Dotted lines show the approximate extents of the coverage areas 120 and 125, which are shown as approximately circular for the purposes of illustration and explanation only. It should be clearly understood that the coverage areas associated with gNBs, such as the coverage areas 120 and 125, may have other shapes, including irregular shapes, depending upon the configuration of the gNBs and variations in the radio environment associated with naturaland man-made obstructions.

Although FIG. 1 illustrates one example of a wireless network, various changes may be made to FIG. 1. For example, the wireless network could include any number of gNBs and any number of UEs in any suitable arrangement. Also, the gNB 101 could communicate directly with any number of UEs and provide those UEs with wireless broadband access to the network 130. Similarly, each gNB 102-103 could communicate directly with the network 130 and provide UEs with direct wireless broadband access to the network 130. Further, the gNBs 101, 102, and/or 103 could provide access to other or additional external networks, such as external telephone networks or other types of data networks.

FIG. 2 illustrates an exemplary base station (BS) utilizing circular antenna arrays designed according to various embodiments of this disclosure. The embodiment of the gNB 102 illustrated in FIG. 2 is for illustration only, and the gNBs 101 and 103 of FIG. 1 could have the same or similar configuration. However, gNBs come in a wide variety of configurations, and FIG. 2 does not limit the scope of this disclosure to any particular implementation of a gNB.

As shown in FIG. 2, the gNB 102 includes multiple antennas 205a-205n, multiple transceivers 210a-210n, a controller/processor 225, a memory 230, and a backhaul or network interface 235.

The transceivers 210a-210n receive, from the antennas 205a-205n, incoming RF signals, such as signals transmitted by UEs in the network 100. The transceivers 210a-210n down-convert the incoming RF signals to generate IF or baseband signals. The IF or baseband signals are processed by receive (RX) processing circuitry in the transceivers 210a-210n and/or controller/processor 225, which generates processed baseband signals by filtering, decoding, and/or digitizing the baseband or IF signals. The controller/processor 225 may further process the baseband signals.

Transmit (TX) processing circuitry in the transceivers 210a-210n and/or controller/processor 225 receives analog or digital data (such as voice data, web data, e-mail, or interactive video game data) from the controller/processor 225. The TX processing circuitry encodes, multiplexes, and/or digitizes the outgoing baseband data to generate processed baseband or IF signals. The transceivers 210a-210n up-converts the baseband or IF signals to RF signals that are transmitted via the antennas 205a-205n.

The controller/processor 225 can include one or more processors or other processing devices that control the overall operation of the gNB 102. For example, the controller/processor 225 could control the reception of UL channel signals and the transmission of DL channel signals by the transceivers 210a-210n in accordance with well-known principles. The controller/processor 225 could support additional functions as well, such as more advanced wireless communication functions. For instance, the controller/processor 225 could support beam forming or directional routing operations in which outgoing/incoming signals from/to multiple antennas 205a-205n are weighted differently to effectively steer the outgoing signals in a desired direction. Any of a wide variety of other functions could be supported in the gNB 102 by the controller/processor 225.

The controller/processor 225 is also capable of executing programs and other processes resident in the memory 230, such as an OS. The controller/processor 225 can move data into or out of the memory 230 as required by an executing process.

The controller/processor 225 is also coupled to the backhaul or network interface 235. The backhaul or network interface 235 allows the gNB 102 to communicate with other devices or systems over a backhaul connection or over a network. The interface 235 could support communications over any suitable wired or wireless connection(s), example, when the gNB 102 is implemented as part of a cellular communication system (such as one supporting 5G/NR, LTE, or LTE-A), the interface 235 could allow the gNB 102 to communicate with other gNBs over a wired or wireless backhaul connection. When the gNB 102 is implemented as an access point, the interface 235 could allow the gNB 102 to communicate over a wired or wireless local area network or over a wired or wireless connection to a larger network (such as the Internet). The interface 235 includes any suitable structure supporting communications over a wired or wireless connection, such as an Ethernet or transceiver.

The memory 230 is coupled to the controller/processor 225. Part of the memory 230 could include a RAM, and another part of the memory 230 could include a Flash memory or other ROM.

Although FIG. 2 illustrates one example of gNB 102, various changes may be made to FIG. 2. For example, the gNB 102 could include any number of each component shown in FIG. 2. Also, various components in FIG. 2 could be combined, further subdivided, or omitted and additional components could be added according to particular needs.

FIG. 3 illustrates an exemplary electronic device for communicating in the networked computing system utilizing circular antenna arrays designed according to various embodiments of this disclosure. The embodiment of the UE 116 illustrated in FIG. 3 is for illustration only, and the UEs 111-115 of FIG. 1 could have the same or similar configuration. However, UEs come in a wide variety of configurations, and FIG. 3 does not limit the scope of this disclosure to any particular implementation of a UE.

As shown in FIG. 3, the UE 116 includes antenna(s) 305, a transceiver(s) 310, and a microphone 320. The UE. 116 also includes a speaker 330, a processor 340, an input/output (I/O) interface (IF) 345, an input 350, a display 355, and a memory 360. The memory 360 includes an operating system (OS) 361 and one or more applications 362.

The transceiver(s) 310 receives, from the antenna 305, an incoming RF signal transmitted by a gNB of the network 100. The transceiver(s) 310 down-converts the incoming RF signal to generate an intermediate frequency (IF) or baseband signal. The IF or baseband signal is processed by RX processing circuitry in the transceiver(s) 310 and/or processor 340, which generates a processed baseband signal by filtering, decoding, and/or digitizing the baseband or IF signal. The RX processing circuitry sends the processed baseband signal to the speaker 330 (such as for voice data) or is processed by the processor 340 (such as for web browsing data).

TX processing circuitry in the transceiver(s) 310 and/or processor 340 receives analog or digital voice data from the microphone 320 or other outgoing baseband data (such as web data, e-mail, or interactive video game data) from the processor 340. The TX processing circuitry encodes, multiplexes, and/or digitizes the outgoing baseband data to generate a processed baseband or IF signal. The transceiver(s) 310 up-converts the baseband or IF signal to an RF signal that is transmitted via the antenna(s) 305.

The processor 340 can include one or more processors or other processing devices and execute the OS 361 stored in the memory 360 in order to control the overall operation of the UE 116. For example, the processor 340 could control the reception of DL channel signals and the transmission of UL channel signals by the transceiver(s) 310 in accordance with well-known principles. In some embodiments, the processor 340 includes at least one microprocessor or microcontroller.

The processor 340 is also capable of executing other processes and programs resident in the memory 360. The processor 340 can move data into or out of the memory 360 as required by an executing process. In some embodiments, the processor 340 is configured to execute the applications 362 based on the OS 361 or in response to signals received from giNBs or an operator. The processor 340 is also coupled to the I/O interface 345, which provides the UE 116 with the ability to connect to other devices, such as laptop computers and handheld computers. The I/O interface 345 is the communication path between these accessories and the processor 340.

The processor 340 is also coupled to the input 350, which includes for example, a touchscreen, keypad, etc., and the display 355. The operator of the UE 116 can use the input 350 to enter data into the UE 116. The display 355 may be a liquid crystal display, light emitting diode display, or other display capable of rendering text and/or at least limited graphics, such as from web sites.

The memory 360 is coupled to the processor 340. Part of the memory 360 could include a. random-access memory (RAM), and another part of the memory 360 could include a. Flash memory or other read-only memory (ROM).

Although FIG. 3 illustrates one example of UE 116, various changes may be made to FIG. 3. For example, various components in FIG. 3 could be combined, further subdivided, or omitted and additional components could be added according to particular needs. As a particular example, the processor 340 could be divided into multiple processors, such as one or more central processing units (CPUs) and one or more graphics processing units (GPUs). In another example, the transceiver(s) 310 may include any number of transceivers and signal processing chains and may be connected to any number of antennas. Also, while FIG. 3 illustrates the UE 116 configured as a mobile telephone or smartphone, UEs could be configured to operate as other types of mobile or stationary devices.

FIG. 4 shows an example of a high-speed backhaul mesh network with IJCAs designed according to various embodiments of this disclosure. In network 400, base station 401 equipped with a UCA communicates with base station 402 via beam 402, with base station 404 via beam 405, with base station 406 via beam 407, with base station 408 via beam 409, with base station 410 via beam 411, and with base station 412 via beam 413. Each of base stations 402, 404, 406, 408, 410, and 412 is also equipped with a UCA.

Among the general problems to be solved when implementing network 400 are:

- The LoS MIMO channel model for TEL bands has inaccuracies when utilizing a planar wave assumption, which inaccuracies are the product of the large phases errors of the “planar array” model.
- In LoS MIMO, misalignments (in azimuth of elevation, or in offsets) can impact the maximum data rate in a communication system.
- Singular value decomposition techniques for MIMO systems can overcome misalignment issues but is computationally cumbersome. Larger arrays require more operations, which can be problematic in dynamic scenarios.
- The geometry of the planar array offers limitations in the robustness (limited range for optimal operation and not applicable for mobile applications) and capacity of the system such that new geometries need to be explored.
- Implementation of low-complexity strategies for robustness in the system are necessary to achieve high spectral efficiency for next generation communication systems.
  
  One specific problem addressed by the present disclosure is the excessive computational complexity overhead for precoded-based THz LoS MIMO system in high data-rate applications.

The present disclosure reduces the complexity of precoder-based LoS MIMO system based on singular value decomposition (SVD) by using analog beam steering techniques with IFFT/FFT. By applying the principles of the present disclosure, the channel matrix can be diagonalized using only analog RF circuitry instead computationally complex procedures with large overheads. This technique uses the intrinsic circulant property of a UCA LoS MIMO channel to allows perfect diagonalization by using just a rotation matrix (of which IFFT/FFT is a special case). In other words, the IFFT/FFT analog system (e.g., Butler Matrix) can replace the SVD precoder.

However, to improve the robustness against angular misalignments in a mesh network (azimuth, elevation) or displacements (offsets), an analog beam steering strategy is proposed to help the IFFT/FFT analog precoder.

Accordingly, the present disclosure designs a uniform circular array assisted with an analog IFFT/FFT precoder to reduce the computational complexity in LoS MIMO backhaul mesh networks.

The present disclosure also incorporates beam steering as a complement for the IFFT/FFT precoder technique, to improve the flexibility of steering the beams in a mesh network to the intended destination.

Moreover, each port in the UCA in the present disclosure is composed of a steerable miniaturized array with beam steering capabilities.

Analysis is begun with a simple case of one TX and one RX, for which analysis of the system is based in a normalized Rician channel where the channel matrix H for M is the number of antennas in the Tx array and N antennas in the Rx array can be described as follows [4]:

H

M
×
N

=

K

K
+
1

⁢

H
LoS

+

1

K
+
1

⁢

H
NLoS

(
1
)

H
LoS

=

[

e

-

jkd

m
,

n

]

M
×
N

,

H
NLoS

∼

CN
⁡
(

0
,

σ
2

⁢
I

)

where H_LoSis the line-of-sight component described by the geometry of the array, k=2 π/λ is the wavenumber of the carrier, λ is the wavelength of the carrier, H_NLoSrepresents the statistical behavior of scatterers modeled as independent and identically distributed complex normal distributed matrix with mean zero and standard deviation equal to one (H_NLoS˜CN(0, I), where I is the identity matrix), and K represents the Rice Factor of the channel, which is the power ratio between the LoS and non-line-of-sight (NLos) components of the channel.

For this channel model, the assumption is that the distance D between the transmitter and receiver arrays is large compared to the inter-antenna spacing d (D>>d), therefore the path gain experiences in each antenna pair between the transmitter and receiver is approximately the same. Therefore, without loss of generality the path gain may be normalized and focus may concentrate on a “phase” analysis.

As reflected in Eq. 1, the channel model is directly related to the geometry of the array, where each element of both arrays is considered an isotropic antenna. For a Tx UCA array at the origin and having M antennas uniformly spaced with the radius R_t, the coordinates of the antenna elements is given by:

0=[0 0 0],

Tx_m=[R_tcos(θ_m), R_tsin(θ_m), 0]^T, (2)

On the opposite side of the link, the Rx UCA array located a distance D meters away from the Tx array and having N antennas uniformly spaced at a radius R_r, the coordinates of the antenna elements is given by:

0=[0 0 D],

Rx_n=R_γ(γ)R_ψ(ψ)[R_rcos(θ_n), R_rsin(θ_n), D]^T+[Δ_x, Δ_y, Δ_z]. (3)

In Eqs. 2 and 3, additional terms to model offsets that may occur when the arrays are deployed (e.g., angular or displacement offsets). Rotations in azimuth (γ) or elevation (ψ) or center shifts [Δ_x, Δ_y, Δ_z] emulate placement of an antenna in a tower for a backhaul link. To simplify the analysis, without loss of generality, the misalignments are assumed to be focused in the receiver end [5]:

R
γ

(
γ
)

=

[

cos
⁡
(
γ
)

0

sin
⁡
(
γ
)

0

1

0

-

sin
⁡
(
γ
)

0

cos
⁡
(
γ
)

]

,

(
4
)

R
ψ

(
ψ
)

=

[

1

0

0

0

cos
⁡
(
ψ
)

-

sin
⁡
(
ψ
)

0

sin
⁡
(
ψ
)

cos
⁡
(
ψ
)

]

Eqs. 2, 3 and 4 describe two UCAs in the x-y plane with a distance D between centers and UCA radii R_t, R_r, θ_mis the angle of the m-th array element at the Tx, where

θ
m

=

2
⁢
π

M

⁢

(
m
)

,

m
∈

(

0
,
…

,

M
-
1

)

,

and similarly θ_nis the angle of the n-th element in the Rx array, where

θ
n

=

2
⁢
π

N

⁢

(
n
)

,

n

∈

(

0
,
…

,

N
-
1

)

.

To apply the Rician channel explained in [4], computation of the Euclidean distance between the m-th Tx antenna and the n-th Rx antenna is necessary, which is computed as follows:

d_m,n=√{square root over (D²+R_t²+R_r²−2R_tR_rcos(2 π(θ_n−θ_mθ₀)))}, (5)

where θ₀is the difference in angular offset between the Tx and Rx UCAs.

FIG. 5 illustrates a coordinate system for the UCA channel model implemented for the analysis herein and discussed above. The Tx array 501 includes M antennas 502, 503, 404, 505, 506 507, 508, and 509 and is as discussed above) centered in the sigin (0=[0 0 0]) with all antennas at a radius R_tfrom the origin and uniformly spaced around the origin, and with the mth antenna elementhaving an angular offset of

θ
m

=

2
⁢
π

M

⁢

(
m
)

,

m
∈

(

0
 
,
…

,

M
-
1

)

.

On the opposite side of the link, the Rx array 511 is placed a distance D meters away from the Tx array 501, at 0=[0 0 D]. The Rx array 511 includes N antennas 512 513, 514, 515. 516, 517, 518, and 519 all at a radius R_rfrom the origin and uniformly spaced around the origin, with the nth Rx antenna element having an angular offset

θ
n

=

2
⁢
π

N

⁢

(
n
)

,

n
∈

(

0
,
…

,

N
-
1

)

.

In the analysis herein, is the carrier wavelength, D is the distance between the Tx and Rx, ψ_Tx, ψ_Rxare the elevation angles for the Tx and Rx, γ_Tx, γ_Rxare the azimuth rotation angles and α_Tx, α_Rxare the angles between the normal vector with respect to the Tx/Rx array and the x′-axis (parallel to the x-axis).

FIG. 6 illustrates an example of the implementation of utilizing the LICAs 501, 511 for high-speed backhaul links, which is the scenario selected for the analysis. The network 600 includes two base stations BS₁601 and BS₂602, with a wireless backhaul link 603 therebetween. However, the subject matter of the present disclosure may be used in fixed wireless access (FWA), and in mobile access scenarios as well.

The capacity of any MIMO channel by assuming an SVD precoding strategy:

H_M×N=U_M×MΣ_M×NV_N×N^† (6)

where U, V are unitary matrices, † indicates the conjugate transpose, and Σ≤diag(σ₁, σ₂, . . . , σ_P) is a diagonal matrix with P elements, where P=min(M, N) and each element in the matrix Σ is ordered from the largest to the smallest (i.e., σ₁≥σ₂≥ . . . σ_R_H>σ_r+1=σ_P=0) (that is, a diagonal matrix of the highest eigenvalues), and where R_H=rank(H) is the rank of the matrix H [4,6].

To compute the capacity, use is made of the work from Shannon [7], Winters [8]. and Foschini [9], who stated that the capacity C in a MIMO channel is computed as:

C
=

max

Rx
:

Tr
⁡
(
Rx
)

=
ρ

⁢
B
⁢

log
2

(

det
⁡
(

I
M

+

HR
x

⁢

H
†

)

)

=

{

C
Water

=

max

P
i

:

∑
i

P
i

≤
P

B
⁢

∑

i
=
1

R
H

⁢

log
2

(

1
+

P
i

P

⁢

γ
i

)

C
EPA

=

B
⁢

∑

i
=
1

R
H

⁢

log
2

(

1
+

γ
i

N

)

(
7
)

where B is the bandwidth, I_Mis the identity matrix of size M, and R_xis a receiver matrix. If the channel is known by the transmitter, then the power

(

P
i

P

)

is allocated by the water-filling power allocation algorithm [6] (C_Water), where π_n²is the noise power and

γ
i

=

σ
i
2

⁢
P

σ
n
2

;

otherwise the power ρ on each eigenmode

(

R
x

=

ρ
N

⁢

I
N

)

is equally distributed and the capacity will be C_EPA.

Without loss of generality, the number of antennas on both link ends may be assumed to be the same (N). The optimal preceding strategy for a MIMO scenario is the use of SVD to estimate the precoder and receiver algorithms. However, as explained in [10], the computational complexity for a SVD precoder-receiver is

CC
MIMO

=

4
⁢

N
3

+

21
⁢

N
2

-

12
⁢
N

6

,

and SVD precoding requires the entire channel matrix to be sent back to the transmitter. When N increases, the feedback data required for this strategy increases significantly.

For this reason, a low complexity strategy is necessary favor arrays with large number of elements (i.e., massive MEM). In [11], the authors proposed decomposing the UPA into a uniform concentric circular array (UCCA), in order to use the intrinsic properties of a LoS MIMO channel for a uniform circular array (UCA).

A UCA LoS MIMO channel in perfect alignment is a circulant matrix, and can be represented as:

H
MIMO

=

F
†

⁢
Δ
⁢
F

→

H

IFFT
-
FFT

=

FH
MINO

⁢

F
†

→

H

IFFT
-
FFT

=
Δ

(
8
)

Δ
=

diag
⁡
(

λ
1

,

λ
2

,
…

,
 

λ
N

)

,

λ
n

=

❘
"[LeftBracketingBar]"

β
0

4
⁢
π

⁢

∑

m
=
1

N

e

-

jkr

m
,

1

r

m
,

1

⁢

e

-
j

⁢
2
⁢

π
⁢
nm

N

❘
"[RightBracketingBar]"

where F is a DFT matrix. A great advantage of this strategy is that the DFT matrix can be implemented with RF analog circuitry (e.g., Butler Matrix). The impact in the computational complexity is vast because the SVD is completely overlapped by an analog process, leaving a diagonal matrix where the complexity is CC_IFFT-FFT=2N. In other words, the interference between the eigenmodes of the channel is completely nullified.

FIG. 7 is a block diagram illustrating an analog IFFT/FFT implementation in a UCA LoS MIMO system, with the IFFT/FFT using RF analog circuitry (e.g., Butler Matrix) that allows the complexity reduction in the processing by replacing the SVD. The IFFT/EFT implementation 700 includes a transmitter 701 and a receiver 702, respectively including UCA 501 and UCA 511. Transmitter 701 includes N inputs receiving N signals x₁. . . x_Nat each of corresponding RF chains 703a-703n. RF analog processing F^† 704 (e.g., a Butler matrix) generates signals for antennas 501, which transmit those signals in beams 710. The transmitted signals are received on beams 720 at antennas 511, which provide the received signals to RF analog processing F 705 (e.g., a Butler matrix) to produce signals for RF chains 706a-706n to output N signals y₁. . . y_N.

The circulant property of the UCA LoS MIMO is susceptible to offsets in azimuth, elevation and displacements between both link ends. These misalignments increase the interference between eigenmodes and so reducing the signal to interference and noise ratio (SINR) and maximum data rate achievable in the channel.

Using the above-described channel model with IFFT-FFT for diagonalization, a strategy to solve the SINR issues products of the angular or displacement offsets that may occurs in a backhaul placement is tested. The idea behind this strategy is to correct the offset by using a phased array circuitry that steers the array hitting the opposite end. This approach is implemented in an orbital angular momentum (0AM) system [12-13] and, due to the similarities between OAM and UCA LoS MIMO, may be used for this purpose.

FIG. 8 is a block diagram illustrating a beamsteering addition to an analog IFFT/FFT implementation in a IJCA LoS MIMO system in accordance with embodiments of the present disclosure. The implementation 800 includes a transmitter 801 and a receiver 802, respectively including UCA 501 and UCA 511. Transmitter 801 includes N inputs receiving signals x₁. . . x_Nat each of corresponding RE chains 803a-803n. RF analog processing F^† 804 (e.g., a Butler matrix) generates signals to be transmitted. However, before those signals are forwarded to antennas 501 for transmission in beams 810, analog circuit 830 “corrects” the phase based on estimated angles γ, ψ on both sides of the link. The transmitted signals are received on beams 820 at antennas 511, which passes the received signals to an analog circuit 831 for phase “correction” before forwarding to RF analog processing F 805 (e.g., a Butler matrix) to produce signals for RE chains 806a-806n to output N signals y₁. . . y_N.

The mathematical model for this strategy is described as follows:

W_D=1_U⊗w_D, w_D=[e^jw¹^D, . . . , e^jw^N^D], V_D=1⊗v_D=[e^−jv¹^D, . . . , e^−jv^N^D], (9)

where ⊗ is a Kronecker product, 1 is the ones vector and 1_Uis the ones vector of size U, and

w_m^D=kR_r(sin(θ_m)sin(ψ)cos(γ)−cos(θ_m)sin((ψ)),

v_m^D=kR_t(sin(θ_n)sin(ψ)cos(γ)−cos(θ_n)sin((ψ)). (10)

As above, R_tand R_rare the radius for antennas in the UCA 501, 511, respectively; θ_n, θ_mare angular offsets for the nth, mth antenna in the UCA 501, 511, respectively; ψ is the elevation angle for the center of UA 511 relative to UCA 501; and γ is the azimuth rotation angle for the center of UCA 511 relative to UCA 501. The resulting channel with beam steering is:

H_IFFT-FFT^BS=(W_D⊙F)H_MIMO(V_D^T⊙F^†), (11)

where ⊙ indicates a Hadamard product. As shown in FIG. 8, V_D^Tis implemented by the analog circuit 830 between RF analog processing 804 and UCA 501 while W_Dis implemented by the analog circuit 831 between UCA 511 and RF analog processing 805.

The present disclosure focuses on LoS MIMO using FFT/IFFT analog precoding to reduce the computational complexity of the system. A similar approach was discussed in [14]—but using a uniform planar array (LPA) in contrast to the UCA design employed in the present disclosure. Furthermore, [12-13] introduce beam steering as a method to steer signals to the intended destination—but with emphasis on the digital (not analog) domain. In present disclosure, an efficient configuration is presented that uses both FFT/IFFT precoding with beam steering, all in the analog domain. Thus, the channel model in [12-13] is completely different than the current channel model employed herein, since the channel model herein establishes a realistic scenario with scatterers (i.e., NLoS paths). Furthermore, beam steering in [12-13] was used in an OAM system, while the present disclosure focuses on near field LoS MIMO communication backhaul networks. In the present disclosure, signals are not sent in multiple modes (as done in OAM), but instead the signal streams are multiplexed.

Finally, instead of implementing the beam steering with an analog phase array network for the entire UCA, as described in [12-13], the system of the present disclosure will work with miniaturized steerable arrays as ports of the UCA providing the steering features, as shown in FIG. 9.

FIG. 9 is a block diagram illustrating beamsteering in a UCA LoS MIMO system using miniaturized steerable arrays as UCA elements in accordance with embodiments of the present disclosure. The implementation 900 includes a transmitter 901 and a receiver 902, respectively including UCA 501 and UCA 511. Transmitter 901 includes N inputs receiving N signals x₁. . . x_Nat each of corresponding RF chains 903a-903n. RF analog processing F^† 904 generates signals for antennas 501, which transmit those signals in beams 910. The transmitted signals are received on beams 920 at antennas 511, which provide the received signals to RF analog processing F 905 to produce signals for RF chains 906a-906n to output N signals y₁. . . y_N.

In the embodiment of FIG. 9, each antenna within UCAs 501, 511 is a miniaturized steerable array 950. The miniaturized steerable array 950 receives one or more of N signals x₁. . . x_Nto be transmitted or one or more of N signals y₁. . . y_Nto be received, together with estimated angles γ, ψ for the respective side of the link. The miniaturized steerable array 950 determines and implements the phase “correction(s)” based on the estimated angles γ, ψ for the respective transmit or receive beam, in accordance with the discussion above. This may offer some advantages over the embodiment of FIG. 8 in steering individual beams. Having a miniaturized steerable array 950 at each antenna port reduces the area of the analog circuitry compared to having a separate phased array (830, 832) analog system. Of course, both the analog circuits 830, 831 (between RF analog processing 904 and UCA 501 and between UCA 511 and RF processing 931) and the miniaturized steerable array 950 at each antenna of UCAs 501, 511 may be implemented together. Regardless, the beam steering capability allows the seamless deployment of the present disclosure in next generation mesh networks.

The effect of the bearnsteering in a pure UCA LoS MIMO channel is analyzed and compared to the use of IFFT/FFT only or SVD by computing the spectral efficiency and capacity of the channel as follows: Assuming a channel matrix H, the SINR of the ith eigenmode is computed by:

S
⁢
I
⁢
N
⁢

R
i

=

P
i

⁢

❘
"[LeftBracketingBar]"

h

i
,

j

❘
"[RightBracketingBar]"

2

∑

j
≠
i

N

⁢

P
j

⁢

❘
"[LeftBracketingBar]"

h

j
,

i

❘
"[RightBracketingBar]"

2

+

σ
n
2

,

(
12
)

where P_iis the power of the ith eigenmode limited by Σ_pP_i=P and σ_n²is the average noise power of the system. The spectral efficiency (in bits-per-second/Hertz [bps/Hz]) can be computed as:

S
⁢
E

=

∑
i

log
2

(

1
+

SINR
i

)

.

(
13
)

Next, the performance of the beamsteering in a pure UCA LoS MIMO scenario is evaluated and compared against the use of IFFT/FFT only and SVD precoder/receiver strategies. The parameters for this analysis are as follows:

R
t

=

R
r

=

R
=

λ
⁢
D

2
⁢

N
(

sin
⁡
(

π
N

)

2

,

(
14
)