The invention generally relates to digital communication and in particular to methods and devices for decoding a data signal.
During the last decades, the design of communication systems has known a considerable evolution in order to satisfy increasing demands in terms of services and applications. The growing number of users and connected machines appeals for conceiving more and more reliable communication platforms and devices capable of providing real-time services with higher capacities.
Multiple-Input Multiple Output (MIMO) technologies have proved themselves as potential candidates to meet such targets. They have made an important contribution in the design of most performing communication systems available today. MIMO technologies have been for example incorporated in several standards such as in wireless LANs (WiMAX IEEE 802.16) and cellular mobile networks (3G and 4G).
MIMO technologies owe their success to their capability to increase data transmission rates by exploiting space and time dimensions for communicating data over a multiplicity of antennas and during a multiplicity of time slots. Space-Time coding techniques are used in transmitter devices to encode flows of information symbols carrying original data. Space-Time decoding techniques are implemented in receiver devices observing outputs of a MIMO channel to estimate the original data conveyed by one or more transmitter devices.
Space-Time coding and decoding techniques can be implemented in a wireless single-user MIMO system accommodating one multi-antenna transmitter device communicating with one multi-antenna receiver device. In such scenario, the multiple inputs of the MIMO system originate from the same transmitter device, and the multiple outputs are received at a single receiver device.
Space-Time coding and decoding techniques can be used in a wireless multi-user MIMO system accommodating a set of users equipped with one or more antennas and communicating with each other. Such communication system is also called ‘distributed MIMO’ since the multiple inputs are distributed in space over the different users. Cellular uplink communication is an example of a distributed MIMO channel. Different user equipments using each with one or more antennas that belong to a same coverage cell may communicate with a base station equipped with multiple antennas.
Space-Time coding and decoding techniques can be used in optical fiber communication systems. For example, the two polarization states of the electrical field of the optical wave or the different propagation modes of multi-mode optical fibers may be exploited to encode and decode a modulated signal carrying a sequence of binary data. Such optical MIMO systems have been identified as promising solutions for providing high transmission rates in optical-fiber links over long distances. Exemplary applications comprise Polarization Division Multiplexed systems (PMD) and Mode Division Multiplexed systems (MDM).
Space-Time coding and decoding techniques can be used in combination with multicarrier techniques using a large number of orthogonal sub-carriers. Exemplary applications comprise OFDM and Filter Bank Multicarrier (FBMC) systems. OFDM modulation formats are used to combat frequency-selective channels, interference and delays. FBMC systems may be used for example for dynamic access spectrum management and cognitive radio applications.
Space-Time coding and decoding techniques may further be used in combination with multiple access techniques in presence of several transmitters. Multiple access techniques are used to manage the access to shared resources, such as bandwidth, between the different users communicating in a same communication system. Exemplary multiple access techniques are the Code Division Multiple Access (CDMA) used for example in radio communication systems (e.g. 3G standards) and Wavelength Division Multiple Access (WDMA) used for example in optical communication systems.
Due to the multipath and superposition properties of the wireless medium and to the dispersion and multiple reflections of the optical fiber propagation environment, information symbols originating from the multiple inputs are mixed at the receiver device. The received signal or MIMO channel output represents a set of multiple linear combinations of different information symbols sent by one or more users, using one or more antennas, during different time slots and over different sub-carriers. The superposition of the different information symbols results in an inter-symbols interference in each linear combination.
A receiver device in a MIMO system implements a Space-Time decoder for estimating, from the received signal and a channel state matrix, the original data conveyed by one or multiple transmitter devices. It compares the received vector of information symbols with the possible transmitted symbols. Several decoding rules may be used depending on the required performance level and processing capabilities of receiver devices. The optimal decoding rule for uniformly distributed information symbols is known as maximum-likelihood (ML) decoding. It results in the minimum probability of decoding error. An ML decoder decides in favor of the vector of information symbols that is closest to the received signal. The closest vector to the received signal represents the vector that has the minimum Euclidean Distance with respect to the received signal.
ML decoders can be implemented in several ways. Exhaustive search-based implementations require intensive processing and storage capabilities that may exceed the available ones. Alternative ML sequential decoding schemes may be used to provide optimal performance while employing fewer computational and storage resources than the exhaustive search-based methods.
Sequential decoders are based on a QR decomposition of the channel state matrix and perform a tree search in a decoding tree to solve the ML decoding problem. The decoding tree comprises a plurality of nodes, levels, branches and paths. Nodes correspond to the different possible values of the information symbols.
Several ML sequential decoders exist and are generally divided into three families according to the tree-search strategy. Sequential decoders may be based on a depth-first strategy as disclosed for example in:
A breadth-first tree-search strategy may be used as in the Stack decoder disclosed for example in:
Other Sequential decoders may be based on a best-first strategy like the SB-Stack decoder as disclosed for example in the “G. R. Ben-Othman, R. Ouertani, and A. Salah. The spherical bound stack decoder. In Proceedings of International Conference on Wireless and Mobile Computing, pages 322-327, October 2008.”
Space-Time (ST) decoders can be generally categorized as joint, single-stream or sub-block decoders, depending on whether the different streams constituting the vector of original information symbols are detected jointly, individually, or in groups of sub-vectors respectively. Joint decoders offer optimal performance but require a high computational complexity that increases as a function of the size of the constellation and of the number of deployed antennas. The size of the constellation generally impacts the number of nodes to be visited at each level. The number of deployed antennas generally impacts the number of levels in the decoding tree.
Using single-stream decoders, the various information symbols can be decoded individually. Single-stream decoders may rely on a linear decoding approach. In a linear decoding approach, the decoder first creates interference-free data flows to decouple the different information symbols and then delivers an estimation of each symbol separately. Accordingly, the decision on a given information symbol is independent from the remaining estimated symbols. Interference elimination in the first step is realized through a projection of the channel output using a filtering matrix. Zero-Forcing (ZF) and Minimum Mean Squared Error (MMSE) detectors are examples of linear single-stream decoders. Alternatively, Single-stream decoders can operate according to a non-linear decoding approach, the information symbols being estimated individually. However, unlike linear decoders, the estimation of a given symbol is impacted by the previously estimated symbols with non-linear decoders. The Zero Forcing-Decision Feedback Equalizer (ZF-DFE) decoder is an example of a non-linear single-stream decoder. It is known as a Successive Interference Cancellation (SIC) scheme. It uses a QR decomposition of the channel state matrix to recursively determine estimations of each single symbol from previously estimated symbols. Inter-symbol interference is then cancelled recursively, any decoding errors on a given symbol being propagated over the forthcoming estimations thereby inducing performance degradation. Linear and non-linear single-stream decoders require low decoding complexity but offer limited performance. Preprocessing techniques such as Lattice reduction and MMSE-GDFE preprocessing may be applied prior to decoding using such approaches to obtain better performance.
Using sub-block decoders, the vector of information symbols is divided into a plurality of sub-vectors and each sub-vector is decoded separately. The sub-vector division of the information symbols is performed in accordance with a sub-block division of a transmission channel representative matrix.
Certain sub-block decoders apply a combined ML and DFE decoding scheme for wireless MIMO systems using spatial multiplexing of data streams as disclosed in “Won-Joon Choi, R. Negi, and J. M. Cioffi. Combined ML and DFE decoding for the V-BLAST system. IEEE International Conference on Communications. Volume 3, pages 1243-1248, 2000.” Accordingly, the vector of information symbols of a length n is divided into two sub-vectors of lengths p and n-p respectively. In a first decoding phase, the sub-vector comprising p information symbols is estimated using an ML decoder. Using these estimated symbols, the receiver recursively performs an inter-symbol interference cancellation using a decision feedback equalization to determine an estimation of the remaining n p symbols composing the second sub-vector of information symbols. Such 2-block decoding schemes allow the achievement of better performance than ZF-DFE decoding.
Other sub-block decoding schemes have been proposed for Space-Time Coded MIMO systems using linear Space-Time Block Codes (STBC). Particular classes of low-complexity ML-decodable STBCs have been considered such as the family of multi-group decodable codes disclosed in:
Other classes of low-complexity ML-decodable STBCs comprise fast decodable codes as disclosed in:
Still other classes of low-complexity ML-decodable STBCs comprise fast-group decodable codes as disclosed in:
Sub-block decoding in the presence of an STBC that belongs to one of these families of codes may be advantageously performed using the QR decomposition of the channel state matrix. The zero structure of the equivalent transmission channel matrix allows recursive decoding of the various sub-vectors of information symbols with reduced complexity without sacrificing the decoding error performance. Particularly, some sub-vectors of symbols may be estimated in a separate way in parallel allowing for faster and lower-complexity decoding.
The order at which the information symbols are decoded may affect the performance and/or the decoding complexity of ST decoders, essentially the decoding techniques based on the QR decomposition of the channel state matrix.
For example, an ordering of the different information symbols prior to sequential decoding may be implemented to accelerate the phase of the tree-search and therefore reduce the computational complexity required to find the ML solution.
Certain single-stream detectors using the ZF-DFE implement a ordering of the information symbols prior to decoding to reduce the impact of the inter-symbol interference and enhance the performance of ZF-DFE decoding.
Several examples of symbol decoding ordering such as V-BLAST and H-norm ordering have been proposed for ML sequential and single-stream decoders. V-BLAST ordering is disclosed, among other works, in: “G. J. Foschini. Layered Space-Time Architecture for Wireless Communication in a Fading Environment When Using Multi-Element Antennas. Bell Labs Tech. J. Volume 1, pages 41-59. 1996” is identified as the optimal ordering for ZF-DFE decoding. Accordingly, the symbol decoding order is organized according to their signal-to-noise ratios (SNR) in a decreasing order such that the first detected symbol is associated with the highest SNR. H-norm ordering is disclosed in: “M.-O. Damen, H. El-Gamal, and G. Caire. On maximum-likelihood decoding and the search for the closest lattice point. Information Theory, IEEE Transactions on, 49(10):2389-2402, October 2003”. It consists of sorting the information symbols in accordance with a ordering of the column vectors of the channel state matrix according to an increasing order of their Euclidean norm.
To change the symbol decoding order, the ordering of the columns of the channel state matrix is generally changed. In certain decoders, the ordering of the columns of the channel state matrix is performed using a permutation matrix to achieve the desired ordering of the columns.
Existing symbol decoding ordering techniques perform symbol ordering according to a symbol-related ordering criterion. Such techniques may require an intensive computational complexity to find the permutation matrix that satisfies the desired ordering criterion. Their practical implementations may not be possible particularly in presence of a high number of transmit and/or receive antennas. Further, existing ordering techniques may not be applicable to sub-block decoders.
To address these and other problems, there is provided a decoder for decoding a vector of information symbols received through a transmission channel in a communication system, from a received signal and a channel state matrix. The information symbols are selected from a given set of values carrying a set of information bits. The decoder comprises:
The decoder may be configured to determine at least one estimate of a vector of transmitted information symbols from the determined at least one estimate of each sub-vector of information symbols.
In one embodiment, the permutation unit may be configured to determine an upper triangular matrix and an orthogonal matrix from each permuted channel state matrix by performing a QR decomposition of each permuted channel state matrix in the set of permuted channel state matrices. The permutation unit may further comprise dividing each upper triangular matrix determined from each permuted channel state matrix into upper triangular sub-matrices and rectangular sub-matrices.
In one embodiment, the selection criterion used to select at least one permuted channel state matrix according may be related to the determined upper triangular sub-matrices and/or rectangular sub-matrices obtained by the QR decomposition of the permuted channel matrices. In particular, the selection metric may be chosen in a group consisting of the number of the zero components of the rectangular sub-matrices, the diagonal components of said upper triangular sub-matrices, the signal-to-noise-ratio associated to the upper triangular sub-matrices and the conditioning number of the upper triangular sub-matrices and/or the rectangular sub-matrices.
In one embodiment, the division unit may be configured to divide the channel state matrix depending on at least one sub-block decoding parameter. The at least one sub-block decoding parameter may be chosen in a group consisting of a predefined number of sub-blocks, a set of sub-block lengths, and a predefined set of decoding algorithms.
In one embodiment, the number of divided sub-blocks of column vectors of the channel state matrix may be set equal to the number of sub-blocks.
In one embodiment, the number of permuted channel state matrices may be less than or equal to the number of sub-blocks.
In one embodiment, the sub-block decoding unit may be configured to determine estimates of the sub-vectors of information symbols using similar or different decoding algorithms. A decoding algorithm may be chosen in a group consisting of a sequential decoding algorithm, a ZF decoding algorithm, a ZF-DFE decoding algorithm or an MMSE decoding algorithm.
In certain embodiments, the sub-block decoding unit may be further configured to perform a lattice reduction and/or MMSE-GDFE preprocessing on the selected at least one permuted channel state matrix.
In certain embodiments, the sub-block decoding unit may be configured to determine a plurality of estimates of each sub-vector of information symbols for delivering soft-output decisions on the set of information bits carried by the information symbols.
The invention also provides a receiver for receiving and decoding a vector of transmitted information symbols. The receiver comprises a decoder according to any preceding feature for decoding a vector of information symbols.
In one application of the invention in wireless multiple-input multiple-output communication systems, there is provided a wireless device capable of receiving data. The wireless device comprises a receiver for receiving and decoding a vector of transmitted information symbols according to any of the preceding embodiments.
In one application of the invention in optical multiple-input multiple output communication systems, there is provided an optical device capable of receiving data. The optical device comprises a receiver for receiving and decoding a vector of transmitted information symbols according to any of the preceding embodiments.
There is also provided a method of decoding a signal represented by a vector of information symbols received through a transmission channel in a communication system. The transmission channel being represented by a channel state matrix. The information symbols are selected from a given set of values and carry a set of information bits, the method comprising:
The method comprises determining at least one estimate of a vector of transmitted information symbols from the at least one estimate of each sub-vector of information symbols.
The method may further comprise determining a determining an upper triangular matrix and an orthogonal matrix from each permuted channel state matrix by performing a QR decomposition of each permuted channel state matrix in the set of permuted channel matrices, and dividing each upper triangular matrix into upper triangular sub-matrices and rectangular sub-matrices.
In one embodiment, the selection criterion may depend on a selection metric related to the determined upper triangular sub-matrices and/or rectangular sub-matrices.
In a particular embodiment, the selection metric may be chosen in a group consisting of the number of zero components of said rectangular sub-matrices, the diagonal components of the upper triangular sub-matrices, the signal-to-noise-ratio associated to the upper triangular sub-matrices, and the conditioning number of the upper triangular sub-matrices and/or the rectangular sub-matrices.
There is also provided a computer program product for decoding a signal represented by a vector of information symbols received through a transmission channel in a communication system. The transmission channel is represented by a channel state matrix. The information symbols are selected from a given set of values and carry a set of information bits, the computer program product comprising a non-transitory computer readable storage medium; and instructions stored on the non-transitory computer readable storage medium that, when executed by a processor, cause the processor to:
determine a transformed signal from the received signal and the selected at least one permuted channel state matrix and determining at least one estimate of each sub-vector of information symbols from the transformed signal by applying at least one iteration of a decoding algorithm;
The processor is caused to determine at least one estimate of a vector of transmitted information symbols from the determined at least one estimate of each sub-vector of information symbols.
Advantageously, the various embodiments of the invention allow optimizing the ordering of the sub-vectors of information symbols enabling reducing error propagation and therefore reducing the decoding error probability using a sub-block decoder.
Advantageously, in one application of the invention in wireless multi-user MIMO systems, the various embodiments of the invention allow improving the decoding order of the sub-vectors of transmitted information symbols originating from different users. As a result, the overall capacity of the communication system can be enhanced and the total error probability can be reduced.
Advantageously, in one application of the invention in combination with OFDM or FBMC modulation formats, the various embodiments of the invention allow improving the decoding order of the sub-vectors of information symbols transmitted over different sub-carriers, enabling efficient use of the spectral bands.
Advantageously, in one application of the invention in optical communication systems, the various embodiments of the invention allow improving the decoding order of the sub-vectors of information symbols propagating over different modes in a multi-mode optical-fiber, enabling adaptive low-complexity and low-error probability decoding taking into considerations the impairments of the optical transmission channel.
Further advantages of the present invention will become clear to the skilled person upon examination of the drawings and detailed description. It is intended that any additional advantages be incorporated herein.
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate various embodiments of the invention and, together with the general description of the invention given above, and the detailed description of the embodiments given below, serve to explain the embodiments of the invention:
Embodiments of the present invention provide methods, devices and computer program products for decoding a vector of information symbols, received through a transmission channel in a communication system, with an optimized decoding order. Embodiments of the present invention are based on a division of the vector of information symbols into a number of sub-vectors and a corresponding division of the channel state matrix representing the transmission channel into a number of sub-blocks of column vectors. An optimized decoding order is achieved by determining a permuted channel state matrix derived from a permutation of the sub-blocks of column vectors, and transforming the received signal using the permuted channel state matrix. Sub-vectors of information symbols are determined from a division of the transformed signal, and at least one estimate of each sub-vector of information symbols is computed. An estimate of the transmitted signal can thus be determined from the estimates of the different sub-vector of information symbols.
Methods, devices and computer programs according to the various embodiments of the invention may be implemented in communication systems comprising at least one transmitter device (also referred to hereinafter as a “transmitter”) for transmitting a plurality of information symbols, and at least one receiver device (also referred to hereinafter as a “receiver”) for receiving and decoding the information symbols transmitted by one or more transmitter devices.
Transmitter devices may be equipped with one or more transmit antennas and receiver devices may be equipped with one or more receive antennas.
The communication system may be a wireless single-user MIMO system in which a wireless multi-antenna transmitter device communicates a flow of information symbols representing an input data with a wireless multi-antenna receiver device configured to decode the conveyed symbols by the transmitter.
The communication system may be a wireless multi-user MIMO system in which a plurality of wireless transmitter devices and receiver devices communicate with each other. In this case, the communication system may use any multiple access techniques such as Time Division Multiple Access (TDMA), Space-Division Multiple Access (SDMA), CDMA or Frequency Division Multiple Access (FDMA).
The communication system may be an optical fiber-based communication system. The received signal may accordingly correspond to the information symbols transmitted through the different polarization states of the optical fiber or propagating over the different modes of multi-mode fibers. In addition, a multiple access technique such as WDMA may be used in such optical communication systems.
The communication channel may be any linear Additive White Gaussian Noise (AWGN) channel or a multipath channel using single-carrier or multi-carrier modulation formats such as OFDM and FBMC.
In a preferred application of the present invention, the complexity of sub-block decoding of a signal transmitted over a wireless single-user MIMO system may be reduced without sacrificing error performance. Exemplary applications of the sub-block decoding methods and devices include, with no limitation, MIMO decoding in configurations implementable in wireless standards such as the WiFi (IEEE 802.11n), the cellular WiMax (IEEE 802.16e), the cooperative WiMax (IEEE 802.16j), the Long Term Evolution (LTE), the LTE-advanced and the 5G ongoing standardization.
For illustration purposes only, the following description will be made with reference to a wireless single-user MIMO system accommodating a transmitter device equipped with nt≧1 transmit antennas and a receiver device equipped with nr≧1 receive antennas for decoding information symbols sent by the transmitter. However, the skilled person will readily understand that the various embodiments of the invention apply in other communication systems such as wireless distributed MIMO systems and optical MIMO systems. Generally, the invention may be integrated in any communication system characterized by a lattice representation of the channel output at receiver devices.
Referring to
The MIMO system may present a symmetric configuration. As used herein, a symmetric configuration refers to a configuration in which case the transmitter and the receiver are equipped with the same number of antennas nt=nr. Alternatively, the MIMO configuration may be asymmetric, in which case the number nr of receive antennas differs from the number nt of transmit antennas. In particular, in order to avoid a rank deficiency problem, the number nr of receive antennas is larger than the number nt of antennas at the transmitter.
The transmitter 10 can convey a signal to a receiver 11 over a noisy wireless MIMO channel. The transmitter 10 can be implemented in different devices or systems capable of operating in a wireless environment, such as for example in a user equipment or a mobile station. The transmitter may be fixed or mobile. The transmitter 10 may comprise for example:
The transmitter 10 may be configured to encode a received flow of information bits as data input using a FEC encoder 101 implementing for example a convolutional code. The encoded binary signal may be then modulated into a symbol vector sc using the modulator 103. Different modulation schemes may be implemented such as 2q-QAM or 2q-PSK with 2q symbols or states. The modulated vector sc may be a complex-value vector comprising κ complex-value symbols s1, s2, . . . , sκ with q bits per symbol.
An information symbol sj has a mean power Es, and can be written in the form:
sj=Re(sj)+iIm(sj) (1)
In equation (1), i denotes the complex number such that i2=−1 and the Re(•) and Im(•) operators output respectively the real and imaginary parts of an input value.
When modulation formats such as 2q-QAM are used, the 2g symbols or states represent a sub-set of the integer field [i]. The corresponding constellation is composed of 2q points representing the different states or symbols. In addition, in the case of squared modulations, the real and imaginary parts of the information symbols belong to the same finite alphabet A=[−(q−1), (q−1)]. The minimum distance dmin of a modulation scheme, represents the Euclidean distance between two adjacent points in the constellation an is equal to 2 in such example.
A Space-Time Encoder 105 may be used to generate a codeword matrix X from the encoded symbols. The space-time encoder 105 may use a linear STBC of length T and may deliver a codeword matrix X of dimension nt×T that belongs to a codebook C and is sent over T time slots. The coding rate of such codes is equal to κ/T complex symbols per channel use, where K is the number of encoded complex-value symbols composing the vector sc=[s1, s2, . . . , sκ]t of dimension κ in this case. When full rate codes are used, the Space-Time Encoder 105 encodes κ=ntT complex-value symbols. An example of STBCs is the Perfect Codes. Perfect codes provide full coding rates by encoding a number κ=nt2(T=nt) of complex information symbols and satisfy a non-vanishing determinant property.
The Space-Time Encoder 105 may use a spatial multiplexing scheme known as V-BLAST scheme by multiplexing the received complex-value information symbols over the different transmit antennas without performing a coding in the time dimension.
The codeword so constructed may be converted from the time domain to the frequency domain using a multicarrier modulation technique, using for example OFDM or FDMC modulators, and spread over the transmit antennas 107. Signals may be sent from the transmit antennas 107 optionally after filtering, frequency transposition and amplification.
The receiver 11 may be configured to receive and decode a signal communicated by the transmitter 10 in a wireless network through a transmission channel (also referred to as a “communication channel”) subject to fading and interference and represented by a complex-value channel matrix Hc. In addition, the communication channel may be noisy, affected for example by a Gaussian Noise.
The receiver 11 may be integrated in a base station such as a Node-B in a cellular network, an access point in a local area network or ad-hoc networks or any other interfacing device operating in a wireless environment. The receiver 11 may be fixed or mobile. In one exemplary embodiment, the receiver 11 may comprise:
The receiver 11 implements a reverse processing of the processing performed in the transmitter 10. Accordingly, if a single-carrier modulation is used at the transmitter rather than a multi-carrier modulation, then the nr OFDM of FBMC demodulators may be replaced by corresponding single-carrier demodulators.
Referring to
Even if not limited to such applications, the invention has certain advantages in recursive sub-block decoding applications. The following description will be made with reference to an application to recursive sub-block decoding for illustration purpose only.
The permutation unit 203 may further comprise a permutation generation unit 303 configured to determine a plurality of orderings πq and corresponding permutation matrices Pq for q=1, . . . , N!, where N is a predefined number of sub-blocks. In a preferred embodiment of the invention, the set of permuted channel state matrices Hq comprises at least two permuted channel state matrices. As used herein, a permuted channel state matrix Hq refers to a matrix resulting from the permutation of the columns of the channel state matrix H using the corresponding ordering πq. The permuted matrices thus determined may be fed into a QR decomposer 307.
The QR decomposer 307 may be configured to perform a QR decomposition of each permuted channel state matrix Hq such that Hq=QqRq where Qq is an orthogonal matrix and Rq is an upper triangular matrix.
The permutation unit 203 may further comprise a matrix division unit 309 configured to divide, for q=1, . . . , N!, the upper triangular matrices Rq into N+N(N+1)/2 sub-matrices comprising N upper triangular sub-matrices Rq(k), k=1, . . . , N and N(N+1)/2 rectangular sub-matrices Bq(kj), k=1, . . . , N, j=k+1, . . . , N. The permutation unit 203 may further comprise a matrix selection unit 311 configured to select, among the computed permuted channel state matrice one permuted channel matrix Hopt and its corresponding upper triangular matrix R, orthogonal matrix Q, ordering πopt and permutation matrix Popt according to a selection criterion C.
These divided sub-matrices may have been previously stored in memory.
Using the sub-vectors s(k) and {tilde over (y)}(k) and the decomposed sub-matrices R(k) and B(kj), a set of sub-blocks (SB)k may be defined. For each index k=1, . . . , N−1, a sub-block (SB)k may be defined as (SB)k={lk, s(k), R(k), {tilde over (y)}(k), {tilde over (w)}(k), D(k), B(kj), j=k+1, . . . , N}. For k=N, the corresponding sub-block is given by (SB)N={lN, s(N), R(N), {tilde over (y)}(N), {tilde over (w)}(N), D(N)}.
The sub-block decoding unit 207 may further comprise N symbol estimation units 403 and N−1 successive interference cancellation units 405. The sub-block decoding unit 207 may comprise also a SIC unit 405 associated with a sub-block (SB)k and configured to calculate a vector
The skilled person will readily understand that the invention is not limited to the use of an estimation unit 403 for each sub-block. Alternatively a unique symbol estimation unit 403 or a set of symbol estimation units 403 (the set comprising less unit than the total number of sub-blocks) may be used to determine the estimate of each sub-block.
In one application of the present invention to a wireless Rayleigh fading multiple antenna system for decoding a signal sent from a transmitter equipped with nt transmit antennas using a V-BLAST spatial multiplexing scheme and 2q-QAM modulation, to a receiver equipped with nr receive antennas with nr≧nt, the received complex-value signal may be written in the form:
yc=Hcsc+wc (2)
In equation 2, yc is an nr-dimensional vector, sc denotes the complex-value vector of transmitted information symbols of dimension nt. The complex-value nr×nt matrix Hc represents the channel state matrix comprising the fading gains. In a Rayleigh fading channel, the entries of the channel state matrix Hc are of independent identically distributed (i.i.d) complex Gaussian type. The channel matrix may be known or estimated in coherent transmissions at the receiver using estimation techniques. In addition to the multipath fading effects, the transmission channel may be noisy. The noise may result from the thermal noise of the system components, inter-user interference and intercepted interfering radiation by antennas. The total noise may be modeled by a zero-mean Additive White Gaussian Noise of variance σ2 per real-value dimension modeled in equation (2) by the nr-dimensional complex-value vector wc.
In another embodiment of the invention to coded systems using a linear STBC to encode a modulated symbol vector sc comprising κ complex-value symbols, the received signal is an nr×T matrix Yc written in the complex-value form as:
Yc=HcX+Wc (3)
In such an embodiment, the noise is represented by the nr×T complex-value matrix Wc of Gaussian i.i.d. zero-mean entries of variance σ2 per real and imaginary parts.
Given the channel output, the receiver may attempt to generate an estimate of the original vector of information symbols.
In step 501, a complex-to-real conversion may be performed to determine a real-value form of the received signal.
For example, in one embodiment using a spatial multiplexing scheme, the system in equation (2) may be transformed into:
The Re(•) and Im(•) operators in equation (4) designate the real and imaginary parts of each element composing the underlying vector or matrix.
Equation (4) can be written in a lattice representation form as:
y=Hs+w (5)
Alternatively, in one embodiment using a linear Space-Time Block code of length T and encoding K symbols, the real-value expression of the channel output can be written in the lattice representation form of equation (5) where the equivalent channel matrix is the real-value 2nrT×2κ matrix Heq given by:
Heq=(ITH)G (6)
The 2ntT×2κ matrix G designates a real-value matrix known as a generator matrix or coding matrix of the linear Space-Time Block code. IT denotes the identity matrix of dimension T and the operator {circle around (×)} is the Kronecker matrices product.
In an application of the invention to an asymmetric MIMO configuration with nt<nr, a lattice representation in the form of equation (5) can also be obtained by performing the complex-to-real conversion of step 501 to the equivalent system given by:
U†yc=DV†sc+U†wc (7)
The matrices U and V are unitary matrices obtained, together with matrix D, from the singular value decomposition of the matrix Hc=UDVt. D is a diagonal matrix having positive diagonal entries representing the singular values of the matrix Hc.
Both spatial multiplexing and Space-Time Block coded symmetric and asymmetric MIMO schemes permit similar real-value lattice representations of the channel output given by equation (5). To facilitate the understanding of the following embodiments, the following description will thus be made with reference to a spatial multiplexing scheme and involving a symmetric MIMO configuration where the transmitter and receiver are equipped with the same number of antennas nt=nr, for illustration purposes only. Accordingly, the real-value vectors y, s and w in equation (5) will be represented as n-dimensional vectors with n=2nt=2nr and the equivalent real-value channel matrix H will be represented by a square n×n matrix. The vector s comprises the real and imaginary parts of the original complex information symbols composing the vector sc.
To perform recursive sub-block decoding, a set of predefined sub-block decoding parameters comprising at least one sub-block decoding parameter may be initially received or retrieved from memory in step 503. The sub-block decoding parameters may comprise a target number of sub-blocks N (preferably equal to at least 2), a set of sub-block lengths lk, k=1, . . . , N satisfying Σk−1Nlk=N, and/or a set of sub-block decoding algorithms D(k),k=1, . . . , N. The lengths lk,k=1, . . . , N may be equal or different. The decoding algorithms may be similar or distinct. The following description will be made with reference to sub-block decoding parameters comprising these three types of parameters (N, lk,k=1, . . . , N, D(k),k=1, . . . , N).
A division of the real-value channel state matrix into sub-blocks may be performed in step 505 in accordance with a sub-vector division of the vector of information symbols s and the vector y, using the sub-block decoding parameters (N, lk,k=1, . . . , N). Specifically, the vector of real information symbols s may be divided into N sub-vectors such that
A sub-vector s(k) of index k has a length lk and comprises lk real symbols. Accordingly, the matrix H may be divided into N sub-blocks of column vectors such that H=[H(1)|H(2)| . . . |H(N)]. A sub-block of column vectors H(k) of index k may be seen as a rectangular matrix of dimension n×lk.
Using the sub-block division of the matrix H and the sub-vector division of the vector s, two ordered sets and and may be defined. The ordered set may be in the form =(SV1, . . . , SVN) where a component SVk corresponds to the sub-vector s(k) of information symbols of index k. The order of the components SVk may correspond to the decoding order of the sub-vectors s(k). The ordered set may be represented in the form =(SM1, . . . , SMN), where a component SMk corresponds to the sub-block of column vectors H(k) of index k. The order of the components SMk corresponds to the order of the sub-blocks of columns in the matrix H.
The columns of the channel matrix H are then ordered to change the symbol decoding order. In order to change the decoding order of the sub-vectors of information symbols, the ordering of the set components SVk and SMk may be changed using the defined sets and .
In step 507, a set of N! permutation matrices Pq,q=1, . . . , N! and a set of N! permuted channel matrices Hq,q=1, . . . , N! may be determined. A permutation matrix Pq of index q corresponds to an ordering πq of the sets and into the sets q and q. As used herein, a permutation matrix refers to a matrix used to permute an ordered set of N sub-vectors is an orthogonal N×N matrix of binary entries, while conventional symbol-related ordering schemes such as V-BLAST and H-norm ordering correspond to n×n binary permutation matrices.
An ordering πq can be represented in the form
where a component SVk of index k is permuted to the component πq(SVk). The permutation matrix Pq corresponding to the ordering πq is a matrix with all zero entries except that in row k, the entry of the index corresponding to πq(SVk) is equal to 1. Corresponding reordered sets q and q are then given by q=(πq(SV1), . . . , πq(SVN)) and q=(πq(SM1), . . . , πq(SMN)). Changing the sub-vector decoding order according to an ordering πq may be therefore obtained by determining the permuted vector sper,q and permuted matrix Hq corresponding respectively to the ordered set q and q. The reverse ordering πq−1 allows to determine the original vector s by ordering the permuted vector sper,q.
To illustrate the derivation of a permutation matrix corresponding to a desired ordering of the sub-vectors of information symbols, the following example of n=4, N=3, l=1, l2=2, l3=1 is considered.
Accordingly, the vector
is divided into three sub-vectors as
such that s(1)=[s1],
and s(3)=[s4]. The matrix H=[h1|h2|h3|h4] comprising four column vectors h1,h2,h3 and h4 is correspondingly divided into three sub-blocks such that H=[H(1)|H(2)|H(3)] where H(1)=[h1], H(2)=[h2|h3] and H(3)=[h4]. The ordered sets and are given by =(SV1,SV2,SV3) and =(SM1, SM2, SM3).
For such a setting, there exist six possible orderings of the sub-vectors of information symbols. One possible ordering allows obtaining a permuted vector given by
It corresponds to the ordering π1 of the set given by
The corresponding permutation matrix is then given by
and the reordered sets 1 and 1 are accordingly given by 1=(SV3,SV1,SV2) and 1=(SM3,SM1,SM2). The permuted vector sper,1 and the permuted channel matrix H1 are therefore obtained by permuting the sub-vectors and sub-blocks of column vectors in accordance with the permuted ordering of the sets 1 and 1 respectively.
In step 509, a QR decomposition of each matrix of the obtained set of permuted channel matrices is performed to determine N! orthogonal matrices Qq and N! upper triangular matrices Rq such that Hq=QqRq for q=1, . . . , N!.
In step 511, a division of the obtained N! upper triangular matrices Rq into sub-matrices is performed. Accordingly, for each q=1, . . . , N!, an upper triangular matrix Rq is divided into
sub-matrices comprising N upper triangular sub-matrices Rq(k), k=1, . . . , N and
rectangular sub-matrices Bq(kj), k=1, . . . , N, j=k+1, . . . , N such that:
A divided upper triangular sub-matrix Rq(k), k=1, . . . , N designates a square matrix of dimension lk×lk.
A divided sub-matrix Bq(kj), k=1, . . . , N; j=k+1, . . . , N designates a rectangular matrix of dimension lk×lj and corresponds to the inter-symbol interference between the sub-vectors sper,q(k) and sper,q(j) of the permuted vector sper,q.
In step 513, at least one permuted channel matrix Hopt and its corresponding upper triangular matrix R, orthogonal matrix Q, ordering πopt and permutation matrix Popt are selected according to a selection criterion C.
In certain embodiments, the selection criterion C may correspond to a maximization or minimization of a selection metric related to the divided sub-matrices of the upper triangular matrices Rq for q=1, . . . , N!. In particular, a selection metric may be related to the components of the divided upper triangular sub-matrices Rq(k), k=1, . . . , N and/or to the components of the divided rectangular sub-matrices Bq(kj), k=1, . . . , N; j=k+1, . . . , N.
In one embodiment, the selection metric may correspond to the number of zero entries in the rectangular sub-matrices Bq(kj). This selection metric may interestingly be used in order to reduce the decoding error propagation by reducing the impact of the interference between the sub-vectors of information symbols depicted by the components of the rectangular sub-matrices Bq(kj). Accordingly, the selected ordering πopt over all possible orderings πq, q=1, . . . , N! may correspond to the ordering which allows obtaining an upper triangular matrix R with the minimum number of zero elements in each sub-matrix Bq(kj) for k=1, . . . , N; j=k+1, . . . , N.
In other embodiments, the selection metric may correspond to the average of the diagonal entries of the upper triangular sub-matrices. Accordingly, the selected ordering πopt may correspond to the ordering which allows maximizing, over all possible orderings πq, q=1, . . . , N!, the minimum average of the diagonal entries of the sub-matrix Rq(k) for k=1, . . . , N. Such an embodiment may be used advantageously when a decoding algorithm D(k) implements a sequential decoding strategy for determining an estimate of the sub-vector of information symbols s(k).
In another embodiment, the selection metric may correspond to the signal-to-noise ratio SNR(k) per sub-vector of information symbols s(k) measured using the upper triangular sub-matrices Rq(k). Accordingly, the selected ordering πopt may correspond to the ordering which maximizes, over all possible orderings πq,q=1, . . . , N!, the minimum SNR(k) for k=1, . . . , N. Such an embodiment may be used when a decoding algorithm D(k) implements a ZF-DFE decoder for determining an estimate of the sub-vector of information symbols s(k).
In still another embodiment, the selection metric may correspond to the conditioning number of the upper triangular sub-matrices. For a matrix U, the conditioning number τ(U)ε[0,1] is given by:
In equation (9), σmin and σmax, correspond respectively to the minimum and maximum singular values of the matrix U. The conditioning number of a given matrix designates an orthogonality measure indicative of the orthogonality of its column vectors. The smaller the conditioning number is, the better the orthogonality of the column vectors. Accordingly, the selected ordering πopt may correspond to the ordering which minimizes, over all possible orderings πq, q=1, . . . , N!, the conditioning number for the divided sub-matrices Rq(k) and/or Bq(kj) for k=1, . . . , N; j=k+1, . . . , N. Minimizing the conditioning number for the sub-matrices associated with a block (SB)k may impact the performance and/or computational complexity of the decoding algorithm D(k). For example, if a decoding algorithm D(k) implements a ZF,MMSE or ZF-DFE decoder, better error performance may be achieved using divided matrices of minimized conditioning numbers.
In step 515, an equivalent system to equation (5) may be determined using the selected permutation. Accordingly, equation (5) may first be rewritten as:
y=Hoptsper+w=QRsper+w (10)
Given the orthogonality of the matrix Q, an equivalent system to equation (10) may be determined according to:
{tilde over (y)}=Qty=Rsper+{tilde over (w)} (11)
In equation (11), {tilde over (w)}=Qtw designates a scaled noise vector. The real-value equivalent system of equation (11) is considered for the estimation of the originally transmitted information symbols.
The ML decoding problem for jointly decoding the information symbols is given by:
ŝper,ML=argmins
In equation (12), A=[Cmin, cmax] designates the alphabet to which belong the real and imaginary parts of the complex-value vector sc composing the real vector s and equivalently the permuted vector Sper. The alphabet may be defined by the bounds cmin and cmax. An ML metric is defined as:
m(s)=∥{tilde over (y)}−Rsper∥2 (13)
In one application of the invention to recursive sub-block decoding, a sub-block decoding may be performed to recover an estimation of the original information symbols. Accordingly, in step 517, a division of the vector {tilde over (y)} into N sub-vectors is performed such that
A sub-vector {tilde over (y)}(k) of index k, for k=1, . . . , N has a lengths lk. The same sub-vector division may be applied to noise vector {tilde over (w)} to determine N sub-vectors {tilde over (w)}(k) of lengths lk such that
The sub-block decoding parameters, divided sub-matrices R(k) and B(kj) of the selected upper triangular matrix R and the divided sub-vectors {tilde over (y)}(k) may be grouped into sub-blocks (SB)k, k=1, . . . , N. A sub-block (SB)k, for k=1, . . . , N−1, may be defined by a set of parameters such that (SB)k={lk, s(k), R(k), {tilde over (y)}(k), {tilde over (w)}(k), D(k), B(kj), j=k+1, . . . , N}, where:
{tilde over (y)}(k)=R(k)s(k)+Σj=k+1NB(kj)s(k)+{tilde over (w)}(k) (14)
For k=N, the sub-block may be defined by (SB)N={lN, s(N), R(N), {tilde over (y)}(N), {tilde over (w)}(N), D(N)} such that:
{tilde over (y)}(N)=R(N)s(N)+{tilde over (w)}(N) (15)
Systems in equations (14) and (15) may be used for the decoding of the various sub-vectors of information symbols.
According to such groups of sub-blocks, the ML decoding metric in equation (13) may be written as:
m(s)=∥{tilde over (y)}−Rsper∥2=∥Σk=1N{tilde over (y)}(k)−(R(k)s(k)+Σj=k+1NB(kj)s(j)∥2 (16)
Accordingly, a sub-block estimation of the original sub-vectors of symbols s(k),k=N, N−1, . . . , 1 is performed recursively in step 521. An initialization may be performed in step 519 corresponding to k=N.
Step 521 may be repeated for each sub-block (SB)k,k=N, N−1, . . . 1 to determine a sub-vector estimation ŝ(k) of the sub-vector of symbols s(k) of the permuted vector sper. For each k=N−1, . . . 1, a sub-vector
If it is determined that all the sub-vectors of symbols have been estimated in step 525, step 529 may be performed to construct an output, from the sub-vectors ŝ(k), k=1, . . . , N, as an estimation ŝc of the complex-value vector of information symbols vector sc. The construction step may comprise three phases. First, a real vector ŝper=[ŝ(1), . . . , ŝ(N)]t may be constructed by aggregating the different sub-vector estimates. Then, an estimate ŝ of the vector of information symbols s is determined by ordering the vector ŝper using the reverse ordering πopt−. Finally, the obtained vectors is converted into the complex vector ŝc=[ŝ1, ŝ2 . . . , ŝn/2]t such that a component ŝj for j=1, . . . . , n/2 is given by:
−ŝj=(ŝ)j+i(ŝ)j+n/2 (17)
In equation (17), (u)j denotes the jth element of a vector u.
According to certain embodiments of the invention, the decoding algorithms D(k), implemented in step 521 for k=1, . . . , N may be similar or different. A decoding algorithm D(k) maybe, but not limited to, any sequential decoding scheme, a ZF, an MMSE or ZF-DFE.
In one embodiment where a sequential decoder is used in a given sub-block (SB)k, the corresponding decoder D(k) delivers an estimate ŝ(k) by minimizing the sub-block metric m(s(k))=∥
Sequential tree-search algorithms such as the Sphere Decoder (SD), the Stack decoder or and the SB-Stack decoder (SB-Stack), may be used to solve equation (18).
Further, in certain embodiments, a preprocessing on the upper triangular sub-matrices R(k) prior to decoding may be performed using for example a lattice reduction and/or an MMSE-GDFE filtering. Preprocessing methods may also be applied on the channel state matrix prior to sub-block division and decoding.
The methods and devices described herein may be implemented by various means. For example, these techniques may be implemented in hardware, software, or a combination thereof. For a hardware implementation, the processing elements of a Space-Time decoder 111 can be implemented for example according to a hardware-only configuration (for example, in one or more FPGA, ASIC or VLSI integrated circuits with the corresponding memory) or according to a configuration using both VLSI and DSP.
While embodiments of the invention have been illustrated by a description of various examples, and while these embodiments have been described in considerable detail, it is not the intent of the applicant to restrict or in any way limit the scope of the appended claims to such detail. Additional advantages and modifications will readily appear to those skilled in the art. The invention in its broader aspects is therefore not limited to the specific details, representative methods, and illustrative examples shown and described. Further, the various embodiments of the invention are not limited to particular types of recursive sub-block decoding, and apply to any other types of sub-block decoding such as Semi-exhaustive Recursive Block decoding disclosed in the patent application EP N° 15306808.5. Further, the various embodiments of the invention apply both to hard and soft decoding.
In one application to soft decoding, methods and devices according to the invention allow generating a list of estimates of the original vector of information symbols. The list thus obtained can be used to calculate the log likelihood ratio values for approximating the extrinsic information of the different information bits carried by the original information symbols. Several iterations of steps 521 to 529 may be performed in order to fill the list of estimates.
Further, while certain embodiments of the invention have been described in relation to a wireless single-user MIMO system, it should be noted that the invention is not limited to such application. The invention may be integrated in any receiver device operating in any linear communication system characterized by a lattice representation of the channel output. The communication system may be wired, wireless or optical fiber-based accommodating single or multiple users, using single or multiple antennas, and single or multi-carrier communication techniques. For example, the present invention may be integrated in a receiver device implemented in a wireless distributed MIMO system. Distributed MIMO may be used for example in cellular uplink communications applied in 3G, 4G and LTE standards. Cooperative communications applied for example in ad-hoc networks (wireless sensor networks, machine-to-machine communications, internet of things . . . ) are also examples of distributed MIMO systems. In addition to wireless networks, the present invention may be integrated in optical receiver devices implemented in optical fiber-based communication systems such as Polarization Division Multiplexing-OFDM (PDM-OFDM) systems.
Further, the invention is not limited to communication devices and may be integrated in signal processing devices such as electronic filters of finite impulse response (FIR) used in audio applications like audio crossovers and audio mastering. Accordingly, certain embodiments of the invention may be used to determine an estimate of an input sequence, given an output sequence of a FIR filter of order M.
In another application, methods, devices and computer program products according to some embodiments of the invention may be implemented in a Global Navigation Satellite System (GNSS), such as IRNSS, Beidou, GLONASS, Galileo; GPS comprising for instance at least a GPS receiver for estimating positioning parameters using for example carrier phase measurements.
Further, methods, devices and computer program products according to some embodiments of the invention may be implemented in cryptographic systems for determining estimates on private secret values used in a cryptographic algorithm for encrypting/decrypting data or messages during their storage, processing or communication. In lattice-based cryptography applications, data/messages are encrypted in the form of lattice points. The decryption of such encrypted data may be advantageously performed according to some embodiments of the invention, enabling for a high probability of success recovery of secret values with a reduced complexity.
Furthermore, the methods described herein can be implemented by computer program instructions supplied to the processor of any type of computer to produce a machine with a processor that executes the instructions to implement the functions/acts specified herein. These computer program instructions may also be stored in a computer-readable medium that can direct a computer to function in a particular manner. To that end, the computer program instructions may be loaded onto a computer to cause the performance of a series of operational steps and thereby produce a computer implemented process such that the executed instructions provide processes for implementing the functions specified herein.
Number | Date | Country | Kind |
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15307154 | Dec 2015 | EP | regional |
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9118446 | Hu | Aug 2015 | B2 |
9271221 | Tong | Feb 2016 | B2 |
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Number | Date | Country |
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15306808.5 | May 2017 | EP |
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Number | Date | Country | |
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20170187433 A1 | Jun 2017 | US |