dB over the set of precoders, depending on the random phase offsets between the antennas. This can be compared with the case of two antennas where the power of the best precoder varies by at most 0.7 dB as a function of the random phase offset.

[0122] Figure 5 is a chart depicting a CCDF 500 of the phase alignment error is shown for the case that the polarizations of the four transmit antennas are the same and the power received from the four antennas transmitting separately is equal so that ^"=^^ = ^} = ^~, in accordance with aspects of the present disclosure. The CCDF 500shows the probability that a given phase alignment error exceeds a particular decibel (dB) value for the coherent, four antenna port precoders in Table 5 (i.e., with same polarization and equal power), in accordance with aspects of the present disclosure. The x-axis tracks the loss due to phase alignment error (in dB), while the y-axis tracks the probability that loss is exceeded.

[0123] From Figure 5, it can be observed that the power corresponding to the best precoder is sensitive to the phase offset J. Furthermore, it should be noted that the phasealignment loss can be greatest when ^" = ^^ = ^} = ^~ for the given azimuth andelevation but will generally be significantly less.

[0124] It can be observed that for four antennas, the power ^^^, ^^ transmitted in aparticular azimuth and elevation with a best precoder within a set of precoders is a random variable that depends on the distribution of the phase offsets J", J^, and J}between the transmit antennas.

[0125] It can be observed that for four antennas, the power for the best precoder over the set of precoders can vary by 3 dB and depends on the values of the random phase offsets J", J^, and J}between the antennas.

[0126] Moreover, it can be observed that because the power variation due to the variations of the random phase offsets of the best precoder over the set of precoders can be very large. Therefore, there is some risk in defining the power as the power for the best precoder at a single snapshot in time.

[0127] In some embodiments, for single-layer uplink MIMO with four antennas, theradiated power ^^^, ^^ for elevation ^ and azimuth ^ can be defined as the averagepower of the best precoder given by 1^^ ^^ ^^^ ()VWX,YVZ = ^ ^ ^ max ^N^^,"O^" + ^^,^O^^e Q + ^ ()^ O^ e S^2^^}^ ^ ^ "^^^^^^ ,} }

[0128] Here ^^,(^^, ^^ denotes the power received from the i-th transmit antenna thatis received by the test equipment on the j-th polarization, where 3 ∈ ^1,2^ and thepolarizations are orthogonal with respect to each other. Here, R^ = ±1 for the i-th antennadepends on the sign of the projection of the antenna pattern onto the second polarization axis relative to the sign of its projection on to the first polarization axis.

[0129] Alternatively, for single-layer uplink MIMO with four antennas, the radiatedpower ^^^, ^^ for elevation ^ and azimuth ^ can be defined as the minimum power ofthe best precoder given by ()Y[\,YVZ Q ()S ()n ^^ = )Q m,)Sin ,)n "^ m^^a^x^^ ^N^^,"O^"," + ^^,^O^^,"e + ^^,}O^},"e + ^^,~O^~,"e N_

[0130] Here ^^,(^^, ^^ denotes the power received from the i-th transmit antenna thatis received by the test equipment on the j-th polarization, where 3 ∈ ^1,2^ and thepolarizations are orthogonal with respect to each other. Here, R^ = ±1 for the i-th antennadepends on the sign of the projection of the antenna pattern onto the second polarization axis relative to the sign of its projection on to the first polarization axis.

[0131] Alternatively, for single-layer uplink MIMO with two antennas, the radiatedpower ^^^, ^^ for elevation ^ and azimuth ^ can be defined as the maximum power ofthe best precoder given by ^N^ O^ + ^ O^ e() + ^ O^ e() + ^ ^ e() ^^ = max max Q S nN_where ^^,(^^, ^^ denotes the power received from the i-th transmit antenna that is receivedby the test equipment on the j-th polarization, where 3 ∈ ^1,2^ and the polarizations areorthogonal with respect to each other. Here, R" = ±1 and R^ = ±1 for the first and secondtransmit antennas depend on the sign of the projection of the antenna pattern onto the second polarization axis relative to the signits projection on to the first polarization axis.

[0132] Figure 6 illustrates an example signal diagram of a procedure 600 for determining a radiated power, in accordance with aspects of the present disclosure. In an implementation, a UE 602 can include two transmit antennas, transmissions from which are received at a test equipment 604. In certain embodiments, the UE 602 is an implementation of the UE 104, described above.

[0133] In aspects of the described techniques, a UE 602 receives (at 606) from the test equipment 604, and the test equipment 604 transmits, an instruction, message, or indication to use a precoder (or a sequence of precoders) for a multi-antenna transmission.

[0134] The UE 602 transmits (at 608) from a first antenna, to the test equipment 604 according to a first precoder, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment. Accordingly, the test equipment 604 receives the first transmission from the first antenna of the UE, and (at 610) measures radiated power of the first transmission from the first antenna for a first radiated power measurement.

[0135] The UE 602 transmits (at 612) from a second antenna, to the test equipment 604 according to the precoder, a second transmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment. Accordingly, the test equipment 604 receives the second transmission from the second antenna of the UE, and (at 614) measures radiated power of the second transmission from the second antenna for a second radiated power measurement.

[0136] The test equipment 604 (at 616) determines a radiated power ^^^, ^^ for anazimuth ^ and elevation ^ relative to the UE of the multi-antenna transmission based at least in part on the precoder and the radiated power measurements for each of the two orthogonal polarizations of the separate transmissions from the individual antennas of the UE.

[0137] While the procedure 600 is described for a UE 602 with two transmit antennas, in other embodiments the UE 603 may have four transmit antennas. In such embodiments, the UE 602 transmits additional transmissions for additional radiated power measurements for each of the two orthogonal polarizations, i.e., a third transmission for a third radiated power measurement for each of the two orthogonal polarizations and a fourth second transmission for a fourth radiated power measurement for each of the two orthogonal polarizations. Here, the UE transmits according to single- antenna precoders, as described herein.

[0138] Figure 7 illustrates an example of a UE 700 in accordance with aspects of the present disclosure. The UE 700 may include a processor 702, a memory 704, a controller 706, and a transceiver 708. The processor 702, the memory 704, the controller 706, or the transceiver 708, or various combinations thereof or various components thereof may be examples of means for performing various aspects of the present disclosure as described herein. These components may be coupled (e.g., operatively, communicatively, functionally, electronically, electrically) via one or more interfaces.

[0139] The processor 702, the memory 704, the controller 706, or the transceiver 708, or various combinations or components thereof may be implemented in hardware (e.g., circuitry). The hardware may include a processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or other programmable logic device, or any combination thereof configured as or otherwise supporting a means for performing the functions described in the present disclosure.

[0140] The processor 702 may include an intelligent hardware device (e.g., a general- purpose processor, a DSP, a central processing unit (CPU), an ASIC, a field programmable gate array (FPGA), or any combination thereof). In some implementations, the processor 702 may be configured to operate the memory 704. In some other implementations, the memory 704 may be integrated into the processor 702. The processor 702 may be configured to execute computer-readable instructions stored in the memory 704 to cause the UE 700 to perform various functions of the present disclosure.

[0141] The memory 704 may include volatile or non-volatile memory. The memory 704 may store computer-readable, computer-executable code including instructions that, when executed by the processor 702, cause the UE 700 to perform various functions described herein. The code may be stored in a non-transitory computer-readable mediumsuch the memory 704 or another type of memory. Computer-readable media includes both non-transitory computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A non- transitory storage medium may be any available medium that may be accessed by a general-purpose or special-purpose computer.

[0142] In some implementations, the processor 702 and the memory 704 coupled with the processor 702 may be configured to cause the UE 700 to perform various functions (e.g., operations, signaling) of a radio node (e.g., sensing transmitter node and / or sensing receiver node) described herein (e.g., executing, by the processor 702, instructions stored in the memory 704). In some implementations, the processor 702 may include multiple processors and the memory 704 may include multiple memories. One or more of the multiple processors may be coupled with one or more of the multiple memories, which may be individually or collectively, configured to perform various functions (e.g., operations, signaling) of the UE 700 as disclosed herein.

[0143] The processor 702 coupled with the memory 704 may be configured to cause the UE 700 to receive, from a test equipment, an instruction to use a multi-antenna precoder for a multi-antenna transmission, wherein the test equipment determines a radiated power for an azimuth and an elevation relative to the UE 700 based at least in part on the multi-antenna precoder and radiated power measurements of separate transmissions from individual antennas of the UE 700.

[0144] The processor 702 coupled with the memory 704 may be configured to cause the UE 700 to transmit from a first antenna, to the test equipment according to a first single-antenna precoder for transmission from the first antenna, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment. Further, the processor 702 coupled with the memory 704 may be configured to cause the UE 700 to transmit from a second antenna, to the test equipment according to a second single-antenna precoder for transmission from the second antenna, a second transmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment.

[0145] Additionally, the multi-antenna transmission may be based at least in part on a codebook that includes the multi-antenna precoder in a set of precoders. In some embodiments, the multi-antenna transmission includes a random phase offset between thefirst transmission from the first antenna of the UE 700 and the second transmission from the second antenna of the UE 700, where the polarizations of the transmit antennas (e.g., first and second antennas) are non-aligned.

[0146] In certain embodiments, the radiated power at the azimuth and the elevation relative to the UE 700 is based on a calculated power of the multi-antenna precoder averaged over the random phase offset based at least in part on the first radiated power measurement for each of the two orthogonal polarizations of the first transmission and the second radiated power measurement of the second transmission. In such embodiments, the multi-antenna precoder may be a best performing precoder determined as a function of the random phase offset of the set of precoders based on the calculated power of each precoder averaged over the random phase offset.

[0147] In certain embodiments, the radiated power is based on a calculated power of the multi-antenna precoder minimized over the random phase offset based at least in part on the first radiated power measurement for each of the two orthogonal polarizations of the first transmission and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission. In such embodiments, the multi- antenna precoder may be a best performing precoder determined as a function of the random phase offset of the set of precoders based on the calculated power of each precoder for a worst case of the random phase offset.

[0148] The controller 706 may manage input and output signals for the UE 700. The controller 706 may also manage peripherals not integrated into the UE 700. In some implementations, the controller 706 may utilize an operating system (OS) such as iOS®, ANDROID®, WINDOWS®, or other operating systems. In some implementations, the controller 706 may be implemented as part of the processor 702.

[0149] In some implementations, the UE 700 may include at least one transceiver 708. In some other implementations, the UE 700 may have more than one transceiver 708. The transceiver 708 may represent a wireless transceiver. The transceiver 708 may include one or more receiver chains 710, one or more transmitter chains 712, or a combination thereof.

[0150] A receiver chain 710 may be configured to receive signals (e.g., control information, data, packets) over a wireless medium. For example, the receiver chain 710may include one or more antennas for receiving the signal over the air or wireless medium. The receiver chain 710 may include at least one amplifier (e.g., a low-noise amplifier (LNA)) configured to amplify the received signal. The receiver chain 710 may include at least one demodulator configured to demodulate the received signal and obtain the transmitted data by reversing the modulation technique applied during transmission of the signal. The receiver chain 710 may include at least one decoder for decoding / processing the demodulated signal to receive the transmitted data.

[0151] A transmitter chain 712 may be configured to generate and transmit signals (e.g., control information, data, packets). The transmitter chain 712 may include at least one modulator for modulating data onto a carrier signal, preparing the signal for transmission over a wireless medium. The at least one modulator may be configured to support one or more techniques such as amplitude modulation (AM), frequency modulation (FM), or digital modulation schemes like phase-shift keying (PSK) or quadrature amplitude modulation (QAM). The transmitter chain 712 may also include at least one power amplifier configured to amplify the modulated signal to an appropriate power level suitable for transmission over the wireless medium. The transmitter chain 712 may also include one or more antennas for transmitting the amplified signal into the air or wireless medium.

[0152] Figure 8 illustrates an example of a processor 800 in accordance with aspects of the present disclosure. The processor 800 may be an example of a processor configured to perform various operations in accordance with examples as described herein. The processor 800 may include a controller 802 configured to perform various operations in accordance with examples as described herein. The processor 800 may optionally include at least one memory 804, which may be, for example, an L1 / L2 / L3 cache. Additionally, or alternatively, the processor 800 may optionally include one or more arithmetic-logic units (ALUs) 806. One or more of these components may be in electronic communication or otherwise coupled (e.g., operatively, communicatively, functionally, electronically, electrically) via one or more interfaces (e.g., buses).

[0153] The processor 800 may be a processor chipset and include a protocol stack (e.g., a software stack) executed by the processor chipset to perform various operations (e.g., receiving, obtaining, retrieving, transmitting, outputting, forwarding, storing, determining, identifying, accessing, writing, reading) in accordance with examples asdescribed herein. The processor chipset may include one or more cores, one or more caches (e.g., memory local to or included in the processor chipset (e.g., the processor 800) or other memory (e.g., random access memory (RAM), read-only memory (ROM), dynamic RAM (DRAM), synchronous dynamic RAM (SDRAM), static RAM (SRAM), ferroelectric RAM (FeRAM), magnetic RAM (MRAM), resistive RAM (RRAM), flash memory, phase change memory (PCM), and others).

[0154] The controller 802 may be configured to manage and coordinate various operations (e.g., signaling, receiving, obtaining, retrieving, transmitting, outputting, forwarding, storing, determining, identifying, accessing, writing, reading) of the processor 800 to cause the processor 800 to support various operations in accordance with examples as described herein. For example, the controller 802 may operate as a control unit of the processor 800, generating control signals that manage the operation of various components of the processor 800. These control signals include enabling or disabling functional units, selecting data paths, initiating memory access, and coordinating timing of operations.

[0155] The controller 802 may be configured to fetch (e.g., obtain, retrieve, receive) instructions from the memory 804 and determine subsequent instruction(s) to be executed to cause the processor 800 to support various operations in accordance with examples as described herein. The controller 802 may be configured to track memory address of instructions associated with the memory 804. The controller 802 may be configured to decode instructions to determine the operation to be performed and the operands involved. For example, the controller 802 may be configured to interpret the instruction and determine control signals to be output to other components of the processor 800 to cause the processor 800 to support various operations in accordance with examples as described herein. Additionally, or alternatively, the controller 802 may be configured to manage flow of data within the processor 800. The controller 802 may be configured to control transfer of data between registers, arithmetic logic units (ALUs), and other functional units of the processor 800.

[0156] The memory 804 may include one or more caches (e.g., memory local to or included in the processor 800 or other memory, such RAM, ROM, DRAM, SDRAM, SRAM, MRAM, flash memory, etc. In some implementations, the memory 804 may reside within or on a processor chipset (e.g., local to the processor 800). In some otherimplementations, the memory 804 may reside external to the processor chipset (e.g., remote to the processor 800).

[0157] The memory 804 may store computer-readable, computer-executable code including instructions that, when executed by the processor 800, cause the processor 800 to perform various functions described herein. The code may be stored in a non-transitory computer-readable medium such as system memory or another type of memory. The controller 802 and / or the processor 800 may be configured to execute computer-readable instructions stored in the memory 804 to cause the processor 800 to perform various functions. For example, the processor 800 and / or the controller 802 may be coupled with or to the memory 804, the processor 800, the controller 802, and the memory 804 may be configured to perform various functions described herein. In some examples, the processor 800 may include multiple processors and the memory 804 may include multiple memories. One or more of the multiple processors may be coupled with one or more of the multiple memories, which may, individually or collectively, be configured to perform various functions herein.

[0158] The one or more ALUs 806 may be configured to support various operations in accordance with examples as described herein. In some implementations, the one or more ALUs 806 may reside within or on a processor chipset (e.g., the processor 800). In some other implementations, the one or more ALUs 806 may reside external to the processor chipset (e.g., the processor 800). One or more ALUs 806 may perform one or more computations such as addition, subtraction, multiplication, and division on data. For example, one or more ALUs 806 may receive input operands and an operation code, which determines an operation to be executed. One or more ALUs 806 be configured with a variety of logical and arithmetic circuits, including adders, subtractors, shifters, and logic gates, to process and manipulate the data according to the operation. Additionally, or alternatively, the one or more ALUs 806 may support logical operations such as AND, OR, exclusive-OR (XOR), not-OR (NOR), and not-AND (NAND), enabling the one or more ALUs 806 to handle conditional operations, comparisons, and bitwise operations.

[0159] The processor 800 may support various functions (e.g., operations, signaling) in accordance with examples as disclosed herein. For example, the controller 802 coupled with the memory 804 may be configured to, capable of, or operable to cause the processor800 to receive, from a test equipment, an instruction to use a multi-antenna precoder for a multi-antenna transmission, wherein the test equipment determines a radiated power foran azimuth and an elevation (e.g., ^^^, ^^ for an azimuth ^ and elevation ^) relative to aUE based at least in part on the multi-antenna precoder and radiated power measurements of separate transmissions from individual antennas of the UE; transmit from a first antenna, to the test equipment according to the a first single-antenna precoder for transmission from the first antenna, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment; and transmit from a second antenna, to the test equipment according to a second single-antenna precoder for transmission from the second antenna, a second transmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment. Additionally, the controller 802 coupled with the memory 804 may be configured to, capable of, or operable to cause the processor 800 to perform one or more functions (e.g., operations, signaling) of the UE as described herein.

[0160] In various implementations, the processor 800 may support the various functions (e.g. operations, signaling) of a test equipment, in accordance with examples as disclosed herein. For example, the controller 802 coupled with the memory 804 may be configured to, capable of, or operable to cause the processor 800 to receive, from a first antenna of a UE, a first transmission (e.g., according to a first single-antenna precoder); determine a first radiated power measurement for each of two orthogonal polarizations based on a measured radiated power of the first transmission; receive, from a second antenna of the UE, a second transmission; determine a second radiated power measurement for each of the two orthogonal polarizations based on a measured radiatedpower of the second transmission; and determine a radiated power (e.g., ^^^, ^^ for anazimuth ^ and elevation ^) of a multi-antenna transmission based at least in part on a multi-antenna precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission, and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission. Additionally, the controller 802 coupled with the memory 804 may be configured to, capable of, or operable to cause the processor 800 to perform one or more functions (e.g., operations, signaling) of the test equipment as described herein.

[0161] Figure 9 illustrates an example of a NE 900 in accordance with aspects of the present disclosure. In some implementations, the NE 900 implements a test equipment204. The NE 900 may include a processor 902, a memory 904, a controller 906, and a transceiver 908. The processor 902, the memory 904, the controller 906, or the transceiver 908, or various combinations thereof or various components thereof may be examples of means for performing various aspects of the present disclosure as described herein. These components may be coupled (e.g., operatively, communicatively, functionally, electronically, electrically) via one or more interfaces.

[0162] The processor 902, the memory 904, the controller 906, or the transceiver 908, or various combinations or components thereof may be implemented in hardware (e.g., circuitry). The hardware may include a processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or other programmable logic device, or any combination thereof configured as or otherwise supporting a means for performing the functions described in the present disclosure.

[0163] The processor 902 may include an intelligent hardware device (e.g., a general- purpose processor, a DSP, a CPU, an ASIC, an FPGA, or any combination thereof). In some implementations, the processor 902 may be configured to operate the memory 904. In some other implementations, the memory 904 may be integrated into the processor 902. The processor 902 may be configured to execute computer-readable instructions stored in the memory 904 to cause the NE 900 to perform various functions of the present disclosure.

[0164] The memory 904 may include volatile or non-volatile memory. The memory 904 may store computer-readable, computer-executable code including instructions when executed by the processor 902 cause the NE 900 to perform various functions described herein. The code may be stored in a non-transitory computer-readable medium such the memory 904 or another type of memory. Computer-readable media includes both non- transitory computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A non-transitory storage medium may be any available medium that may be accessed by a general-purpose or special-purpose computer.

[0165] In some implementations, the processor 902 and the memory 904 coupled with the processor 902 may be configured to cause the NE 900 to perform various functions (e.g., operations, signaling) described herein (e.g., executing, by the processor 902, instructions stored in the memory 904). In some implementations, the processor 902 mayinclude multiple processors and the memory 904 may include multiple memories. One or more of the multiple processors may be coupled with one or more of the multiple memories, which may be individually or collectively, configured to perform various functions (e.g., operations, signaling) of the NE 900 as disclosed herein.

[0166] The processor 902 coupled with the memory 904 may be configured to cause the NE 900 to receive, from a first antenna of a UE, a first transmission (e.g., according to a first single-antenna precoder) and measure radiated power of the first transmission from the first antenna for a first radiated power measurement for each of two orthogonal polarizations. In other words, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to determine a first radiated power measurement for each of the two orthogonal polarizations based on a measured radiated power of the first transmission.

[0167] The processor 902 coupled with the memory 904 may be configured to cause the NE 900 to receive, from a second antenna of the UE, a second transmission (e.g., according to a second single-antenna precoder) and measure the radiated power of the second transmission from the second antenna for a second radiated power measurement for each of the two orthogonal polarizations. In other words, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to determine a second radiated power measurement for each of the two orthogonal polarizations based on a measured radiated power of the second transmission.

[0168] The processor 902 coupled with the memory 904 may be configured to cause the NE 900 to determine a radiated power of a multi-antenna transmission based at least in part on a multi-antenna precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission, and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

[0169] Additionally, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to calculate a TRP of the multi-antenna transmission by integrating multiple radiated power measurements over a unit sphere. In some embodiments, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to transmit an instruction to use a first single-antenna precoder for the first transmission, a second single-antenna precoder for the second transmission, and the multi-antenna precoder for a simultaneous transmission from multiple antennas.

[0170] In some embodiments, the multi-antenna transmission from the UE is based at least in part on a codebook that includes the multi-antenna precoder in a set of precoders. In certain embodiments, the multi-antenna transmission includes a random phase offset between the first transmission from the first antenna of the UE and the second transmission from the second antenna of the UE, where the polarizations of the transmit antennas (e.g., first and second antennas of the UE) are non-aligned.

[0171] In certain embodiments, to determine the radiated power, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to calculate a power of the precoder averaged over the random phase offset based at least in part on the first radiated power measurement for each of the two orthogonal polarizations of the first transmission and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission. In such embodiments, the multi-antenna precoder may be a best performing precoder determined as a function of the random phase offset of the set of precoders based on the calculated power of each precoder averaged over the random phase offset.

[0172] In certain embodiments, to determine the radiated power, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to calculate aradiated power as ^ = ~ √^VWX,YVZ ^"," + ^",^ + ^^," + ^^,^ + ^ NO^","^^," + R"R^O^",^^^,^N, where P1,1polarization, where P1,2 represents the first radiated power measurement received on a second polarization, where P2,1 represents the second radiated power measurement received on the first polarization, where P2,2 represents the second radiated powermeasurement received on the second polarization, and where R" = ±1 and R^ = ±1depend on the sign of the projection of the antenna patternthe second polarization axis relative to the sign of its projection on to the first polarization axis.

[0173] In certain embodiments, to determine the radiated power, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to calculate a power of the precoder minimized over the random phase offset based at least in part on the first radiated power measurement for each of the two orthogonal polarizations of the first transmission and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission. In such embodiments, the multi- antenna precoder may be a best performing precoder determined as a function of therandom phase offset of the set of precoders based on the calculated power of each precoder for a worst case of the random phase offset.

[0174] In certain embodiments, to determine the radiated power, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to calculate aradiated power as ^Y[\,YVZ = ^"," + ^",^ + ^^," + ^^,^ + √2 NO^","^^," + R"R^O^",^^^,^N ,where P1,1 polarization,second polarization, where P2,1 represents the second radiated power measurement received on the first polarization, where P2,2represents the second radiated powermeasurement received on the second polarization, and where R" = ±1 and R^ = ±1depend on the sign of the projection of the antenna pattern onto the second polarizationaxis relative to the sign of its projection on to the first axis.

[0175] In some embodiments, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to receive, from one or more additional antennas of the UE, respective additional transmissions according to one or more single-antenna precoders. In such embodiments, the processor 902 coupled with the memory 904 may be configured to cause the NE 900 to determine the radiated power of the multi-antenna transmission based at least in part on the multi-antenna precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission from the first antenna, the second radiated power measurement for each of the two orthogonal polarizations of the second transmission from the second antenna, and one or more additional radiated power measurements for each of the two orthogonal polarizations of the respective additional transmissions measured individually from the one or more additional antennas.

[0176] In certain embodiments, the multi-antenna transmission includes a number of random phase offsets that is one less than a number of transmit antennas of the UE, and the polarizations of the transmit antennas of the UE are non-aligned. Here, the transmit antennas of the UE include at least the first antenna, the second antenna, and the one or more additional antennas. In one embodiment, the multi-antenna precoder is a best performing precoder of a set of precoders, determined as a function of the random phase offsets based on a calculated power of each precoder averaged over the random phase offsets. In another embodiment, the multi-antenna precoder is a best performing precoderof the set of precoders, determined as a function of the random phase offsets based on a calculated power of each precoder for a worst case of minimum power.

[0177] The controller 906 may manage input and output signals for the NE 900. The controller 906 may also manage peripherals not integrated into the NE 900. In some implementations, the controller 906 may utilize an operating system such as iOS®, ANDROID®, WINDOWS®, or other operating systems. In some implementations, the controller 906 may be implemented as part of the processor 902.

[0178] In some implementations, the NE 900 may include at least one transceiver 908. In some other implementations, the NE 900 may have more than one transceiver 908. The transceiver 908 may represent a wireless transceiver. The transceiver 908 may include one or more receiver chains 910, one or more transmitter chains 912, or a combination thereof.

[0179] A receiver chain 910 may be configured to receive signals (e.g., control information, data, packets) over a wireless medium. For example, the receiver chain 910 may include one or more antennas for receiving the signal over the air or wireless medium. The receiver chain 910 may include at least one amplifier (e.g., a low-noise amplifier (LNA)) configured to amplify the received signal. The receiver chain 910 may include at least one demodulator configured to demodulate the received signal and obtain the transmitted data by reversing the modulation technique applied during transmission of the signal. The receiver chain 910 may include at least one decoder for decoding / processing the demodulated signal to receive the transmitted data.

[0180] A transmitter chain 912 may be configured to generate and transmit signals (e.g., control information, data, packets). The transmitter chain 912 may include at least one modulator for modulating data onto a carrier signal, preparing the signal for transmission over a wireless medium. The at least one modulator may be configured to support one or more techniques such as amplitude modulation (AM), frequency modulation (FM), or digital modulation schemes like phase-shift keying (PSK) or quadrature amplitude modulation (QAM). The transmitter chain 912 may also include at least one power amplifier configured to amplify the modulated signal to an appropriate power level suitable for transmission over the wireless medium. The transmitter chain 912 may also include one or more antennas for transmitting the amplified signal into the air or wireless medium.

[0181] Figure 10 depicts one embodiment of a method 1000 in accordance with aspects of the present disclosure. In various embodiments, the operations of the method 1000 may be implemented by a UE, as described herein. In some implementations, the UE may execute a set of instructions to control the function elements of the UE to perform the described functions.

[0182] At step 1002, the method may include receiving, from a test equipment, an instruction to use a multi-antenna precoder for a multi-antenna transmission, where the test equipment determines a radiated power for an azimuth and an elevation relative to the UE based at least in part on the multi-antenna precoder and radiated power measurements of separate transmissions from individual antennas of a UE. The operations of step 1002 may be performed in accordance with examples as described herein. In some implementations, aspects of the operations of step 1002 may be performed by a UE as described with reference to Figure 7.

[0183] At step 1004, the method may include transmitting from a first antenna, to the test equipment according to a first single-antenna precoder for transmission from the first antenna, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment. The operations of step 1004 may be performed in accordance with examples as described herein. In some implementations, aspects of the operations of step 1004 may be performed by a UE as described with reference to Figure 7.

[0184] At step 1006, the method may include transmitting from a second antenna, to the test equipment according to a second single-antenna precoder for transmission from the second antenna, a second transmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment. The operations of step 1006 may be performed in accordance with examples as described herein. In some implementations, aspects of the operations of step 1006 may be performed a UE as described with reference to Figure 7.

[0185] It should be noted that the method 1000 described herein describes one possible implementation, and that the operations and the steps may be rearranged or otherwise modified and that other implementations are possible.

[0186] Figure 11 illustrates a flowchart of a method 1100 in accordance with aspects of the present disclosure. The operations of the method may be implemented by a test equipment, as described herein. In some implementations, the test equipment may execute a set of instructions to control the function elements of the test equipment to perform the described functions. It should be noted that the method described herein describes a possible implementation, and that the operations and the steps may be rearranged or otherwise modified and that other implementations are possible.

[0187] At step 1102, the method may include receiving, from a first antenna of a UE, a first transmission. The operations of step 1102 may be performed in accordance with examples as described herein. In some implementations, aspects of the operations of step 1102 may be performed by a test equipment or a NE as described with reference to Figure 9.

[0188] At step 1104, the method may include determining a first radiated power measurement for each of two orthogonal polarizations based on a measured radiated power of the first transmission. The operations of step 1104 may be performed in accordance with examples as described herein. In some implementations, aspects of the operations of step 1104 may be performed by a test equipment or a NE as described with reference to Figure 9.

[0189] At step 1106, the method may include receiving, from a second antenna of the UE, a second transmission. The operations of step 1106 may be performed in accordance with examples as described herein. In some implementations, aspects of the operations of step 1106 may be performed a test equipment or a NE as described with reference to Figure 9.

[0190] At step 1108, the method may include determining a second radiated power measurement for each of the two orthogonal polarizations based on a measured radiated power of the second transmission. The operations of step 1108 may be performed in accordance with examples as described herein. In some implementations, aspects of the operations of step 1108 may be performed a test equipment or a NE as described with reference to Figure 9.

[0191] At step 1110, the method may include determining a radiated power of a multi-antenna transmission based at least in part on a multi-antenna precoder, the firstradiated power measurement for each of the two orthogonal polarizations of the first transmission, and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission. The operations of step 1110 may be performed in accordance with examples as described herein. In some implementations, aspects of the operations of step 1110 may be performed by a test equipment or a NE as described with reference to Figure 9.

[0192] It should be noted that the method 1100 described herein describes one possible implementation, and that the operations and the steps may be rearranged or otherwise modified and that other implementations are possible.

[0193] The description herein is provided to enable a person having ordinary skill in the art to make or use the disclosure. Various modifications to the disclosure will be apparent to a person having ordinary skill in the art, and the generic principles defined herein may be applied to other variations without departing from the scope of the disclosure. Thus, the disclosure is not limited to the examples and designs described herein but is to be accorded the broadest scope consistent with the principles and novel features disclosed herein.

Claims

CLAIMS What is claimed is:

1. A test equipment for wireless communication, comprising: at least one memory; and at least one processor coupled with the at least one memory and configured to cause the test equipment to: receive, from a first antenna of a user equipment (UE), a first transmission; determine a first radiated power measurement for each of two orthogonal polarizations based on a measured radiated power of the first transmission; receive, from a second antenna of the UE, a second transmission; determine a second radiated power measurement for each of the two orthogonal polarizations based on a measured radiated power of the second transmission; and determine a radiated power of a multi-antenna transmission based at least in part on a multi-antenna precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission, and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

2. The test equipment of claim 1, wherein the at least one processor is configured to cause the test equipment to calculate a total radiated power (TRP) of the multi- antenna transmission by integrating multiple radiated power measurements over a unit sphere.

3. The test equipment of claim 1, wherein the at least one processor is configured to: transmit an instruction to use a first single-antenna precoder for the first transmission, a second single-antenna precoder for the second transmission, and the multi-antenna precoder for a simultaneous transmission from multiple antennas.

4. The test equipment of claim 1, wherein the multi-antenna transmission from the UE is based at least in part on a codebook that includes the multi-antenna precoder in a set of precoders.

5. The test equipment of claim 4, wherein the multi-antenna transmission includes a random phase offset between the first transmission from the first antenna of the UE and the second transmission from the second antenna of the UE, and wherein a first polarization of the first antenna of the UE and a second polarization of the second antenna of the UE are non-aligned.

6. The test equipment of claim 5, wherein, to determine the radiated power, the at least one processor is configured to cause the test equipment to calculate a power of the multi-antenna precoder averaged over the random phase offset based at least in part on the first radiated power measurement for each of the two orthogonal polarizations of the first transmission and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

7. The test equipment of claim 6, wherein the multi-antenna precoder is a best performing precoder as a function of the random phase offset of the set of precoders based on the calculated power of each precoder averaged over the random phase offset.

8. The test equipment of claim 5, wherein, to determine the radiated power, the at least one processor is configured to cause the test equipment to calculate a radiated power as ^ ~ √^VWX,YVZ = ^"," + ^",^ + ^^," + ^^,^ + ^ NO^","^^," +received on the first polarization, where P1,2represents the first radiated power measurement received on the second polarization, where P2,1 represents the second radiated power measurement received on the first polarization, and where P2,2represents the second radiated power measurement received on the second polarization.

9. The test equipment of claim 5, wherein, to determine the radiated power, the at least one processor is configured to cause the test equipment to calculate a powerof the multi-antenna precoder minimized over the random phase offset based at least in part on the first radiated power measurement for each of the two orthogonal polarizations of the first transmission and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

10. The test equipment of claim 9, wherein the multi-antenna precoder is a best performing precoder as a function of the random phase offset of the set of precoders based on the calculated power of each precoder for a worst case of the random phase offset.

11. The test equipment of claim 5, wherein, to determine the radiated power, the at least one processor is configured to cause the test equipment to calculate a radiated power as ^Y[\,YVZ = ^"," + ^",^ + ^^," + ^^,^ + √2 NO^","^^," +received on the first polarization, where P1,2represents the first radiated power measurement received on the second polarization, where P2,1 represents the second radiated power measurement received on the first polarization, and where P2,2represents the second radiated power measurement received on the second polarization.

12. The test equipment of claim 1, wherein the at least one processor is configured to cause the test equipment to: receive, from one or more additional antennas of the UE, respective additional transmissions according to one or more single-antenna precoders; and determine the radiated power of the multi-antenna transmission based at least in part on the multi-antenna precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission from the first antenna, the second radiated power measurement for each of the two orthogonal polarizations of the second transmission from the second antenna, and one or more additional radiated power measurements for each of the twoorthogonal polarizations of the respective additional transmissions measured individually from the one or more additional antennas.

13. A method performed by a test equipment, the method comprising: receiving, from a first antenna of a user equipment (UE), a first transmission; determine a first radiated power measurement for each of two orthogonal polarizations based on a measured radiated power of the first transmission; receiving, from a second antenna of the UE, a second transmission; determine a second radiated power measurement for each of the two orthogonal polarizations based on a measured radiated power of the second transmission; and determining a radiated power of a multi-antenna transmission based at least in part on a multi-antenna precoder, the first radiated power measurement for each of the two orthogonal polarizations of the first transmission, and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

14. A user equipment (UE) for wireless communication, comprising: at least one memory; and at least one processor coupled with the at least one memory and configured to cause the UE to: receive, from a test equipment, an instruction to use a multi-antenna precoder for a multi-antenna transmission, wherein the test equipment determines a radiated power for an azimuth and an elevation relative to the UE based at least in part on the multi- antenna precoder and radiated power measurements of separate transmissions from individual antennas of the UE; transmit from a first antenna, to the test equipment according to a first single-antenna precoder for transmission from the first antenna, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment; andtransmit from a second antenna, to the test equipment according to a second single-antenna precoder for transmission from the second antenna, a second transmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment.

15. The UE of claim 14, wherein the multi-antenna transmission is based at least in part on a codebook that includes the multi-antenna precoder in a set of precoders, wherein the multi-antenna transmission includes a random phase offset between the first transmission from the first antenna of the UE and the second transmission from the second antenna of the UE, and wherein respective polarizations of transmit antennas are non-aligned, the transmit antennas comprising the first antenna and the second antenna.

16. The UE of claim 15, wherein the radiated power at the azimuth and the elevation relative to the UE is based on a calculated power of the multi-antenna precoder averaged over the random phase offset based at least in part on the first radiated power measurement for each of the two orthogonal polarizations of the first transmission and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

17. The UE of claim 16, wherein the multi-antenna precoder is a best performing precoder determined as a function of the random phase offset of the set of precoders based on the calculated power of each precoder averaged over the random phase offset.

18. The UE of claim 15, wherein the radiated power is based on a calculated power of the multi-antenna precoder minimized over the random phase offset based at least in part on the first radiated power measurement for each of the two orthogonal polarizations of the first transmission and the second radiated power measurement for each of the two orthogonal polarizations of the second transmission.

19. The UE of claim 18, wherein the multi-antenna precoder is a best performing precoder determined as a function of the random phase offset of the set of precoders based on the calculated power of each precoder for a worst case of the random phase offset.

20. A processor for wireless communication, comprising: at least one controller coupled with at least one memory and configured to cause the processor to: receive, from a test equipment, an instruction to use a multi-antenna precoder for a multi-antenna transmission, wherein the test equipment determines a radiated power for an azimuth and an elevation relative to a user equipment (UE) based at least in part on the multi-antenna precoder and radiated power measurements of separate transmissions from individual antennas of the UE; transmit from a first antenna, to the test equipment according to a first single-antenna precoder for transmission from the first antenna, a first transmission for a first radiated power measurement for each of two orthogonal polarizations at the test equipment; and transmit from a second antenna, to the test equipment according to a second single-antenna precoder for transmission from the second antenna, a second transmission for a second radiated power measurement for each of the two orthogonal polarizations at the test equipment.

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