WO2016085373A1

WO2016085373A1 - Methods and nodes for enabling determination of data in a radio signal

Info

Publication number: WO2016085373A1
Application number: PCT/SE2014/051405
Authority: WO
Inventors: Ather GATTAMI
Original assignee: Telefonaktiebolaget Lm Ericsson (Publ)
Priority date: 2014-11-25
Filing date: 2014-11-25
Publication date: 2016-06-02

Abstract

A transmitting node (900), a receiving node (902), and methods therein for supporting determination of input data encoded as data symbols which are transmitted in amplitude modulated pulses.The transmitting node (900) pre-codes (900b, 900c) the data symbols based on a circulant matrix C describing Inter- Symbol-Interference, ISI, between the pulses, and transmits (900d) the amplitude modulated pulses with amplitudes corresponding to the pre-coded data symbols using a time separation ρ Taccording to a Faster-than-Nyquist, FTN, technique. The receiving node then receives and samples (902a) the radio signal and performs determination of the input data by decoding (902b-d) the data symbols based on the circulant matrix C.

Description

METHODS AND NODES FOR ENABLING DETERMINATION OF DATA IN A

RADIO SIGNAL

Technical field

The present disclosure relates generally to a transmitting node, a receiving node and methods therein, for enabling determination of input data encoded as data symbols, the data symbols being transmitted by the transmitting node to the receiving node as a radio signal with consecutive amplitude modulated pulses

Background

In recent years, different types of wireless networks have been developed to provide radio communication for various wireless devices in different areas such as cells. The wireless networks, also commonly referred to as cellular or mobile networks, are constantly improved to provide better capacity, quality and coverage to meet the demands from subscribers using services and increasingly advanced terminals for communication, such as smartphones and tablets, which often require considerable amounts of bandwidth and resources for data transport in the networks. Therefore, it is often a challenge to achieve high capacity and good performance, e.g. in terms of high data throughput, low latency and low rate of dropped or lost data, in the radio communication between base stations in the wireless network and various wireless devices communicating with the base stations.

In the field of radio communication in wireless networks, the terms "wireless device" and "User Equipment, UE" are commonly used and may represent any mobile phone, tablet or laptop computer capable of radio communication with a wireless network including receiving downlink signals transmitted from a serving network node and sending uplink signals to the network node. Further, the terms

"network node", "base station" and "Node B" are commonly used in this field and may represent any node of a wireless network that can communicate uplink and downlink radio signals with wireless devices or UEs.

Throughout this disclosure, the terms "transmitting node" and "receiving node" are used in the sense that the transmitting node transmits radio signals, either uplink or downlink, which are received by the receiving node. Consequently, when the transmitting node is a network node the receiving node is a wireless device, and conversely when the transmitting node is a wireless device the receiving node is a network node. This disclosure is thus valid for both uplink radio signals and downlink radio signals. Further, the term "data" may refer to any information conveyed in the radio signals from the transmitting node to the network node, such as any payload data and signaling data, and the examples and embodiments to be described below are not limited in this respect.

As indicated above, it is of great interest to achieve high data throughput in radio communications taking place in a wireless network when data is communicated in radio signals from a transmitting node to a receiving node. One efficient method of achieving high bitrate is to apply pulse amplitude modulation of the data for communicating data symbols where each data symbol is carried by an amplitude modulated pulse and may comprise several bits of information. A series of such consecutive pulses are transmitted in a pulse train, each pulse carrying a data symbol. In this case it is important that the receiving node can detect the amplitude of each pulse correctly to avoid data errors. This may however be difficult since consecutive pulses tend to interfere with one another, called Inter-Symbol- Interference, IS I, when transmitted as a pulse train. An example of a radio communication is schematically shown in Fig. 1 where a network node 100 transmits data in downlink radio signals to a wireless device 102. In this process the network node 100 has thus some input data to transmit and network node 100 basically encodes the input data on a radio signal in a first action 1 :1 and transmits the radio signal to the wireless device 102 in a next action 1 :2. A further action 1 :3 illustrates that the wireless device 102 decodes the incoming radio signal to extract the input data, hopefully acquiring the same data that was encoded at the network node 100 in action 1 :1 .

Fig. 2 illustrates the basic operation of a transmitting node 200 and a receiving node 202, e.g. the above network node 100 and wireless device 102, respectively, when pulse amplitude modulation is used. The transmitting node 200 comprises a pulse generator function 200a which generates pulses with amplitudes that correspond to some encoded input data a[n]. Each pulse thus represents a data symbol carrying a number of information bits according to the pulse amplitude modulation applied where the information bits may represent some input data to be transmitted. The pulses are commonly referred to as "Nyquist" pulses of a certain sampling rate T.

These pulses are transmitted as a radio signal s(t) by a transmitter function 200b in the transmitting node 200 and the radio signal s(t) propagates over a radio channel to the receiving node 202. During this propagation the signal is affected, i.e. corrupted or distorted, by noise w(t) before it is received by a receiver function 202a in the receiving node 202 as a received signal r(t), such that r(t) = s(t) + w(t)

The noise w(t) that affects propagating radio signals in this way is commonly regarded as a static "white Gaussian noise" for simplicity, which basically does not change over time. The received signal is then sampled by a sampler function 202b in the receiving node 202 which produces a series of samples y[n]. The receiving node 202 then tries to estimate the input data a[n] from the samples y[n]. It is naturally desirable that this estimation is made with as low error probability as possible.

One known way of increasing the data rate in this communication is to use a so- called "Faster-than-Nyquist, FTN" technique where the amplitude modulated pulses are transmitted separated in time shorter than the Nyquist sampling rate T. This can be formulated as transmitting the amplitude modulated pulses separated by the time pTwhere 0 < p < 1. Thereby, the number of data symbols and information bits communicated per time can be increased. However, it is a problem that the process of estimating the original input data from the samples obtained at the receiving node can be very complex when the FTN technique is employed, particularly when relatively large block-lengths of data are used in the radio communication. Briefly described, the estimation process is based on a predefined matrix G whose elements basically describe the Inter- Symbol-Interference, IS I , that occurs between the transmitted pulses. The matrix G used in this process is thus known in beforehand and it is defined depending on the pulse shape and FTN rate used.

Each transmitted pulse is thus subjected to interference from contiguous pulses in the transmission which gives rise to the IS I, and the matrix G thus describes the correlation between different pulses in the transmission. The matrix G is used for pre-coding the data at the transmitting node and for decoding the data at the receiving node. A process called "G-to-minus-half, GTMH, pre-coding", which is well-known in this field, is typically used in a very complex computational operation requiring a number of multiplications. For example, if the block-length N is 1000 bits, the number of multiplications required for encoding and decoding each pulse is in the magnitude of 1000.000. The FTN technique is discussed in more detail in the Master of Science Thesis "Low complexity algorithms for Faster-Than-Nyquist Signaling" by Emil Ringh, Stockholm 2013. Summary

It is an object of embodiments described herein to address at least some of the problems and issues outlined above. It is possible to achieve this object and others by using a transmitting node, a receiving node and methods therein as defined in the attached independent claims. According to one aspect, a method is performed by a transmitting node in radio communication with a receiving node, for supporting determination of input data encoded as data symbols, the data symbols being transmitted to the receiving node as a radio signal with consecutive amplitude modulated pulses. In this method the transmitting node pre-codes the data symbols based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol-

Interference, IS I, between contiguous pulses in the radio signal, and generates the amplitude modulated pulses with amplitudes corresponding to the pre-coded data symbols. The transmitting node then transmits the radio signal with the amplitude modulated pulses using a time separation pT shorter than a sampling rate T used by the receiving node for sampling the radio signal. Thereby, the receiving node is enabled to determine the input data by decoding the data symbols based on the circulant matrix C.

According to another aspect, a transmitting node is arranged to support determination of input data encoded as data symbols when the data symbols are transmitted to a receiving node as a radio signal with consecutive amplitude modulated pulses. The transmitting node comprises means configured to pre-code the data symbols based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal. This pre-coding operation may be performed by a precoding module in the transmitting node.

The transmitting node also comprises means configured to generate the amplitude modulated pulses with amplitudes corresponding to the pre-coded data symbols. This generating operation may be performed by a generating module in the transmitting node. The transmitting node also comprises means configured to transmit the radio signal with the amplitude modulated pulses using a time separation pT shorter than a sampling rate 7^" used by the receiving node for sampling the radio signal, thereby enabling the receiving node to determine the input data by decoding the data symbols based on the circulant matrix C. This transmitting operation may be performed by a transmitting module in the transmitting node.

According to another aspect, a method is performed by a receiving node in radio communication with a transmitting node, for determination of input data encoded as data symbols, the data symbols being received from the transmitting node as a radio signal with consecutive amplitude modulated pulses. In this latter method, the receiving node receives the radio signal with the amplitude modulated pulses having a time separation pT shorter than a sampling rate 7 used by the receiving node for sampling the radio signal. The amplitude modulated pulses have amplitudes corresponding to data symbols which have been pre-coded by the transmitting node based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal. The receiving node then obtains samples y_n of the amplitude modulated pulses in the received radio signal, and modifies the samples y_n based on a circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, IS I , between contiguous pulses in the radio signal. The receiving node further decodes the data symbols by finding a Maximum Likelihood Estimate of the data symbols based on the modified samples y, and finally determines the input data based on the decoded data symbols.

According to another aspect, a receiving node is arranged to perform

determination of input data encoded as data symbols received from a transmitting node as a radio signal with consecutive amplitude modulated pulses. The receiving node comprises means configured to receive the radio signal with the amplitude modulated pulses having a time separation pTshorter than a sampling rate 7 used by the receiving node for sampling the radio signal, wherein the amplitude modulated pulses have amplitudes corresponding to data symbols which have been pre-coded by the transmitting node based on a circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, IS I, between contiguous pulses in the radio signal. This receiving operation may be performed by a receiving module in the receiving node.

The receiving node also comprises means configured to obtain samples y_n of the amplitude modulated pulses in the received radio signal. This obtaining activity may be performed by an obtaining module in the receiving node. The receiving node further comprises means configured to modify the samples y_n based on a predefined circulant matrix C comprising elements that are correlated to Inter- Symbol-lnterference, IS I , between contiguous pulses in the radio signal. This modifying operation may be performed by a modifying module in the receiving node. The receiving node further comprises means configured to decode the data symbols by finding a Maximum Likelihood Estimate of the data symbols based on the modified samples y. This decoding operation may be performed by a decoding module in the receiving node. The receiving node further comprises means configured to determine the input data based on the decoded data symbols. This determining operation may be performed by a determining module in the receiving node.

A circulant matrix is a fairly accurate approximation of the correlation between different pulses in an amplitude modulated pulse transmission but it is far less complex to use in the pre-coding and decoding operations than the conventionally used matrix G mentioned above which is typically a so-called Toeplitz matrix. Thus, by using the above transmitting and receiving nodes and methods therein, data can be communicated between the nodes with significantly reduced complexity as compared to conventional solutions. The above methods and nodes may be configured and implemented according to different optional embodiments to accomplish further features and benefits, to be described below.

Brief description of drawings

The solution will now be described in more detail by means of exemplary embodiments and with reference to the accompanying drawings, in which:

Fig. 1 is a scenario illustrating a radio communication between a network node and a wireless device, according to the prior art.

Fig. 2 is a block diagram illustrating some basic functions in a transmitting node and a receiving node for radio communication, according to the prior art. Fig. 3 is a diagram illustrating a schematic model of a radio communication process, where the solution may be used.

Fig. 4 is a diagram illustrating how the amplitude of a single transmitted pulse varies over a finite time duration.

Fig. 5 is a diagram illustrating how the amplitude of a transmitted train of consecutive pulse varies over a time period.

Fig. 6 is a flow chart illustrating a procedure in a transmitting node, according to further possible embodiments. Fig. 7 is a flow chart illustrating a procedure in a receiving node, according to further possible embodiments.

Fig. 8 is a block diagram illustrating a transmitting node and a receiving node in more detail, according to further possible embodiments. Fig. 9 is a block diagram illustrating procedures performed in a transmitting node and in a receiving node, according to further possible embodiments.

Detailed description

Briefly described, a solution is provided to reduce the complexity when pre-coding data symbols at the transmitting node and when decoding the data symbols at the receiving node when the above-described FTN technique and a matrix with elements describing the ISI are used. In conventional solutions, a matrix referred to as the Toeplitz matrix has been used in the above-mentioned GTMH process for pre-coding data symbols at the transmitting node and for decoding the data symbols at the receiving node, resulting in the above-described complexity, e.g. requiring around 1000.000 multiplications for encoding and decoding each data symbol when a block-length N of 1000 bits is used. The complexity of using such a matrix is in a magnitude of 0(N²) multiplications.

In the solution described herein, however, the Toeplitz matrix is replaced by a circulant matrix which is used instead for pre-coding the data symbols at the transmitting node and for decoding the data symbols at the receiving node. A circulant matrix is a fairly accurate approximation of the correlation between different pulses in an amplitude modulated pulse transmission but it is far less complex to use in the pre-coding and decoding operations than the Toeplitz matrix. The circulant matrix comprises elements which are arranged in rows such that the elements in each row are obtained by shifting the elements in a preceding row one step such that the last element in the preceding row is placed as the first element of the row. As a result, the complexity of using a circulant matrix in the pre-coding and decoding operations is in a magnitude of 0(N log(N)) multiplications, which means that the complexity for each pulse is reduced from 1000.000 to 1000 multiplications when a block-length N of 1000 bits is used.

First, it will be described in more detail with reference to Fig. 3 how the

transmitting process 300 and the receiving process 302 are executed at the transmitting node and the receiving node, respectively, when the FTN technique is used in general, thus transmitting input data a[n] as a radio signal with amplitude modulated pulses g"(t) separated in time shorter than the Nyquist sampling rate 7. In other words, the amplitude modulated pulses are transmitted separated by the time pTwhere 0 < p < 1. It is shown that the transmitting process 300 comprises generating the pulses g_j {t) by applying a pulse filter 300a on the input data a[n] before transmitting the signal s(t) over a radio channel 304. The transmitted signal s(t) becomes s t) = ^ a[k] ^■ p g_T(t - k pT)

k where Jp g_T(t - n pT) describes the pulse shape when using the FTN technique as normalized to avoid increase of the transmit power. The transmitted radio signal is affected by white Gaussian noise w(t) when propagating over the radio channel 304, which may be referred to as an Analog White Gaussian Noise, AWGN, channel. The transmitted radio signal s(t) is thereby more or less distorted to become the received radio signal r(t) as r(t) = s(t) + w(t)

The receiving process 302 comprises sampling the received radio signal r(t) using a matched filter 302a to optimize the Signal-to-Noise Ratio, SNR, and get a set of data points or samples y[n] that is sufficient for performing determination of the input data, where

oo

j r t)^■ Jp g_T(t - n pT) Given the samples y, the receiving node then has the task of trying to determine the input data a[n] with as low probability of error as possible. The samples y relate to the data a and the noise w as y = Ga + G^²w where G is the Toeplitz matrix with elements G_{m n} given by

oo

^Gm,n = j Jp g_T(t - n pT) ^■ Jp g_T(t - m pT) dt

— 00 It will now be described how the above-mentioned GTMH precoding scheme can be used in the transmitting process 300. The GTMH precoding is based on the above formulation to make a precoding that takes into consideration the structure of the ISI, as described by the Toeplitz matrix G, rather than just regarding it as plain noise. Instead of using the communicated data symbols a as the amplitudes for the pulses, precoded data symbols a are used for representing the pulse amplitudes as a = G^~^²a

The data symbols a are taken from some finite alphabet A. Then the original signal input/output relationship between input a, noise w, and output y can be "diagonalized" as y = G^~lii2y = a + w which means that the receiving node needs to solve the following:

G¹'²y = y .

When applying the above GTMH precoding scheme in the procedure shown in Fig. 3, a GTMH precoder in the transmitting node creates precoded data symbols a[n] from the input data a[n] and applies the pulse filter 300a to the data symbols a[n] before transmission. Correspondingly, a GTMH decoder in the receiving node creates decoded samples [n] from the samples y[n] coming from the matched filter 302a. The final determination of the input data a[n] can then be applied to the decoded samples [n] which may be done using an estimation algorithm previously applied for an ISI-free case.

In practice, all amplitude modulated pulses have a finite duration when transmitted in a radio signal, see Fig. 4 which illustrates a prototype filter for a single pulse with the amplitude variation over time l(f) in a duration from time -4 to time 4. It can be seen that the amplitude has a symmetric variation around the amplitude of 0 on either side of the actual amplitude top of 1 which occurs at time 0. When a series of such consecutive pulses are transmitted in a pulse train, as shown in Fig. 5, each pulse will be interfered by a number of adjacent pulses due to their amplitude variations illustrated in Fig. 4, which are added to the actual amplitude top of the pulse. This is how the above-mentioned ISI occurs in a pulse amplitude modulated radio signal created by super position of the pulses in a pulse train, as of Fig. 5. For instance, the pulse with its top at time 0 in Fig. 5 will not overlap with the pulses with their tops occurring at time 8, 9, 10, ... , etc. This means that there is no ISI between the pulse with its top at time 0 and the pulses with tops at time instances greater than or equal to 8.

Mathematically, this super position of pulses in a pulse train will correspond to a matrix with a banded structure, i.e. the above-mentioned Toeplitz matrix G. For instance, if each pulses is overlapped by only a single neighboring pulse, the Toeplitz matrix G is

In the case of Fig. 5 where several pulses overlap, a greater number of nonzero elements would be comprised in matrix G since 8 consecutive pulses overlap, and therefore Gi , G₂, ... , G₈ will be nonzero in the Toeplitz matrix G. In general, if the number of future pulses overlapping with a certain pulse is r-1 , then Gi , G2, . ,G_r will be nonzero, resulting in the above-mentioned high complexity. It was mentioned above that the complexity in the transmitting and receiving nodes can be greatly reduced by using a predefined circulant matrix C instead of the Toeplitz matrix G in the precoding and decoding operations, which will now be described in more detail. It was also mentioned above that the circulant matrix is a fairly accurate approximation of the correlation between different pulses in an amplitude modulated pulse transmission. The Toeplitz matrix G can therefore be replaced by the circulant matrix C without changing the signal Ga too much. It is assumed that the predefined circulant matrix C is known at the transmitting and receiving nodes given the pulse shape and FTN rate used and also by the block length N used. The circulant matrix C is thus an NxN matrix with N rows and N columns.

In the example where r = 2, the circulant matrix C would be

By using the circulant matrix C, it is an advantage that it is not a very complex operation to decouple the sampled signal y - Ca + C^1/2w into multiple parallel independent components, or "streams", at the receiving node when a Fast Fourier Transform, FFT, precoding is used. To accomplish this, a "lambda matrix" Λ is obtained based on a Singular Value Decomposition, SVD, of the circulant matrix C given by C = ΙΙΛΙ , where U = IFFT(a), U^* = FFT(a) for a vector a of the input data, wherein IFFT is an Inverse Fast Fourier Transform and the lambda matrix Λ

IS

The precoding and decoding operations will be described in more detail later An example of how the solution may be employed will now be described with reference to the flow chart in Fig. 6 which illustrates a procedure with actions performed by a transmitting node in radio communication with a receiving node, to accomplish the functionality described above. The transmitting node is operative to support determination of input data encoded as data symbols, the data symbols being transmitted to the receiving node as a radio signal with consecutive amplitude modulated pulses.

A first action 600 illustrates that the transmitting node "obtains" input data which is to be transmitted in the form of data symbols to the receiving node in the radio communication. For example, the input data may be stored or generated locally in the transmitting node or it may come from another node or equipment connected to the transmitting node. The solution is not limited to any particular type of input data or how it is obtained. The data symbols to be transmitted with an FTN signal can be represented as a vector a = ( ₀, <½__!). In a next action 602, the transmitting node pre-codes the data symbols based on a predefined circulant matrix C comprising elements that are correlated to Inter- Symbol-lnterference, IS I , between contiguous pulses in the radio signal. In a possible embodiment, pre-coding the data symbols may comprise:

- obtaining a lambda matrix Λ based on a Singular Value Decomposition, SVD, of the circulant matrix C given by C = IIAIT, where U = IFFT(a), U* = FFT(a) for a vector a of the input data a,, wherein IFFT is an Inverse Fast Fourier Transform, r Transform and the lambda matrix A is

- rescaling the input data a, with lambda A, according to the lambda matrix A to obtain rescaled input data b; = A, ^' a, for i = 0, N-1 , and

- forming the pre-coded data symbols a by performing an Inverse Fast Fourier Transform, IFFT, on the rescaled input data b, . In this embodiment, the lambda matrix is known to the transmitting and receiving nodes and it can therefore be considered as being predefined as well.

Another action 604 illustrates that the transmitting node generates the amplitude modulated pulses with amplitudes corresponding to the pre-coded data symbols. In another possible embodiment, generating the amplitude modulated pulses may comprise forming a Faster-than-Nyquist, FTN, signal s(t) as:

where 0 < p < 1 and gj denotes the amplitude modulated pulses.

The transmitting node then finally transmits the radio signal with the amplitude modulated pulses using a time separation pT shorter than a sampling rate T used by the receiving node for sampling the radio signal, in a final action 606. Thereby, the receiving node is enabled to determine the input data, as represented by the pre-coded data symbols, by decoding the data symbols based on the circulant matrix C.

It is thus an advantage of this solution that the complexity is reduced in both the transmitting node and in the receiving node. This is because the pre-coding of the data symbols is based on the predefined circulant matrix C in the transmitting node, and also the decoding of the data symbols is based on the circulant matrix C in the receiving node, which can both be done with a significant reduction of multiplications as compared to the conventional use of the Toeplitz matrix G. This is because the circulant matrix C has properties that enable the IFFT-based precoding at the transmitting node in the manner described above and also FFT- based decoding at the receiving node to be described below. This in turn allows for using a much simpler, and less costly, processor in either node. Furthermore, the pre-coding and decoding operations will also be more robust and reliable with less data errors.

An example of how the solution may be employed will now be described with reference to the flow chart in Fig. 7 which illustrates a procedure with actions performed by a receiving node in radio communication with a transmitting node, to accomplish the functionality described above. The receiving node is operative for determination of input data encoded as data symbols, the data symbols being received from the transmitting node as a radio signal with consecutive amplitude modulated pulses. A dashed arrow between Figs 6 and 7 indicates schematically that the radio signal with the amplitude modulated pulses transmitted by the transmitting node in action 606 of Fig. 6 is received by the receiving node in the procedure of Fig. 7.

A first action 700 illustrates that the receiving node receives the radio signal with the amplitude modulated pulses having a time separation pT shorter than a sampling rate 7^" used by the receiving node for sampling the radio signal. Action 700 thus corresponds to action 606 above. The received amplitude modulated pulses have amplitudes corresponding to data symbols which have been pre- coded by the transmitting node, as described for action 602 above, based on a predefined circulant matrix C comprising elements that are correlated to Inter- Symbol-lnterference, ISI, between contiguous pulses in the radio signal.

Another action 702 illustrates that the receiving node obtains samples y_n of the amplitude modulated pulses in the received radio signal. In a possible

embodiment, the receiving node may obtain the samples y_n by applying a matched filter on the amplitude modulated pulses.

In a further action 704, the receiving node modifies the obtained samples y_n based on a circulant matrix C comprising elements that are correlated to Inter- Symbol-lnterference, ISI, between contiguous pulses in the radio signal. In another possible embodiment, the receiving node may modify the obtained samples y_n by: - obtaining a lambda matrix Λ based on a Singular Value Decomposition, SVD, of the circulant matrix C given by C = ΙΙΛΙ , where U = IFFT(a), U^* = FFT(a) for a vector a of the input data a,, wherein IFFT is an Inverse Fast Fourier Transform, FFT is a Fast Fourier Transform and the lambda matrix Λ is

- performing a Fast Fourier Transform, FFT, on the samples y_n , and

- rescaling the FFT samples y with a lambda inverse A; ^~1/2 according to the lambda matrix Λ to obtain the modified samples y.

In a further possible embodiment, the receiving node may form the FFT samples y as y = FFT(y = U^*y = A^1/2a + A^1/2v = A^ a + v) and y\ = lj(ai + Vi for i = 0, N-1 , wherein v = U^*w is Gaussian white noise. In another possible embodiment, the receiving node may form the modified samples y as

Having modified the samples y_n based on the circulant matrix C in action 704, the receiving node decodes the data symbols by finding a Maximum Likelihood Estimate of the data symbols which thus represent the input data, based on the modified samples y, in an action 706. The receiving node finally determines the input data based on the decoded data symbols, in a final action 708.

The block diagram in Fig. 8 illustrates a detailed but non-limiting example of how a transmitting node 800 and a receiving node 802, respectively, may be structured to bring about the above-described solution and embodiments thereof. In this figure, the transmitting node 800 and the receiving node 802 may be configured to operate according to any of the examples and embodiments of employing the solution as described above, where appropriate, and as follows. Each of the transmitting node 800 and the receiving node 802 is shown to comprise a processor "P", a memory "M" and a communication circuit "C" with suitable equipment for transmitting and receiving radio signals in the manner described herein.

The communication circuit C in each of the transmitting node 800 and the receiving node 802 thus comprises equipment configured for communication with each other over a radio interface using a suitable protocol for radio communication depending on the implementation. The solution is however not limited to any specific types of data or protocols.

The transmitting node 800 comprises means configured or arranged to perform at least some of the actions 600-606 of the flow chart in Fig. 6 in the manner described above. Further, the receiving node 802 comprises means configured or arranged to perform the actions 700-706 of the flow chart in Fig. 7 in the manner described above. These actions may be performed by means of functional modules in the respective processor P in the transmitting node 800 and the receiving node 802 as follows.

The transmitting node 800 is arranged to support determination of input data encoded as data symbols when the data symbols are transmitted to a receiving node as a radio signal with consecutive amplitude modulated pulses . The transmitting node 800 comprises means configured to pre-code the data symbols based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal. This pre-coding activity may be performed by a precoding module 800a in the transmitting node 800, e.g. in the manner described for action 602 above.

The transmitting node 800 also comprises means configured to generate the amplitude modulated pulses with amplitudes corresponding to the pre-coded data symbols. This generating activity may be performed by a generating module 800b in the transmitting node 800, e.g. in the manner described for action 604 above. The transmitting node 800 also comprises means configured to transmit the radio signal with the amplitude modulated pulses using a time separation pT shorter than a sampling rate T used by the receiving node for sampling the radio signal, thereby enabling the receiving node to determine the input data by decoding the data symbols based on the circulant matrix C. This transmitting activity may be performed by a transmitting module 800c in the transmitting node 800, e.g. in the manner described for action 606 above. The receiving node 802 is arranged to perform determination of input data encoded as data symbols received from a transmitting node as a radio signal with consecutive amplitude modulated pulses. The receiving node 802 comprises means configured to receive the radio signal with the amplitude modulated pulses having a time separation pT shorter than a sampling rate T used by the receiving node for sampling the radio signal, wherein the amplitude modulated pulses have amplitudes corresponding to data symbols which have been pre-coded by the transmitting node based on a circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, IS I, between contiguous pulses in the radio signal. This receiving activity may be performed by a receiving module 802a in the receiving node 802, e.g. in the manner described for action 700 above.

The receiving node 802 also comprises means configured to obtain samples y_n of the amplitude modulated pulses in the received radio signal. This obtaining activity may be performed by an obtaining module 802b in the receiving node 802, e.g. in the manner described for action 702 above. The receiving node 802 further comprises means configured to modify the samples y_n based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol- lnterference, IS I, between contiguous pulses in the radio signal. This modifying activity may be performed by a modifying module 802c in the receiving node 802, e.g. in the manner described for action 704 above. The receiving node 802 further comprises means configured to decode the data symbols by finding a

Maximum Likelihood Estimate of the data symbols based on the modified samples y. This decoding activity may be performed by a decoding module 802d in the receiving node 802, e.g. in the manner described for action 706 above. The receiving node 802 further comprises means configured to determine the input data based on the decoded data symbols. This determining activity may be performed by a determining module 802e, e.g. in the manner described for action 708 above.

It should be noted that Fig. 8 illustrates various functional modules in the transmitting node 800 and the receiving node 802, respectively, and the skilled person is able to implement these functional modules in practice using suitable software and hardware. Thus, the solution is generally not limited to the shown structures of the transmitting node 800 and the receiving node 802, and the functional modules 800a-c and 802a-e therein may be configured to operate according to any of the features and embodiments described in this disclosure, where appropriate.

The functional modules 800a-c and 802a-e described above can be implemented in the transmitting node 800 and in the receiving node 802, respectively, by means of program modules of a respective computer program comprising code means which, when run by the processor P causes the transmitting node 800 and the receiving node 802 to perform the above-described actions and procedures. Each processor P may comprise a single Central Processing Unit (CPU), or could comprise two or more processing units. For example, each processor P may include a general purpose microprocessor, an instruction set processor and/or related chips sets and/or a special purpose microprocessor such as an Application Specific Integrated Circuit (ASIC). Each processor P may also comprise a storage for caching purposes.

Each computer program may be carried by a computer program product in each of the transmitting node 800 and the receiving node 802 in the form of a memory having a computer readable medium and being connected to the processor P. The computer program product or memory M in each of the transmitting node 800 and the receiving node 802 thus comprises a computer readable medium on which the computer program is stored e.g. in the form of computer program modules or the like. For example, the memory M in each node may be a flash memory, a

Random-Access Memory (RAM), a Read-Only Memory (ROM) or an Electrically Erasable Programmable ROM (EEPROM), and the program modules could in alternative embodiments be distributed on different computer program products in the form of memories within the respective transmitting node 800 and receiving node 802.

The solution described herein may be implemented in each of the transmitting node 800 and the receiving node 802 by a computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to carry out the actions according to any of the above

embodiments, where appropriate. The solution may also be implemented at each of the transmitting node 800 and the receiving node 802 in a carrier containing the above computer program, wherein the carrier is one of an electronic signal, optical signal, radio signal, or computer readable storage medium.

Finally, an example of how the solution may work in practice will now be described with reference to Fig. 9 which illustrates operations in a transmitting node 900 and in a receiving node 902 in accordance with several of the embodiments described above. The first set of operations 900a-d are executed by the transmitting node 900.

Initially, input data to be transmitted is obtained in an operation 900a, e.g. data being stored or generated locally at the transmitting node 900 and/or data received from another entity. Then the input data is rescaled with lambda according to the above-described lambda matrix in an operation 900b, thus obtaining rescaled input data. Pre-coded data symbols a are then formed by performing an Inverse Fast Fourier Transform, IFFT, on the rescaled input data, in an operation 900c. Finally, amplitude modulated pulses with amplitudes corresponding to the pre- coded data symbols are generated and transmitted as a radio signal, in an

operation 900d. The operations 900a-d may thus be executed in accordance with embodiments described above in connection with Fig. 6.

The second set of operations 902a-d are executed by the receiving node 902, which more or less reverses the operations of the transmitting node 900 as follows. The radio signal transmitted by the transmitting node 900 in operation 900d is received and sampled in an operation 902a. A Fast Fourier Transform, FFT, is then performed on the samples in an operation 902b, thus obtaining FFT samples. The FFT samples are then rescaled with lambda inverse according to the lambda matrix, thus obtaining modified samples, in an operation 902c. Finally, an estimate of the input data is determined, i.e. the data symbols are decoded, by finding a Maximum Likelihood Estimate of the input data based on the modified samples, in an operation 902d. The process of finding a Maximum Likelihood Estimate is well-known as such in the art and it is therefore not necessary to describe here in any detail.

While the solution has been described with reference to specific exemplifying embodiments, the description is generally only intended to illustrate the inventive concept and should not be taken as limiting the scope of the solution. For example, the terms "transmitting node", "receiving node", "circulant matrix" and "lambda matrix" have been used throughout this disclosure, although any other corresponding entities, functions, and/or parameters could also be used having the features and characteristics described here. The solution is defined by the appended claims.

Claims

1. A method performed by a transmitting node (800) in radio communication with a receiving node (802), for supporting determination of input data encoded as data symbols, the data symbols being transmitted to the receiving node as a radio signal with consecutive amplitude modulated pulses, the method comprising:

- pre-coding (602) the data symbols based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal,

- generating (604) the amplitude modulated pulses with amplitudes corresponding to the pre-coded data symbols, and

- transmitting (606) the radio signal with the amplitude modulated pulses using a time separation pT shorter than a sampling rate Tused by the receiving node for sampling the radio signal, thereby enabling the receiving node to determine the input data by decoding the data symbols based on the circulant matrix C.

2. A method according to claim 1 , wherein pre-coding the data symbols comprises:

- obtaining a "lambda matrix" Λ based on a Singular Value Decomposition, SVD, of the circulant matrix C given by C = UAU^* where U = IFFT(a), U^* = FFT(a) for a vector a of the input data a,, wherein IFFT is an Inverse Fast Fourier Transform, r Transform and the lambda matrix A is

- rescaling the input data a,- with lambda A; according to the lambda matrix A to obtain rescaled input data b; = A, ^' a, for i = 0, N-1 , and

- forming the pre-coded data symbols a by performing an Inverse Fast Fourier Transform, IFFT, on the rescaled input data b; .

3. A method according to claim 2, wherein generating (604) the amplitude modulated pulses comprises forming a Faster-than-Nyquist, FTN, signal s(t) as:

where 0 < p < 1 and gj denotes the amplitude modulated pul

4. A transmitting node (800) arranged to support determination of input data encoded as data symbols when the data symbols are transmitted to a receiving node as a radio signal with consecutive amplitude modulated pulses, the transmitting node (800) comprising means configured to:

- pre-code (800a) the data symbols based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal,

- generate (800b) the amplitude modulated pulses with amplitudes corresponding to the pre-coded data symbols, and

- transmit (800c) the radio signal with the amplitude modulated pulses using a time separation pT shorter than a sampling rate 7^" used by the receiving node for sampling the radio signal, thereby enabling the receiving node to determine the input data by decoding the data symbols based on the circulant matrix C.

5. A transmitting node (800) according to claim 4, wherein the transmitting node (800) is configured to pre-code the data symbols by:

- obtaining a "lambda matrix" Λ based on a Singular Value Decomposition, SVD, of the circulant matrix C given by C = IIAIT, where U = IFFT(a), U^* = FFT(a) for a vector a of the input data a,, wherein IFFT is an Inverse Fast Fourier Transform, FFT is a Fast Fourier Transform and the lambda matrix A is

- rescaling the input data a,- with lambda A,- according to the lambda matrix Λ to obtain rescaled input data b_t =

^' a,- for i = 0, N-1 , and

5 6. A transmitting node (800) according to claim 5, wherein the transmitting node (800) comprising means configured to generate the amplitude modulated pulses by forming a Faster-than-Nyquist, FTN, signal s(t) as:

where 0 < p < 1 and gr-r denotes the amplitude modulated pulses.

7. A method performed by a receiving node (802) in radio communication o with a transmitting node (802), for determination of input data encoded as data symbols, the data symbols being received from the transmitting node as a radio signal with consecutive amplitude modulated pulses, the method comprising:

- receiving (700) the radio signal with the amplitude modulated pulses having a time separation pT shorter than a sampling rate Tused by the receiving node for5 sampling the radio signal, wherein the amplitude modulated pulses have

amplitudes corresponding to data symbols which have been pre-coded by the transmitting node based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal, 0 - obtaining (702) samples y_n of the amplitude modulated pulses in the received radio signal,

- modifying (704) the samples y_n based on a circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal, - decoding (706) the data symbols by finding a Maximum Likelihood Estimate of the data symbols based on the modified samples y, and

- determining (708) the input data based on the decoded data symbols.

8. A method according to claim 7, wherein the receiving node (802) obtains the samples y_n by applying a matched filter on the amplitude modulated pulses.

9. A method according to claim 7 or 8, wherein modifying (704) the samples y_n comprises:

- obtaining a lambda matrix Λ based on a Singular Value Decomposition, SVD, of the circulant matrix C given by C = UAIT, where U = IFFT(a), U* = FFT(a) for a vector a of the input data a,, wherein IFFT is an Inverse Fast Fourier Transform, r Transform and the lambda matrix A is

- performing a Fast Fourier Transform, FFT, on the samples y_n , and

- rescaling the FFT samples y with lambda inverse

according to the lambda matrix A to obtain the modified samples y.

10. A method according to claim 9, wherein the receiving node (802) forms the FFT samples y as y = FFT(y) = U^*y = A^1/2a + A^1/2v = Λ½(α + v) and y\ = li(ai + Vi) for i = 0, N-1 , wherein v = U^*w is Gaussian white noise.

11 . A method according to claim 10, wherein the receiving node (802) forms the modified samples y as

9i = h^→l2 i = ¾ +

12. A receiving node (802) arranged to perform determination of input data encoded as data symbols received from a transmitting node as a radio signal with consecutive amplitude modulated pulses, the receiving node (802) comprising means configured to: - receive (802a) the radio signal with the amplitude modulated pulses having a time separation pT shorter than a sampling rate Tused by the receiving node for sampling the radio signal, wherein the amplitude modulated pulses have amplitudes corresponding to data symbols which have been pre-coded by the transmitting node based on a circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal,

- obtain (802b) samples y_n of the amplitude modulated pulses in the received radio signal,

- modify (802c) the samples y_n based on a predefined circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal,

- decode (802d) the data symbols by finding a Maximum Likelihood Estimate of the data symbols based on the modified samples y, and

- determine (802e) the input data based on the decoded data symbols.

13. A receiving node (802) according to claim 12, wherein the receiving node (802) is configured to obtain the samples y_n by applying a matched filter on the amplitude modulated pulses.

14. A receiving node (802) according to claim 12 or 13, wherein the receiving node (802) is configured to modify the samples y_n by: - obtaining a lambda matrix Λ based on a Singular Value Decomposition, SVD, of the circulant matrix C given by C = UAIT, where U = IFFT(a), U* = FFT(a) for a vector a of the input data a,, wherein IFFT is an Inverse Fast Fourier Transform, FFT is a Fast Fourier Transform and the lambda matrix Λ is

- performing a Fast Fourier Transform, FFT, on the samples y_n , and

- rescaling the FFT samples y with lambda inverse A, ^{~1 2} according to the lambda matrix Λ to obtain the modified samples y.

15. A receiving node (802) according to claim 14, wherein the receiving node (802) is configured to form the FFT samples y as y = FFT(y) = U^*y = A^1/2a + A^1/2v = Α (α + v) and y\ = lj(ai + Vi for i = 0, N-1 , wherein v = U^*w is Gaussian white noise.

16. A receiving node (802) according to claim 15, wherein the receiving node (802) is configured to form the modified samples y as

17. A computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to carry out the method according to any one of claims 1 -3 and 7-1 1.

18. A carrier containing the computer program of claim 17, wherein the carrier is one of an electronic signal, optical signal, radio signal, or computer readable storage medium.

19. A transmitting node (800) arranged to support determination of input data encoded as data symbols when the data symbols are transmitted to a receiving node as a radio signal with consecutive amplitude modulated pulses, the transmitting node (800) comprising: - a pre-coding module (800a) configured to pre-code the data symbols based on a predefined circulant matrix C comprising elements that are correlated to Inter- Symbol-lnterference, ISI, between contiguous pulses in the radio signal,

- a generating module (800b) configured to generate the amplitude modulated pulses with amplitudes corresponding to the pre-coded data symbols, and

- a transmitting module (800c) configured to transmit the radio signal with the amplitude modulated pulses using a time separation pT shorter than a sampling rate 7 used by the receiving node for sampling the radio signal, thereby enabling the receiving node to determine the input data by decoding the data symbols based on the circulant matrix C.

20. A receiving node (802) arranged to perform determination of input data encoded as data symbols received from a transmitting node as a radio signal with consecutive amplitude modulated pulses, the receiving node (802) comprising:

- a receiving module (802a) configured to receive the radio signal with the amplitude modulated pulses having a time separation pTshorter than a sampling rate 7 used by the receiving node for sampling the radio signal, wherein the amplitude modulated pulses have amplitudes corresponding to data symbols which have been pre-coded by the transmitting node based on a circulant matrix C comprising elements that are correlated to Inter-Symbol-lnterference, ISI, between contiguous pulses in the radio signal,

- an obtaining module (802b) configured to obtain samples y_n of the amplitude modulated pulses in the received radio signal,

- a modifying module (802c) configured to modify the samples y_n based on a predefined circulant matrix C comprising elements that are correlated to Inter- Symbol-Interference, ISI, between contiguous pulses in the radio signal,

- a decoding module (802d) configured to decode the data symbols by finding a Maximum Likelihood Estimate of the data symbols based on the modified samples y, and - a determining module (802e) configured to determine the input data based on the decoded data symbols