Patent ID: 12218780

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The structure and use of disclosed embodiments are discussed in detail below. It should be appreciated, however, that the present disclosure provides many applicable concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific structure and use of embodiments, and do not limit the scope of the disclosure.

FIG.1illustrates an example communications system100. Communications system100includes an access node105serving user equipments (UEs), such as UEs120. In a first operating mode, communications to and from a UE passes through access node105. In a second operating mode, communications to and from a UE do not pass through access node105, however, access node105typically allocates resources used by the UE to communicate when specific conditions are met. Communication between a UE and access node pair occur over uni-directional communication links, where the communication links between the UE and the access node are referred to as uplinks130, and the communication links between the access node and UE is referred to as downlinks135.

Access nodes may also be commonly referred to as Node Bs, evolved Node Bs (eNBs), next generation (NG) Node Bs (gNBs), master eNBs (MeNBs), secondary eNBs (SeNBs), master gNBs (MgNBs), secondary gNBs (SgNBs), network controllers, control nodes, base stations, access points, transmission points (TPs), transmission-reception points (TRPs), cells, carriers, macro cells, femtocells, pico cells, and so on, while UEs may also be commonly referred to as mobile stations, mobiles, terminals, tablets, laptop PCs, users, subscribers, stations, and the like. Access nodes may provide wireless access in accordance with one or more wireless communication protocols, e.g., the Third Generation Partnership Project (3GPP) long term evolution (LTE), LTE advanced (LTE-A), 5G, 5G LTE, 5G NR, sixth generation (6G), High Speed Packet Access (HSPA), the IEEE 802.11 family of standards, such as 802.11a/b/g/n/ac/ad/ax/ay/be, etc. While it is understood that communications systems may employ multiple access nodes capable of communicating with a number of UEs, only one access node and two UEs are illustrated for simplicity.

As discussed previously, in time division duplex (TDD) communication systems, channel information for a first channel may be obtained through channel measurements of a second channel due to channel reciprocity. As an example, channel information for a downlink channel may be obtained through channel measurements of a corresponding uplink channel due to channel reciprocity. However, the reciprocity that applies for instantaneous channel state information (CSI) does not hold in frequency division duplex (FDD) communication systems where training and measurements of the first channel, along with information feedback is required.

Due to the large number of antennas present in massive multiple input multiple output (MIMO) communication systems, the computational complexity associated with downlink channel training and the feedback overhead associated with information feedback is very large. The computational complexity is further exacerbated in computationally limited UEs, which may be incapable of providing computational resources needed to train, or generate the channel information and feedback information.

Furthermore, in the case of wideband transmissions, inter-symbol interference (ISI) becomes a critical issue because, due to multipath channel fading, the transmitted signal arrives at the receiver at different times on different paths. Orthogonal frequency division multiplexing (OFDM) has been adopted in 4G and 5G communication systems to combat ISI and simplify receiver design. Because multipath fading introduces frequency selectivity, there is significant channel variance on different frequency subbands. With only spatial channel covariance, channel training has to be processed independently along with the frequency domain, which leads to increased training complexity and overhead. Because the channel spatial covariance only includes channel statistics related to the spatial (or equivalently, angular) domain, a key component of channel characteristics is missed, namely, delays over different channel paths.

According to an example embodiment, methods and apparatus are provided that utilize high dimensional (HiDi) channel characteristics to capture both spatial (angular) and delay information of a channel. As an example, a spatial-frequency covariance matrix is transformed from the power angle delay spectrum rather than the power angle spectrum for the spatial channel covariance matrix. Information regarding the radio environment of a gNB or the coverage of the gNB may help improve the network performance (e.g., spectrum access, user handover, radio resource management, and so on). HiDi provides an improved radio environment map because it captures multi-dimensional channel characteristics.

In an embodiment, the conversion of the spatial-frequency covariance on the downlink based on the uplink observation allows for improving the downlink channel training or cross subband channel filtering in FDD communication systems. However, besides FDD communication systems, the conversion of the spatial-frequency covariance may be applied to any communication system that operates on multiple frequency bands with the same antenna array aperture, as long as the carrier frequency spacing between any two bands is not too great. Additionally, assumption that the power angle delay spectrum on these frequency bands is the same (or approximately the same) remains valid. The ability to obtain HiDi channel statistics of a first frequency band by converting HiDi channel statistics of a second frequency band benefits the system design on the first frequency band by enabling efficient wideband channel training, beam management, and so on, without requiring the determination of the HiDi channel statistics of the first frequency band through training.

FIG.2Aillustrates a communication system200used in presenting a signal model utilized in the discussion presented herein. Communication system200includes an access node205and a UE210. Access node205includes an antenna array with M antennas207, while UE210includes a single receive antenna212. For a discrete spatial channel model, assuming that there are L channel paths, the channel response at the antenna array (denoted h(t)=[hi(t), . . . , hM(t)]T) may be expressed as

h⁡(t)=∑l=1L⁢cl(t)⁢a⁡(θl,ϕl)⁢δ⁡(t-τl),(1)
where a(θl, ϕl)=[a1(θl, ϕl), . . . , aM(θl, ϕl)]Tis a normalized beam vector on the channel from the angle of arrival (AoA) θ based on the antenna location and

am(θ,ϕ)=e-j⁢2⁢πλ⁢k⁡(θ,ϕ)T⁢um,
k(θ, ϕ)=[sin(θ)sin(ϕ), cos(θ)sin(ϕ), cos(ϕ)]T, θ∈[−π, π], ϕ∈[0, π], and umis in the three-dimensional (3-D) spatial coordinates of antenna in.

FIG.2Billustrates a diagram250of a 3-D vector of a channel path255. Channel path255may be represented in angular form with angles θ260and ϕ262or in Cartesian coordinate form as sin θ sin ϕ270(in the X axis), cos θ sin ϕ272(in the Y axis), and cos ϕ274(in the Z axis).

If a two-dimensional (2-D) antenna array is considered, then k(θ)=[sin(θ), cos(θ)]Tand umis the 2-D spatial coordinates of antenna in. Additionally, in Equation (1), cl(t), θl, ϕl, and τlare the instantaneous complex channel gain, the horizontal and vertical AoA, and the delay of the l-th path, respectively, and δ(⋅) is the delta function with δ(0)=1 and 0 otherwise. Then{cl(t)}=pl. The channel statistics can be specified as the power angle delay profiles, i.e., {pl, θl, ϕl, τl}l=1L. Without including the large scale channel parameters, e.g., pathloss or receive signal-to-noise ratio (SNR) in general, it is assumed that Σlpl=1.

In the discussion presented herein, the focus is on 2-D systems. However, the example embodiments presented are operable with 3-D systems for any planar antenna array. Therefore, the focus on 2-D systems should not be construed as being limiting to the spirit of the example embodiments.

Considering wideband systems with OFDM modulation, after FFT at the receiver, the fading channel in the frequency domain on subcarrier k is expressible as

h[k]⁢(t)=F⁢h⁡(t)=1NF⁢∑l=1L⁢cl(t)⁢a⁡(θl)⁢e-j⁢2⁢π⁢k⁢fs⁢c⁢τι,(2)
where fscis the subcarrier spacing and NFis the Fast Fourier Transfer (FFT) size.

Given the instantaneous channel in the frequency domain, channel measurements may be taken at different subcarriers k1, k2, . . . , kN, i.e., h [k1], . . . , h [kN]. The channel measurements may be vectorized as

h=Δ[h[k1]T,…,h[kN]T]T.(3)

A first version of the spatial-frequency covariance (a form of HiDi channel statistics) is expressible as

RSF=𝔼⁢{h~⁢h~H}=[𝔼⁢{h[k1]⁢h[k1]H}𝔼⁢{h[k1]⁢h[k2]H}…𝔼⁢{h[k1]⁢h[kN]H}𝔼⁢{h[k2]⁢h[k1]H}𝔼⁢{h[k2]⁢h[k2]H}…𝔼⁢{h[k2]⁢h[kN]H}⋮⋮⋱⋮𝔼⁢{h[kN]⁢h[k1]H}𝔼⁢{h[kN]⁢h[k2]H}…𝔼⁢{h[kN]⁢h[kN]H}].(4)

From Equation (2), each subblock{h[ki]h[kj]H} in Equation (4) is expressible as

𝔼⁢{h[ki]⁢h[kj]H}=𝔼⁢{∑l=1L⁢cl1⁢a⁡(θll)⁢e-j⁢2⁢π⁢ki⁢fs⁢c⁢τl1⁢∑l2=1L⁢cl2*⁢a⁡(θl2)H⁢ej⁢2⁢π⁢kj⁢fs⁢c⁢τl2}=𝔼⁢{∑l=1L⁢❘"\[LeftBracketingBar]"cl❘"\[RightBracketingBar]"2⁢a⁡(θl)⁢a⁡(θl)H⁢e-j⁢2⁢π⁢(ki-kj)⁢fs⁢c⁢τl}=∑l=1L⁢pl⁢a⁡(θl)⁢a⁡(θl)H⁢e-j⁢2⁢π⁢(ki-kj)⁢fs⁢c⁢τl,(5)
where the second equality follows the assumption that the complex channel gain of each path clis independent.

From Equation (5),{h[ki]h[kj]H} depends only on the difference of the subcarriers, i.e., Δkij=ki−kj, instead of the absolute values of kior kj. Hence, when ki=kj, Δkij=0. Then,

𝔼⁢{h[ki]⁢h[ki]H}=∑l=1L⁢pl⁢a⁡(θl)⁢a⁡(θl)H,∀i,(6)
which reduces to the wideband spatial covariance R.

Based on the above observation, it is possible to rewrite Equation (4) and define a new version of spatial-frequency covariance. The channel on a frequency subcarrier k,

k+Δk1,…,kΔkNSF-1′,
i.e., h[k], h[k+Δk1], . . . ,

h[k],h[k+Δk1],…,h[k+ΔkNSF-1],
is selected, where {Δki} are the frequency lags considered in the spatial-frequency covariance. Furthermore, the following are set: Δki≠Δkjand Δki≠0, ∀ i, j.

The spatial channels on these subcarriers with different frequency lags are vectorized to obtain

h˘=Δ[h[k]T,h[k+Δk1]T⁢…,h[k+ΔkNS⁢F-1]T]T.(7)

The new spatial-frequency covariance matrix, defined as

RSF=𝔼⁢{h˘⁢h˘H}=[𝔼⁢{h[k]⁢h[k]H}𝔼⁢{h[k]⁢h[k+Δk1]H}…𝔼⁢{h[k]⁢h[k+ΔkNSF-1]H}𝔼⁢{h[k+Δk1]⁢h[k]H}𝔼⁢{h[k+Δk1]⁢h[k+Δk1]H}…𝔼⁢{h[k+Δk1]⁢h[k+ΔkNSF-1]H}⋮⋮⋱⋮𝔼⁢{h[k+ΔkNSF-1]⁢h[k]H}𝔼⁢{h[k+ΔkNSF-1]⁢h[k+Δk1]H}…𝔼⁢{h[k+ΔkNSF-1]⁢h[k+ΔkNSF-1]H}]=[R0RΔk1H…RΔkNSF-1HRΔk1R0…RΔkNSF-2H⋮⋮⋱⋮RΔkNSF-1RΔkNSF-2…R0],(8)
where NSFis the number of frequency lags in the covariance including the zero lag and

RΔki={h[k+Δki]⁢h[k]H}=∑l=1L⁢pl⁢a⁡(θl)⁢a⁡(θl)H⁢e-j⁢2⁢π⁢Δki⁢fs⁢c⁢τl.(9)

From Equation (9), the new spatial-frequency covariance matrix is not dependent on an arbitrary subcarrier k, but on all frequency lags Δki, with the first frequency lag being zero lag.

Also the path power plis a function of the path angle and delay. For the continuous case, a continuous function representing power angle delay spectrum ρ(θ, τ) is used. Then the block entries of spatial-frequency covariance matrix as the function of ρ(θ, τ) are expressible as

RΔki=∫0+∞∫-ππρ⁡(θ,τ)⁢a⁡(θ)⁢a⁡(θ)H⁢e-j⁢2⁢π⁢Δki⁢fsc⁢τ⁢d⁢θ⁢d⁢τ,i=0,⋯,NSF-1.(10)

Naturally, ∫0+∞∫−ππρ(θ, τ)dθdτ<+∞ due to the total channel power constraint. In practice, it is assumed that there is a largest delay spread threshold on the channel delay, denoted as τDS. Later, an asymptotic result is obtained by takin τDSto ∞. For a given τDS,

RΔki=∫0τDS∫-ππρ⁡(θ,τ)⁢a⁡(θ)⁢a⁡(θ)H⁢e-j⁢2⁢π⁢Δki⁢fsc⁢τ⁢d⁢θ⁢d⁢τ.(11)
RSFis a Hermitian. For the uplink (UL) and the downlink (DL) in FDD communication systems,

RΔkiU⁢L=∫0τD⁢S∫-ππρ⁡(θ,τ)⁢aU⁢L(θ)⁢aU⁢L(θ)H⁢e-j⁢2⁢π⁢Δki⁢fs⁢c⁢τ⁢d⁢θ⁢d⁢τ(12)RΔkiDL=∫0τDS∫-ππρ⁡(θ,τ)⁢aDL(θ)⁢aDL(θ)H⁢e-j⁢2⁢π⁢Δki⁢fsc⁢τ⁢d⁢θ⁢d⁢τ,(13)
where the entries for aUL(θ) and aDL(θ) are expressible as

amU⁢L(θ)=e-j⁢2⁢πλU⁢L⁢k⁡(θ)TumandamD⁢L(θ)=e-j⁢2⁢πλD⁢L⁢k⁡(θ)Tum,
respectively.

According to an example embodiment, methods and apparatus for obtaining the spatial-frequency covariance matrix RSFof a FDD communication system are provided. The spatial-frequency covariance matrix may be determined in accordance with measurements of the channels made at difference subcarriers.

FIG.3illustrates an example process300for generating the spatial-frequency covariance of a communication system. Process300may be used in FDD or multiband communication systems. Process300may also be used as input for TDD systems. Process300includes a frequency domain channel estimation unit305, a time-frequency offset compensation unit310, a spatial-frequency vectorization unit315, and a spatial-frequency correlation unit320. Frequency domain channel estimation unit305is configured to derive channel estimates (in the frequency domain) of the channels of the communication system from received signals. Time-frequency offset compensation unit310is configured to provide compensation for the time offsets present in the channel estimates. Spatial-frequency vectorization unit315is configured to vectorize the time compensated channel estimates. Spatial-frequency correlation unit320is configured to correlate the vectorized channel estimates to determine the spatial-frequency covariance.

FIG.4illustrates an exemplary space-frequency frame structure400of a communication system as a function of time and frequency.FIG.4also illustrates space-frequency covariance. Space-frequency diagram400displays MT distinct time-frequency frames405-407, one for each of the MT transmit antennas. Also illustrated inFIG.4are time-frequency resources used for estimating the channels, such as resources410-413of time-frequency frame407, as well as similar resources of time-frequency frames405and406. The space-frequency covariance, including the cross correlations, for the resources on different subcarriers and different antennas are illustrated inFIG.4as arrowed lines (for example, arrowed lines420and similar arrowed lines of time-frequency frames405and406). The resources used for estimating the channels are pilot signals that are usually separated by a constant number of subcarriers. The space-frequency covariance depends on the frequency difference between subcarriers and not arbitrary subcarrier locations. As an example resource410is spaced one subcarrier away from resource411, which is spaced one subcarrier away from resource412, and so on.

According to an embodiment, a conversion of the spatial-frequency covariance for a first frequency band to the spatial-frequency covariance for a second frequency band is provided. The ability to convert an existing spatial-frequency covariance to another spatial-frequency covariance may eliminate training requirements, thereby reducing computational requirements and communication overhead, and improve overall communication performance. As an example, in a FDD communication system, the spatial-frequency covariance for an uplink channel may be obtained using uplink transmissions and computations. However, because the instantaneous channel for the downlink is not known, UE measurements and feedback are needed to determine the spatial-frequency covariance in the downlink. Being able to convert the spatial-frequency covariance for the uplink channel from uplink measurement into the spatial-frequency covariance for the downlink channel without UE measurement and feedback would facilitate the efficient channel training and reduce training and feedback overhead. As another example, the spatial-frequency covariance for a first frequency band may be converted from the spatial-frequency covariance for a second frequency band, again with similar savings in computational resources and communication overhead.

Although the discussion focuses on spatial and frequency domain conversion, the example embodiments presented herein are also operable with single domain conversion. As an example, in a situation where the first frequency band and the second frequency band are the same, then spatial-frequency domain conversion becomes only spatial domain conversion (because the frequency domain does not change). Therefore, the discussion of spatial-frequency domain conversion should not be construed as being limiting to the scope of the example embodiments.

FIG.5illustrates a flow diagram of example operations500occurring in a device converting spatial-frequency covariance RSF. Operations500may be indicative of operations occurring in a device as the device converts the spatial-frequency covariance. The device may be an access node. The device may also be a UE (or other similar devices). The device may alternatively be a separate device configured for generating spatial-frequency covariance for communicating devices utilizing information provided by the communicating devices. As an example, the device may be a device located in the communication system dedicated to receiving channel information from communicating devices and converting spatial-frequency covariance for the communicating devices.

Operations500begin with the device obtaining a spatial-frequency covariance of the uplink RSFUL(block505). The device may make channel measurements and generate the spatial-frequency covariance based on transmissions occurring in the uplink. As an example, the device may include an implementation of process300ofFIG.3to generate spatial-frequency covariance. Alternatively, the device may receive channel measurements or frequency domain channel estimates from a communicating device and the device generates the spatial-frequency covariance based on the channel measurements or the frequency domain channel estimates. As an example, the device may include an implementation of process300ofFIG.3to generate spatial-frequency covariance from the received channel measurements or the frequency domain channel estimates.

The device estimates the power angle delay spectrum (PADS) for the uplink (block507). In an embodiment, a technique based on a projection onto the Hilbert space is utilized to estimate the PADS. Without specifying any one particular carrier frequency band, the spatial-frequency covariance is vectorized and is expressible as
r=vec([{{RSF},{RSF}]),
where vec (X) denotes a vectorizing operation that vectorizes the matrix X into a vector. The n-th entry of r, rn, is then expressible as
rn=∫0τDS∫−ππρ(θ,τ)gn(θ,τ)dθdτ,n=1, . . . ,N,(14)
where gn(θ, τ) is the entry of vectorized angular and delay term

c⁢a⁡(θ)⁢a⁡(θ)H⁢e-j⁢2⁢π⁢Δki⁢fs⁢c⁢τ
corresponds to rn, with real and imaginary parts separated, i.e., the mapping from [−π, π]×[0, τDS]→, c is the normalization factor which is defined as, and N is total number of entries rUL,i.e., N=2 (M2−M)NSF. The normalization is a scaling factor, which may not affect the results for any given τDSbecause the normalization simply scales the PADS with a common factor. The normalization will be scaled back with the conversion. However, the normalization is important to form the solution when τDSgoes to infinity.

A Hilbert spaceof a real function in L2space with inner product is defined, and is expressible as
(f,g=∫0τDS∫−ππf(θ,τ)g(θ,τ)dθdτ.(15)
The L−2 norm is then defined as

f2=Δ〈f,f〉=∫0τD⁢S∫-ππf2(θ,τ)⁢d⁢θ⁢d⁢τ.(16)
Equation (14) may be rewritten as
rn=ρ,gn,n=1, . . . ,N.(17)
Then, for the uplink,
rnUL=ρ,gnUL,n=1, . . . ,N(18)
where gnULis the entry of

caUL(θ)⁢aUL(θ)H⁢e-j⁢2⁢π⁢Δki⁢fsc⁢τ
corresponding to rnUL.

Therefore, the problem becomes: for a given {rnUL} and {gnUL(θ, τ)}, the PADS ρ(θ, T) is estimated. The solution involves solving a linear equation array if the PADS ρ is a discrete vector of the quantized pair (θ, τ). However, {ρ(θ, τ)} is a continuous function of the 2-D variables (θ, τ), and the problem becomes intractable with conventional methods.

In order to solve the PADS estimation in Equation (18), the problem may be reformulated and solve the problem with the projection method in Hilbert space. First, without loss of generality, it is assumed that gnUL(θ, τ), n=1, . . . , N′ are the linearly independent vector subset of all gnUL(θ, τ), n=1, . . . , N. Then the subspace V of ρ∈specified by {gnUL(θ, τ)}n=1N′is defined as

V=△⋂n=1N⁢Vn⁢Vn=△{ρ∈ℋ:〈ρ,gnUL〉=rnUL},n=1⁢…,N′.(19)

To obtain the estimation of PADS ρ(θ, T), the minimum norm criterion is considered, i.e.,

ρˆ(θ,τ)=argminρ∈Vρ2,(20)
where the subspace V is defined in Equation (19). The solution of Equation (20) will be the orthogonal projection of PADS ρ(θ, τ) on the orthogonal subspace of the linear variety V, which will be the projection to the subspace V. The estimate of PADS is then expressible as

ρˆ(θ,τ)=∑n=1N′⁢αn⁢gnU⁢L(θ,τ),(21)
where {αn} are the solution of linear equations, which are expressible as

〈g1U⁢L,g1U⁢L〉⁢α1+〈g1U⁢L,g2U⁢L〉⁢α2+…+〈g1U⁢L,gNU⁢L〉⁢αN′=r1U⁢L⋮⋮〈gN′U⁢L,g1U⁢L〉⁢α1+〈gN′U⁢L,g2U⁢L〉⁢α2+…+〈gN′U⁢L,gN′U⁢L〉⁢αN′=rN′U⁢L.(22)

If α=[α1, . . . , αN′]T, the linear array of Equation (22) may be rewritten as
Gα=rUL,  (23)
where G is defined as

G=[〈g1UL,g1UL〉…〈g1UL,gN′UL〉⋮⋱⋮〈gN′UL,g1UL〉…〈gN′UL,gN′UL〉].(24)

The above linear equations (Equation (24)) are guaranteed to have at least one solution. From Equation (21), it is seen that the PADS can be represented as the weighted sum of independent basis functions of angles and delays, gnUL(θ, τ), with weights αn, n=1, . . . , N′. In mathematics, a basis function is an element of a particular basis for a function space. The basis functions may enable the representation of a more complex function based on the simpler basis functions. Every continuous function in the function space may be represented as a linear function of basis functions, just as every vector in a vector space may be represented as a linear combination of basis vectors. From equations (22)-(24), estimating PADS becomes estimating the weights α As explained before, gn(θ, τ) is the entry of vectorized angular and delay function of

ca⁡(θ)⁢a⁡(θ)H⁢e-j⁢2⁢π⁢Δki⁢fsc⁢τ
with real and imaginary parts separated. Therefore, the basis functions gn(θ, τ), n=1, . . . , N′, depend on the antenna structure, e.g. antenna positions, the carry frequency of the frequency band, and frequency lags Δki. In general, the basis functions do not change over the UEs. However, when the UE changes or the channel statistics for the UE changes, the power angle delay spectrum of the UE may still be represented as a linear combination in Equation (21) with the same basis functions gn(θ, T) but with different coefficients or weights αn.

The device determines a frequency domain conversion for the spatial-frequency covariance (block509). In order to obtain the spatial-frequency covariance in the downlink, it is assumed that the same PADS92(θ, τ) applies. After obtaining the estimated PADS {circumflex over (ρ)}(θ, τ), by using Equation (21), for example, the following is obtained for the downlink

rˆnD⁢L=〈ρˆ,gnD⁢L〉=∑n′=1N′⁢αn′⁢〈gn′U⁢L,gnD⁢L〉,(25)
where {circumflex over (r)}nDLis the estimate of n-th entry of rDLand rDL=vec ([{RSF},{RSF}]). Then, the vectorized spatial-frequency covariance in the downlink is expressible as
{circumflex over (r)}DL=Qα,(26)
where Q is the frequency domain conversion for the HiDi channel statistics and is expressible as

Q=[〈g1UL,g1DL〉…〈gN′UL,g1DL〉⋮⋱⋮〈gN′UL,gNDL〉…〈gN′UL,gNDL〉].(27)

The device converts the spatial-frequency covariance of the uplink to spatial-frequency covariance of the downlink (block511). The device may convert the spatial-frequency covariance of the uplink to the spatial-frequency covariance of the downlink by reforming the spatial-frequency covariance of the downlink from the vectorized spatial-frequency covariance in the uplink. As an example, the reforming of the spatial-frequency covariance in the downlink may proceed in a manner that is in reverse of the way that the vectorized spatial-frequency covariance in the uplink is formed. The device communicates in accordance with the spatial-frequency covariance of the downlink (block513). As an example, the device uses the spatial-frequency covariance of the downlink to perform training and facilitate downlink transmissions to other devices.

Although the discussion presented herein focuses on converting the spatial-frequency covariance in the downlink from the spatial-frequency covariance in the uplink, the example embodiments presented herein are operable for converting the spatial-frequency covariance of a first frequency band to the spatial-frequency covariance of a second frequency band. The conversion of the spatial-frequency covariance from the uplink spatial-frequency covariance to the downlink spatial-frequency covariance may be viewed as a special case of the first frequency band and the second frequency band, where the first frequency band is the uplink and the second frequency band is the downlink. Therefore, the discussion of uplink and downlink should not be construed as being limiting to the scope of the example embodiments.

FIG.6Aillustrates a flow diagram of example operations600occurring in a device estimating the PADS for the uplink. Operations600may be indicative of operations occurring in a device as the device estimates the PADS for the uplink. Operations600may be an example implementation of block507ofFIG.5. Although the discussion focuses on uplink and downlink, the example embodiments are operable for any two frequency bands. In such a situation, the uplink would be a first frequency band and the downlink would be a second frequency band.

Input to operations600may include the spatial-frequency covariance RSFUL, which may be determined in accordance with measurements of the uplink (block602). Operations600begin with the device selecting non-repeating entries of RSFULand vectorizing RSFULto form a real vector rSFUL(block605). The selection may be based on hermitian or other data structure, such as Toeplitz or block Teoplitz structures. As an example, the real vector rSFULis expressible as
rSFUL=Vec{{{RSFUL},{RSFUL}}.

The device forms an estimation matrix G (block607). The estimation matrix G may be formed in accordance with parameters of the communication system, including the antenna structure (such as aperture, spacing, polarization, etc.), carrier frequency of the uplink, configured frequency spacings or lags, and so on). As an example, estimation matrix G may be formed as shown in Equation (24).

The device estimates the PADS (block609). The estimation of the PADS may be performed in accordance with the real vector rSFULand the estimation matrix G, and may include solving Equation (23), for example. The estimated PADS is as expressed as Equation (21). The device outputs the estimation output α (block611). The device outputs the weights α of the estimated PADS, for example.

FIG.6Billustrates a flow diagram of example operations650occurring in a device converting the spatial-frequency covariance for the uplink RD to the spatial-frequency covariance for the downlink RSFDL. Operations65omay be indicative of operations occurring in a device as the device converts the spatial-frequency covariance for the uplink RSFDLto the spatial-frequency covariance for the downlink RD. Operations650may be an example implementation of blocks509and511ofFIG.5. Although the discussion focuses on uplink and downlink, the example embodiments are operable for any two frequency bands. In such a situation, the uplink would be a first frequency band and the downlink would be a second frequency band.

Input to operations65omay include the estimation output α, such as produced by a device performing block611ofFIG.6A(block652). Operations650begin with the device forming a conversion matrix Q (block655). The conversion matrix may be formed in accordance with parameters of the communication system, including the antenna structure (such as aperture, spacing, polarization, etc.), carrier frequency of the uplink and the downlink, configured frequency spacings or lags, and so on). As an example, the conversion matrix Q may be formed as shown in Equation (27).

The device obtains the vectorized form of the spatial-frequency covariance for the downlink rSFDL(block657). The vectorized form of the spatial-frequency covariance being obtained by multiplying the estimation output α (provided as input to operations650) and the conversion matrix Q formed in block655, and may be expressible as rDL=Qα, for example. The device reforms the spatial-frequency covariance matrix RSFDL(block659). The RSFDLmay be reformed from the vectorized form of the spatial-frequency covariance for the downlink rSFDL. The RSFDLmay be formed in a reverse manner from forming the spatial-frequency covariance for the uplink rSFULwith rSFUL=Vec{{{RSFDL},{RSFUL}}, such as in block605ofFIG.6A, for example. As an example, RD may be formed using a reversal of the process used to determine rSFUL=Vec{{{RSFUL},{RSFUL}}. In other words, given that rSFULis known, RSFDLmay be determined.

It is also possible to obtain solutions for general array configurations. If it is defined that

φm,m′(θ)=△k⁡(θ)T⁢um-k⁡(θ)T⁢um′,
men gnUL(θ, τ) as an entry of

vec⁡({ca⁡(θ)⁢a⁡(θ)H⁢e-j⁢2⁢π⁢Δki⁢fs⁢c⁢τ},{ca⁡(θ)⁢a⁡(θ)H⁢e-j⁢2⁢π⁢Δki⁢fs⁢c⁢τ})
may be represented as

gnUL(θ,τ)=12⁢π⁢τD⁢S⁢cos⁡(2⁢πλUL⁢φm,m′(θ)+2⁢π⁢Δki⁢fs⁢c⁢τ)(28)
for the real term, and

gnUL(θ,τ)=-12⁢π⁢τDS⁢sin⁡(2⁢πλUL⁢φm,m′(θ)+2⁢π⁢Δki⁢fs⁢c⁢τ)(29)
for the imaginary term.

So there is one-one mapping between n and four tuple {m, m′, i, IR/I} where IR/Iindicates whether it is an entry corresponding to the real term or imaginary term. An explicit expression for the mapping is not defined, rather it is simply defined as n=M(m, m′, i, IR/I) for the purpose of general presentation. Also for any given finite τDS, the normalization factor does not impact the results as it just scales every entry of G and Q matrices with the same value. However, as will be seen below, it is critical to obtain the asymptotic results when the case τDS→∞ is considered.

Due to separation of the real and imaginary parts, the matrix G in Equation (24) can be expressed as

G=[].(30)

The entries inare expressible as

[]n1,n2=〈gn1UL,gn2UL〉=12⁢π⁢τD⁢S⁢∫0τD⁢S∫-ππ[]n1,n2⁢(θ,τ)⁢d⁢θ⁢d⁢τ,(31)where[]n1,n2⁢(θ,τ)=cos⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢π⁢Δki1⁢fsc⁢τ)⁢cos⁡(2⁢πλUL⁢φm2,m2′(θ)+2⁢π⁢Δki2⁢fs⁢c⁢τ)=12⁢{cos(2⁢π(Δki1-Δki2)⁢fs⁢c⁢τ)⁢cos(2⁢πλUL⁢(φm1,m1′(θ)-φm2,m2′(θ)))-sin(2⁢π(Δki1-Δki2)⁢fs⁢c⁢τ)⁢sin⁡(2⁢πλUL⁢(φm1,m1′(θ)-φm2,m2′(θ)))+cos(2⁢π(Δki1+Δki2)⁢fs⁢c⁢τ)⁢cos⁡(2⁢πλUL⁢(φm1,m1′(θ)+φm2,m2′(θ)))-sin(2⁢π(Δki1+Δki2)⁢fs⁢c⁢τ)⁢sin⁡(2⁢πλUL⁢(φm1,m1′(θ)+φm2,m2′⁢2⁢(θ)))}.
Therefore, the entries ofare expressible as

[]n1,n2=12⁢{sin⁢c(2⁢π(Δki1-Δki2)⁢fs⁢c⁢τD⁢S)⁢Fm1,m1′,m2,m2′c-(λUL)+1-cos(2⁢π(Δki1-Δki2)⁢fs⁢c⁢τD⁢S)2⁢π(Δki1-Δki2)⁢fs⁢c⁢τD⁢S⁢Fm1,m1′,m2,m2′,s-(λUL)+sin⁢c(2⁢π(Δki1+Δki2)⁢fs⁢c⁢τD⁢S)⁢Fm1,m1′,m2,m2′c+(λU⁢L)+1-cos(2⁢π(Δki1+Δki2)⁢fs⁢c⁢τD⁢S)2⁢π(Δki1+Δki2)⁢fs⁢c⁢τD⁢S⁢Fm1,m1′,m2,m2′s+(λUL)},(32)wherem1,m1′,m2,m2′c-(λ)=12⁢π⁢∫-ππcos⁡(2⁢πλ⁢(φm1,m1′(θ)-φm2,m2′(θ)))⁢d⁢θ,(33)m1,m1′,m2,m2′s-(λ)=12⁢π⁢∫-ππsin⁡(2⁢πλ⁢(φm1,m1′(θ)-φm2,m2′(θ)))⁢d⁢θ,m1,m1′,m2,m2′c+(λ)=12⁢π⁢∫-ππcos⁡(2⁢πλ⁢(φm1,m1′(θ)+φm2,m2′(θ)))⁢d⁢θ,m1,m1′,m2,m2′s+(λ)=12⁢π⁢∫-ππsin⁡(2⁢πλ⁢(φm1,m1′(θ)+φm2,m2′(θ)))⁢d⁢θ.
Similarly,

[]n1,n2⁢(θ,τ)=△-cos⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢πΔki1⁢fsc⁢τ)⁢sin⁡(2⁢πλUL⁢φm2,m2′(θ)+2⁢π⁢Δki2⁢fsc⁢τ)(34)[]n1,n2⁢(θ,τ)=△-sin⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢π⁢Δki1⁢fsc⁢τ)⁢cos⁡(2⁢πλUL⁢φm2,m2′(θ)+2⁢π⁢Δki2⁢fsc⁢τ)(35)[]n1,n2⁢(θ,τ)=△sin⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢π⁢Δki1⁢fsc⁢τ)⁢sin⁡(2⁢πλUL⁢φm2,m2′(θ)+2⁢π⁢Δki2⁢fsc⁢τ).(36)Then[]n1,n2=12⁢π⁢τDS⁢∫0τDS∫-ππ[]n1,n2⁢(θ,τ)⁢d⁢θ⁢d⁢τ=12⁢{-1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′c-(λUL)+sin⁢c⁢(2⁢π(Σki1-Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s-(λUL)⁢1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′c+(λUL)-sin⁢c⁢(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s+(λUL)},(37)[]n1,n2=12⁢π⁢τDS⁢∫0τDS∫-ππ[]n1,n2⁢(θ,τ)⁢d⁢θ⁢d⁢τ=12⁢{1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′c-(λUL)-sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s-(λUL)⁢1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′c+(λUL)-sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s+(λUL)},[]n1,n2=12⁢π⁢τDS⁢∫0τDS∫-ππ[]n1,n2⁢(θ,τ)⁢d⁢θ⁢d⁢τ=12⁢{sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′c-(λUL)+1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′s-(λUL)-sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′c+(λUL)-1-cos⁢(2⁢π⁢(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′s+(λUL)}.
For some special entries when

Δki1=Δki2,
the following are valid

sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)=1,(38)1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDS=0,(39)
and when

Δki1=Δki2=0,
the following are valid

sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)=1,(40)1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDS=0.(41)

In order to obtain the conversion matrix Q, again due to separation of the real and imaginary components, the block matrix is rewritten as

Q=[Qℛ𝒥Q𝒥ℛQ𝒥𝒥].(42)
The first entries inare expressible as

[]n1,n2=〈gn1UL,gn2DL〉=12⁢π⁢τDS⁢∫0τDS∫-ππ[]n1,n2⁢(θ,τ)⁢d⁢θ⁢d⁢τ,(43)where[]n1,n2⁢(θ,τ)=cos⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢π⁢Δki1⁢fsc⁢τ)⁢cos⁡(2⁢πλDL⁢φm2,m2′(θ)+2⁢π⁢Δki2⁢fsc⁢τ)=12⁢{cos(2⁢π(Δki1-Δki2)⁢fsc⁢τ)⁢cos⁡(2⁢πλUL⁢φm1,m1′(θ)-2⁢πλDL⁢φm2,m2′(θ))-sin(2⁢π(Δki1-Δki2)⁢fsc⁢τ)⁢sin⁡(2⁢πλUL⁢φm1,m1′(θ)-2⁢πλUL⁢φm2,m2′(θ))+cos(2⁢π(Δki1+Δki2)⁢fsc⁢τ)⁢cos⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢πλUL⁢φm2,m2′(θ))-sin(2⁢π(Δki1+Δki2)⁢fsc⁢τ)⁢sin⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢πλUL⁢φm2,m2′(θ))}.

The entries inare expressible as

[]n1,n2=12⁢{sin⁢c⁢(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′c-(λUL,λDL)+1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′s-(λUL,λDL,)+sin⁢c⁢(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′c+(λUL,λDL)+1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′s+(λUL,λDL)},wherem1,m1′,m2,m2′c-(λ1,λ2)=12⁢π⁢∫-ππcos⁡(2⁢πλ1⁢φm1,m1′(θ)-2⁢πλ2⁢φm2,m2′(θ))⁢d⁢θ,(45)m1,m1′,m2,m2′s-(λ1,λ2)=12⁢π⁢∫-ππsin⁡(2⁢πλ1⁢φm1,m1′(θ)-2⁢πλ2⁢φm2,m2′(θ))⁢d⁢θ,m1,m1′,m2,m2′c+(λ1,λ2)=12⁢π⁢∫-ππcos⁡(2⁢πλ1⁢φm1,m1′(θ)+2⁢πλ2⁢φm2,m2′(θ))⁢d⁢θ,m1,m1′,m2,m2′s+(λ1,λ2)=12⁢π⁢∫-ππsin⁡(2⁢πλ1⁢φm1,m1′(θ)+2⁢πλ2⁢φm2,m2′(θ))⁢d⁢θ.

The following are defined

[]n1,n2⁢(θ,τ)=-cos⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢π⁢Δki1⁢fsc⁢τ)⁢sin⁡(2⁢πλDL⁢φm2,m2′(θ)+2⁢π⁢Δki2⁢fsc⁢τ)⁢[F~21]n1,n2⁢(θ,τ)=-sin⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢π⁢Δki1⁢fsc⁢τ)⁢cos⁡(2⁢πλDL⁢φm2,m2′(θ)+2⁢π⁢Δki2⁢fsc⁢τ)⁢[]n1,n2⁢(θ,τ)=sin⁡(2⁢πλUL⁢φm1,m1′(θ)+2⁢π⁢Δki1⁢fsc⁢τ)⁢sin⁡(2⁢πλDL⁢φm2,m2′(θ)+2⁢π⁢Δki2⁢fsc⁢τ).(46)

Similarly, the other three subblock matrices of Q are expressible as

[]n1,n2=12⁢π⁢τDS⁢∫0τDS∫-ππ[]n1,n2⁢(θ,τ)⁢d⁢θ⁢d⁢τ=12⁢{-1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′c-(λUL,λDL)+sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s-(λUL,λDL,)+1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′c+(λUL,λDL)-sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s+(λUL,λDL)},(47)-sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s+(λUL,λDL)},[]n1,n2=12⁢π⁢τDS⁢∫0τDS∫-ππ[F~21]n1,n2⁢(θ,τ)⁢d⁢θ⁢d⁢τ=12⁢{1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′c-(λUL,λDL)-sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s-(λUL,λDL,)+1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′c+(λUL,λDL)-sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′s+(λUL,λDL)},(48)[]n1,n2=12⁢π⁢τDS⁢∫0τDS∫-ππ[]n1,n2⁢(θ,τ)⁢d⁢θ⁢d⁢τ=12⁢{sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′c-(λUL,λDL)+1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′s-(λUL,λDL,)-sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)m1,m1′,m2,m2′c+(λUL,λDL)-1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDSm1,m1′,m2,m2′s+(λUL,λDL)}.(49)

In the general case, the largest delay spread may go to infinity, i.e., τDS→∞. Because the function gn(θ, τ) is normalized with τDS, it is now possible to take limit of τDS→∞ on the results obtained above. The asymptotic results for the following four terms, together with above special cases, are expressible as

limτDS→"\[Rule]"+∞sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)={1,Δki1=Δki2;0,Δki1≠Δki2,(50)limτDS→"\[Rule]"+∞sin⁢c⁢(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)=1,Δki1=Δki2=0;0,otherwise,(51)limτDS→"\[Rule]"+∞1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDS=0,(52)limτDS→"\[Rule]"+∞1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDS=0.(53)

Then for the G matrix, when

Δki1≠Δki2,
the following is known
[]n1,n2=[]n1,n2=[]n1,n2=[]n1,n2=0.  (54)
When

Δki1=Δki2,
the following is known

[]n1,n2={12m1,m1′,m2,m2′c-(λUL)+12m1,m1′,m2,m2′c+(λUL),Δki1=Δki2=0,12m1,m1′,m2,m2′c-(λUL),Δki1=Δki2≠0;(55)[]n1,n2={12m1,m1′,m2,m2′s-(λUL)-12m1,m1′,m2,m2′s+(λUL),Δki1=Δki2=0,12m1,m1′,m2,m2′s-(λUL),Δki1=Δki2≠0;(56)[]n1,n2={-12m1,m1′,m2,m2′s-(λUL)+12m1,m1′,m2,m2′s+(λUL),Δki1=Δki2=0,-12m1,m1′,m2,m2′s-(λUL),Δki1=Δki2≠0;(57)[]n1,n2={12m1,m1′,m2,m2′c-(λUL)-12m1,m1′,m2,m2′c+(λUL),Δki1=Δki2=0,12m1,m1′,m2,m2′c-(λUL),Δki1=Δki2≠0.(58)

From Equation (58), for cases

Δki1=Δki2≠0,
the entries of submatrices []n1,n2are the exact same as those of []n1,n2.

Similarly for the conversion matrix Q, when

Δki1≠Δki2,
the following is known
[]n1,n2=[]n1,n2=[]n1,n2=[]n1,n2=0.  (59)
When

Δki1=Δki2,
the following is known

[]n1,n2={12m1,m1′,m2,m2′c-(λUL,λDL)+12m1,m1′,m2,m2′c+(λUL,λDL),Δki1=Δki2=0,12m1,m1′,m2,m2′c-(λUL,λDL),Δki1=Δki2≠0;(60)[]n1,n2={12m1,m1′,m2,m2′s-(λUL,λDL)-12m1,m1′,m2,m2′s+(λUL,λDL),Δki1=Δki2=0,12m1,m1′,m2,m2′s-(λUL,λDL),Δki1=Δki2≠0;(61)[]n1,n2={-12m1,m1′,m2,m2′s-(λUL,λDL)+12m1,m1′,m2,m2′s+(λUL,λDL),Δki1=Δki2=0,-12m1,m1′,m2,m2′s-(λUL,λDL),Δki1=Δki2≠0;(62)[]n1,n2={12m1,m1′,m2,m2′c-(λUL,λDL)-12m1,m1′,m2,m2′c+(λUL,λDL),Δki1=Δki2=0,12m1,m1′,m2,m2′c-(λUL,λDL),Δki1=Δki2≠0.(63)

From Equations (54) and (59), it is seen that the off-diagonal submatrices in the estimation and conversion matrices are all zero now. The advantage of this result is that the power angle delay spectrum can be estimated independently for each frequency lag. For example for

Δki1=Δki2=0,
number delay is exactly the same as the estimated power angle delay as the delay information is absent in R0UL, with Δki=0. As the dimension increases, the computation complexity increases exponentially. With the frequency lag independent estimation and conversion in the asymptotic results, the complexity increases only linearly on the frequency lags for HiDi spatial-frequency covariance. The complexity is then very low for the high dimensional data processing. However, because the estimation and conversion are independent over different frequency lags, the estimation of

RΔki
on one Δkidoes not help the estimation on the other frequency.

FIG.7Aillustrates a flow diagram of example operations700occurring in a device estimating the PADS for the uplink with asymptotic solutions. Operations700may be indicative of operations occurring in a device as the device estimates the PADS for the uplink with asymptotic solutions. Based on the asymptotic solutions, the estimation PADS can be performed independently for each frequency lag with the covariance submatrices

RΔkiUL⁢in⁢RSFUL.
operations700may De an example implementation of block507ofFIG.5. Although the discussion focuses on uplink and downlink, the example embodiments are operable for any two frequency bands. In such a situation, the uplink would be a first frequency band and the downlink would be a second frequency band.

Input to operations700may include the spatial-frequency covariance RSFUL, which may be determined in accordance with measurements of the uplink (block702). Operations700begin with the device obtaining the subblock matrices of the spatial-frequency covariance RSFUL(block705). The device may decompose the spatial-frequency covariance RD to obtain the subblock matrices, which are denoted RSF,ΔkiULfor example. The device selects non-repeating entries of RSF,ΔkiULand vectorizing RSF,ΔkiULto form real vectors rSF,ΔkiUL(block707). The selection may be based on hermitian or other data structure, such as Toeplitz or block Teoplitz structures. As an example, the real vectors rSF,ΔkiULis expressible as
rSF,ΔkiUL={{{RSF,ΔkiUL},{RSF,ΔkiUL}},i=1, . . . ,NSF.

The device forms an estimation matrices GΔki(block709). The estimation matrices GΔkimay be formed for each frequency lag and may be formed in accordance with parameters of the communication system, including the antenna structure (such as aperture, spacing, polarization, etc.), carrier frequency of the uplink, configured frequency spacings or lags, and so on). As an example, estimation matrices GΔkimay be formed as shown in Equation (30).

The device estimates the PADS (block711). The estimation of the PADS may be performed in accordance with the real vectors rSF,ΔkiULand the estimation matrices GΔki, and may include solving the equation GΔkiαΔki=rSF,ΔkiULand obtain the PADS in a form of equation {circumflex over (p)}Δki(θ, τ)=ΣnαΔki,ngΔki,n(θ, τ), for example. The device outputs the estimation outputs αΔki=1, . . . , NSF(block713). The device outputs the weights αΔkiof the estimated PADS, for example.

FIG.7Billustrates a flow diagram of example operations750occurring in a device converting the spatial-frequency covariance for the uplink RSFULto the spatial-frequency covariance for the downlink RSFDL, with asymptotic solutions. Based on the asymptotic solutions, the frequency domain conversion can be performed independently for each frequency lag to obtain the covariance submatrices

RΔkiDL⁢in⁢RSLDL.
Operations750may be indicative of operations occurring in a device as the device converts the spatial-frequency covariance for the uplink RSFULto the spatial-frequency covariance for the downlink RSFDL, with asymptotic solutions. Operations750may be an example implementation of blocks509and511ofFIG.5. Although the discussion focuses on uplink and downlink, the example embodiments are operable for any two frequency bands. In such a situation, the uplink would be a first frequency band and the downlink would be a second frequency band.

Input to operations750may include the estimation outputs αΔki=1, . . . , NSF, such as produced by a device performing block713ofFIG.7A(block752). Operations750begin with the device forming conversion matrices QΔki(block755). The conversion matrices may be formed for each frequency lag in accordance with parameters of the communication system, including the antenna structure (such as aperture, spacing, polarization, etc.), carrier frequency of the uplink and the downlink, configured frequency spacings or lags, and so on). As an example, the conversion matrices QΔkimay be formed as shown in Equation (42) and Equations (60)-(63).

The device obtains the subblock matrices of the vectorized form of the spatial-frequency covariance for the downlink rSF,ΔkiDL(block757). The vectorized form of the spatial-frequency covariance being obtained by multiplying the estimation outputs αΔki(provided as input to operations750) and the conversion matrices QΔkiformed in block755, and may be expressible as rSF,ΔkiDL=QΔkiαΔkifor example. The device reforms the subblock matrices of the spatial-frequency covariance matrix for each frequency lag RSF,ΔkiDL(block759). The RSF,ΔkiDLmay be reformed from the vectorized form of the spatial-frequency covariance for the downlink rSF,ΔkiDL. The RSF,ΔkiDLmay be formed in a reverse manner from forming the spatial-frequency covariance for the uplink rSFDLwith rSF,ΔkiUL={{{RSF,ΔkiUL},{RSF,ΔkiUL}}, such as in block707ofFIG.7A, for example. The device reconstructs the spatial-frequency covariance in the downlink (block761). The spatial-frequency covariance in the downlink RSFDLmay be reconstructed from the converted subblock matrices RSF,ΔkiDL, i=1, . . . , NSF, for example.

According to an example embodiment, conversions of spatial-frequency covariance for multi-panel antenna arrays are provided. In addition to the conversion in the frequency domain (i.e., estimate the spatial-frequency covariance in one carrier frequency and convert the spatial-frequency covariance to another carrier frequency), the example embodiments presented herein are operable for conversions in the spatial domain. In a first embodiment, two antenna panels serve different frequency bands. In such an embodiment, the related antenna locations in a first antenna panel may not be the same as the antenna locations in a second antenna panel.

FIGS.8A and8Billustrate antenna panels with the antenna panels serving different frequency bands. A first antenna panel800(shown inFIG.8A) includes antennas805that serve a first frequency band and a second antenna panel810(shown inFIG.8B) includes antennas815that serve a second frequency band. First antenna panel800and second antenna panel810have different antenna placements.FIG.8Cillustrate a third antenna panel820serving two different frequency bands. Third antenna panel820includes a plurality of antennas825. Plurality of antennas825comprise a first subset of antennas (shown as solid X's) and a second subset of antennas (shown as dashed X's), where the first subset of antennas serves a third frequency band and the second subset of antennas serves a fourth frequency band.

In the second scenario, the two antenna panels have different steering directions, i.e., facing towards the different angles.FIGS.9A and9Billustrate antenna panels with different steering directions. A first antenna panel900(shown inFIG.9A) has antennas905serving a first steering direction (θ1, ϕ1)907, and a second antenna panel910(shown inFIG.9B) antennas915serving a second steering direction (θ2, ϕ2)917.

For the discussion of either scenario, it is assumed that the far field assumption still holds for both panels so that each anenna array experiences the same physical power angle delay channel spectrum, with the difference being on the antenna array response.

In the scenario with multiple antenna arrays with different antenna locations (as depicted inFIGS.8A-8C), the estimation of the PADS for one panel is the same as discussed previously. A difference in the process lies with the conversion. The frequency conversion and the spatial conversion are discussed together.

FIG.10illustrates a flow diagram of example operations moo occurring in a device converting spatial-frequency covariance where the device has two antenna panels serving different frequency bands. Operations moo may be indicative of operations occurring in a device (such as an access node, a UE, or a dedicated device configured to convert spatial-frequency covariance) as the device converts spatial-frequency covariance, where the device has two antenna panels serving different frequency bands. Although the discussion focuses on two antenna panels, the example embodiments are operable in a situation were the device has an antenna array with two subsets of antenna elements, with each subset serving a different frequency band. Therefore, the discussion of antenna panels should not be construed as being limiting to the scope of the example embodiments.

Operations moo begin with the device obtaining a spatial-frequency covariance of a first antenna panel, e.g., antenna panel A, RSFA(block1005). The device may make channel measurements and generate the spatial-frequency covariance based on transmissions occurring in a first frequency band. As an example, the device may include an implementation of process300ofFIG.3to generate spatial-frequency covariance. Alternatively, the device may receive channel measurements or frequency domain channel estimates from a communicating device and the device generates the spatial-frequency covariance based on the channel measurements or the frequency domain channel estimates. As an example, the device may include an implementation of process300ofFIG.3to generate spatial-frequency covariance from the received channel measurements or the frequency domain channel estimates.

The device estimates the PADS for the antenna panel A in the first frequency band (block1007). The estimated PADS for the antenna panel A may be determined in accordance with the spatial-frequency covariance of the first antenna panel A in the first frequency band. In an embodiment, a technique based on a projection onto the Hilbert space is utilized to estimate the PADS. As an example the device may include an implementation of process600inFIG.6Ato estimate PADS based on whole RSFA, or an implementation of process650inFIG.6Bto estimate PADS for each frequency lag with the subblock matrices in RSF,ΔkiAin RSFAfor each frequency lag.

The device determines a domain conversion for the spatial-frequency covariance (block1009). The domain conversion converts the space and frequency domains of the spatial-frequency covariance of the first antenna panel A in the first frequency domain to spatial-frequency covariance of a second antenna panel B in a second frequency domain. In addition to determining the domain conversion, the device may also determine if single domain conversion or joint domain conversion is being performed. As an example, single domain conversion involves only spatial domain conversion, while joint domain conversion involves both spatial and frequency domain conversion. The device converts the spatial-frequency covariance of the first antenna panel A in the first frequency band to spaital-frequency covariance of the second antenna panel B in the second frequency band (block mu). The device may convert the spatial-frequency covariance of the first antenna panel A in the first frequency band to the spatial-frequency covariance of the second antenna panel B in the second frequency band by reforming the spatial-frequency covariance of the second antenna panel B in the second frequency band from the vectorized spatial-frequency covariance of the first antenna panel A in the first frequency band. As an example, the reforming of the spatial-frequency covariance of the second antenna panel B in the second frequency band may proceed in a manner that is in reverse of the way that the vectorized spatial-frequency covariance of the first antenna panel A in the first frequency band is formed. The device communicates in accordance with the spatial-frequency covariance of the second antenna panel B in the second frequency band (block1013). As an example, the device uses the spatial-frequency covariance of the second antenna panel B in the second frequency band to perform training and facilitate downlink transmissions to other devices.

FIG.11Aillustrates a flow diagram of example operations1100occurring in a device converting spatial-frequency covariance in the spatial and frequency domains for two antenna panels at different locations. Operations1100may be indicative of operations occurring in a device (such as an access node, a UE, or a dedicated device configured to convert spatial-frequency covariance) as the device converts spatial-frequency covariance, where the device has two antenna panels located at different locations. Operations1100may be also indicative of operations occurring in two devices as a processor in central unit that connects the two devices or a processor in one device that connect the other device. Although the discussion focuses on two antenna panels, the example embodiments are operable in a situation were the device has an antenna array with two subsets of antenna elements, with each subset serving a different frequency band. Therefore, the discussion of antenna panels should not be construed as being limiting to the scope of the example embodiments.

Input to operations1100may include the PADS estimation output α for the first antenna panel A, where the PADS estimation output may be based on the RSF,AUL, from measurements made on the first antenna panel A in the first frequency band (block1102). Operations1100begin with the device forming a conversion matrix(block1105). The conversion matrix may be formed in accordance with the antenna structure of the first antenna panel A and a second antenna panel B (such as aperture, spacing, polarization, antenna element spacing, etc.), carrier frequencies of the first antenna band and the second antenna band, configured frequency spacings or lags, and so on).

The device obtains the vectorized form of the spatial-frequency covariance of the second antenna panel B in the second frequency band rSF,BUL(block1107). The vectorized form of the spatial-frequency covariance being obtained by multiplying the PADS estimation output α (provided as input to operations1100) and the conversion matrixformed in block1105, and may be expressible as rSF,BDL=α, for example. The device reforms the spatial-frequency covariance matrix RSF,BDL(block1109). The RSF,BDLmay be reformed from the vectorized form of the spatial-frequency covariance of the second antenna panel B in the second frequency band rSF,BDL. The rSF,BDLmay be formed in a reverse manner from forming the spatial-frequency covariance for the first antenna panel A in the first frequency band rSF,AULwith rSF,AUL=Vec{{RSF,AUL},{RSF,AUL}}, for example.

FIG.11Billustrates a flow diagram of example operations1150occurring in a device converting spatial-frequency covariance in the spatial and frequency domains for two antenna panels with different locations, with asymptotic solutions. Operations1150may be indicative of operations occurring in a device (such as an access node, a UE, or a dedicated device configured to convert spatial-frequency covariance) as the device converts spatial-frequency covariance, with asymptotic solutions, where the device has two antenna panels located at different locations. Although the discussion focuses on two antenna panels, the example embodiments are operable in a situation were the device has an antenna array with two subsets of antenna elements, with each subset serving a different frequency band. Therefore, the discussion of antenna panels should not be construed as being limiting to the scope of the example embodiments.

Input to operations1150may include the PADS estimation outputs αΔki=1, . . . , NSF(block1152). Operations1150begin with the device forming conversion matricesΔki(block1155). The conversion matrices may be formed for each frequency lag in accordance with parameters of the communication system, including the antenna structure (such as aperture, antenna element spacing, polarization, etc.), carrier frequency of the first frequency band and the second frequency band, configured frequency spacings or lags, and so on).

The device obtains the subblock matrices of the vectorized form of the spatial-frequency covariance of the second antenna panel B in the second frequency band rSF,B,ΔkiDL(block1157). The vectorized form of the spatial-frequency covariance may be obtained for different locations, such as at the different antenna element locations. The vectorized form of the spatial-frequency covariance being obtained by multiplying the PADS estimation output α (provided as input to operations1150) and the conversion matrixΔkiformed in block1155, and may be expressible as rSF,B,ΔkiDL=ΔkiαΔki, for example. The device reforms the subblock matrices of the spatial-frequency covariance matrix RSF,B,ΔkiDL(block1159). The RSF,B,ΔkiDLmay be reformed from the vectorized form of the spatial-frequency covariance of the second antenna panel B in the second frequency band rSF,B,ΔkiDL. The RSF,B,ΔkiDLmay be formed in a reverse manner from forming the spatial-frequency covariance for the first antenna panel A in the first frequency band rSFwith rSF=Vec{{{RSF},{RSF}}, for example. The device reconstructs the spatial-frequency covariance of the second antenna panel B in the second frequency band RSFDL(block1161). The spatial-frequency covariance of the second antenna panel B in the second frequency band RSFDLmay be reconstructed from the subblock matrices RSF,B,ΔkiDL, for example.

Let umA, m=1, . . . , MAbe the locations of antennas for one panel, e.g., antenna panel A, from which the channel is measured and the spatial-frequency covariance is obtained, and umB, m=1, . . . , MBbe the locations of antennas for a second panel, e.g., antenna panel B, for the covariance conversion. Furthermore, let gnUL,A(θ, τ) be an entry of the vectorized real and imaginary components of the matrix

caUL,A(θ)⁢aUL,A(θ)H⁢e-j⁢2⁢π⁢Δki⁢fsc⁢τ
and gnDL,B(θ, τ) as an entry of the vectorized real and imaginary components of the matrix

caDL,B(θ)⁢aDL,B(θ)H⁢e-j⁢2⁢π⁢Δki⁢fsc⁢τ
with the index of the one-one mapping expressible as n=(m, m′, i, IR/I).
Given the location of umA, it is possible to compute φm,m′(θ) with umAas φm,m′A(θ)=k (θ)TumA−k (θ)Tum′A. The estimation matrix G may be determined using Equations (32) to (37) for a given τDSor using Equations (54) to (58) for asymptotic delay spread.

The covariance for antenna panel B on a frequency associated with antenna panel B being expressible as

r^nDL,B=〈ρ^,gnDL,B〉=∑n′=1N′⁢αn′⁢〈gn′UL,A,gnDL,B〉,(64)
where the inner products,gn′ULA, gnDL,B, form the conversion matrixfor the two antenna panels with different antenna locations. Similarly as before, with separation of real and imaginary parts, the conversion matrixcan be rewritten into 4 subblock matrices expressible as

Q⌣=[].(65)

Denoting φm,m′B(θ)=k(θ)TumB−k(θ)Tum′Bfor antenna panel B, the conversion matrix Q are expressible as

m1,m1′,m2,m2′c-(λ1,λ2)=12⁢π⁢∫-ππcos⁡(2⁢πλ1⁢φm1,m1′A(θ)-2⁢πλ2⁢φm2,m2′B(θ))⁢d⁢θ,(66)m1,m1′,m2,m2′s-(λ1,λ2)=12⁢π⁢∫-ππsin⁡(2⁢πλ1⁢φm1,m1′A(θ)-2⁢πλ2⁢φm2,m2′B(θ))⁢d⁢θ,m1,m1′,m2,m2′c+(λ1,λ2)=12⁢π⁢∫-ππcos⁡(2⁢πλ1⁢φm1,m1′A(θ)+2⁢πλ2⁢φm2,m2′B(θ))⁢d⁢θ,m1,m1′,m2,m2′s+(λ1,λ2)=12⁢π⁢∫-ππsin⁡(2⁢πλ1⁢φm1,m1′A(θ)-2⁢πλ2⁢φm2,m2′B(θ))⁢d⁢θ.

Because the integral of the inner product can be separated on spatial and delay domains, the integral on the delay main formatrix remains the same as that for Q matrix itself. The results share the same structure except that the spatial domain integrals result in thefunctions as in Equation (66). The conversion matrixfor a given finite τDSis obtained with its entriesgnULA, gnDL,Bin the same forms as that of Q as in Equations (44), and (47) to (49) but with allfunctions in Equation (45) replaced with the correspondingfunctions in Equation (66), and the asymptotic expressions with the entries of the conversion matrix in the forms of Equations (59) to (63) but replacingfunctions in Equation (45) with the correspondingfunctions in Equation (66).

FIG.12Aillustrates a flow diagram of example operations1200occurring in a device converting spatial-frequency covariance in the spatial and frequency domains for two antenna panels with different steering directions. Operations1200may be indicative of operations occurring in a device (such as an access node, a UE, or a dedicated device configured to convert spatial-frequency covariance) as the device converts spatial-frequency covariance, where the device has two antenna panels with different steering directions. Although the discussion focuses on two antenna panels, the example embodiments are operable in a situation were the device has an antenna array with two subsets of antenna elements, with each subset serving a different frequency band. Therefore, the discussion of antenna panels should not be construed as being limiting to the scope of the example embodiments.

Input to operations1200may include the PADS estimation output α for the first antenna panel A, where the PADS estimation output may be based on the RSF,AULfrom measurements made on the first antenna panel A in the first frequency band (block1202). Operations1200begin with the device forming a conversion matrix(block1205). The conversion matrix may be formed in accordance with the antenna structure of the first antenna panel A and a second antenna panel B (such as aperture, spacing, polarization, antenna element spacing, etc.), carrier frequencies of the first antenna band and the second antenna band, configured frequency spacings or lags, and so on).

The device obtains the vectorized form of the spatial-frequency covariance of the second antenna panel B in the second frequency band rSF,BDL(block1207). The vectorized form of the spatial-frequency covariance being obtained by multiplying the PADS estimation output α (provided as input to operations1200) and the conversion matrixformed in block1105, and may be expressible as rSF,BDL=α, for example. The device reforms the spatial-frequency covariance matrix RSF,BDL(block1209). The RSF,BDLmay be reformed from the vectorized form of the spatial-frequency covariance of the second antenna panel B in the second frequency band rSF,BDL. The RSF,BDLmay be formed in a reverse manner from forming the spatial-frequency covariance for the first antenna panel A in the first frequency band rSF,AULwith rSF,AUL=vec{{{RSF,AUL},{RSF,AUL}}, for example.

FIG.12Billustrates a flow diagram of example operations occurring in a device converting spatial-frequency covariance in the spatial and frequency domains for two antenna panels with different steering directions, with asymptotic solutions. Operations1250may be indicative of operations occurring in a device (such as an access node, a UE, or a dedicated device configured to convert spatial-frequency covariance) as the device converts spatial-frequency covariance, with asymptotic solutions, where the device has two antenna panels with different steering directions. Although the discussion focuses on two antenna panels, the example embodiments are operable in a situation were the device has an antenna array with two subsets of antenna elements, with each subset serving a different frequency band. Therefore, the discussion of antenna panels should not be construed as being limiting to the scope of the example embodiments.

Input to operations1250may include the PADS estimation outputs αΔki=1, . . . , NSF(block1252). Operations1250begin with the device forming conversion matricesΔki(block1255). The conversion matrices may be formed for each frequency lag in accordance with parameters of the communication system, including the antenna structure (such as aperture, antenna element spacing, polarization, etc.), carrier frequency of the first frequency band and the second frequency band, configured frequency spacings or lags, and so on).

The device obtains the subblock matrices of the vectorized form of the spatial-frequency covariance of the second antenna panel B in the second frequency band rSF,B,ΔkiDL(block1257). The vectorized form of the spatial-frequency covariance may be obtained for different locations, such as at the different antenna element locations. The vectorized form of the spatial-frequency covariance being obtained by multiplying the PADS estimation output α (provided as input to operations1250) and the conversion matrixΔkiformed in block1155, and may be expressible as rSF,B,ΔkiDL=ΔkiαΔki, for example. The device reforms the subblock matrices of the spatial-frequency covariance matrix RSF,B,ΔkiDL(block1259). The RSF,B,ΔkiDLmay be reformed from the vectorized form of the spatial-frequency covariance of the second antenna panel B in the second frequency band rSF,B,ΔkiDL. The RSF,B,ΔkiULmay be formed in a reverse manner from forming the spatial-frequency covariance for the first antenna panel A in the first frequency band RSFDLwith rSFUL=Vec{{{RSFUL},{RSFUL}}, for example. The device reconstructs the spatial-frequency covariance of the second antenna panel B in the second frequency band RSFDL(block1261). The spatial-frequency covariance of the second antenna panel B in the second frequency band RSFDLmay be reconstructed from the subblock matrices RSF,B,ΔkiDL, for example.

In the scenario with antenna arrays with different steering directions, it is assumed that the steering directions of two co-located antenna arrays have an angle difference θΔ. It is assumed that the related locations of the antenna elements are the same for the two antenna panels, i.e., {um}. The steering angle of the antenna array can be translated into the location coordinates. Therefore, if the locations of the antenna elements in two antenna arrays are placed in a global coordinate reference system, the information of antenna steering direction is contained in the location of the antenna elements. Hence, the results presented above may be applied directly to obtaining the conversion for the two panels with different steering direction. However, because the only difference is angle, a more efficient solution may be provided, particularly, when it is subsequently applied to a regular array (e.g., a uniform linear array (ULA)).

Because the PADS is estimated based on one antenna array, the estimation procedure will be the same as discussed previously. The conversion, however, has to take into account the difference of the antenna steering direction. Given the estimated power angle delay spectrum estimate {circumflex over (ρ)}(θ, τ) from one panel, the spatial-frequency covariance matrix on the other panel and a different band can be obtained as

rnDL,B=〈ρ^(θ,τ),gn(θ+θΔ,τ)〉=∑n′=1N′⁢αn′⁢〈gn′UL,A(θ,τ),gnDL,B(θ+θΔ,τ)〉,(67)
where the inner products,gn′ULA(θ, τ), gnDL,B(θ+θΔ,τ), form the conversion matrixfor the scenario. Again, with separation of the real and imaginary parts, the conversion matrixmay be rewritten into four subblock matrices expressible as

Q⌣=[].(68)

Let

m1,m1′,m2,m2′c-(λ1,λ2,θΔ)=12⁢π⁢∫-ππcos⁡(2⁢πλ1⁢φm1,m1′A(θ)-2⁢πλ2⁢φm2,m2′B(θ+θΔ))⁢d⁢θ,(69)m1,m1′,m2,m2′s-(λ1,λ2,θΔ)=12⁢π⁢∫-ππsin⁡(2⁢πλ1⁢φm1,m1′A(θ)-2⁢πλ2⁢φm2,m2′B(θ+θΔ))⁢d⁢θ,m1,m1′,m2,m2′c+(λ1,λ2,θΔ)=12⁢π⁢∫-ππcos⁡(2⁢πλ1⁢φm1,m1′A(θ)+2⁢πλ2⁢φm2,m2′B(θ+θΔ))⁢d⁢θ,m1,m1′,m2,m2′s+(λ1,λ2,θΔ)=12⁢π⁢∫-ππsin⁡(2⁢πλ1⁢φm1,m1′A(θ)+2⁢πλ2⁢φm2,m2′B(θ+θΔ))⁢d⁢θ.

The conversion matrixfor a given finite τDSwith the resulting entriesgn′ULA(θ, τ), gnDL,B(θ+θΔ, τ)in the same forms as that of Q as in Equations (44), and (47) to (49) but replacing all Q functions in Equation (45) with the correspondingfunctions in Equation (68), and the asymptotic expressions with the entries in the same forms as in Equations (59) to (63) but replacing Q functions in Equation (45) withfunctions in Equation (66).

The spatial-frequency conversion for general antenna array configurations are presented above. The results involve complex integrals based on antennas as in the F,,, andfunctions.

According to an example embodiment, spatial-frequency conversion for ULAs are provided. ULAs are commonly used in massive MIMO communication systems. The ULAs have an equal antenna spacing d. Explicit solutions are provided.

With ULAs, the antenna response α(θ) is a beam vector and is expressible as

a⁡(θ)=[1,e-j⁢2⁢π⁢dλ⁢sin⁢θ,…,e-j⁢2⁢π⁢dλ⁢(M-1)⁢sin⁢θ]T.(70)
It is easily seen that for ULAs, R0is Toeplitz Hermitian and

{RΔki}
are Toeplitz matrices. Therefore, for R0, only the first column is needed and the conversion for the first column is obtained. There are total 2M−1 real entries after the separation of real and imaginary values of the complex entries. For

RΔki
with Δki≠0, there are 2(2M−1) independent real values for each Δki. So the total number of independent entries is (NSF−1)(4M−2)+2M−1. Because for each entry there is a function gn(θ, τ), the number of independent functions is then N′=(NSF−1)(4M−2)+2M−1.

The estimation matrix G and the conversion matrix Q for ULA may be determined as follows. First, φm,m′(θ)=(m−m′)sin(θ). In order to compute the F andfunctions, due to symmetric antenna structure, the angle region for the integrals in the inner product can be reduced to

[-π2,π2].
The normalization factor is then 1/π. The F functions for ULA is expressible as

m1,m1′,m2,m2′c-(λ)=1π⁢∫-π2π2cos⁡(2⁢π⁢dλ⁢((m1-m1′)-(m2-m2′))⁢sin⁡(θ))⁢d⁢θ=J0(2⁢π⁢dλ⁢((m1-m1′)-(m2-m2′))),(71)m1,m1′,m2,m2′s-(λ)=1π⁢∫-π2π2sin⁡(2⁢πλ⁢((m1-m1′)-(m2-m2′))⁢sin⁡(θ))⁢d⁢θ=0,m1,m1′,m2,m2′c+(λ)=1π⁢∫-π2π2cos⁡(2⁢π⁢dλ⁢((m1-m1′)+(m2-m2′))⁢sin⁡(θ))⁢d⁢θ=J0(2⁢π⁢dλ⁢((m1-m1′)+(m2-m2′))),m1,m1′,m2,m2′s+(λ)=1π⁢∫-π2π2sin⁡(2⁢πλ⁢((m1-m1′)+(m2-m2′))⁢sin⁡(θ))⁢d⁢θ=0.
The four submatrices of the G matrix are expressible as

[]n1,n2=12⁢{sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-(m2-m2′)))+sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)⁢J0(2⁢π⁢dλUL⁢((m1-m1′)+(m2-m2′)))},[]n1,n2=12⁢{-1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDS⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-(m2-m2′)))⁢1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDS⁢J0(2⁢π⁢dλUL⁢((m1-m1′)+(m2-m2′)))},[]n1,n2=12⁢{1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDS⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-(m2-m2′)))⁢1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDS⁢J0(2⁢π⁢dλUL⁢((m1-m1′)+(m2-m2′)))},[]n1,n2=12⁢{sin⁢c⁢(2⁢π⁢(Δki1-Δki2)⁢fsc⁢τDS)⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-(m2-m2′)))-sin⁢c⁢(2⁢π⁢(Δki1+Δki2)⁢fsc⁢τDS)⁢J0(2⁢π⁢dλUL⁢((m1-m1′)+(m2-m2′)))}.

Similarly, thefunctions as obtain in Equation (45) are expressible as

m1,m1′,m2,m2′c-(λ1,λ2)=J0(2⁢π⁢dλ1⁢(m1-m1′)-2⁢π⁢dλ2⁢(m2-m2′)),m1,m1′,m2,m2′s-(λ1,λ2)=0,m1,m1′,m2,m2′c+(λ1,λ2)=J0(2⁢π⁢dλ1⁢(m1-m1′)+2⁢π⁢dλ2⁢(m2-m2′))⁢m1,m1′,m2,m2′s+(λ1,λ2)=0.(72)
Consequently, the submatrices for Q are expressible as

[]n1,n2=12⁢{sin⁢c(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-2⁢π⁢dλDL⁢(m2-m2′))+sin⁢c(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)⁢J0(2⁢π⁢dλUL⁢(m1-m1′)+2⁢π⁢dλDL⁢(m2-m2′))},[]n1,n2=12⁢{-1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDS⁢J0(2⁢π⁢dλUL⁢(m1-m1′)-2⁢π⁢dλDL⁢(m2-m2′))+1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDS⁢J0(2⁢π⁢dλUL⁢(m1-m1′)+2⁢π⁢dλDL⁢(m2-m2′))},[]n1,n2=12⁢{1-cos(2⁢π(Δki1-Δki2)⁢fsc⁢τDS)2⁢π(Δki1-Δki2)⁢fsc⁢τDS⁢J0(2⁢π⁢dλUL⁢(m1-m1′)-2⁢π⁢dλDL⁢(m2-m2′))+1-cos(2⁢π(Δki1+Δki2)⁢fsc⁢τDS)2⁢π(Δki1+Δki2)⁢fsc⁢τDS⁢J0(2⁢π⁢dλUL⁢(m1-m1′)+2⁢π⁢dλDL⁢(m2-m2′))},[]n1,n2=12⁢{sin⁢c⁢(2⁢π⁢(Δki1-Δki2)⁢fsc⁢τDS)⁢J0(2⁢π⁢dλUL⁢(m1-m1′)-2⁢π⁢dλDL⁢(m2-m2′))-sin⁢c⁢(2⁢π⁢(Δki1+Δki2)⁢fsc⁢τDS)⁢J0(2⁢π⁢dλUL⁢(m1-m1′)+2⁢π⁢dλDL⁢(m2-m2′))}.(73)
For the G and Q submatrices, the results for some special cases when

Δki1=Δki2,
as described in Equations (38) to (41) can be applied, which simplify the matrices significantly.
The asymptotic expressions for a communication system with ULA considering τDSgoing to infinity are determined. By applying asymptotic results in Equations (50) to (53), there zeros for all the submatrices in both G and Q when

Δki1≠Δki2
as in Equations (54) and (59). For the cases when

Δki1=Δki2,
the G submatrices are expressible as

[]n1,n2={12⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-(m2-m2′)))+12⁢J0(2⁢π⁢dλUL⁢((m1-m1′)+(m2-m2′))),Δki1=Δki2=0,12⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-(m2-m2′))),Δki1=Δki2≠0[]n1,n2=0,[]n1,n2=0,[]n1,n2={12⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-(m2-m2′)))-12⁢J0(2⁢π⁢dλUL⁢((m1-m1′)+(m2-m2′)))Δki1=Δki2=0,12⁢J0(2⁢π⁢dλUL⁢((m1-m1′)-(m2-m2′)))Δki1=Δki2≠0,
and the Q submatrices are expressible as

[]n1,n2={12⁢J0⁢(2⁢π⁢dλUL⁢(m1-m1′)-2⁢π⁢dλD⁢L⁢(m2-m2′))+12⁢J0⁢(2⁢π⁢dλUL⁢(m1-m1′)+2⁢π⁢dλD⁢L⁢(m2-m2′)),⁢Δki1=Δki2=012⁢J0⁢(2⁢π⁢dλUL⁢(m1-m1′)-2⁢π⁢dλD⁢L⁢(m2-m2′))Δki1=Δki2≠0(74)[]n1,n2=0,[]n1,n2=0,[]n1,n2={12⁢J0⁢(2⁢π⁢dλUL⁢(m1-m1′)-2⁢π⁢dλD⁢L⁢(m2-m2′))-12⁢J0⁢(2⁢π⁢dλUL⁢(m1-m1′)+2⁢π⁢dλD⁢L⁢(m2-m2′)),⁢Δki1=Δki2=012⁢J0⁢(2⁢π⁢dλUL⁢(m1-m1′)-2⁢π⁢dλD⁢L⁢(m2-m2′))Δki1=Δki2≠0

FIG.13Aillustrates a diagram1300of two ULA antenna arrays with different antenna spacings. As shown inFIG.13A, a first antenna array1305has an antenna spacing of dA1307, while a second antenna array1310has an antenna spacing of dB1312.FIG.13Billustrates a diagram1350of two ULA antenna arrays with different steering directions. As shown inFIG.13B, a first antenna array1355has a first facing direction1357and a second antenna array1365has a second facing direction1367. The two antenna arrays have a facing direction difference of θA1370.

In the situation where the communication system has two ULAs with different antenna spacings dAand dB, the following are known
φm,m′A(θ)=(m−m′)dAsin(θ)
φm,m′B(θ)=(m−m′)dBsin(θ).  (75)
As discussed previously, the PADS for one antenna panel is determined using the techniques presented herein, and for the ULA, the G matrix specified in Equation (74) is used.

In order to obtain the conversion matrix for both spatial and frequency domains, thefunctions from Equation (66) for ULA are expressible as

m1,m1′,m2,m2′c-(λ1,λ2)=J0(2⁢π⁢dAλ1⁢(m1-m1′)-2⁢π⁢dBλ2⁢(m2-m2′)),m1,m1′,m2,m2′s-(λ1,λ2)=0,m1,m1′,m2,m2′c+(λ1,λ2)=J0(2⁢π⁢dBλ1⁢(m1-m1′)+2⁢π⁢dBλ2⁢(m2-m2′))⁢m1,m1′,m2,m2′s+(λ1,λ2)=0.(76)
The Q̆ submatrices are expressible as

[]n1,n2=12⁢{sin⁢c⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)⁢J0(2⁢π⁢dAλU⁢L⁢(m1-m1′)-2⁢π⁢dBλD⁢L⁢(m2-m2′))+sin⁢c⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)⁢J0(2⁢π⁢dAλU⁢L⁢(m1-m1′)+2⁢π⁢dBλD⁢L⁢(m2-m2′))},[]n1,n2=12⁢{-1-cos⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S⁢J0(⁠2⁢π⁢dAλU⁢L⁢(m1-m1′)-2⁢π⁢dBλD⁢L⁢(m2-m2′))+1-cos⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1+Δki2)⁢fs⁢c⁢τD⁢S⁢J0(2⁢π⁢dAλU⁢L⁢(m1-m1′)+2⁢π⁢dBλD⁢L⁢(m2-m2′))},[]n1,n2=12⁢{1-cos⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1-Δki2)⁢fs⁢c⁢τD⁢S⁢J0(⁠2⁢π⁢dAλU⁢L⁢(m1-m1′)-2⁢π⁢dBλD⁢L⁢(m2-m2′))+1-cos⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1+Δki2)⁢fS⁢c⁢τD⁢S⁢J0(2⁢π⁢dAλU⁢L⁢(m1-m1′)+2⁢π⁢dBλD⁢L⁢(m2-m2′))},[]n1,n2=12⁢{sin⁢c⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)⁢J0(2⁢π⁢dAλU⁢L⁢(m1-m1′)-2⁢π⁢dBλD⁢L⁢(m2-m2′))-sin⁢c⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)⁢J0(2⁢π⁢dAλU⁢L⁢(m1-m1′)+2⁢π⁢dBλD⁢L⁢(m2-m2′))}.(77)

Considering the case where τDS→∞, the asymptotic results for thesubmatrices for

Δki1=Δki2
are expressible as

[]n1,n2={12⁢J0⁢(2⁢π⁢dAλUL⁢(m1-m1′)-2⁢π⁢dBλD⁢L⁢(m2-m2′))+12⁢J0⁢(2⁢π⁢dAλUL⁢(m1-m1′)+2⁢π⁢dBλD⁢L⁢(m2-m2′)),⁢Δki1=Δki2=012⁢J0⁢(2⁢π⁢dAλUL⁢(m1-m1′)-2⁢π⁢dBλD⁢L⁢(m2-m2′))Δki1=Δki2≠0(78)[]n1,n2=0,[]n1,n2=0,[]n1,n2={12⁢J0⁢(2⁢π⁢dAλUL⁢(m1-m1′)-2⁢π⁢dBλD⁢L⁢(m2-m2′))-12⁢J0⁢(2⁢π⁢dAλUL⁢(m1-m1′)+2⁢π⁢dBλD⁢L⁢(m2-m2′)),⁢Δki1=Δki2=012⁢J0⁢(2⁢π⁢dAλUL⁢(m1-m1′)-2⁢π⁢dBλD⁢L⁢(m2-m2′))Δki1=Δki2≠0.

In the situation where the communication system has two ULAs with different steering directions, the facing direction difference θΔrepresents the angular difference in the steering directions. As previously discussed, the PADS remains the same. In order to obtain the conversion matrix, thefunctions are determined as follows, and the function φm,m′(θ) of two antenna panels are as provided in Equation (75).

First, denote

B⌣1,m1,m1′=2⁢π⁢dAλ1⁢(m1-m1′),and⁢B⌣2,m2,m2′=2⁢π⁢dBλ2⁢(m2-m2′),and(79)Cm1,m1′,m2,m2′-(λ1,λ2,θΔ)=B⌣1,m1,m1′2+B⌣2,m2,m2′2-2⁢B⌣1,m1,m1′⁢B⌣1,m1,m1′⁢cos⁡(θΔ),(80)Cm1,m1′,m2,m2′-(λ1,λ2,θΔ)=B⌣1,m1,m1′2+B⌣2,m2,m2′2+2⁢B⌣1,m1,m1′⁢B⌣1,m1,m1′⁢cos⁡(θΔ),ψm1,m1′,m2,m2′-(λ1,λ2,θΔ)=tan-1(-B⌣2,m2,m2′⁢sin⁡(θΔ)B⌣1,m1,m1′-B⌣2,m2,m2′⁢cos⁢(θΔ))ψm1,m1′,m2,m2′+(λ1,λ2,θΔ)=tan-1(B⌣2,m2,m2′⁢sin⁡(θΔ)B⌣1,m1,m1′+B⌣2,m2,m2′⁢cos⁢(θΔ)).
Additionally, the H (c, φ) function is defined as

H⁡(c,φ)=Δ1π⁢∫-π2π2sin⁡(c⁢sin⁡(θ+φ))⁢d⁢θ.(81)

Then, from Equation (69), with the integration range changed to [−π/2, π/2], thefunctions expressible as
m1,m′1,m2,m′2c−(λ1,λ2,θΔ)=J0(Cm1,m′1,m2,m′2−(λ1,λ2,θΔ)),
m1,m′1,m2,m′2s−(λ1,λ2,θΔ)=H(Cm1,m′1,m2,m′2−(λ1,λ2,θΔ),ψm1m′1,m2m′2−(λ1,λ2,θΔ))
m1,m′1,m2,m′2c+(λ1,λ2,θΔ)=J0(Cm1,m′1,m2,m′2+(λ1,λ2,θΔ)),
m1,m′1,m2,m′2s+(λ1,λ2,θΔ)=H(Cm1,m′1,m2,m′2+(λ1,λ2,θΔ),ψm1m′1,m2m′2−(λ1,λ2,θΔ))  (82)

The Q̆ submatrices are expressible as

[]n1,n2=12⁢{sin⁢c⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)⁢J0(Cm1,m1′,m2,m2′-(λ1,λ2,θΔ))+1-cos⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1-Δki2)⁢fs⁢c⁢τD⁢S⁢H⁢(Cm1,m1′,m2,m2′-(λ1,λ2,θΔ),ψm1,m1′,m2,m2′-(λ1,λ2,θΔ))+sin⁢c⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)⁢J0(Cm1,m1′,m2,m2′+(λ1,λ2,θΔ))+1-cos⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1+Δki2)⁢fs⁢c⁢τD⁢S⁢H⁡(Cm1,m1′,m2,m2′+(λ1,λ2,θΔ),ψm1,m1′,m2,m2′+(λ1,λ2,θΔ))},(83)[]n1,n2=12⁢{-1-cos⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1-Δki2)⁢fs⁢c⁢τD⁢S⁢J0(Cm1,m1′,m2,m2′-(λ1,λ2,θΔ))+sin⁢c⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)⁢H⁡(Cm1,m1′,m2,m2′-(λ1,λ2,θΔ),ψm1,m1′,m2,m2′-(λ1,λ2,θΔ))+1-cos⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1+Δki2)⁢fs⁢c⁢τD⁢S⁢J0(Cm1,m1′,m2,m2′+(λ1,λ2,θΔ)),-sin⁢c⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)⁢H⁡(Cm1,m1′,m2,m2′+(λ1,λ2,θΔ),ψm1,m1′,m2,m2′+(λ1,λ2,θΔ))}[]n1,n2=12⁢{1-cos⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1-Δki2)⁢fs⁢c⁢τD⁢S⁢J0(2⁢π⁢dAλUL⁢(m1-m1′)-2⁢π⁢dBλDL⁢(m2-m2′))-sin⁢c⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)⁢H⁡(Cm1,m1′,m2,m2′-(λ1,λ2,θΔ),ψm1,m1′,m2,m2′-(λ1,λ2,θΔ))[]n1,n2=12⁢{sin⁢c⁡(2⁢π⁡(Δki1-Δki2)⁢fsc⁢τD⁢S)⁢J0(2⁢π⁢dAλUL⁢(m1-m1′)-2⁢π⁢dBλDL⁢(m2-m2′))+sin⁢c⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)⁢J0(Cm1,m1′,m2,m2′+(λ1,λ2,θΔ))-sin⁢c⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)⁢J0(2⁢π⁢dAλUL⁢(m1-m1′)+2⁢π⁢dBλDL⁢(m2-m2′))+1-cos⁡(2⁢π⁡(Δki1+Δki2)⁢fsc⁢τD⁢S)2⁢π⁡(Δki1+Δki2)⁢fs⁢c⁢τD⁢S⁢H⁡(Cm1,m1′,m2,m2′+(λ1,λ2,θΔ),ψm1,m1′,m2,m2′+(λ1,λ2,θΔ))}.

In the case of infinite τDS, the asymptotic results formatrices for

Δki1=Δki2
are expressible as

[]n1,n2={12⁢J0(Cm1,m1′,m2,m2′-)+12⁢J0⁢(Cm1,m1′,m2,m2′+)),Δki1=Δki2=012⁢J0⁢(Cm1,m1′,m2,m2′-)Δki1=Δki2≠0(84)[]n1,n2={12⁢H⁡(Cm1,m1′,m2,m2′-,ψm1,m1′,m2,m2′-)-12⁢H⁢(Cm1,m1′,m2,m2′+,ψm1,m1′,m2,m2′+)Δki1=Δki2=012⁢H⁢(Cm1,m1′,m2,m2′-⁢(λ1,λ2,θΔ),ψm1,m1′,m2,m2′+)⁢(λ1,λ2,θΔ))Δki1=Δki2≠0,[]n1,n2={-12⁢H⁡(Cm1,m1′,m2,m2′-,ψm1,m1′,m2,m2′-)-12⁢H⁢(Cm1,m1′,m2,m2′+,ψm1,m1′,m2,m2′+)Δki1=Δki2=0-12⁢H⁢(Cm1,m1′,m2,m2′-,ψm1,m1′,m2,m2′+)Δki1=Δki2≠0,[]n1,n2={12⁢J0⁢(Cm1,m1′,m2,m2′-)-12⁢J0⁢(Cm1,m1′,m2,m2′+),Δki1=Δki2=012⁢J0⁢(Cm1,m1′,m2,m2′-)Δki1=Δki2≠0,
where the function inputs (λ1, λ2, θΔ) are dropped for notational simplicity.

FIG.14illustrates an example communication system1400. In general, the system1400enables multiple wireless or wired users to transmit and receive data and other content. The system1400may implement one or more channel access methods, such as code division multiple access (CDMA), time division multiple access (TDMA), frequency division multiple access (FDMA), orthogonal FDMA (OFDMA), single-carrier FDMA (SC-FDMA), or non-orthogonal multiple access (NOMA).

In this example, the communication system1400includes electronic devices (ED)1410a-1410c, radio access networks (RANs)1420a-1420b, a core network1430, a public switched telephone network (PSTN)1440, the Internet1450, and other networks1460. While certain numbers of these components or elements are shown inFIG.14, any number of these components or elements may be included in the system1400.

The EDs1410a-1410care configured to operate or communicate in the system1400. For example, the EDs1410a-1410care configured to transmit or receive via wireless or wired communication channels. Each ED1410a-1410crepresents any suitable end user device and may include such devices (or may be referred to) as a user equipment or device (UE), wireless transmit or receive unit (WTRU), mobile station, fixed or mobile subscriber unit, cellular telephone, personal digital assistant (PDA), smartphone, laptop, computer, touchpad, wireless sensor, or consumer electronics device.

The RANs1420a-1420bhere include base stations1470a-1470b, respectively. Each base station1470a-1470bis configured to wirelessly interface with one or more of the EDs1410a-1410cto enable access to the core network143o, the PSTN144o, the Internet1450, or the other networks1460. For example, the base stations1470a-1470bmay include (or be) one or more of several well-known devices, such as a base transceiver station (BTS), a Node-B (NodeB), an evolved NodeB (eNodeB), a Next Generation (NG) NodeB (gNB), a Home NodeB, a Home eNodeB, a site controller, an access point (AP), or a wireless router. The EDs1410a-1410care configured to interface and communicate with the Internet1450and may access the core network1430, the PSTN1440, or the other networks1460.

In the embodiment shown inFIG.14, the base station1470aforms part of the RAN1420a, which may include other base stations, elements, or devices. Also, the base station1470bforms part of the RAN1420b, which may include other base stations, elements, or devices. Each base station1470a-1470boperates to transmit or receive wireless signals within a particular geographic region or area, sometimes referred to as a “cell.” In some embodiments, multiple-input multiple-output (MIMO) technology may be employed having multiple transceivers for each cell.

The base stations1470a-1470bcommunicate with one or more of the EDs1410a-1410cover one or more air interfaces1490using wireless communication links. The air interfaces1490may utilize any suitable radio access technology.

It is contemplated that the system1400may use multiple channel access functionality, including such schemes as described above. In particular embodiments, the base stations and EDs implement 5G New Radio (NR), LTE, LTE-A, or LTE-B. Of course, other multiple access schemes and wireless protocols may be utilized.

The RANs1420a-1420bare in communication with the core network1430to provide the EDs1410a-1410cwith voice, data, application, Voice over Internet Protocol (VoIP), or other services. Understandably, the RANs1420a-1420bor the core network1430may be in direct or indirect communication with one or more other RANs (not shown). The core network1430may also serve as a gateway access for other networks (such as the PSTN1440, the Internet1450, and the other networks1460). In addition, some or all of the EDs1410a-1410cmay include functionality for communicating with different wireless networks over different wireless links using different wireless technologies or protocols. Instead of wireless communication (or in addition thereto), the EDs may communicate via wired communication channels to a service provider or switch (not shown), and to the Internet1450.

AlthoughFIG.14illustrates one example of a communication system, various changes may be made toFIG.14. For example, the communication system1400could include any number of EDs, base stations, networks, or other components in any suitable configuration.

FIGS.15A and15Billustrate example devices that may implement the methods and teachings according to this disclosure. In particular,FIG.15Aillustrates an example ED1510, andFIG.15Billustrates an example base station1570. These components could be used in the system1400or in any other suitable system.

As shown inFIG.15A, the ED1510includes at least one processing unit1500. The processing unit1500implements various processing operations of the ED1510. For example, the processing unit1500could perform signal coding, data processing, power control, input/output processing, or any other functionality enabling the ED1510to operate in the system1400. The processing unit1500also supports the methods and teachings described in more detail above. Each processing unit1500includes any suitable processing or computing device configured to perform one or more operations. Each processing unit1500could, for example, include a microprocessor, microcontroller, digital signal processor, field programmable gate array, or application specific integrated circuit.

The ED1510also includes at least one transceiver1502. The transceiver1502is configured to modulate data or other content for transmission by at least one antenna or NIC (Network Interface Controller)1504. The transceiver1502is also configured to demodulate data or other content received by the at least one antenna1504. Each transceiver1502includes any suitable structure for generating signals for wireless or wired transmission or processing signals received wirelessly or by wire. Each antenna1504includes any suitable structure for transmitting or receiving wireless or wired signals. One or multiple transceivers1502could be used in the ED1510, and one or multiple antennas1504could be used in the ED1510. Although shown as a single functional unit, a transceiver1502could also be implemented using at least one transmitter and at least one separate receiver.

The ED1510further includes one or more input/output devices1506or interfaces (such as a wired interface to the Internet1450). The input/output devices1506facilitate interaction with a user or other devices (network communications) in the network. Each input/output device1506includes any suitable structure for providing information to or receiving information from a user, such as a speaker, microphone, keypad, keyboard, display, or touch screen, including network interface communications.

In addition, the ED1510includes at least one memory1508. The memory1508stores instructions and data used, generated, or collected by the ED1510. For example, the memory1508could store software or firmware instructions executed by the processing unit(s)1500and data used to reduce or eliminate interference in incoming signals. Each memory1508includes any suitable volatile or non-volatile storage and retrieval device(s). Any suitable type of memory may be used, such as random access memory (RAM), read only memory (ROM), hard disk, optical disc, subscriber identity module (SIM) card, memory stick, secure digital (SD) memory card, and the like.

As shown inFIG.15B, the base station1570includes at least one processing unit1550, at least one transceiver1552, which includes functionality for a transmitter and a receiver, one or more antennas1556, at least one memory1558, and one or more input/output devices or interfaces1566. A scheduler, which would be understood by one skilled in the art, is coupled to the processing unit1550. The scheduler could be included within or operated separately from the base station1570. The processing unit1550implements various processing operations of the base station1570, such as signal coding, data processing, power control, input/output processing, or any other functionality. The processing unit1550can also support the methods and teachings described in more detail above. Each processing unit1550includes any suitable processing or computing device configured to perform one or more operations. Each processing unit1550could, for example, include a microprocessor, microcontroller, digital signal processor, field programmable gate array, or application specific integrated circuit.

Each transceiver1552includes any suitable structure for generating signals for wireless or wired transmission to one or more EDs or other devices. Each transceiver1552further includes any suitable structure for processing signals received wirelessly or by wire from one or more EDs or other devices. Although shown combined as a transceiver1552, a transmitter and a receiver could be separate components. Each antenna1556includes any suitable structure for transmitting or receiving wireless or wired signals. While a common antenna1556is shown here as being coupled to the transceiver1552, one or more antennas1556could be coupled to the transceiver(s)1552, allowing separate antennas1556to be coupled to the transmitter and the receiver if equipped as separate components. Each memory1558includes any suitable volatile or non-volatile storage and retrieval device(s). Each input/output device1566facilitates interaction with a user or other devices (network communications) in the network. Each input/output device1566includes any suitable structure for providing information to or receiving/providing information from a user, including network interface communications.

FIG.16is a block diagram of a computing system1600that may be used for implementing the devices and methods disclosed herein. For example, the computing system can be any entity of UE, access network (AN), mobility management (MM), session management (SM), user plane gateway (UPGW), or access stratum (AS). Specific devices may utilize all of the components shown or only a subset of the components, and levels of integration may vary from device to device. Furthermore, a device may contain multiple instances of a component, such as multiple processing units, processors, memories, transmitters, receivers, etc. The computing system160oincludes a processing unit1602. The processing unit includes a central processing unit (CPU)1614, memory1608, and may further include a mass storage device1604, a video adapter1610, and an I/O interface1612connected to a bus1620.

The bus1620may be one or more of any type of several bus architectures including a memory bus or memory controller, a peripheral bus, or a video bus. The CPU1614may comprise any type of electronic data processor. The memory1608may comprise any type of non-transitory system memory such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), read-only memory (ROM), or a combination thereof. In an embodiment, the memory1608may include ROM for use at boot-up, and DRAM for program and data storage for use while executing programs.

The mass storage1604may comprise any type of non-transitory storage device configured to store data, programs, and other information and to make the data, programs, and other information accessible via the bus1620. The mass storage1604may comprise, for example, one or more of a solid state drive, hard disk drive, a magnetic disk drive, or an optical disk drive.

The video adapter1610and the I/O interface1612provide interfaces to couple external input and output devices to the processing unit1602. As illustrated, examples of input and output devices include a display1618coupled to the video adapter1610and a mouse, keyboard, or printer1616coupled to the I/O interface1612. Other devices may be coupled to the processing unit1602, and additional or fewer interface cards may be utilized. For example, a serial interface such as Universal Serial Bus (USB) (not shown) may be used to provide an interface for an external device.

The processing unit1602also includes one or more network interfaces1606, which may comprise wired links, such as an Ethernet cable, or wireless links to access nodes or different networks. The network interfaces1606allow the processing unit1602to communicate with remote units via the networks. For example, the network interfaces1606may provide wireless communication via one or more transmitters/transmit antennas and one or more receivers/receive antennas. In an embodiment, the processing unit1602is coupled to a local-area network1622or a wide-area network for data processing and communications with remote devices, such as other processing units, the Internet, or remote storage facilities.

It should be appreciated that one or more steps of the embodiment methods provided herein may be performed by corresponding units or modules. For example, a signal may be transmitted by a transmitting unit or a transmitting module. A signal may be received by a receiving unit or a receiving module. A signal may be processed by a processing unit or a processing module. Other steps may be performed by a calculating unit or module, a determining unit or module, an estimating unit or module, a projecting unit or module, a reconstructing unit or module, an obtaining unit or module, a reforming unit or module, or a generating unit or module. The respective units or modules may be hardware, software, or a combination thereof. For instance, one or more of the units or modules may be an integrated circuit, such as field programmable gate arrays (FPGAs) or application-specific integrated circuits (ASICs).

Although the present disclosure and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the scope of the disclosure as defined by the appended claims.