Description:FIELD OF INVENTION
[0001] Embodiments of the present disclosure relate to electronic communication system and more
particularly relate to an efficient successive interference cancellation decoder for a MIMO
communication system.
RELATED ART
[0002] A MIMO (Multiple Input and Multiple Output) communication system employs multiple
antennas for transmission of information and/or multiple antennas for receiving the information.
Information in the form of symbols is transmitted over the multiple antennas and correspondingly
received on multiple antennas as is well known in the art. In certain MIMO communication systems,
one (say a first) symbol is transmitted over multiple antennas at a given time and another (say a
second) symbol is transmitted over multiple antennas at a second time instance so on and so forth.
This is often referred to as spatial diversity. In certain other MIMO communication systems,
multiple symbols (say a set of symbols) are transmitted over the corresponding multiple antennas at
a given time instance and another set of symbols are transmitted over multiple antennas at a second
time instance so on and so forth. This is often referred to as spatial multiplicity or spatial
multiplexing. Decoding or detecting the symbols in the latter system (spatial multiplicity) is more
challenging due to transmission of multiple symbols at the same time; as signal (symbol)
transmitted from one antenna interfere with the other symbol transmitted from other antenna. In
general, when multiple symbols are transmitted simultaneously over the same time slot and
frequency resources, the receiver needs to remove the effect of the channel (noise, delay and fading
etc) as well as remove the effect of the inter-mixing of the symbols (interference) from different
transmitter antennas.
[0003] Conventionally, several techniques are used for estimating/decoding/detecting/extracting the
signal at the receiver. For example, in certain conventional techniques, the data is pre-coded at the
transmitted with the knowledge of the channel state/statistics/behavior. This may reduce the data
rate or needs additional information of the channel at the receiver. In certain other conventional
techniques, a SIC (Successive interference cancellation (SIC), as is well known in the art) based
decoders are employed. In such SIC decoder, the Channel characteristic (the matrix representing the
channel) is first decomposed for performing the SIC. For example, if the channel characteristic is
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represented by matrix [H]and the set of symbols are represented by matrix [X] then the received
signals may be represented as [Y]=[H][X]. Conventional decomposing of the matrix [H] using QR
decomposition technique is well known in the art. However, such SIC decoders can result in colored
noise at the receiver for different symbols resulting in increased symbol errors for a given signal-tonoise
ratio (SNR). Further, QR decomposition based SIC decoding techniques are complex and
computationally intensive. These QR based decoders are popular, but they operate on the full
channel matrix making it more complex, numerically sensitive and computationally intensive. That
apart, channel matrix decomposition based SIC decoders in general can generate colored noise thus
enhancing the probability of error while detecting the symbols for the given signal to noise ratio.
[0004] In certain other conventional decoders, more exhaustive search operations are performed for
all possible symbol combinations. These techniques are also referred as sphere decoding in the field
of art. Apparently the technique is computationally intensive and provides a sub-optimal solution
where the search range for the symbols is limited within a small radius of a sphere.
SUMMARY
[0005] According to an aspect, method of decoding a set of symbols from the plurality of signals
received on multiple antennas of a receiver in a MIMO (Multiple input and Multiple Output)
communication system, the method comprises receiving a first set of signals on a corresponding a
first set of antennas, receiving a channel characteristics corresponding to the first set of signals,
wherein the channel characteristics are arranged in a first matrix form, performing Hermitian
transform on the channel characteristic to form a second matrix, wherein the second matrix is a
covariant matrix, performing Cholesky decomposition on the second matrix to generate a third
matrix, wherein the third matrix is a triangular matrix, performing successive interference
cancellation using the third matrix and the first set of signal to generate an estimate of the set of
symbols.
[0006] According to another aspect, comprising the method further comprises partitioning the
second matrix into sub matrices that are of the order less than the order of the second matrix and
performing the Cholesky decomposition and their inverse recursively on the partitioned sub
matrices which reduces the computations as well as memory requirements in embedded
applications.
BRIEF DESCRIPTION OF DRAWINGS
[0007] FIG. 1 is an example MIMO communication system in an embodiment.
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[0008] FIG.2 is a block diagram of an example receiver signal processor in one embodiment.
[0009] FIG. 3 is a block diagram illustrating the manner in which the receiver signal processor may
be implemented in an embodiment.
[0010] FIG. 4A is a block diagram illustrating the manner in which the Cholesky decomposition
may be performed in an embodiment.
[0011] FIG. 4B illustrates the recursive Cholesky decomposition.
DETAILED DESCRIPTION OF THE PREFERRED EXAMPLES
[0012] FIG. 1 is an example MIMO communication system in an embodiment. The environment
100 is shown comprising a signal source 110, symbols generator 120, transmit (side) signal
processor 130, transmit (side) RF section 140, MIMO transmitter antenna 150, channel 155, MIMO
receiver antenna 160, receive (side) RF section 170, receiver (side) signal processor 180, output
device 190.Each element is further described below.
[0013] The signal source 110 provides the information for transmitting over the communication
channel 155. The information source may be audio, video, radar signal, media signal, data etc. In
certain embodiment the signal source 110 may comprise microphone, video camera, database, data
repository etc. The information provided by the signal source 110 may be in analog form or digital
form.
[0014] The symbols generator 120 receives the information and converts the information into
sequence of symbols. The symbol generator may employ any known encoding techniques (also
referred to as modulation techniques) such as Amplitude modulation (PAM, QAM, etc.,) Phase
Shift Keying, Frequency Shift Keying (QPSK, MSK, etc.,) as is well known in the art. Each symbol
may carry piece of information corresponding to one bit or two bits or four bits, etc. The symbols
thus generated is provided to the transmit signal processor 130.
[0015] The transmit (side) signal processor 130 generates the signal for transmission over MIMO
antenna array 150. The transmit signal processor 130 may perform one of spatial diversity or spatial
multiplicity transmission pattern or combinations thereof. For example, transmit signal processor
130 may configure the transmit RF section 140 and MIMO antenna 150 to transmit a set of symbols
over a corresponding set of antennas in MIMO antenna 150. That is, a set of symbols may be
transmitted in a first time slot over plurality of antennas. Accordingly, the signals are routed to
different antennas through the transmit RF section 140. The transmitted symbols in a given time slot
may be represented as X=[x1, x2, …xn], wherein the x1, x2, …xn representing the set of symbols.
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The signal configured for transmission over the antennas is provided to RF section 140. The
processor 130 may control the circuit elements in blocks 120, 140, and 150 to cause transmission of
multiple symbols over the multiple MIMO antenna elements. The transmit RF section 140 performs
signal condition operations such as power gain, frequency conversion, filter operation, impedance
matching etc., as is well known in the art. The signals ready for transmission over antennas are
provided to the antenna 150.
[0016] The MIMO transmitter antenna 150 comprises array of antennas (elements)150A-150P, each
capable of transmitting a signal/symbol. In one embodiment, the antenna elements 150A-150P
transmit different symbols in one time slot. That is each antenna element 150A-150P transmit
different symbol over channel 155 at same time or overlapping in time. The channel 155 may be
wireless channel capable of propagating electromagnetic waves in RF frequency range. P may be
greater than or equal number of symbols “N” in the set of symbols.
[0017] The MIMO receiver antenna 160 comprises array of antenna element 160A-160M capable of
receiving signal from the channel 155. In one embodiment, the antenna elements 160A-160M are
configured to effectively receive the signal transmitted from the antenna 150. For example, the
frequency range, dimension, direction, and power sensitivity of the antenna 160 are adjusted or
correspond to that of the antenna 150. The received raw RF signal is provided to the receive RF
section 170.
[0018] The receive RF section 170 receives the RF signal from the antenna 160 (M number of
signals from M antennas) and perform signal conditioning operations on each signal (in conjunction
with unit 140) such as amplification, frequency down conversion, filter operation, impedance
matching operations etc. In certain embodiment the receive RF section 170 may also perform analog
to digital conversion to provide the M streams of received signals in digital form. In certain
embodiment the number of receiver antenna M may be greater than or equal to “N”
[0019] The receiver signal processor 180 extracts the symbols from the M streams of received
signals. The extracted symbols are provided to output devices 190. The output device may comprise
storage device, media player, another transmitter, etc. The received signal streams may be
represented as Y=[y1, y2, …yM], wherein M may be greater than N wherein N is equal to the total
transmitted symbols x1, x2, …xN in a given time period. In one embodiment, the receiver signal
processor 180 is implemented with reduced complexity providing estimate of transmitted symbols
x1, x2, …xN with less probability of error (more accurate with the transmitted symbols) for a given
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signal to noise ratio. The manner in which the receiver signal processor 180 may be implemented in
an embodiment is further described below.
[0020] FIG. 2 is a block diagram of an example receiver signal processor in one embodiment. In the
block 210, the receiver 180 receives streams of signals (signal streams)from the multiple antennas
and also receives data representing the characteristic of the channel 155 (often referred to as channel
transfer function).The characteristic of the channel may be stored in a memory prior to receiving the
streams of signal or the characteristic of the channel may be received dynamically in real-time along
with the streams of signals. The characteristic of the channel may be represented in the matrix form
as [H] of order MXN, when the number of transmitted symbols is N and number of receiver antenna
in the array 160 is M. Thus, M represents the number of streams/receiver antennas. The
characteristic of the channel may be represented as:
=
h ? h
? ? ?
h
? h

in that, the h...h
(in general h
for all values of i from 1 to N and j from 1 to M) representing
characteristic of the channel between ith transmit antenna to jth receive antenna elements.
[0021] The M streams of signals received may be represented as:
=

?

wherein, y1 corresponds to signal received on antenna 1, y2 corresponds to signal received on
antenna 2, so on so forth with yM corresponds to signal received on Mth antenna. The [H] may
corresponds to or take values corresponding to the time instant of receiving the [Y] streams. The
received signal [Y] may be the transmitted signal [X] that is modified/affected by the channel [H]
and a noise component. Thus, received signal [Y] may be represented as:
(1) =

?

=
h ? h
? ? ?
h
? h

?

+ ,
wherein K is noise component and
= … denotes the transmitted symbols X =[x1, ...xN].
[0022] In the block 220, the receiver 180 converts (or determines the symmetry) of the general
characteristic of the channel to a symmetric representation of characteristics. In one embodiment the
receiver 180 may perform Hermitian transformation operation on the [H] to generate an N X N
symmetric channel matrix where N is less than M. The Hermitian transformed matrix [H] may be
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represented as [H]H. In one embodiment, the Hermitian transformation may be performed on the
relation (1) above. Thus, the relation (1) may be represented as:
(2)
= =
+ . In that, the operator representing the Hermitian operation
or covariance of the respective matrix and is a symmetric square matrix of order N X N.
Theterm represents the instance of a coloured noise vector generated from the spatially white
noise vector K.
[0023] In the block 230, the receiver 180, converts the coloured noise to white noise. In one
embodiment, the receiver 180 performs Cholesky decomposition of the symmetric channel matrix
to obtain the triangular matrix. For example, the Cholesky decomposition may be performed
on obtained in the relation (2) and convert the coloured noise to white noise. The
decomposition operation may be represented as:
(3)
=
=
+ . In that, the operator represents inverse of
Cholesky matrix L. The relation (3) may be represented as:
(4)
=
+ =
+ .The term represents the instance of
spatially white noise vector obtained from the colored noise vector.
[0024] In the block 240, the receiver 180, perform iterative estimation of the symbols by first
estimating the lowest dependency stream. As it may be appreciated that, the (transpose of the
Cholesky decomposition matrix) is an upper triangle matrix, and thus, symbols may be derived by
performing SIC decoding technique. Accordingly, the receiver 180 performs iterative SIC decoding
to determine estimate … of the symbols X. Further since is a white noise, the
symbols so extracted are having lesser probability of error for a given signal to noise ratio (SNR). It
may be appreciated that: the technology is described with mathematical relations for definitiveness
and accuracy of the description so that a person of the relevant skill shall be able to exploit the
details and implement the technology without ambiguity. The implementation of the same may be
performed using any known hardware such as system on chip (SOC), computer processors
executing the set of instructions etc. The manner in which the hardware implementation may be
further simplified is described below.
[0025] FIG. 3 is a block diagram illustrating the manner in which the receiver signal processor may
be implemented in an embodiment. The signal processor 300 is shown comprising Hermitian
8
Transformers 310, Cholesky decomposer 320 and SIC decoder 330. Each element further described
below.
[0026] The Hermitian Transformers 310 receives the stream of data from the M number of antennas
on path 301. The stream of data may be represented as samples of the signal that is digitised to Q
bits. The number of bits (Q) may be set to 32 bits, 64 bits, 128 bits etc., Thus, each element in the
matrix Y represents the sample of the received signal on a corresponding antenna sampled at a
given time instance. For example, the y1 representing the digital value of the sample received from
antenna 1 at time instance t1, y2 representing the digital value of the sample received from antenna
2 at time instance t1, so on so forth. Similarly, the Hermitian transformer 310 also receives the
channel characteristics arranged in two dimensional arrays (similar to Matrix H) for processing. The
characteristic of the channels may be iteratively updated during the decoding process and may
correspond to the estimated channel behaviour at the time of the sampling of the received signal Y.
Each element in the array may be represented using number of bits such as 32, 64, 128 etc. In
particular, the value of each element in the channel matrix represents the channel response between
a transmitting antenna and a receiving antenna. In one embodiment, the Hermitian transformer 310
implemented to convert the matrix Y, H and K to its conjugate transpose form. In that, K is a
predefined noise component in the received vector signal Y that may be updated dynamically based
on the channel characteristic/model. The Hermitian transformed matrices are represented as HH, YH
and KH and are provided for further processing to Cholesky decomposer. In one embodiment the
Hermitian Transformers 310 may be implemented by way of VLSI circuit model in the form of an
Intellectual Property (IP) core that may be integrated with the other processing circuit module.
[0027] Similarly, the Cholesky decomposer 320 performs Choleskey decomposition operation on
the digital data HHH, YH and KH to produce Cholesky decomposed data L-1HHH, L-1YH, and L-1KH
respectively. In that, L-1HHH is an upper triangular matrix of the form:
=
! !" !
0 !"" !"
0 0 !
.
The may be obtained by first performing the L (Cholesky decomposition) operation, its inverse
computation and then by performing the transpose of the same.
[0028] The SIC decoder 330 estimates of the received symbol from the relation (4) by back
substitution as: = wherein the is the inverse of the . For example, the SIC decoder
may first determine/estimate the using relation = ! + Noise. Similarly, next the may
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be determined using relation = !, + !, + %&'(). In a similar way other
symbols may be estimated iteratively. The (first) symbol(s) estimated in one step of SIC may be
stored in the memory and fetched for determining the next symbol in the next step of SIC. The
estimated symbols are provided on path 399. The manner in which the Cholesky decomposer 320
may be implemented is further described below.
[0029] FIG. 4A is a block diagram illustrating the manner in which the Cholesky decomposition
may be performed in an embodiment. In block 410, the channel characteristic data in the twodimensional
array form and that is symmetrical is received. For example the received Channel data
may be in the form of a square matrix of order NXN. In one embodiment, the channel data received
in the form of channel covariance matrix that comply to the requirement that every element hi,j = h* j,i
in the two dimensional array/matrix. In that,h*j,i representing the complex conjugate of hi,j for every i
and j.
[0030] In block 420, the Cholesky decomposer 320 creates/partitions sub array/sub matrices that are
of the order less than the order of the array/matrix received in block 410. In other words, the
Cholesky decomposer 320 may partition the received channel matrix/array into multiple sub
matrices or arrays. For example, considering the received channel matrix is of the order N X N
where N=2n, then the channel matrix may be portioned into four matrices of order N/2 X N/2. In
that, The Cholesky decomposer, perform the operation of Cholesky decomposition recursively on
the partitioned matrices by considering one by one. FIG. 4B illustrates the recursive Cholesky
decomposition. As shown there the 451 is the received symmetric channel matrix of order N X N.
The 461-464 representing the portioned submatrices of order N/2 X N/2. The 471-474 represents the
Cholesky decomposed matrices corresponding to the 461-464. As may be appreciated,
[461]=[471][471]T, [462]=[472][472]T, [463]=[462]T=[473][473]T and [464] = [473][473]T+
[474][474]T. In that [ ] representing the matrix. Thus, Cholesky decomposition of any matrix may be
derived from the decompositions of the sub-matrices or the partitioned matrices. It may be
understood that above partitioning with equal dimensions N/2 x N/2 is given here for illustration
only and the technique is applicable for any division of N = N1 + N2, N1 not equal to 0 and N2 not
equal to zero.
[0031] In block 430, Cholesky decomposer 320 constructs the upper triangle matrix from the
elements of the decomposed sub matrices. For example, the elements of the matrix 471, 473 and
474 are combined to first form the lower triangle matrix and then transpose operation is performed
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to obtain the upper triangle matrix. Accordingly, the computational complexity is further reduced.
Hence the receiver 180 may operate at a relatively lower SNR conditions with reduced complexity
(both in terms of hardware and/or processing power) and that does not produce colored noise.
[0032] 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. For
example, a similar method of Hermitian matrix conversion, Cholesky decomposition and recursive
symbol estimation using Successive Interference Cancellation (SIC) is relevant when the number
of receive antennas M is smaller than the number of transmit antennas N, with suitable changes in
(1)-(4) for the order in which H is multiplied with Y to obtain to Hermitian matrix format. 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:I/We Claim:
1. A method of decoding a set of symbols from the plurality of signals received on
multiple antennas of a receiver in a MIMO (Multiple input and Multiple Output) communication
system, the method comprising:
receiving a first set of signals on a corresponding a first set of antennas;
receiving a channel characteristic corresponding to the first set of signals, wherein the channel
characteristics are arranged in a first matrix form;
performing Hermitian transform on the channel characteristic to form a second matrix, wherein the
second matrix is a covariant matrix;
performing Cholesky decomposition on the second matrix to generate a third matrix, wherein the
third matrix is a triangular matrix;
performing successive interference cancellation using the third matrix and the first set of signal to
generate an estimate of the set of symbols.
2. The method of claim 1, wherein the first set of received signals is equal to:
=

?

=
h ? h
? ? ?
h
? h

?

+ , in that, h...h
representing the channel
characteristics in the first matrix form, ?
representing the first set of signals,?
representing the estimate of the set of symbols and K representing the Noise.
3. The method of claim 2, wherein said performing Hermitian transform comprise the
operation represented by the relation:

= =
+ , in that the operation representing the Hermitian operation on
H, H representing the channel characteristic in the first matrix form, and
representing a matrix of
the estimate of the set of symbols.
4. The method of claim 3, wherein said performing Cholesky decomposition comprise
the operation represented by the relation:

=
=
+ , In that, the operator represents the said Cholesky
decomposition operator.
5. The method of claim 4, further comprising partitioning the second matrix into sub
matrices that are of the order less than the order of the second matrix and performing the Cholesky
decomposition and its inverse recursively on the partitioned sub matrices.
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6. The method of claim 5, further creating the spatially white noise vector and
performing successive interference cancellation on the symbols to decode the data symbols.
7. A method, system, and apparatus for communication system comprising one or more
features described in the specifications and drawings.