DESC:DESCRIPTION
FIELD OF INVENTION
[0001] Embodiments of the present disclosure relate to wireless transceivers and more
particularly relate to method, system and apparatus for optimal hybrid beamforming in a multiple
antenna wireless system.
RELATED ART
[0002] Wireless transceivers often employ RF antennas for radiating and collecting the RF signal
(electromagnetic waves) for transmitting and receiving wireless signals. For example, wireless
communication system such as 3G/4G/5G systems, RADAR systems and object detection systems
employ RF antennas to transmit and receive RF signals. The antenna radiates the RF signal energy
in all directions. Thus, the energy transmitted in any desired direction is lesser than the total
energy/strength radiated by the antenna. In order to enhance the transmitted RF signal strength
(gain) in a particular direction, beam forming techniques are employed. In the beam forming
technique multiple phase shifted version of the RF signal are transmitted or received on a plurality
of antennas (antenna array) as is well known in the art. The conventional beam forming technique
is further described in the literature titled Multibeam Antenna Technologies for 5G Wireless
Communications by Wei Hong, et al, published in IEEE transactions on antennas and
propagation, vol. 65, no. 12, December 2017, which is incorporated herein by reference. Briefly,
beam forming (generating multiple phase shifted signals) is performed in analog mode, digital
mode and hybrid mode.
[0003] FIG. 1A illustrates an example conventional analog beamforming. As shown there, the
antennas 110A-N receives the RF signals, the phase shifters 120A-N shift the phase of the
corresponding received RF signals, the combiner 130 combines the phases sifted RF signals. The
multiplier 140 and local oscillator (LO) 145, converts the RF signal received from the combiner to
base band signal for further processing. The combined RF signal provided by combiner 130 is
represented by relation:
(1) Y = S WiXi
????
=0 ,
In that, Xi represents signals received from antennas, Wi represents the weights (phases shift and
gain) provided to the corresponding ones of Xi signals. Accordingly, as the number of antennas are
increased to reduce the beam width, the Wi requires to be in smaller phase values (at least when
beams are required to be steered in smaller angle or good angular resolution) . The analog
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conventional beam forming places limitation (at least in terms of the analog hardware part) on the
smaller phase values in Wi.
[0004] FIG. 1B illustrates an example conventional digital beam forming. As shown there, the
antennas 110A-N receives the RF signals, the mixers 150A-N mixes the RF signals on
corresponding channels 116A-N with a reference signal from LO 160 to convert each RF signal to
respective baseband signals 157A-N. Digital Beam former170 performs beam forming to provide
baseband beams on paths 171 and 172. The beamformer output Y may be represented using
relation:
(2) Y = ????,
in that, W represents a weight matrix and X represents the input baseband signal vector.
[0005] As is well known in the art, the conventional digital beam former 170 may perform
digitization of the RF signal and may perform matrix multiplication with the weight matrix. Due
to digital processing with large bit width multipliers, a smaller beam width (high resolution) may
be obtained. In other words, a smaller phase shifts may be achieved in the digital processing,
thereby accommodating any desired beam direction and resolution. However, the digital beam
former increases the complexity of the hardware as the number of base band converter (base band
processing channels) increase with increasing number of receiving/transmitting antennas.
[0006] FIG. 1C illustrates an example conventional hybrid beam forming. As shown there, the
antennas 110A-N receives the RF signals, the analog beam former 180 generates set of beams
181A-D, the Base band processing channel 185A-D converts the RF beam 181A-181D to
corresponding baseband beam 186A-D, digital beam former 190 performs digital beam forming
on the base band signals 186A-D to generate digitized beams 191 A-C.
[0007] As is well known in the art, the number of base band converting channels is reduced due to
first level of analog beam forming (180) and the benefits of smaller phase angles (high resolution)
are obtained by employing the digital beam former (190) . The conventional hybrid beam former
reduces the hardware complexity by reducing the number of baseband processing channels.
However, such reduction in the hardware causes the reduced flexibility at the digital beam former.
[0008] US Patent US10, 979, 117 (Granted to the current applicant of this patent application)
overcomes some of the disadvantages of the above mentioned prior at. However, the technology
as taught in US 10, 979, 117 is not optimal when the antennas are sparsely connected to analog
beamforming channels.
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SUMMARY
[0009] According to an aspect, a radio frequency receiver comprises a set of antennas for
receiving an RF signal over a communication channel represented by a channel matrix Hd, a
plurality of analog beamformer for generating plurality of analog beams, wherein each analog
beam former is coupled to a subset of antennas comprising a fewer number antennas in the set of
antennas, a mixer for combining the plurality of analog beams to provide a down converted signal,
and a digital beam former for generating a plurality of digital beams, wherein a set of analog
weights (FR) of the plurality of analog beamformer and a set of digital weights (FB) of the digital
beamformer are selected such that effective beam formed by their product FB FR is orthogonal and
spans the same space as columns of the channel matrix Hd.
[0010] According to another aspect, the digital beam former providing a signal yb= FB FR Hd P s
+ FB FR n, in that s representing the signal transmitted into the channel Hd, P representing the
precoder matrix at a transmitter transmitting the signal s and n representing a receiver noise.
[0011] According to yet another aspect, the plurality of antennas are arranged over set of patches
on the radio frequency receiver wherein, the set of patches are physically at different positions, the
subset of antennas are derived from one or more patches in the set of patches.
[0012] According to yet another aspect, a method in a radio frequency communication system
comprising a set of analog beam former and a digital beam former comprises constructing a first
matrix order T X M where in M representing a number of analog beamformer in the set of analog
beamformer and T representing number of antenna, wherein the first matrix is sparse with non
zero values according to the number antennas coupled to correspond analog beamformer and rest
being zero values, determining a first set of weights corresponding to the non zero elements in the
first matrix by minimizing an angle between the vector spaces spanned by an ideal set of weights
and an another set of weights, wherein the ideal set of weights being ideal values and the another
set of weights comprising all possible sparse orthogonal weights as allowed by the sparse antenna
coupling and determining a weight matrix as a transformation matrix between a basis vectors of
the two vector spaces and adapting the weight matrix for implementing the digital beamformer.
[0013] According to yet another aspect, a radio frequency transmitter comprises a set of antennas
for transmitting an RF signal over a communication channel, a plurality of analog beamformer for
generating plurality of analog beams, wherein each analog beam former is coupled to a subset of
antennas comprising a fewer number antennas in the set of antennas, a digital beam former for
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generating a plurality of digital beams, and a mixer for combining the plurality of digital beams to
provide a upconverted signal, wherein a set of analog weights of the plurality of analog
beamformer and a set of digital weights of the digital beamformer maintain a relation: WR WB ˜
V, in that WB representing weights of the digital beamformer, the WR representing weights of the
analog beamformer and V representing a right singular vectors of the communication channel
matrix Hd.
BRIEF DESCRIPTION OF DRAWINGS
[0014] FIG. 1A illustrates an example conventional analog beam forming.
[0015] FIG. 1B illustrates an example conventional digital beam forming.
[0016] FIG. 1C illustrates an example conventional hybrid beam forming.
[0017] FIG. 2A is an example RF receiver system in an embodiment.
[0018] FIG. 2B illustrates an example device 299 in which the antenna elements are
distributively/sparsely located instead of a regular (geometrical) array.
[0019] FIG. 3 is a block diagram illustrating a transmitter in an embodiment.
[0020] FIG. 4 is a block diagram illustrating a communication system 400 comprising both
transmitter 401 and receiver 402.
[0021] FIG. 5 illustrates the weight computation in one embodiment.
DETAILED DESCRIPTION OF THE PREFERRED EXAMPLES
[0022] FIG. 2A is an example RF receiver system in an embodiment. The receiver 201 is shown
comprising antenna array 210, analog beamformers 220, Mixer 230, Digital Beam former 240,
decoder 260 and input/output (I/O) devices 270. Each block is further described below.
[0023] The antenna array 210 is shown comprising antennas (antenna elements) 210A-210N. The
antenna array 210 is employed to determine the angle of arrival (beamforming as is well known).
The antenna array 210 is configured for a MIMO (Multiple Input and Multiple Output) operation.
In one embodiment the antenna elements 210A-210N are distributively located on a device. FIG.
2B illustrates an example device 299 in which the antenna elements are distributively/sparsely
located instead of a regular (geometrical) array. As shown there, the antenna elements are formed
on edges and at centre (for illustration) in patches 280A-280K. Each patch 280A-280K houses a
finite number of antenna elements that may not be equal in number. The device 299 may be a
mobile device operative on 5G protocol or 5G communication links. Such sparse arrangement of
antenna may be required on a device to optimise on the space, at least.
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[0024] The analog beamformers 220 receives the signal from the antenna array 210 and perform
analog beam forming. The analog beamformers 220 is shown comprising plurality of analog beam
formers 220A-220L. Each analog beam former 220A-220L may receive a signal from selected set
of antennas. For example, the beamformer 220A may receive signal from antenna 210A-C (for
example, not shown), the beamformer 220B may receive signal from antenna 210D-210G, the
beamformer 220C may receive signal from antenna 210A, 210D, 210F-210H, etc. Each
beamformer 220A-220L may receive the signal from the antennas located in different patches
280A-280K, or from a same patch, etc. Since only a few antenna elements are coupled to each
analog beamformer, the weight matrix representing the analog beamforming by the analog beam
former 220A-220L may be sparse and is of the form:
[
??1 0 ??3
0 ??2 0
0 0 0
0 … .0 0
??3 … .0 0
0 … . ??4 ??5
]
in that, each row representing the analog beamformer in the plurality of beam former with X’s
representing the antennas coupled to the corresponding analog beam former and 0’s representing
the unconnected antennas to the respective beamformer in the respective position of an array X1-
XT (210A-210N).
[0025] Each analog beamformer 220A-220L provides the Beams to the mixer 230. The Mixer
230 mixes the received RF beams from the analog beamformers 220A-220L with a reference
signal to generate a corresponding number of beams in the intermediate frequency band (referred
to as IF Beams). The Mixer 230 may also combine the signal and provide the combined signal as
a baseband (BB) signal to the digital beamformer 240. The number of IF/BB beams corresponds
to number of beamformers. The IF/BB beams are provided to Digital Beam former 240.
[0026] The Digital Beamformer 240 performs digital beamforming on the received IF beams. In
one embodiment, the digital beamformer 240 is operative to generate M number of base band
beams. The Digital beam former may be implemented to provide a desired beam resolution. The
beam formed at the output of the digital beam former is dependent on the values in the analog
beamformers 220 and digital beam former 240. In one embodiment, the based band signal formed
at the output of the digital beamformer may be represented as:
(1) yb= FB FR Hd P s + FB FR n (also referred to as signal model).
[0027] Wherein, yb representing the based band signal at the output of the digital beamformer
240, FB representing the weight matrix of the digital beam former 240, FR representing the weight
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matrix of the analog beam former 220, Hd representing the downlink channel matrix (transfer
function), s representing the signal (data/information) intended for transmitting at a transmitter, P
representing the precoder matrix at the transmitter, P s = S representing signal transmitted into
the channel Hd, and n representing the receiver noise. In one embodiment, the values (weights) FB
and FR is set such that the product FB FR =U, wherein the U is left singular vectors (also referred
to as matrix) of Hd.
[0028] Decoder 260 decodes the data and information from the output of the digital beam former
240. Due to the weight selected in the analog beamformer 220 and the digital beamformer 240, the
signal to noise ratio is increased and/or the interference between the spatial channels are
minimised even when the antennas are sparsely connected to the analog beamformer. The
decoded information is provided to the I/O device 270 for performing several control operations
and/or further processing. The I/O devices 270 may comprise one or more of memory device,
communication modem, data ports, etc.
[0029] In conjunction, a transmitter may transmit the signal s forming a beam through analog and
digital beamformer. FIG. 3 is a block diagram illustrating a transmitter in an embodiment. The
transmitter 300 is shown comprising an antenna array 310, analog beamformers 320, Mixer 330,
Digital Beam former 340, Encoder 360 and data source 370. In that, the analog beamformers 320
are selectively coupled to the antennas to form sparse matrix. The digital beam former operate in
base band or in the IF band to generate plurality of digital beam from the base band signal
generated by the encoder. The encoder 360 generates the digital signal representing the data from
the data source 370. In other words, the transmitter 300 (elements) operate conjunctively to the
receiver 200. Accordingly, in one embodiment the signal s transmitted on the channel may be
represented as:
(2) S= WR WB s
[0030] In that, WB representing the weight matrix of the digital beam former 340, WR is
representing the weight matrix of the analog beam former 320, s representing the encoded
baseband signal. In one embodiment, the values (weights) WB and WR is set such that the product
WR WB =V, wherein the V is right singular matrix of Hd. While description is provided with the
downlink channel for illustration, the technology may be adopted to uplink channel (with the
corresponding up link channel matrix Hu) by maintaining the order and rank of the weight
matrixes.
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[0031] FIG. 4 is a block diagram illustrating a communication system 400 comprising both
transmitter 401 and receiver 402. In that, the transmitter 401 and receiver 402 may be one of a
base station (BS) and user equipment (UE). The base station may be one of the 4G and 5G
network base station and UE may be a mobile phone connecting to base station. In an
embodiment, both UE and base station may house both transmitter 401 and receiver 402 as
transceiver for both transmission and reception of 4G/5G or any other such communication signal.
[0032] The transmitter 401 is shown comprising layer mapping unit 410, Digital beamformer
(DBF) 420, RF Mixer 430 analog beamformer and Power Amplifier (ABF & PA) 440A-440M,
transmit antenna 449A-T. Similarly the receiver 402 is shown comprising receiving antennas
460A-R, analog beamformer and Power Amplifier (ABF & PA) 465A-465N, RF mixer 470,
digital beam former (DBF) 480, layer de-multiplexer 490. In that the weight determination unit
450 is shown coupled to the DBF 420 and 480, ABF &PA 440A-440M and 460A-440N.
[0033] In the transmitter, the layer mapping unit 410 perform layer mapping of user code words
(multiple user data) to the number of analog beamformers (ABF) as is well known in the field of
4G/5G communication system. For example, when the antenna array 449A-449T and 460A-T are
operated as MIMO system providing spatial multiplexing capabilities, the layer mapping unit 410
maps the code words to the desired number of layers that are spatially multiplexed using the
transmit and receive antenna array. Digital beamformer (DBF) 420 is shown providing M beams
to the RF mixer 430. The DBF 430 may be implemented similar to digital beam former 340. The
RF Mixer 430 receives the M digital beams from the DBF 420 and performs up-conversion to
generate corresponding M number of RF beams. The RF beams are provided to the corresponding
ABF &PA 440A-440M. The ABF &PA 440A-440M spreads the M beams to T antennas 449A-
449T. As shown there each analog beam former is coupled to fewer numbers of antennas (Fewer
than T). Thus, forming a sparsely connected antenna network. The ABF &PA 440A-440M may
be coupled to antennas sparsely as described with reference to FIG. 3.
[0034] Similarly, the receiver section 402 operates in conjunction with the transmitter 402. As
shown there, the R number of antennas 460A-R receives the signal through the channel (4G/5G).
The antennas 460A-R are sparsely coupled to the ABF & PA 465A-465N. That is only a fewer
number of antennas are coupled to each ABF & PA 465A-465N. As shown, the ABF & PA 465A-
465N provides N channels to the RF mixer 470 to combine and down covert the N channels of RF
analog beamformer signals. The combined and down converted N channel signal is provided to
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the DBF 480 for digital beam forming. The digital beamformer 480 may be implemented similar
to the DBF 240. The layer de-multiplexer 490 operates to de-multiplex the code words from L
number of layers to form user data streams.
[0035] In the above MIMO communication system 400 with T transmit antennas at the transmitter
and R receive antennas at the receiver, the transmit antennas are fed by analog beamformers
which spread the M channel input to the T antennas. The M channels of the analog beamformers
are fed by L spatial layers of user signal through a digital beamformer. As an example, if T = 64,
M = 8, and 4 = L = M, each analog beamformer is connected to at most 8 antennas in a nonoverlapping
manner. Similarly, the receiver uses N channels output after the analog beamformer,
K spatial channels after the digital beamformer. For instance, say R = 16, N = 4 and 2 = K = N.
The channel (not shown) is assumed to be quasi-stationary with individual elements of the channel
matrix H drawn from random variables for every coherence period (for example, circularly
symmetric, complex Gaussian (CSCG) random variables with zero mean and unit variance).
[0036] Each beam former DBF 420 and 480 and ABF & PA 440A-440M and 465A-465N
comprises phase shifters and gain unit (as is well known and also as illustrated in the US 10, 979,
117). The phase angle and the gain (amplitude) value of the phase shifter and the gain unit
together referred to as the weights. The weight computation unit 490 determines and sets the
weights of the beamformers DBF 420 and 480 and ABF & PA 440A-440M and 465A-465N.
[0037] FIG. 5 illustrates the weight computation in one embodiment. In block 510, the weight
computation unit 490 construct sparse orthogonal matrices which can be employed as Analog
beamforming weights of ABF & PA 440A-440M and/or 465A-465N. In block 520, the weight
computation unit 490 determines the optimal sparse orthogonal weights from the two set of
weights (one being ideal desired and other being a set of all possible sparse orthogonal weights as
allowed by the sparse antenna geometry chosen by the antenna design) by minimizing the angle
between the vector spaces spanned by the two sets of weights. In block 530, the weight
computation unit 490 compute the digital beamforming matrix as the transformation matrix
between the basis vectors of the two vector spaces (corresponding to the ideal desired singular
vectors matrix and best possible sparse orthogonal weights). Further describing with reference to
FIG. 4 and 5, the weight computation unit 490 may determine the transmit beamforming as below.
[0038] Considering number of transmit antennas is T, and the transmit antennas are split across M
RF-BB chains with D = T/M antennas per chain. That is, the analog beamformer associated with
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each RF-BB chain has D number of antenna elements. Thus in the equation (2), H has dimensions
R X T, the analog beamformer WR has dimensions T X M, the digital beamformer WB has
dimensions M X L, the user signal vector s has dimensions L X 1 and the receiver noise vector n
has dimensions R X 1. Wherein, L representing the number of layers used in the communication.
It may be appreciated that, the analog beamformer Matrix WR is sparse, as only D antennas are
attached to every RF chain. This imposes certain structure in WR, apart from the restrictions in the
precision available for the phase shift and amplitude control. That is, the analog weights can be
selected, only from a finite set of allowable phase shifts and amplitude scales. In one embodiment,
as the M strongest right singular vectors of the channel matrix Hd form the optimal transmit
beamforming (precoding) matrix, P, the weight computation unit 490 selects P = WR WB = V1:L,
wherein V1:L denotes the dominant L right singular vectors of Hd.
[0039] In that, the structure of WR is obtained based on the hardware constraints such as the
number of antennas per RF-BB chain, precision available for the phase, amplitude control and the
total transmit power per transmission, per RF-BB chain. Based on these constraints, the sparse
orthogonal matrices may be constructed using the well known complex orthogonal design (COD)
for space time block codes (STBC) techniques. Thus, by selecting the COD (which meets the
dimensions required for each Analog beam former) as base code matrix, the sparse orthogonal
matrices may be constructed meeting the constraints, which can be used as the analog
beamforming matrix, WR. In one embodiment, the number of columns in COD is chosen such
that, the analog beamformer output forms sufficient statistics represented by: ybs= WH
bs (X+N).
Wherein, where X denotes the array signal matrix with dimensions Nant X K, the beam space
weight matrix Wbs has dimensions Nbs X Nant, K denotes the number of snapshots of array data
and N is the observation noise and Nant is the number of antennas connected to one analog
beamformer.
[0040] To approximate the right singular vectors to maximize the achieved rate, the following
sub-space approximation may be utilized. In other words, WR and WB must meet the requirement
WRWB ˜ V1:L. This approximation required to be valid among all possible matrices of WR and
WB such that capacity is maximized. That is, the best analog beamformers may be selected by
solving the linear programming relation:
(3) W*
R = arg max || WH
R V1:L||2
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[0041] Similarly, Digital beamformer weights WB may be selected after determining the weights
of the analog beamformer using the relation WB =WH
R V, since it is desirable to approximate V
as the product of WR and WB.
[0042] While determining the WR and WB for transmitter, the receiver weights are presumed to be
ideal and vice a versa. However, when both transmitter and receivers are incorporated in a single
chip, the WR and WB for both transmitter part and the receiver part (say 401 and 402) may be
determined by combining the process described with reference to receiver and transmitter above
in the following manner. At first, the channel matrix is made available at both the transmitter and
receiver separately and both of them independently compute their optimal transmitter beamformer
matrices and receiver beamformer matrices.
[0043] In the next step, The transmitter (base station) transmits approximately orthogonal beam
weights WR,F WB,F ˜ F1:M, wherein WB,F is taken as IMXM and F1:M denotes M columns of any
orthogonal matrix such as normalized Fourier matrix. To ensure that the M columns chosen from
F1:T span the same space where UE is present, all T dimensions are scanned ahead of this data
transmission, i.e., at the initial beam acquisition time such as PBCH decoding, to ensure that
transmitter identifies the tight set of M columns. UE also uses N columns of a similar orthogonal
beam weights matrix corresponding to normalized Fourier matrix FB,F FR,F ˜ F1:N, wherein
FB,F=INXN.
[0044] In the next step, the receiver (490) estimates the channel matrix Hd, computes the optimal
beamforming matrices FB, FR for the chosen number of layers K, and uses them as uplink transmit
beamforming matrices. Due to determination of the weights as described above practical
constraints on the hybrid and analog beamformer architectures may be effectively overcome
without iteration of design and with computational deterministic.
[0045] While various embodiments of the present disclosure have been described above, it should
be understood that they have been presented by way of example only, and not limitation. Thus, the
breadth and scope of the present disclosure should not be limited by any of the above-discussed
embodiments but should be defined only in accordance with the following claims and their
equivalents. ,CLAIMS:CLAIMS
I/We Claim,
1. A radio frequency receiver comprising:
a set of antennas for receiving an RF signal over a communication channel represented
by a channel matrix Hd;
a plurality of analog beamformer for generating plurality of analog beams, wherein each
analog beam former is coupled to a subset of antennas comprising a fewer number antennas
in the set of antennas;
a mixer for combining the plurality of analog beams to provide a down converted signal;
and
a digital beam former for generating a plurality of digital beams,
wherein a set of analog weights (FR) of the plurality of analog beamformer and a set of
digital weights (FB) of the digital beamformer are selected such that effective beam formed
by their product FBFR is orthogonal and spans the same space as columns of the channel
matrix Hd.
2. The radio frequency receiver of claim 1 wherein the FR is a sparse matrix of the form:
???? = [
??1 0 ??3
0 ??2 0
0 0 0
0 … .0 0
??3 … .0 0
0 … . ??4 ??5
]
in that, each row representing the analog beamformer in the plurality of beam former with X
representing the antennas coupled and 0’s representing the unconnected antennas to the
respective beamformer in the respective position of an array X1-XT, and FB FR ˜ U, wherein
U representing a left singular vectors of the communication channel matrix Hd.
3. The radio frequency receiver of claim 2, wherein the digital beam former providing a
signal yb= FB FR Hd P s + FB FR n, in that s representing the signal transmitted into the
channel Hd, P representing the precoder matrix at a transmitter transmitting the signal s and n
representing a receiver noise.
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4. The radio frequency receiver of claim 2, wherein the plurality of antennas are arranged
over set of patches on the radio frequency receiver wherein, the set of patches are physically at
different positions, the subset of antennas are derived from one or more patches in the set of
patches.
5. A method in a radio frequency communication system comprising a set of analog beam
former and a digital beam former comprising:
constructing a first matrix order R X M where in M representing a number of analog
beamformer in the set of analog beamformer and R representing number of receive antennas,
wherein the first matrix is sparse with non zero values according to the number antennas
coupled to correspond analog beamformer and rest being zero values;
determining a first set of weights corresponding to the non zero elements in the first
matrix by minimizing an angle between the vector spaces spanned by an ideal set of weights
and an another set of weight, wherein the ideal set of weights being ideal values and the
another set of weights comprising all possible sparse orthogonal weights as allowed by the
sparse antenna coupling; and
determining a weight matrix as a transformation matrix between a basis vectors of the
two vector spaces and adapting the weight matrix for implementing the digital beamformer.
6. A radio frequency transmiter comprising:
a set of antennas for transmiting an RF signal over a communication channel;
a plurality of analog beamformer for generating plurality of analog beams, wherein each
analog beam former is coupled to a subset of antennas comprising a fewer number antennas
in the set of antennas;
a digital beam former for generating a plurality of digital beams; and
a mixer for combining the plurality of digital beams to provide a upn converted signal;
wherein a set of analog weights of the plurality of analog beamformer and a set of digital
weights of the digital beamformer maintain a relation:
WR WB ˜ V, in that WB representing weights of the digital beamformer, the WR
representing weights of the analog beamformer and V representing a right singular vectors of
the communication channel matrix Hd.
14
7. The radio frequency transmitter of claim 6, wherein the WR is a sparse matrix of the
form:
???? = [
??1 0 ??3
0 ??2 0
0 0 0
0 … .0 0
??3 … .0 0
0 … . ??4 ??5
]
in that, each row representing the analog beamformer in the plurality of beam former with X
representing the antennas coupled to the corresponding analog beam former and 0’s
representing the unconnected antennas to the respective beamformer in the respective position
of an array X1-XT.
8. The radio frequency transmitter of claim 7, wherein the plurality of analog beam former
providing a signal S= WR WB s, in that s representing an encoded baseband signal provided to
the digital beam former.
9. The radio frequency transmitter of claim 8, wherein the plurality of antennas are
arranged over set of patches on the radio frequency transmitter wherein, the set of patches are
physically at different positions, the subset of antennas are derived from one or more patches
in the set of patches.
10. A method, system and apparatus providing one or more features as described in the
paragraphs of this specification.