WO2023272447A1

WO2023272447A1 - A suboptimal detector for time frequency packing

Info

Publication number: WO2023272447A1
Application number: PCT/CN2021/102816
Authority: WO
Inventors: Giulio Colavolpe; Tommaso Foggi; Amina Piemontese; Alessandro UGOLINI; Jilong HAN; Ling Liu
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2021-06-28
Filing date: 2021-06-28
Publication date: 2023-01-05
Also published as: EP4342082A1

Abstract

A soft-output symbol detector (500) for detecting one or more symbol streams from a received signal (101) representing multiple time-frequency packed linearly modulated signals (101a). The detector (600) comprises one or more processors (601) configured to: process the received signal (101) to compute a proper joint probability mass function (102); form a factor graph (103) by performing an exact factorisation of the joint probability mass function (102); compute marginals (104a) of the joint probability mass function (102) by performing a message-passing algorithm on nodes (103a, 103b) of the factor graph (103); and detect the symbol stream (s) (105a) in dependence on the computed marginals (104a). Detecting the symbol stream (s) (105a) in dependence on the computed marginals (104a) enables the detection to be based on the exact factorisation of the proper joint probably mass function (102) of the received signal (101).

Description

A SUBOPTIMAL DETECTOR FOR TIME FREQUENCY PACKING

FIELD OF THE INVENTION

This invention relates to detecting symbol streams from a received signal, for example, the received signal representing multiple time-frequency packed linearly modulated signals.

BACKGROUND

Symbol streams can be detected from a received signal representing multiple time-frequency packed linearly modulated signals.

Implementing Faster-than-Nyquist (FTN) techniques may involve the compression of the transmitted symbols in time. This compression may introduce intentional intersymbol interference (ISI) . The ISI may degrade the performance in terms of mutual information, but may increase the spectral efficiency, as the time resource occupancy is reduced.

Further, a frequency compression may be introduced among carriers, so that intercarrier interference (ICI) arises, but a further increase of spectral efficiency may be possible. The combined compression in time and frequency is known as time-frequency packing (TFP) .

The transmission of a linear modulation, for example quadrature amplitude modulation (QAM) and phase shift keying (PSK) , over a channel that introduces both ISI and ICI belong to a general class of linear channels. The following systems also belong to the same class (i) code division multiple access (CDMA) systems, (ii) multiple input multiple output (MIMO) systems, (iii) orthogonal frequency division multiplexing (OFDM) systems with ICI, and (iv) storage systems with 2-dimensional ISI.

There are papers which propose suboptimal soft-input soft-output (SISO) detection algorithms for linear channels. One example is G. Colavolpe, D. Fertonani, and A. Piemontese, “SISO detection over linear channels with linear complexity in the number of interferers, ” IEEE Journal of Selected Topics in Signal Processing, vol. 5, pp. 1475-1485, December, 2011, in which the algorithm complexity is linear in the number of interferers. However, this algorithm may not produce a good performance in the TFP scenario mentioned above.

Other algorithms may have a complexity which is quadratical in the number of interferers and can be adopted for TFP implementations as well. They are shown in these papers, X. Wang and H.V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA, ” IEEE Trans. Commun., vol. 47, pp. 1046-1061, July 1999, H. El Gamal and E. Geraniotis, “Iterative multiuser detection for coded CDMA signals in AWGN and fading channels, ” IEEE J. Select. Areas Commun., vol. 18, pp. 30-41, Jan. 2000. and J. Boutros and G. Caire, “Iterative multiuser joint decoding: unified framework and asymptotic analysis, ” IEEE Trans. Inform. Theory, vol. 48, pp. 1772-1793, July 2002. These are based on a Gaussian approximation of the interference, which addresses multiuser detection for CDMA systems.

The same algorithm has also been extended to MIMO, ISI channels in (M. Tuchler, A.C. Singer, and R. Koetter, “Minimum mean square error equalization using a priori information, ” IEEE Trans. Signal Processing, vol. 50, pp. 673–683, Mar. 2002., M. Tuchler, R. Koetter, and A.C. Singer, “Turbo equalization: Principles and new results, ” IEEE Trans. Commun., vol. 55, pp. 754-767, May 2002, and R.J. Drost and A.C. Singer, “Factor-graph algorithms for equalization, ” IEEE Trans. Signal Processing, vol. 55, pp. 2052-2065, May 2007. ) , and FDM systems with ICI (see F. Beidas, H. El Gamal, and S. Kay, “Iterative interference cancellation for high spectral efficiency satellite communications, ” IEEE Trans. Commun., vol. 50, pp. 31-36, Jan. 2002. ) .

As said, the algorithms have a complexity which increases quadratically with the number of interferers. So the implementation may be unaffordable in TFP systems.

In A. Piemontese and G. Colavolpe, “A novel graph-based suboptimal multiuser detector for FDM-CPM transmissions, ” IEEE Trans. Wireless Commun., vol. 9, pp. 2812-2819, September 2010 an algorithm is disclosed that uses a FG and SPA framework. However, the algorithm is tailored for of continuous phase modulations (modulations with constant envelope and a continuous phase) . Hence, the nodes of the FGs represent different factors.

In F. Rusek and A. Prlja, “Optimal channel shortening for MIMO and ISI channels, ” IEEE Trans. Wireless Commun., vol. 11, pp. 810-818, Feb. 2012 and A. Modenini, F. Rusek, and G. Colavolpe, “Adaptive rate-maximizing channel shortening for ISI channels, ” IEEE Commun. Letters, vol. 19, pp. 2090–2093, Dec. 2015 a channel shortener (CS) technique is described. The CS technique may allow a reduction in complexity of the detection stage by properly computing a reduced channel response by taking into account all the interfering signals in a limited number of channel coefficients. This detector is designed for systems with time packing only. In other words, the detector may not be directly applied to TFP systems.

It is desirable to develop a detector and method that overcomes the above problems.

SUMMARY

According to a first aspect there is provided a soft-output symbol detector for detecting one or more symbol streams from a received signal representing multiple time-frequency packed linearly modulated signals. The detector comprises one or more processors configured to: process the received signal to compute a proper joint probability mass function; form a factor graph by performing an exact factorisation of the joint probability mass function; compute marginals of the joint probability mass function by performing a message-passing algorithm on nodes of the factor graph; and detect the symbol stream (s) in dependence on the computed marginals.

Detecting the symbol stream (s) in dependence on the computed marginals enables the detection to be based on the exact factorisation of the proper joint probably mass function of the received signal.

In some implementations, the detector may be configured to jointly detect symbol streams of multiple users in the received signal.

Configuring the detector to jointly detect symbol streams of multiple users in the received signal enables the detector to be used for multiple users.

In some implementations, the detector may be configured to jointly detect multiple symbol streams from a same user in the received signal.

Configuring the detector to jointly detect multiple symbol streams from a same user in the received signal enables the detector to be used for complex symbol streams from a single user.

In some implementations, the detector may be configured to disregard symbol streams in adjacent bandwidths.

Configuring the detector to disregard symbol streams in adjacent bandwidths enables simplification of the detector in situations where the interference in negligible.

In some implementations, the exact factorisation of the joint probability mass function involves a combined variable representing the transmitted symbols and properly defined states for each time or frequency interval.

Configuring the detector to perform exact factorisation of the joint probability mass function with a combined variable enables the factorisation to be dependent, or based, on both the transmitted symbols and the properly defined state for each time or frequency interval.

In some implementations, the combined variable introduces cycles in the factor graph.

Configuring the detector so that the combined variable introduces cycles in the factor graph enables the performance and/or complexity of the detector to be varied by the introduction of the combined variable.

In some implementations, the factorisation of the joint probability mass function comprises variable nodes and factor nodes.

Configuring the detector so that the factorisation comprises variable nodes and factor nodes enables the detector to plot the variable nodes to represent the variables, and to plot the factor nodes to represent the factors.

In some implementations, the factorisation of the joint probability mass function comprises variable nodes that stretch the variables into the combined variable.

In some implementations, the stretching of the variables does not introduce approximations.

In some implementations, the stretching of the variables is so as to increase a minimum cycle length of the factor graph.

Stretching the variables into the combined variables enables the length of the minimum cycle to be increased. In an implementation with cycles, the detector may function iteratively to provide an approximation of the exact marginals. In this way, longer cycles may provide a better approximation.

In some implementations, the factorisation of the joint probability function is:

In some implementations, the message-passing process is iterative and/or convergent.

When the detector is configured so that the message-passing process is iterative and/or convergent, the message-passing process may take several attempts, but the message-passing process may converge on good approximations of the correct, or true, values.

In some implementations, the joint probability mass function is an a-posteriori probability mass function of a time-sequence of properly defined states.

In some implementations, the detector is a sub-optimal multi-user detector.

The detector being a sub-optimal detector enables simplifications in the detection of the symbol stream which may reduce the complexity.

In some implementations, the processor is configured to operate a computational complexity that is related linearly to a number of users. The number of users may also be known as subcarriers.

Configuring the processor to operate a computational complexity that is related linearly to a number of users, or subcarriers, enables the complexity and size of the overall detector to be suitable for the implementation.

According to a second aspect there is provided a method for estimating one or more symbol streams from a received signal representing multiple time-frequency packed linearly modulated signals. The method comprises: processing the received signal to compute a proper joint probability mass function; forming a factor graph by performing an exact factorisation of the joint probability mass function; computing the marginals of the joint probability mass function by performing a message-passing algorithm on nodes of the factor graph; and detecting the symbol stream (s) in dependence on the computed marginals.

According to a third aspect there is provided a computer program which, when executed by a computer, causes the computer to perform the method of claim 16. The computer program may be stored on a non-transitory computer-readable storage medium.

According to a fourth aspect there is provided a receiver for detecting a symbol stream in a received signal comprising multiple symbol streams. The receiver comprises: a bank of matched filters for performing matched filtering of the received signal in dependence on each of a plurality of filter responses to form a plurality of first filtered signals; a downsampler for downsampling each of the first filtered signals to form a plurality of downsampled signals; a secondary filter for filtering each of the downsampled signals with a multidimensional channel shortener to form a plurality of second filtered signals; and a detector for detecting the symbol stream in the second filtered signals.

Using a secondary filter to filter each of the downsampled signals with a multidimensional channel shortener and detecting the symbol stream from the output of the channel shortener enables the detector to operate on a reduced size graph, which may reduce the complexity of the receiver.

In some implementations, the multidimensional channel shortener

is computed as a multidimensional matrix with size U×U×L _r+1 in accordance with:

where L _r is the length of the desired channel response.

In some implementations, the detector is configured to perform detection using a channel response computed in dependence on the multidimensional channel shortener.

In some implementations, the detector is configured to perform detection using a channel response computed in accordance with:

where I (U) is an identity matrix with size U.

In some implementations, the received signal is a multiuser signal.

By configuring the receiver to receive a multiuser signal enables the receiver to be used for multiple users.

In some implementations, the detector is configured to output a plurality of detected symbol streams representing substreams of the received signal and the receiver comprises a plurality of detectors, each detector being arranged to detect a substream of the transmitted signal.

BRIEF DESCRIPTION OF THE FIGURES

The present invention will now be described by way of example with reference to the accompanying drawings. In the drawings:

Figure 1 schematically illustrates an exemplary embodiment of the stages of a soft-output symbol detector.

Figure 2 schematically illustrates an exemplary embodiment of a factor graph of an optimal detector.

Figure 3 schematically illustrates an exemplary embodiment of a factor graph of a suboptimal detector.

Figure 4 illustrates an example method for estimating one or more symbol streams from a received signal.

Figure 5 illustrates an example of an apparatus configured to perform the methods described herein.

Figure 6 schematically illustrates an exemplary embodiment of the architecture of a receiver.

DETAILED DESCRIPTION

The apparatuses and methods described herein concern detecting one or more symbol streams from a received signal and receiving a symbol stream in a received signal.

Embodiments of the present system may tackle one or more of the problems previously mentioned by detecting the symbol stream (s) in dependence on the computed marginals. In this way, the detection can be based on the exact factorisation of the proper joint probably mass function of the received signal.

Figure 1 shows the framework of the sum-product algorithm (SPA) and the factor graphs (FGs) 103, used to derive optimal and suboptimal detectors. In some embodiments, the detector may be a sub-optimal multi-user detector. In other words, simplifications may be made in the detection of the symbol stream. In other embodiments, the detector may be an optimal detector.

The FGs 103 and the SPA represent a framework configured to compute, either in an exact or in an approximate way, the marginals 104a of the joint probability mass function 102.

In detection problems, where x= {x _k} are the transmitted symbols and y= {y _k} are the received samples from the received signal 101, maximum a-posteriori probability MAP symbol detection is given by Equation 1.

The strategy may require the computation of the marginals P (x _k|y) , that can be obtained from a joint probability mass function 102 P (x, σ|y) , where σ= {σ _k} are proper hidden variables, through the FG/SPA framework. In this way, the framework may be used to implement optimal, or suboptimal, MAP detection strategies.

Given the joint probability mass function 102 P (x, σ|y) to be marginalized, the detector may carry out the following steps:

The detector may obtain a received signal 101. The received signal 101 may represent multiple time-frequency packed linearly modulated signals 101a. In other words, the multiple time-frequency packed linearly modulated signals 101a may be adjacent to one another.

The detector is configured to process the received signal 101 to compute a proper joint probability mass function 102. In some embodiments, the joint probability mass function 102 may be an a-posteriori probability mass function of a time-sequence of properly define states.

The detector is configured to form a factor graph 103 by performing an exact factorisation of the joint probability mass function 102. In other words, the joint probability mass function 102 may be expressed as a product of factors. This factorisation may be arbitrary in the sense that the factors may be clustered into one. Different factorisations may provide different marginalisation algorithms.

The exact factorisation of the joint probability mass function 102 may involve a combined variable 102a, 102b. The combined variable 102a, 102b may represent the transmitted symbols 102a and the properly defined states 102b for each time or frequency interval.

The factorisation of the joint mass probability function 102 may be carried out using a specific smart factorisation of the transmitted symbols given the received samples. The joint mass probability function 102 may be expressed in closed form. Depending on how the factors are collected, the factor graph 103 may or may not comprise cycles. This may depend on whether the many factors are collected in one or if the factors are represented separately.

If the factor graph 103 does not comprise cycles, then the application of a SPA may result in an optimal MUD detector.

If the factor graph comprises cycles, then the application of the SPA may result in a suboptimal MUD detector with different performance/complexity trade-offs. In implementations where the factor graph 103 includes cycles, the detector may function iteratively to provide approximations of the marginals 104a.

The processors of the detector may be configured to be in a onw-to-one correspondence with the nodes of the factor graph 103. The factor graph 103 may comprise a bypartite graph with at least two types of nodes. One type of node is a variable node 103a, usually denoted with circles as shown in Figure 1, which represents the variables ( {x _k} and {σ _k} only, since at the receiver, samples {y _k} are known. Another type of node is a factor node 103b, usually represented with squares as shown in Figure 2, which represent the factors.

The detector is configured to compute marginals 104a of the joint probability mass function 102 by performing a message-passing algorithm on nodes 103a of the factor graph 103. The message-passing algorithm may be the SPA. The marginals may be computed exactly, where the factor graph 103 does not comprise cycles. As shown illustratively in Figure 1, the number of computed marginals 104a may correspond to the number of nodes 103a of the factor graph 103. Although, it may be appreciated that the number of computed marginals 104a may not correspond to the number of nodes 103a of the factor graph 103.

In some embodiments, the message-passing process may be iterative. In other words, the message-passing process may take several attempts. Additionally, or alternatively, the message-passing process may be convergent. In other words, the message-passing process may converge on good approximations of the correct, or true, values.

The factorisation of the joint probability mass function 102 may comprise variable nodes 103a that stretch the variables into the combined variable 102a, 102b. In other words, the stretching of the variables may increase the girth, or the length of the minimum cycle of the factor graph 103. It is preferable that the stretching of the variable does not introduce approximations, so that the performance of the detector is maintained.

The detector is configured to detect the symbol stream (s) 105a from the received signal 101 in dependence on the computed marginals 104a. In other words, the detector may use the data in the computed marginals 104a to control the detection of the symbol streams (s) 105a. As shown illustratively in Figure 1, the number of symbol streams (s) 105a may correspond to the number of time-frequency packed linearly modulated signals 101a of the received signal 101. Although, it may be appreciated that the number of symbol streams (s) 105a may not correspond to the number of time-frequency packed linearly modulated signals 101a of the received signal 101.

This detector FG/SPA framework may be conveniently used to derive new algorithms with very good trade-offs between performance and complexity.

The detector may be configured to jointly detect symbol streams 105a of multiple users in the received signal. In this way, this may enable the detector to be used for multiple users.

Additionally, or alternatively, the detector may be configured to disregard symbol streams 105a in adjacent bandwidths. Particularly, where the interference between adjacent symbol streams 105a is negligible, this may simplify the detector.

Additionally, or alternatively, the detector may be configured to jointly detect multiple symbol streams 105a from a same user in the received signal. In this way, this may enable the detector to be used for complex symbol streams from a single user.

The application of the FG/SPA framework, in the detector, which represents the joint a-posteriori probability (APP) of the received signals from all users may lead to a factorisation that may be implemented by exploiting the forward-backward message-passing BCJR algorithm. This may provide the optimal APPs.

A technical problem with the prior art is due to the high complexity of a multi-user detector (MUD) receiver. This may be prohibitive in practice, as, for instance, a quadrature phase shift keying (QPSK) modulated signal with just U=3 and L=3 would imply a detector with 262144 states, which is unfeasible.

The resulting algorithm may be made of different single-user detectors (SUDs) , one for each carrier, or user, that exchange information. In this way, any SUD will exchange information only with the SUDs processing the adjacent carriers, or users. In this way, the processor is configured to operate a computational complexity that is related linearly to a number of users. Additionally, a two-dimensional channel shortener (CS) technique may be implemented to further reduce the complexity. CS technique may provide a reduction the complexity of the detection stage by properly computing a reduced channel response which takes account of the interfering signals in a limited number of channel coefficients.

The detector will now be described in more detail.

In an exemplary embodiment, the detector is designed in a time frequency packing (TFP) scenario and is a suboptimal detector designed by employing the FG/SPA framework. The exemplary suboptimal detector is implemented for a multicarrier transmission with U carries, or users.

The received signal 101 may be defined by Equation 2.

is the vector containing the K symbols transmitted on carrier, or user, l and x= (x ⁽¹⁾ ^T, x ⁽²⁾ ^T, ..., x ^(U) T) ^T.

In Equation 2, f ^(l) is the lth carrier, or user, frequency and w (t) is the additive white Gaussian noise (AWGN) .

A sufficient statistic for MAP symbol detection may be obtained through a bank of U filters matched to the pulses p ^(l) (t) , l=1, 2, ..., U (Ungerboeck model) . y is defined as y= (y ^(1) T, y ^(2) T, ..., y ^(U) T) .

The joint probability mass function of the output given the input is defined by Equation 3.

In Equation 3, matrix G is a block matrix and G ^(l, m) denotes the (l, m) submatrix with K rows and K columns accounting for the correlation between carriers, or users, l and m. The entries are defined by Equation 4.

In Equation 4, the submatrices may have a Toeplitz structure that may be properly exploited.

By defining

and

Equations 5 to 10 may express a possible factorization of the joint a posteriori probability mass function.

I(x _k, σ _k, σ _k+1) =P (σ _k+1|σk, x _k) (10)

Figure 2 schematically illustrates an exemplary embodiment of the corresponding factor graph. The factor graph 200 comprises

variable nodes

201, 202, 203 and

factor nodes

204, 205.

Since this FG has no cycles, the application of the SPA to it gives the optimal marginal APPs

The message-passing resulting algorithm may take the form of a forward-backward BCJR algorithm.

Figure 3 schematically illustrates an exemplary embodiment of an alternative factor graph representing the same joint probability mass function. The factor graph 300 comprises

variable nodes

303, 306, 308, 312, 314, 316, 318, 322, 324, 326, 328 and

factor nodes

301, 302, 304, 305, 307, 309, 310, 311, 313, 315, 317, 319, 320, 321, 323, 325, 327. The factorisation in the suboptimal detector is given by Equation 11. In this exemplary embodiment, the factorisation is still an exact factorisation. We simply further factorized some terms.

This FG contains cycles. Hence the application of the SPA to it provides approximations of the marginal APPs

The resulting algorithm is suboptimal.

The corresponding factor graph 200 has cycles of length 4. In this way, the application of the SPA results in a suboptimal algorithm. Thus, in this exemplary embodiment, stretching is used to preserve the information of the original factor graph, and we obtain a factor graph with longer cycles (length 12) . In this exemplary embodiment, the SPA applied to this factor graph is still iterative and leads to approximate APPs.

In this exemplary embodiment, further simplification may be introduced by assuming that the interference among non-adjacent users is negligible. The corresponding factorization and factor graph 300, shown in Figure 3, are defined by Equation 12.

In this way, the suboptimal detector may comprise single-user detectors (illustrated by the

boxes

309, 310, 319, 320 in Figure 3) , neglecting ICI, and nodes

that mitigate the interference among users. The complexity related to these nodes increases only linearly with U.

Additionally, an extended adaptive channel shortening technique for MUD may be used. The algorithm relies on a training phase based on known symbols and designs, a shortened channel response with a desired length, and a channel shortening filter. The design may be based on the computation of the error between the transmitted symbols and a bank of U MMSE filters which are used to filter the outputs of the front-end stage. The errors may be used to compute the cross-correlations between the different users. The autocorrelations of the error may be collected in a multidimensional matrix

with size U×U×L _r.

The matrix block, with matrix size UL _r×UL _r, is defined by Equation 13.

In Equation 13,

are submatrices of

The matrix with size U×U is computed as defined in Equation 14.

The computation of U ₀, a matrix of size U×U, is defined by Equation 15.

A multidimensional matrix

with size U×U×L _r+1 is computed as defined in Equation 16.

A channel shortener is computed as a multidimensional matrix with size U×U×L _r+1 as defined in Equation 17.

The shortened channel response may only differ from

as defined by Equation 18.

In Equation 18, I (U) is the identity matrix with size U.

Figure 4 summarises an example of a method 400 for estimating one or more symbol streams from a received signal representing multiple time-frequency packed linearly modulated signals. At step 401, the method 400 comprises processing the received signal to compute a proper joint probability mass function. At step 402, the method 400 comprises forming a factor graph by performing an exact factorisation of the joint probability mass function. At step 403, the method 400 comprises computing the marginals of the joint probability mass function by performing a message-passing algorithm on nodes of the factor graph. At step 404, the method 400 comprises detecting the symbol stream (s) in dependence on the computed marginals.

An example of an apparatus 500 configured to implement the methods described herein is schematically illustrated in Figure 5. The apparatus 500 may comprise, or provide, the detector 500. The detector 500 may be implemented on an electronic device, such as in a field-programmable gate array (FPGA) or a very large-scale integration (VSLI) chip.

The detector 500 comprises a processor 501 configured to process the datasets in the manner described herein. For example, the processor 501 may be implemented as a computer program running on a programmable device such as a Central Processing Unit (CPU) . The detector 500 comprises a memory 502 which is arranged to communicate with the processor 501. Memory 502 may be a non-volatile memory. The processor 501 may also comprise a cache (not shown in Figure 5) , which may be used to temporarily store data from memory 502. The detector 500 may comprise more than one processor 501 and more than one memory 502. The memory 502 may store data that is executable by the processor 501. The processor 501 may be configured to operate in accordance with a computer program stored in non-transitory form on a machine-readable storage medium. The computer program may store instructions for causing the processor 501 to perform its methods in the manner described herein.

Specifically, the soft-output symbol detector 500 may comprise one or more processors 501. The processor (s) 501 may be configured to operate a computational complexity that is related linearly to a number of users. The detector 500 may process the received signal to compute a proper joint probability mass function. The detector 500 may form a factor graph by performing an exact factorisation of the joint probability mass function. The detector 500 may compute the marginals of the joint probability mass function by performing a message-passing algorithm on nodes of the factor graph. The detector 500 may detect the symbol stream (s) in dependence on the computed marginals.

The receiver 600 may be used to detect a symbol stream in a received signal 601 comprising multiple symbol streams. As described herein, in relation to the detector, the received signal may be a multiuser, or multi-carrier, signal.

The implementation of the algorithms in the receiver 600 are preferably provided within the electronic processing at receive side, as shown in Figure 6.

The receiver 600 may comprise a bank of matched

filters

605, 606, 607 for performing matched filtering of the received signal 601. In the exemplary embodiment shown in Figure 6, there are three matched

filters

605, 606, 607. The filtering of the received signal 601 may be in dependence on each of a plurality of

filter responses

602, 603, 604. In other words, the filtering may take account of the

filter responses

602, 603, 604. The filtering of the received signal 601 is carried out to form a plurality of first filtered signals.

The receiver 600 may comprise a downsampler. The downsampler may be used to downsample each of the first filtered signals to form a plurality of downsampled signals. Each of the plurality of downsampled signals may be formed from a corresponding first filtered signal.

The receiver 600 may comprise a secondary filter 608. The secondary filter 608 may be used to filter all the signals at the output of the bank of matched filters with a multidimensional channel shortener. The multidimensional channel shortener, denoted by

may provide further filtering to each of the downsampled signals. The output of the secondary filter 608 may be a plurality of second filtered signals.

The multidimensional channel shortener

may be computed as a multidimensional matrix with size U×U×L_r+1 in accordance with Equation 19, where L_r is the length of the desired channel response.

The receiver 600 may comprise a detector 609. The second filtered signals may be inputted into the detector 609. The detector 609 may detect the symbol stream in the second filtered signals. The detector 609 may be a MUD. The detector 609, or MUD, may operate on a reduced size graph, or trellis, defined by the computed reduced channel response

The detector 609 may carry out, or perform, the detection using a channel response computed in dependence on the multidimensional channel shortener

In other words, the detector 609 may use the output from the secondary filter 608 to carry out the detection.

The detector 609 may carry out, or perform, the detection using a channel response computed in accordance with Equation 20, where I (U) is an identity matrix with size U.

The detector 609 may be configured to output a plurality of detected symbol streams. Each of the plurality of detected symbol streams may correspond to a second filtered signal. The plurality of detected symbol streams may represent substreams of the received signal.

The receiver 600 may also comprise

different decoders

610, 611, 612. The receiver 600 may comprise

N decoders

610, 611, 612 corresponding to N matched

filters

605, 606, 607 It may be appreciated that, in alternative embodiments, the number of

decoders

610, 611, 612 may not correspond to the number of matched

filters

605, 606, 607. In the exemplary embodiment shown in Figure 6, the receiver 600 comprises three

decoders

610, 611, 612 corresponding to the three matched

filters

605, 606, 607. The decoders may be arranged to detect a substream of the transmitted signal.

Each iteration between the detectors 609, the

decoders

610, 611, 612, and the nodes

may be updated and used to compute the branch metrics of each single-user detector.

The apparatus 500 illustrated in Figure 5 may also comprise, or provide, the

receiver

500, 600 as described herein.

The applicant hereby discloses in isolation each individual feature described herein and any combination of two or more such features, to the extent that such features or combinations are capable of being carried out based on the present specification as a whole in the light of the common general knowledge of a person skilled in the art, irrespective of whether such features or combinations of features solve any problems disclosed herein, and without limitation to the scope of the claims. The applicant indicates that aspects of the present invention may consist of any such individual feature or combination of features. In view of the foregoing description, it will be evident to a person skilled in the art that various modifications may be made within the scope of the invention.

Claims

A soft-output symbol detector (500) for detecting one or more symbol (105a) streams from a received signal (101) representing multiple time-frequency packed linearly modulated signals (101a) , the detector (500) comprising one or more processors (501) configured to:

process the received signal (101) to compute a proper joint probability mass function (102) ;

form a factor graph (103) by performing an exact factorisation of the joint probability mass function (102) ;

compute marginals (104a) of the joint probability mass function (102) by performing a message-passing algorithm on nodes (103a, 103b) of the factor graph (103) ; and

detect the symbol stream (s) (105a) in dependence on the computed marginals (104a) .
A detector (500) as claimed in claim 1, wherein the detector (500) is configured to jointly detect symbol streams (105a) of multiple users in the received signal (101) .
A detector (500) as claimed in claim 1 or claim 2, wherein the detector (500) is configured to jointly detect multiple symbol streams (105a) from a same user in the received signal (101) .
A detector (500) as claimed in claim 2, wherein the detector (500) is configured to disregard symbol streams (105a) in adjacent bandwidths.
A detector (500) as claimed in any preceding claim, wherein the exact factorisation of the joint probability mass function (102) involves a combined variable (102a, 102b) representing the transmitted symbols (102a) and properly defined states (102b) for each time or frequency interval.
A detector (500) as claimed in claim 5, wherein the combined variable (102a, 102b) introduces cycles in the factor graph (103) .
A detector (500) as claimed in any preceding claim, wherein the factorisation of the joint probability mass function (102) comprises variable nodes (103a) and factor nodes (103b) .
A detector (500) as claimed in claim 7 as dependent on claim 5, wherein the factorisation of the joint probability mass function (102) comprises variable nodes that stretch the variables into the combined variable.
A detector (500) as claimed in claim 8, wherein the stretching of the variables does not introduce approximations.
A detector (500) as claimed in claim 8 or claim 9, wherein the stretching of the variables is so as to increase a minimum cycle length of the factor graph (103) .
A detector (500) as claimed in any preceding claim, wherein the factorisation of the joint probability mass function (102) is:
A detector (500) as claimed in any preceding claim, wherein the message-passing process is iterative and/or convergent.
A detector (500) as claimed in any preceding claim, wherein the joint probability mass function (102) is an a-posteriori probability mass function of a time-sequence of properly defined states.
A detector (500) as claimed in any preceding claim, wherein the detector (500) is a sub-optimal multi-user detector (500) .
A detector (500) as claimed in any preceding claim, wherein the processor (501) is configured to operate a computational complexity that is related linearly to a number of users.
A method (400) for estimating one or more symbol streams from a received signal representing multiple time-frequency packed linearly modulated signals, the method comprising:

processing (401) the received signal to compute a proper joint probability mass function;

forming (402) a factor graph by performing an exact factorisation of the joint probability mass function;

computing (403) marginals of the joint probability mass function by performing a message-passing algorithm on nodes of the factor graph; and

detecting (404) the symbol stream (s) in dependence on the computed marginals.
A computer program which, when executed by a computer, causes the computer to perform the method (400) of claim 16.
A receiver (500, 600) for detecting a symbol stream in a received signal (601) comprising multiple symbol streams, the receiver (600) comprising:

a bank of matched filters (605, 606, 607) for performing matched filtering of the received signal (601) in dependence on each of a plurality of filter responses (602, 603, 604) to form a plurality of first filtered signals;

a downsampler for downsampling each of the first filtered signals to form a plurality of downsampled signals;

a secondary filter (608) for filtering each of the downsampled signals with a multidimensional channel shortener to form a plurality of second filtered signals; and

a detector (609) for detecting the symbol stream in the second filtered signals.
A receiver (500, 600) as claimed in claim 18, wherein the multidimensional channel shortener
is computed as a multidimensional matrix with size U×U×L _r+1 in accordance with:

where L _r is the length of the desired channel response.
A receiver (500, 600) as claimed in claim 18 or claim 19, wherein the detector (609) is configured to perform detection using a channel response computed in dependence on the multidimensional channel shortener.
A receiver (500, 600) as claimed in claim 20 as dependent on claim 19, wherein the detector (609) is configured to perform detection using a channel response computed in accordance with:

where I (U) is an identity matrix with size U.
A receiver (500, 600) as claimed in any of claims 18 to 21, wherein the received signal is a multiuser signal.
A receiver (500, 600) as claimed in any of claims 18 to 22, wherein the detector (609) is configured to output a plurality of detected symbol streams representing substreams of the received signal and the receiver comprises a plurality of detectors, each detector being arranged to detect a substream of the transmitted signal.