TECHNICAL FIELD

The present disclosure generally relates to wireless mobile communication systems, and particularly, to hybrid digital-analog beamforming in communication systems.

BACKGROUND

Mobile data is experiencing a phenomenal growth, and a paradigm shift is necessary in allocation, utilization and management of new resources. The concept of massive multiple-input multiple-output (MIMO) is a key enabler for increasing spectral efficiency. Massive MIMO may facilitate multi-stream transmission and increase gains of an effective channel, resulting in higher gains of spatial multiplexing and improved signal-to-noise ratio.

In fully digital beamforming in massive MIMO systems, there is one antenna element per each radio frequency (RF) chain, and beamforming is performed in baseband, wherein exercising full control over signal amplitude and phase is possible. In practice, however, the number of RF chains may be much less than the number of antenna elements. As a result, fully digital beamforming may be infeasible. Instead, hybrid (digital-analog) beamforming may be performed in baseband as well as in RF. Digital signal processing may be employed in baseband (in baseband precoder and in baseband combiner) to eliminate interference, and phase shifters in RF (in RF precoder and RF combiner) may be utilized to steer an RF beam to a desired direction.

Quality of service (QoS) is of paramount importance in future networks. Ignoring a users' QoS and instead focusing on spectral efficiency may lead to users' dissatisfaction and eventual migration to other service providers. A user may simultaneously request several services (e.g., web browsing, video streaming, messaging, etc.), each with a different QoS requirement in a single-user system or different users may request various services in a multi-user system. When a user simultaneously requests several services, QoS-aware systems are needed. Conventional hybrid beamforming methods mostly optimize a global measure of performance for an aggregate of all data streams without considering QoS for individual data streams when transmit power is minimized. In contrast, spectral efficiency of each data stream may be constrained to an acceptable value in QoS-aware systems when transmit power is minimized.

A QoS-aware massive MIMO system may be designed by minimizing transmit power while satisfying per data stream mean-squared-error (MSE) constraints. When a baseband precoder performs channel diagonalization and a baseband combiner is minimum MSE (MMSE) combiner, data may be transmitted over multiple sub-channels chosen from an effective channel gain matrix. By channel diagonalization, MSE of different streams may be independent and inversely proportional to both sub-channel gains and transmit power levels. Transmit power of each data stream may be minimized when the respective sub-channel gain of data streams, i.e., respective eigenvalues of an effective channel gain matrix, is maximized. Eigenvalues of effective channel gain matrix may be maximized by adopting eigen-beamforming at both transmitter and receiver, i.e., by adopting right and left eigenvectors of effective channel gain matrix as transmit and receive beamforming vectors, respectively.

In conventional hybrid beamforming, RF precoders and RF combiners may be utilized to perform eigen-beamforming. However, since RF precoders and RF combiners include only exponential entries, they may not be equal to the right and left eigenvectors of effective channel gain matrix. Therefore, RF precoders and RF combiners may provide approximations of the right and left eigenvectors of effective channel gain matrix. In determining the approximation, only phase information in eigenvectors of effective channel gain matrix may be utilized and amplitudes of eigenvectors may be ignored, resulting in small gains for sub-channels. To compensate for low gains, transmit power may be increased. In other words, QoS may be satisfied in the conventional hybrid beamforming but excessive transmit power may be required.

There is, therefore, a need for a hybrid beamforming method that guarantees per data stream QoS requirements. There is also a need for a hybrid beamforming method that minimizes transmit power of base station by maximizing effective channel gain matrix.

SUMMARY

This summary is intended to provide an overview of the subject matter of the present disclosure, and is not intended to identify essential elements or key elements of the subject matter, nor is it intended to be used to determine the scope of the claimed implementations. The proper scope of the present disclosure may be ascertained from the claims set forth below in view of the detailed description below and the drawings.

In one general aspect, the present disclosure describes an exemplary method for hybrid digital-analog beamforming in communication systems. An exemplary method may include obtaining a plurality of transmit phase shifted signals, obtaining a plurality of transmit signals from the plurality of transmit phase shifted signals, and transmitting the plurality of transmit signals on a set of wireless channels. In an exemplary embodiment, obtaining the plurality of transmit phase shifted signals may include obtaining a hybrid precoding matrix FH. In an exemplary embodiment, hybrid precoding matrix FHmay be obtained by utilizing one or more processors. In an exemplary embodiment, hybrid precoding matrix FHmay be obtained based on a plurality of dominant right eigenvectors of a first effective channel matrix. An exemplary first effective channel matrix may be associated with a set of channel matrices. In an exemplary embodiment, hybrid precoding matrix FHmay include a product of a digital precoding matrix FBB(1)and an analog precoding matrix FRF. In an exemplary embodiment, each entry of analog precoding matrix FRFmay include one of zero or a respective complex value with unit magnitude. In an exemplary embodiment, each channel matrix in the set of channel matrices may be associated with a base station (BS) and a respective user equipment (UE) in a set of UE.

In an exemplary embodiment, obtaining the plurality of transmit phase shifted signals may further include obtaining a digital precoding matrix FBB(2)based on the hybrid precoding matrix FH, obtaining a plurality of digitally precoded symbols based on digital precoding matrix FBB(2), obtaining a plurality of frequency-upconverted signals from the plurality of digitally precoded symbols, and generating the plurality of transmit phase shifted signals from the plurality of frequency-upconverted signals.

In an exemplary embodiment, digital precoding matrix FBB(2)may be obtained by utilizing the one or more processors. In an exemplary embodiment, digital precoding matrix FBB(2)may be obtained based on a second effective channel matrix associated with hybrid precoding matrix FHand the set of channel matrices. In an exemplary embodiment, the plurality of digitally precoded symbols may be obtained by utilizing the one or more processors. In an exemplary embodiment, the plurality of digitally precoded symbols may be obtained by multiplying a transmit vector and a digital precoding matrix FBB. An exemplary transmit vector may include a plurality of transmit symbols. In an exemplary embodiment, digital precoding matrix FBBmay be equal to FBB(1)FBB(2).

In an exemplary embodiment, an amplitude and a phase of each of the plurality of frequency-upconverted signals may be associated with a respective digitally precoded symbol of the plurality of digitally precoded symbols. In an exemplary embodiment, a number NtRFof the plurality of transmit RF chains may satisfy a condition according to NtRF≥NSwhere NSis a number of the plurality of transmit symbols. In an exemplary embodiment, the plurality of transmit phase shifted signals may be generated by utilizing a plurality of transmit phase shifters of the BS. In an exemplary embodiment, the plurality of transmit phase shifted signals may be generated by phase shifting the plurality of frequency-upconverted signals based on analog precoding matrix FRF.

In an exemplary embodiment, the plurality of transmit signals may be transmitted by utilizing a plurality of transmit antennas of the BS. In an exemplary embodiment, the set of wireless channels may be associated with the set of channel matrices. In an exemplary embodiment, a number Ntof the plurality of transmit antennas may satisfy a condition according to NtRF<Nt.

In an exemplary embodiment, obtaining the hybrid precoding matrix FHmay include obtaining a hybrid combining matrix WH,uin a set of hybrid combining matrices and generating hybrid precoding matrix FHbased on hybrid combining matrix WH,u. In an exemplary embodiment, hybrid combining matrix WH,umay be obtained by utilizing the one or more processors. In an exemplary embodiment, hybrid combining matrix WH,umay be obtained based on a plurality of dominant left eigenvectors of a channel matrix Huin the set of channel matrices. In an exemplary embodiment, hybrid combining matrix WH,umay be associated with a uthUE in the set of UE where 1≤u≤U and U is a size of the set of UEs. In an exemplary embodiment, hybrid combining matrix WH,umay include a product of a digital combining matrix WBB,u(1)and an analog combining matrix WRF,u0. In an exemplary embodiment, each entry of analog combining matrix WRF,umay include one of zero or a respective complex value with unit magnitude.

An exemplary method may further include obtaining a uthplurality of estimated symbols by computing a digital combining matrix WBB,u(2), transmitting a uthcombiner set to the uthand generating the uththe plurality of estimated symbols based on the uthcombiner set. In an exemplary embodiment, the uthplurality of estimated symbols may be computed according to an operation defined by WBB,u(2)=(Heff,uF1BB,u(2)FBB,u(2)HHeff,uH+Rñ,u)−1Heff,uFBB,u(2)where Heff,u=WH,uHHuFH, Rñ,u=WH,uHRn,uWH,u, and Rn,uis a covariance matrix of a noise vector at the uthUE. In an exemplary embodiment, the uthcombiner set may be transmitted by the BS. In an exemplary embodiment, the uthcombiner set may include digital combining matrix WBB,u(1), digital combining matrix WBB,u(2), and analog combining matrix WRF,u. In an exemplary embodiment, the uththe plurality of estimated symbols may be generated by the uthUE.

In an exemplary embodiment, generating the uthplurality of estimated symbols may include receiving the uthcombiner set, receiving a uthplurality of receive signals associated with the plurality of transmit signals, obtaining a uthplurality of receive phase shifted signals from the uthplurality of receive signals, obtaining a uthplurality of frequency-downconverted signals from the uthplurality of receive phase shifted signals, and computing the uthplurality of estimated symbols based on the uthplurality of frequency-downconverted signals.

In an exemplary embodiment, the uthcombiner set may be received by the uthUE. In an exemplary embodiment, the uthplurality of receive signals may be received by utilizing a uthplurality of receive antennas of the uthUE. In an exemplary embodiment, the uthplurality of receive phase shifted signals may be obtained by utilizing a uthplurality of receive phase shifters of the uthUE. In an exemplary embodiment, the uthplurality of receive phase shifted signals may be obtained by phase shifting the uthplurality of receive signals based on analog combining matrix WRF,u. In an exemplary embodiment, the uthplurality of frequency-downconverted signals may be obtained by utilizing a uthplurality of receive RF chains of the uthUE. In an exemplary embodiment, an amplitude and a phase of each of the uthplurality of frequency-downconverted signals may be associated with a respective receive phase shifted signal of the uthplurality of receive phase shifted signals. In an exemplary embodiment, a number Nr,uRFof the uthplurality of receive RF chains may satisfy a condition according to Nr,uRF≥Nuwhere Nuis a number of the uthplurality of estimated symbols. In an exemplary embodiment, the number of the uthplurality of receive RF chains may satisfy another condition according to Nr,uRF<Nr,uwhere Nr,uis a number of the uthplurality of receive antennas. In an exemplary embodiment, the uthplurality of estimated symbols may be computed by utilizing the one or more processors. In an exemplary embodiment, the uthplurality of estimated symbols may be computed by multiplying a receive vector by a digital combining matrix WBB,u. In an exemplary embodiment, the receive vector may include the uthplurality of frequency-downconverted signals. In an exemplary embodiment, digital combining matrix WBB,umay be equal to WBB,u(1)WBB,u(2).

In an exemplary embodiment, obtaining hybrid combining matrix WH,umay include setting each entry of an RF combining matrixWRF(0)to one of zero or a respective complex value, and repeating a first iterative process until a first termination condition is satisfied. An exemplary complex value may include a unit amplitude and a random phase.

In an exemplary embodiment, an rthiteration of the first iterative process may include computing a baseband combining matrixWBB(r)and computing an RF combining matrixWRF(r). In an exemplary embodiment, baseband combining matrixWBB(r)may be computed according to an operation defined byWBB(r)=(WRF(r−1)HWRF(r−1))−1WRF(r−1)HVFwhere r≥1 is an integer and VFincludes the plurality of dominant left eigenvectors. In an exemplary embodiment, RF combining matrixWRF(r)may be computed by one of setting a (k, l)thentry ofWRF(r)to a first value or setting the (k, l)thentry ofWRF(r)to one of zero or a second value. An exemplary first value may be equal to e−j∠βk,l(1)where

βk.l(1)=∑n=1Nr,uRF⁢ξk,n*⁢Wl,n,
ξk,n=Vk,n−Σi≠lejφk,iWi,n, Vk,nis a (k, n)thentry of VF, Wl,nis an (l, n)thentry ofWBB(r), and ejφk,iis a (k, l)thentry ofWRF(r−1). An exemplary second value may be equal to e−j∠βk,l(2)where βk,l(2)=

∑n=1Nr,uRF⁢Vk,n*⁢Wl,n.
An exemplary first termination condition may be defined according to ∥WRF(r−1)WBB(r−1)−VFμF−∥WRF(r)WBB(r)−VF∥F≤∈Wwhere ∈Wis a first threshold and ∥.∥Fis a Frobenius norm. In an exemplary embodiment, hybrid combining matrix WH,umay be equal toWRF(r1)WBB(r1)where r1is a total number of iterations of the first iterative process when the first termination condition is satisfied. In an exemplary embodiment, analog combining matrix WRF,umay be equal toWRF(r1). In an exemplary embodiment, the digital combining matrix WBB,u(1)may be equal toWBB(r1).

In an exemplary embodiment, generating hybrid precoding matrix FHmay include setting each entry of an RF precoding matrixFRF(0)to one of zero or a respective complex value, and repeating a second iterative process until a second termination condition is satisfied. An exemplary complex value may include a unit amplitude and a random phase.

In an exemplary embodiment, an rthiteration of the second iterative process may include computing a baseband precoding matrixFBB(r)and computing an RF precoding matrixFRF(r). In an exemplary embodiment, baseband precoding matrixFBB(r)may be computed according to an operation defined byFBB(r)=(FRF(r−1)HFRF(r−1))−1FRF(r−1)HVWwhere VWincludes the plurality of dominant right eigenvectors of the first effective channel matrix. In an exemplary embodiment, the first effective channel matrix may be equal to WmuHmuwhere Hmu=[H1T. . . HUT]Tand Wmuis a block diagonal matrix. In an exemplary embodiment, each diagonal block of Wmumay include a respective hybrid combining matrix in the set of hybrid combining matrices.

In an exemplary embodiment, RF precoding matrixFRF(r)may be computed by one of setting a (q, s)thentry ofFRF(r)to a third value or setting the (q, s)thentry ofFRF(r)to one of zero or a fourth value. An exemplary third value may be equal to e−j∠γq,s(1)where γq,s(1)=

∑n=1NtRF⁢δq,n*⁢Fs,n,δq,n=Vq,n-∑i≠s⁢eq,ij⁢⁢θ⁢Fi,n,Vq,n
is a (q, n)thentry of VW, Fs,nis an (s, n)thentry ofFBB(r), and ejθq,iis a (q, i)thentry ofFRF(r−1). An exemplary fourth value may be equal to e−j∠γq,s(2)where γq,s(2)=Σn=1NtRFV*q,nFs,n. An exemplary second termination condition may be defined according to ∥FRF(r−1)FBB(r−1)−VW∥F−∥FRF(r)FBB(r)−VW∥F≤∈Fwhere ∈Fis a second threshold. In an exemplary embodiment, hybrid precoding matrix FHmay be equal to FRF(r2)FBB(r2)where r2is a total number of iterations of the second iterative process when the second termination condition is satisfied. In an exemplary embodiment, the analog precoding matrix FRFmay be equal toFRF(r2). In an exemplary embodiment, digital precoding matrix FBB(1)may be equal toFBB(r2).

In an exemplary embodiment, obtaining the digital precoding matrix FBB(2)may include obtaining a precoding matrix FBB,u(2). In an exemplary embodiment, precoding matrix FBB,u(2)may be associated with the uthUE. In an exemplary embodiment, obtaining precoding matrix FBB,u(2)may include setting a unitary matrix V1,uto Nuleast dominant right eigenvectors of an interference channelHu, setting a unitary matrix V2,uto a plurality of right eigenvectors of

Rn~,u-12⁢Heff,u⁢V1,u,
obtaining a transmit power allocation matrix Pu, and computing precoding matrix FBB,u(2).

In an exemplary embodiment, interference channelHumay be equal to [Heff,1T, . . . , Heff,u−1T, Heff,u+1T, . . . , Heff,UT]Twhere U>1. In an exemplary embodiment, transmit power allocation matrix Pumay be obtained based on the set of channel matrices, hybrid precoding matrix FH, and the hybrid combining matrices set. In an exemplary embodiment, transmit power allocation matrix Pumay include a diagonal matrix. In an exemplary embodiment, each diagonal entry of transmit power allocation matrix Pumay include a respective non-negative value. In an exemplary embodiment, precoding matrix FBB,u(2)may be computed according to an operation defined by

FBB,u(2)=V1,u⁢V2,u⁢Pu12.
In an exemplary embodiment, digital precoding matrix FBB(2)may be equal to [FBB,1(2), . . . , FBB,U(2)].

In an exemplary embodiment, obtaining transmit power allocation matrix Pumay include computing a kthdiagonal entry pu,kof transmit power allocation matrix Puaccording to one of a first operation or a second operation. In an exemplary embodiment, the first operation may be defined by pu,k=1/λu,k−1(ρu,k−1−1) where λu,kis a kthdominant eigenvalue

Rn~,u-12⁢Heff,u⁢V1,u,
and ρu,kis a kthmaximum acceptable mean squared error of the uthUE. In an exemplary embodiment, the second operation may be defined by

pu,k=max⁡(μλu,k-12-λu,k-1,0)
where μ satisfies a condition according to

Σu=1U⁢Σk=1Ns⁢max⁡(μλu,k-12-λu,k-1,0)=Pmax,
and Pmaxis a power budget of the BS.

In an exemplary embodiment, obtaining digital precoding matrix FBB(2)may include obtaining a precoding matrix FBB,1(2). In an exemplary embodiment, digital precoding matrix FBB(2)may be associated with a first (1st) UE in the set of UEs set. In an exemplary embodiment, obtaining precoding matrix FBB,1(2)may include setting a unitary matrix V3to a plurality of right eigenvectors of

Rn~,1-12⁢Heff,1,
obtaining a transmit power allocation matrix P1, and computing precoding matrix FBB,1(2)based on transmit power allocation matrix P1. In an exemplary embodiment, transmit power allocation matrix P1may be obtained based on the set of channel matrices, hybrid precoding matrix FH, and the set of hybrid combining matrices. In an exemplary embodiment, transmit power allocation matrix P1may include a diagonal matrix. In an exemplary embodiment, each diagonal entry of transmit power allocation matrix P1may include a respective non-negative value. In an exemplary embodiment, precoding matrix FBB,1(2)may be computed according to an operation defined by

FB⁢B,1(2)=V3⁢P112.
In an exemplary embodiment, digital precoding matrix FBB(2)may be equal to FBB,1(2).

In an exemplary embodiment, obtaining transmit power allocation matrix P1may include computing a kthdiagonal entry p1,kof transmit power allocation matrix P1according to one of a third operation and a fourth operation. In an exemplary embodiment, the third operation may be defined by p1,k=1/λ1,k−1(ρ1,k−1−1) where λ1,kis a kthdominant eigenvalue of

Rn~,1-12⁢Heff,1,
and ρ1,kis a kthmaximum acceptable mean squared error of the first (1st) UE. In an exemplary embodiment, the fourth operation may be defined by

p1,k=max⁡(μλ1,k-12-λ1,k-1,0)
where μ satisfies a condition according to

Σk=1Ns⁢max⁡(μλ1,k-12-λ1,k-1,0)=Pmax.

Other exemplary systems, methods, features and advantages of the implementations will be, or will become, apparent to one of ordinary skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description and this summary, be within the scope of the implementations, and be protected by the claims herein.

