WO2017133768A1

WO2017133768A1 - A communication apparatus and method for receiving a multicarrier modulation signal

Info

Publication number: WO2017133768A1
Application number: PCT/EP2016/052314
Authority: WO
Inventors: Van Minh Nguyen; Stefano Tomasin
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2016-02-03
Filing date: 2016-02-03
Publication date: 2017-08-10
Also published as: CN108605022A; CN108605022B

Abstract

The invention relates to a communication apparatus (400) for receiving a multicarrier modulation signal (401) over a communication channel, the communication channel being associated with a channel impulse response vector h, the communication apparatus (400) comprising: a time domain filter (403) configured to filter the multicarrier modulation signal (401) on the basis of a plurality of filter coefficients w configured to reduce the delay spread of the multicarrier modulation signal caused by the communication channel; and a determiner (405) configured to determine the plurality of filter coefficients w on the basis of an effective channel impulse response vector b_i, wherein the determiner (405) is configured to determine the effective channel impulse response vector b_i by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b_i-1of the (i - 1)-th iteration on the basis of an adjustment vector d_i _-1, wherein each iterative adjustment of the effective channel impulse response vector b_i _-1 of the (i - 1)-th iteration on the basis of the adjustment vector d_i _-1 comprises an element-wise division or multiplication operation of the effective channel impulse response vector b_i _-1 of the (i - 1)-th iteration with the adjustment vector d_i _-1.

Description

A COMMUNICATION APPARATUS AND METHOD FOR RECEIVING A

MULTICARRIER MODULATION SIGNAL

TECHNICAL FIELD

Generally, the present invention relates to the field of telecommunications. More specifically, the present invention relates to a communication apparatus and method configured to perform time-domain equalization of a multicarrier modulation signal received over a communication channel.

BACKGROUND

Discrete multitoned receiver (DMT) is an orthogonal frequency division multiplexing (OFDM) technique used in the context of wireline communication systems. In DMT, data (e.g., QAM symbols) are organized into blocks of Q samples that are transformed at the transmitter by an inverse discrete Fourier transform (IDFT) and each transformed block is extended with a cyclic prefix (CP) before transmission on the channel. If the channel discrete impulse response, including the effects of transmit and receive filters, is shorter than the duration of the CP, then the CP part at the receiver can be discarded and by taking the discrete Fourier transform (DFT) of the remainder of the received signal a scaled version of the transmitted QAM symbols is obtained (apart from additional noise). In other words, a proper choice of the CP length allows converting a frequency selective channel into a set of Q parallel flat-fading channels. However, the CP lowers the spectral efficiency of the transmission, since it is discarded at the receiver. For long channels and relatively short DFT sizes the impact of the CP on efficiency can be significant. On the other hand, a channel impulse response with a duration exceeding the CP length creates both inter-block interference (IBI) and inter- carrier interference (ICI), which is detrimental to the demodulation performance.

In order to allow for a short CP and still avoid IBI and ICI, a channel shortening technique can be used, also known as time-domain equalization (TEQ). This technique consists in allowing for a CP that is shorter than the channel impulse response, while applying a TEQ filter on the time-domain received signal, such that the resulting channel, i.e. the cascade of the channel and the TEQ filter, is shorter than the CP length. This technique is illustrated in the context of the communication system 100 shown in figure 1 . The communication system 100 comprises the following functional blocks: an inverse FFT (IFFT) block 101 , a block 103 configured to transform the parallel data streams into a serial data stream (P/S) and to add a cyclic prefix (CP) to the serial data stream, the communication channel (characterized by its channel impulse response h) 105, the TEQ filter 107, a block 109 configured to remove the cyclic prefix (xCP) from the serial data stream and to transform the serial data stream into parallel data streams and an FFT block 1 1 1 .

This channel shortening technique increases the complexity of the receiver and requires the TEQ filter coefficients described by a vector w to be constantly adapted to the channel impulse response h. Moreover, in general - and in particular for finite impulse response TEQ filters - it is not possible to force the resulting channel to be shorter than the CP length, thus some residual IBI and ICI will always be present. Therefore, the system performance depends heavily on the quality of the TEQ filter (herein also referred to as shortening filter).

The design of the TEQ filter is a trade-off between performance gain and computational complexity. In this context, the performance gain depends on how well the shortening filter will shorten the channel so that the resulting shorted channel yields a reduced IBI and ICI. In addition, when using an iterative solution for designing the TEQ filter, it has to be made sure that the solution converges after a finite number of iterations.

An overview of different TEQ filter design techniques and algorithms is given in Martin, R. K.; Vanbleu, K.; Ding, M.; Ysebaert, G.; Milosevic, M.; Evans, B. L; Moonen, M. &

Johnson, C. R. "Unification and evaluation of equalization structures and design algorithms for discrete multitone modulation systems", IEEE Transactions on Signal Processing, 2005, 53, 3880-3894.

A lot of known TEQ filter design algorithms require the computation of eigenvectors of matrices and are, thus, computationally highly complex, i.e. with a computational complexity at least of the order of N³ where N is generally the length of the TEQ filter plus the channel length (see, for instance, Martin, R.; Vanbleu, K.; Ding, M.; Ysebaert, G.; Milosevic, M.; Evans, B.; Moonen, M. & Johnson, C. "Implementation Complexity and Communication Performance Tradeoffs in Discrete Multitone Modulation Equalizers", IEEE Transactions on Signal Processing, 2006, 54, 3216-3230). The TEQ filter design algorithm disclosed in Chow, J. S.; Cioffi, J. M. & Bingham, J. A. "Equalizer training algorithms for multicarrier modulation systems", IEEE International Conference on Communications, ICC 1993, 1 993, 2, 761 -765 (hereinafter referred to as reference [3]) reduces the complexity to the order of Aflog(N) by using an iterative solution based on a Fast Fourier Transform (FFT) instead of a matrix inversion. It is, however, well known that this TEQ filter design algorithm suffers from the so-called instable

convergence problem, which turns out to be even more critical than the computational complexity. The iterative TEQ filter design algorithm disclosed in Lopez-Valcarce, R. "Minimum delay spread TEQ design in multicarrier systems", IEEE Signal Processing Letters, 2004, 1 1 , 682-685 (hereinafter referred to as reference [4]) is known for its proven convergence and its avoidance of eigenvector computations. This iterative TEQ filter design algorithm, however, still requires one matrix inversion per iteration, which, although better than the other prior art methods mentioned above, is still disadvantageous with respect to computational complexity and memory usage.

The iterative TEQ filter design algorithm disclosed in reference [4] will be described in more detail in the following under reference to figure 2. In this context the following notation is introduced. K denotes the size of the channel impulse response h (including the transmit and receive filters) so that the channel impulse response h can be written as h = [h₀, h_x, ... , /it_f-i]^7*, wherein [... ]^T stands for the standard transpose operator. M denotes the predefined length of the TEQ filter. The TEQ filter coefficients are collected into the /W-size column vector as w = [w₀, ₁₍ ... , w_M_J^r (hereinafter the expressions "TEQ filter" and "TEQ filter coefficients" are used interchangeably). The matrix H is the Toeplitz matrix of size ( + K - 1) x M with the first column being

[/i₀, /ii, ... , /i_/f_i, 0, ... ,0]^T and the first row being [h₀, 0, ... ,0] . The matrix C is defined as the matrix product of the matrix H and its transpose H^r, i.e. C = H^rH. For a given value k, V(/c) denotes the ( + K - 1) x ( + K - 1) diagonal matrix defined by v(/c) =

[0, 1, ... , K + M— 2]^T - k with v(/c) = diag(v(/c)), where diag(x) denotes the diagonal matrix whose diagonal elements are those of the vector x. Finally, N_FFT denotes the OFDM symbol size (FFT size) and L denotes the size of the cyclic prefix (CP) in number of samples. The iterative TEQ filter design algorithm disclosed in reference [4] determines the TEQ filter coefficients, i.e. the TEQ filter, w in such a way as to minimize the channel delay spread as the cost function at each iteration i, i.e.:

Wi = argmin/ty; /!^!) ,

y wherein the cost function / is defined as:

/(y; n) ?g -L \\_q(k)\\* , wherein q = Hy, £(q) = ∑_fe||q(/c) ||² denotes the total energy of q, n is a scalar input, and denotes the center-of-mass of the effective channel b_i_₁ obtained during iteration i - 1, i.e.:

Figure 2 illustrates the iterative algorithm 200 disclosed in reference [4] to solve the optimization problem described above. After obtaining the channel impulse response h (step 201 of figure 2) the TEQ filter w is initialized as follows (step 203 of figure 2, which includes some of further initializations described above):

Wn = ¹ =, o 0

/ ^coo where c₀₀ is the first element of the matrix C. During each iteration i, the iterative algorithm 200 computes the TEQ filter w_t by solving the following equation (see step 207 of figure 2):

A^Wi = C w . This includes one matrix inversion operation of the M x M matrix A^. After normalizing the TEQ filter w_t (step 209 of figure 2), parameters are updated as follows (see steps 21 1 and 213 of figure 2): A; = A_i_₁ + 6?C - 26_iB_i__1> and

= B_i - 6_iC.

The iterative algorithm 200 continues, until a predefined number of iterations has been reached (steps 205, 215 and 217a of figure 2), and provides the TEQ filter w_t of the last iteration (step 217b of figure 2) as the final result.

A possible implementation of the iterative algorithm 200 in the form of a communication apparatus 300 is shown in figure 3. The communication apparatus 300 comprises a parameter initialization block 301 configured to receive the channel impulse response h and the size M of the TEQ filter as input and to provide the initialized TEQ filter coefficients w₀ as output to an iteration block 303 configured to perform the steps 205 to 215 of the iterative algorithm 200 shown in figure 2. To this end, the iteration block 303 of the apparatus 300 comprises a parameter update block 305 and a matrix inversion block 307, wherein the matrix inversion block 307 is configured to perform the matrix inversion required in step 207 of the iterative algorithm 200 shown in figure 2.

In the light of the above, there is a need for an improved communication apparatus and method for receiving a multicarrier modulation signal, which are computationally less complex than the prior art, while providing a performance at least similar to the prior art.

SUMMARY

It is an object of the invention to provide an improved communication apparatus and method for receiving a multicarrier modulation signal, which are computationally less complex than the prior art, while providing a performance at least similar to the prior art.

The foregoing and other objects are achieved by the subject matter of the independent claims. Further implementation forms are apparent from the dependent claims, the description and the figures.

According to a first aspect the invention relates to a communication apparatus for receiving a multicarrier modulation signal, in particular a DMT signal, over a

communication channel, the communication channel being associated with a channel impulse response vector h, the communication apparatus comprising: a time domain filter configured to filter the multicarrier modulation signal on the basis of a plurality of filter coefficients w configured to reduce the delay spread of the multicarrier modulation signal caused by the communication channel; and a determiner configured to determine the plurality of filter coefficients w on the basis of an effective channel impulse response vector bj, wherein the determiner is configured to determine the effective channel impulse response vector b_; by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b^ of the (i - l)-th iteration on the basis of an adjustment vector d^, wherein each iterative adjustment of the effective channel impulse response vector b_i_₁ of the (i - l)-th iteration on the basis of the adjustment vector comprises an element-wise division or multiplication operation of the effective channel impulse response vector b^ of the (i - l)-th iteration with the adjustment vector d^.

Thus, an improved communication apparatus is provided configured to perform time- domain equalization of a multicarrier modulation signal received over a communication channel, which is computationally less complex than prior art devices, while providing a performance at least similar thereto.

In a first possible implementation form of the communication apparatus according to the first aspect as such, the elements of the adjustment vector d^ are defined as the squared distances between a plurality of taps or discrete time indices of the effective channel impulse response vector b_i_₁ of the (i - l)-th iteration and a reference time k __x of the (i - l)-th iteration associated with the effective channel impulse response vector b^_! of the (i - l)-th iteration. In a second possible implementation form of the communication apparatus according to the first implementation form of the first aspect, the determiner is configured to determine the adjustment vector d_i_₁ of the (i - l)-th iteration on the basis of the following equation : d, i-l = v(/c_i_₁) O v(/c_i_₁), wherein Θ denotes the element-wise product, k_{_ denotes the reference time associated with the effective channel impulse response vector b^ of the (i - l)-th iteration and vC/q.i) denotes a vector defined by the following equation: v(fe_i_₁) = [0 L_b - 1] - k with L_b = M + K— 1, wherein M denotes the number of filter coefficients w and K denotes the size of the channel impulse response vector h.

In a third possible implementation form of the communication apparatus according to the second implementation form of the second aspect, the determiner is configured to modify the adjustment vector of the (i - l)-th iteration by setting d^Cn) = 1 for any n = 0, ... , L_b - 1, for which d^in) = 0.

In a fourth possible implementation form of the communication apparatus according to any one of the first to third implementation form of the first aspect, the determiner is configured to determine the reference time associated with the effective channel impulse response vector b^ of the (i - l)-th iteration as the center-of-mass of the plurality of taps of the effective channel impulse response vector of the (£ - l)-th iteration. In a fifth possible implementation form of the communication apparatus according to any one of the first to third implementation form of the first aspect, the determiner is configured to determine the reference time k^ associated with the effective channel impulse response vector of the (i - l)-th iteration by selecting a tap from a window S covering a plurality of taps of the effective channel impulse response vector b^ of the (i - l)-th iteration, wherein the window S has the size L of a cyclic prefix of the multicarrier modulation signal and for which the sum of the powers of the taps covered by the window 5 is a maximum.

In a sixth possible implementation form of the communication apparatus according to the fifth implementation form of the fifth aspect, the determiner is configured to determine the reference time k_i_₁ associated with the effective channel impulse response vector b^ of the (i - l)-th iteration by selecting the tap from the window S that has the largest power of the taps covered by the window S. In a seventh possible implementation form of the communication apparatus according to the first aspect as such or any one of the first to sixth implementation form thereof, the determiner is configured to determine the effective channel impulse response vector b_; by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b^ of the (i - l)-th iteration on the basis of the adjustment vector on the basis of the following equation: hi = b_i_₁ 0 d^, wherein 0 denotes the element-wise division of the effective channel impulse response vector of the (i - l)-th iteration by the adjustment vector d_i_₁ and wherein the effective channel impulse response vector of the first iteration b₀ is equal to the channel impulse response vector h.

In an eighth possible implementation form of the communication apparatus according to the first aspect as such or any one of the first to sixth implementation form thereof, the adjustment vector is chosen to be invariant over iterations, i.e. = d₀ for all iterations i, and the determiner is configured to determine the effective channel impulse response vector b_; by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b^ of the (i - l)-th iteration on the basis of the adjustment vector d^ on the basis of the following equation: hi = bi__! 0 d₀, wherein 0 denotes the element-wise division of the effective channel impulse response vector b_;._! of the (i - l)-th iteration by the adjustment vector d₀ and wherein the effective channel impulse response vector of length L_b of the first iteration b₀ is initialized to the channel impulse response vector h, i.e. b₀ = [h₀, h_x, ... , h_K__x, 0, ... ,0]^T wherein T stands for transpose operator.

In a ninth possible implementation form of the communication apparatus according to the first aspect as such or any one of the first to sixth implementation form thereof, the determiner is configured to determine the effective channel impulse response vector b_; by starting from the channel impulse response vector h and using a single iteration of adjusting the effective channel impulse response vector b₀ of the first iteration on the basis of the adjustment vector d₀ on the basis of the following equation: b_; = b₀ ø d°\ wherein 0 denotes the element-wise division of the effective channel impulse response vector b₀ of the first iteration by the adjustment vector d®¹ that is the adjustment vector d₀ to the element-wise power i and wherein the effective channel impulse response vector of the first iteration b₀ is equal to the channel impulse response vector h. In a tenth possible implementation form of the communication apparatus according to the first aspect as such or any one of the first to ninth implementation form thereof, the determiner is configured to determine the plurality of filter coefficients w on the basis of the effective channel impulse response vector b_; of the i-th iteration on the basis of the following equation: w = C^H^b;, wherein C ¹ denotes the inverse of a matrix C, which is defined as C = H^rH, H^7* denotes the transpose of the matrix H, wherein H denotes the Toeplitz matrix of size ( + K - 1) x M with the first column being [h₀, h_x, ... , h_K__t, 0, ... ,0]^T and the first row being

[h₀, 0, ... ,0] , wherein M denotes the number of the plurality of filter coefficients w, and K denotes the size of the channel impulse response vector h = [/ι₀, /ι₁₍ - ,

In an eleventh possible implementation form of the communication apparatus according to the first aspect as such or any one of the first to tenth implementation form thereof, the determiner is configured to determine the effective channel impulse response vector b_; by iteratively adjusting the channel impulse response vector h on the basis of the adjustment vector di^, as long as a variation measure between the effective channel impulse response b_; of the i-th iteration and the effective channel impulse response b_i_₁ of the (i - l)-th iteration is larger than or equal to a variation measure threshold.

In a twelfth possible implementation form of the communication apparatus according to the first aspect as such or any one of the first to eleventh implementation form thereof, the communication apparatus is configured to deactivate the time domain filter, in case the SNR of the multicarrier modulation signal is smaller than a predefined SNR threshold or in case the transmission distance is shorter than a transmission distance threshold.

According to a second aspect the invention relates to a method for receiving a multicarrier modulation signal, in particular a DMT signal, over a communication channel, the communication channel being associated with a channel impulse response vector h, the method comprising: determining a plurality of filter coefficients w on the basis of an effective channel impulse response vector b_{i ;} wherein the effective channel impulse response vector b_; is determined by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b^ of the (i - 1)- th iteration on the basis of an adjustment vector d^, wherein each iterative adjustment of the effective channel impulse response vector of the (i - l)-th iteration on the basis of the adjustment vector comprises an element-wise division or multiplication operation of the effective channel impulse response vector of the (i - l)-th iteration with the adjustment vector d^; and filtering the multicarrier modulation signal on the basis of the plurality of filter coefficients w configured to reduce the delay spread of the multicarrier modulation signal caused by the communication channel.

The method according to the second aspect of the invention can be performed by the communication apparatus according to the first aspect of the invention. Further features of the method according to the second aspect of the invention result directly from the functionality of the communication apparatus according to the first aspect of the invention and its different implementation forms described above.

According to a third aspect, the invention relates to a computer program comprising program code for performing the method according to the second aspect of the invention or any of its implementation forms when executed on a computer.

The invention can be implemented in hardware and/or software. BRIEF DESCRIPTION OF THE DRAWINGS

Further embodiments of the invention will be described with respect to the following figures, wherein: Fig. 1 shows a schematic diagram of a multicarrier communication system;

Fig. 2 shows a schematic diagram of a method for determining a TEQ filter;

Fig. 3 shows a schematic diagram of a communication apparatus implementing the method shown in figure 2;

Fig. 4 shows a schematic diagram illustrating a communication apparatus for receiving a multicarrier modulation signal according to an embodiment; Fig. 5 shows a schematic diagram illustrating a communication method for receiving a multicarrier modulation signal according to an embodiment; Fig. 6 shows a schematic diagram illustrating a component of a communication apparatus for receiving a multicarrier modulation signal according to an embodiment;

Fig. 7 shows a schematic diagram illustrating a stage of a communication method for receiving a multicarrier modulation signal according to an embodiment;

Fig. 8 shows a schematic diagram illustrating a method of determining a reference time as a stage of a communication method for receiving a multicarrier modulation signal according to an embodiment;

Fig. 9 shows a schematic diagram illustrating a method of determining a reference time as a stage of a communication method for receiving a multicarrier modulation signal according to an embodiment; Fig. 10 shows a schematic diagram illustrating a component of a communication apparatus for receiving a multicarrier modulation signal according to an embodiment;

Fig. 1 1 shows a schematic diagram illustrating a component of a communication apparatus for receiving a multicarrier modulation signal according to an embodiment;

Fig. 12 shows a schematic diagram of a multicarrier communication system for evaluating the performance of a communication apparatus and method according to an embodiment;

Fig. 13 shows a schematic diagram illustrating the convergence performance provided by a communication apparatus and method according to an embodiment in comparison with the prior art;

Fig. 14 shows a schematic diagram illustrating the spectral efficiency provided by a communication apparatus and method according to an embodiment in comparison with the prior art; and

Fig. 15 shows a schematic diagram illustrating the computational complexity performance provided by a communication apparatus and method according to an embodiment in comparison with the prior art. In the various figures, identical reference signs are used for identical or at least functionally equivalent features.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In the following description, reference is made to the accompanying drawings, which form part of the disclosure, and in which are shown, by way of illustration, specific aspects in which the present invention may be placed. It is understood that other aspects may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The following detailed description, therefore, is not to be taken in a limiting sense, as the scope of the present invention is defined be the appended claims.

For instance, it is understood that a disclosure in connection with a described method may also hold true for a corresponding device or system configured to perform the method and vice versa. For example, if a specific method step is described, a corresponding device may include a unit to perform the described method step, even if such unit is not explicitly described or illustrated in the figures. Further, it is understood that the features of the various exemplary aspects described herein may be combined with each other, unless specifically noted otherwise.

Figure 4 shows a schematic diagram of a communication apparatus 400 for receiving a multicarrier modulation signal, in particular a DMT signal, 401 over a communication channel. The properties of the communication channel being can be described by a channel impulse response vector h.

The communication apparatus 400 comprises a time domain or TEQ filter 403 configured to filter the multicarrier modulation signal 401 on the basis of a plurality of filter coefficients w configured to reduce the delay spread of the multicarrier modulation signal caused by the communication channel.

Furthermore, the communication apparatus 400 shown in figure 4 comprises a determiner 405 configured to determine the plurality of filter coefficients w on the basis of an effective channel impulse response vector . To this end, the determiner 405 is configured to determine the effective channel impulse response vector b_; by starting from the channel impulse response vector h, i.e. b₀ = [h₀, h_x, ... , h_K__t, 0, ... ,0]^T, and iteratively adjusting the effective channel impulse response vector of the (i - l)-th iteration on the basis of an adjustment vector d^, wherein each iterative adjustment of the effective channel impulse response vector b_i_₁ of the (i - l)-th iteration on the basis of the adjustment vector comprises an element-wise division or multiplication operation of the effective channel impulse response vector of the (i - l)-th iteration with the adjustment vector d^.

In an embodiment, the elements of the adjustment vector are defined as the squared distances between a plurality of taps of the effective channel impulse response vector b_;._! of the (i - l)-th iteration and a reference time of the (i - l)-th iteration associated with the effective channel impulse response vector of the (£ - l)-th iteration.

Figure 5 shows a schematic diagram of a method 500 for receiving a multicarrier modulation signal, in particular a DMT signal, 401 over a communication channel, wherein the communication channel is associated with a channel impulse response vector h.

The method 500 comprises a first step 501 of determining a plurality of filter coefficients w on the basis of an effective channel impulse response vector b_{i ;} wherein the effective channel impulse response vector b_; is determined by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b^_! of the (i - l)-th iteration on the basis of an adjustment vector d^, wherein each iterative adjustment of the effective channel impulse response vector b^ of the (i - l)-th iteration on the basis of the adjustment vector d^ comprises an element-wise division or multiplication operation of the effective channel impulse response vector b^ of the (i - l)-th iteration with the adjustment vector d^.

Furthermore, the method 500 comprises a second step 503 of filtering the multicarrier modulation signal on the basis of the plurality of filter coefficients w configured to reduce the delay spread of the multicarrier modulation signal 401 caused by the communication channel.

Further implementation forms, embodiments and aspects of the apparatus 400 and the method 500 will be described in the following, under reference to the notation introduced in the context of figures 1 to 3. As will be described in more detail further below, embodiments of the invention make advantageous use of the following formulation of the matrix A_t, which already has been introduced in the context of figures 1 to 3:

Aj = H^rDjH, (1 ) where D_; is a diagonal matrix that will be described in more detail further below. By setting b; = Hwj, the above formulation of A_t allows to obtain the following relations: A^w; = C Wi_! => Η^. = H^. (2) or equivalently:

H^r(D_i_₁b_i - b_i_₁) = 0. (3)

Thus, the vector D^ty - belongs to the null space of the matrix H^7* and a solution of equation (3) is given by the following equation:

D^bi - bi^ O. (4)

Equation (4) allows to easily compute b_; by a simple element-wise division since is diagonal. As a result, the eigenvector computation and matrix inversion required by conventional solutions can be eliminated by making use of equation (4). In the following, it will be briefly shown that the matrix A_t can be expressed in the form defined in equation (1 ). The set of update equations used by the iterative algorithm 200 shown in figure 2 is identical to the following equation:

where rij denotes the center-of-mass of the taps of the effective communication channel b₍. It can be seen that V²(/q) is diagonal for any reference time k_t. Thus, by setting:

one obtains A_t as defined in equation (1 ). In an embodiment shown in figures 6 and 7, the determiner 405 of the communication apparatus 400 and the method 500 implement an iterative algorithm comprising essentially the following steps, wherein i denotes the iteration number: 1 . Initialize parameters (steps 701 and 703 of figure 7).

2. Compute b_; from using the proposed formulation D^ = b^ (step 709 of figure 7).

3. Compute the reference time k_t from the obtained channel b_; (step 707 of figure 7).

4. Update parameters (step 707 of figure 7).

5. Evaluate stopping conditions and stop iterative algorithm if the conditions are

satisfied (steps 705, 71 1 , 713 and 715 of figure 7).

As described above, in the iterative algorithm 200 the reference time is computed as the center-of-mass of the channel. In an embodiment, the reference time is computed in a different advantageous way, which will be described in the following under reference to figures 8 and 9. The effective channel to be computed for the reference time can be expressed as b_; = (b₍(0), ... , _i L_b - 1)) with L_b being its length. The window of the size of the CP, L, that has the maximum energy is computed as: S = (n^*, n^* + Ι, .,. , η^* + L - 1), (7) with n^* = argmax E^Ub^ +;)ll²- (8)

n=0,...,L¾-L From the selected window 5, the reference time k_t of b_; can be computed as the tap of S that has the maximum power, i.e.:

/c^ argmaxllbiO II². (9)

jes For a channel that is much longer than the cyclic prefix, which, in turn, is the object of channel shortening, the center-of-mass can fall outside of the most significant part of the channel, since it is weighted by the tap delay. By contrast, the proposed method ensures that during each iteration the resulting shortened channel always contains the strongest energy part of the channel, thus enhances the signal-to-noise ratio in a better way than the state-of-the-art solutions can do. In an initialization phase, the effective communication channel of length L_b = M + K— 1 for the first iteration is set to the actual communication channel, i.e. b₀ =

[/ι₀,/ΐ_ι, ... , Ηκ^, Ο, ... ,0]^T for instance, by the parameter initialization block 601 shown in figure 6 or in step 703 of figure 7.

For each iteration i≥ 1 performed by the iteration block 602 of the embodiment of the determiner 405 shown in figure 6, the reference time of the previous using preferably the solution described in the context of figures 8 and 9 is computed, for instance, by the reference time computation block 603 shown in figure 6. On the basis of this reference time k_i_₁ a vector v is computed as follows, for instance, by the block 605 shown in figure 6 or in step 707 of figure 7: v(fe_i_₁) = [0 L_b - 1] - /q.i, (10) with L_b = M + K - 1. This vector vC/c^) allows computing the adjustment vector d_i_₁ on the basis of the following equation: di-^ vft-O O vifei. , (1 1 ) wherein O denotes the element-wise product, i.e. the element-by-element multiplication. In an embodiment the adjustment vector can be further modified by setting

= 1 for any n = 0, ... , L_b - 1, for which

= 0. On the basis of this adjustment vector di__t the new effective channel (coefficients) b_; can be computed in step 709 of figure 7 as follows: b_; = b^_! 0 d_t_ 1; (12) wherein 0 denotes the element-wise division, i.e. an element-by-element division. This computational step can be implemented by means of an element-wise multiplication block 609 as shown in figure 6 (or alternatively an element-vise division block). In an embodiment, the effective channel vector b_; is then normalized to unit power (see step 709 of figure 7), i.e.:

(13)

£(b;)^' The iterative process performed by the iteration block 602 of the embodiment of the determiner 405 shown in figure 6 can be terminated, when the variation of the coefficients obtained during two subsequent iterations, is smaller than a predefined threshold e, i.e., when:

.^llbi-iir II*

This termination policy can be controlled by the iteration block 602, which can decide either to feedback the resulting vector b_; to the next iteration loop or to terminate the iteration process (see also steps 71 1 and 713 of figure 7).

Finally, the filter coefficients w are obtained on the basis of the following equation (see step 715 of figure 7): w = C^"1H^rb_i. (15)

This computation can be realized by two blocks of matrix multiplication 61 1 and 615 in cascade as shown in figure 6. It is worth mentioning that the preferred embodiment for determining the reference time described above has a beneficial impact on the frame synchronization of the system. Thus, embodiments of the invention employing the preferred method of determining the reference time provide an improvement in this respect as well. In addition to performance improvement, another advantage of the synchronization solution provided by embodiments of the invention is that it makes use of the available information provided by the TEQ training algorithm in figure 8, thereby minimizing the computational complexity.

Comparing the determiner 405 of the communication apparatus 400 shown in figure 6 with the conventional communication apparatus 300 shown in figure 3, one will appreciate that the determiner 405 shown in figure 6 uses an element-wise multiplication (or division) component during iterations, whereas the conventional communication apparatus 300, which implements the iterative algorithm disclosed in reference [4], requires at least one matrix inversion component and two matrix multiplication operations.

In an embodiment, the reference time is chosen as invariant over iterations, i.e., k_{i+ 1} = k_t . Hence d_; = d₀ for all iterations i. As a result, b_; = 0 d₀ . A determiner 405 of a communication apparatus 400 according to such an embodiment is shown in figure 10, where the parameter update block 605 of the communication apparatus shown in figure 6 is no longer necessary. As the blocks 1001 , 1009, 101 1 , 1013 and 1015 of the determiner 405 shown in figure 10 essentially correspond to the blocks 601 , 609, 61 1 , 613 and 615 of the determiner 405 shown in figure 6, reference is made to the above description of figure 6.

In an embodiment of the communication, apparatus 400 with the determiner 405 shown in figure 1 1 , the proposed solution is realized in a forward computational way without the need for an iterative loop. In this embodiment an additional input parameter Λ specifies the requirement targeted for the TEQ filter design. For example, Λ can be either the maximum number of expected iterations or the target signal-to-interference ratio of the final effective channel b_t. On the basis of the input parameter Λ the variable n can be computed as the number of equivalent iterations once by the parameter initialization block 1 101 of the determiner 405 shown in figure 1 1 . Subsequently, the vector 1 0 d₀ is raised in block 1 108 to the element-wise power n, i.e. an n-time element-wise product. As the blocks 1 101 , 1 109, 1 1 1 1 , 1 1 13 and 1 1 15 of the determiner 405 shown in figure 1 1 essentially correspond to the blocks 601 , 609, 61 1 , 613 and 615 of the determiner 405 shown in figure 6, reference is made to the above description of figure 6.

In an embodiment, the communication apparatus 400 is configured to deactivate the time domain filter 403, in case the SNR of the multicarrier modulation signal 401 is smaller than a predefined SNR threshold or in case the loop length, i.e. transmission distance, is shorter than a predefined transmission distance threshold.

Embodiments of the invention provide amongst others for the following advantages vis-avis the prior art. The algorithm implemented by embodiments of the invention is guaranteed to converge. The spectral efficiency is significantly improved. The

computational complexity is reduced. In the following these advantages provided by embodiments of the invention will be described in more detail.

The performance of embodiments of the invention is evaluated using a typical ADSL channel, which has been simulated using a conventional channel simulator. The performance of a TEQ filter is evaluated in terms of the resulting spectral efficiency. The simulation model used to evaluate the spectral efficiency is illustrated in figure 12. In the communication, system 100 shown in figure 12 the block 108 ("Time Sync") performs a time synchronization based on the maximum energy window detection described above. More specifically, it searches over the effective channel b the window S of size L that has the maximum energy as given in equation (7). Then the receiver time is set to n^* as defined in equation (8). The noise and interference power on a subcarrier m is estimated on the basis of the following equation: m ⁼ E{ II ^Ym - ^Xm^Bm l|²}> (16) wherein B = FFT(b). In this example the data X has been set to unit transmit power. The SINR estimate is thus given by:

SINR_m = ^. (17) The average spectral efficiency in b/s/Hz is then given by:

P = _j^l!^-^il + SINRm). (18)

Moreover, the computational complexity of a TEQ filter design algorithm is evaluated in terms of the number of equivalent real multiplication-and-accumulates ("MACs"). In the algorithm disclosed in prior art reference [3] typically about 460 iterations are required to design the TEQ filter. Moreover, in many cases it seems difficult to establish convergence as the TEQ filter coefficients exhibit significant variations even after a large number of iterations. Typical lengths of the TEQ filter are 1 12 taps for the algorithms disclosed in references [3] and [4], and 600 taps for the algorithm implemented in embodiments of the invention.

The convergence of algorithm implemented in embodiments of the invention can be easily proven mathematically. Figure 13 shows the convergence over iterations as obtained from a simulation of its cost function (i.e. the channel delay spread as defined in the context of the iterative algorithm 200) and the signal-to-interference ratio (SIR). The signal-to- interference ratio is the ratio between the channel energy captured within the CP part and the energy outside of the CP that creates inter-block and inter-carrier interference.

Obviously, a greater SIR corresponds to a better channel. As can be taken from the left plot of figure 13, embodiments of the invention allow shortening the channel delay spread and, consequently, the channel in a better way than the iterative algorithm 200. More importantly, the right plot of figure 13 shows that the algorithm as implemented in embodiments of the invention enhances the channel SIR much better than the conventional iterative algorithm 200.

Figure 14 shows two plots for evaluating the spectral efficiency of the algorithm

implemented in embodiments of the invention as a function of the SNR. The left plot of figure 14 shows the spectral efficiency, and the right plot shows the performance gain when no channel shortening is used.

In the high SNR regime, the algorithm implemented in embodiments of the invention greatly improves the performance, as the performance gain attains 80% compared to 40% of the conventional iterative algorithm 200 disclosed in reference [4]. It seems that this improvement is due to the fact that the algorithm implemented in embodiments of the invention substantially "squeezes" the channel and, thus, efficiently suppresses the interblock interference in the high SNR regime. In the low SNR regime, where noise is more important than inter-block interference, the "squeezing" of the channel leads to a noise enhancement and, hence, to a performance degradation.

Figure 15 shows three plots for evaluating the computational complexity of the algorithm implemented in embodiments of the invention in terms of the numbers of equivalent real multiplication-and-accumulates (MAC) as a function of the number of iterations. The plot on the left side of figure 15 shows the number of MACs as a function of the number of iterations for the conventional algorithm disclosed in reference [3], the plot in the middle of figure 15 shows the same for the conventional iterative algorithm 200 disclosed in reference [4] and the plot on the right side of figure 15 shows the same for the algorithm implemented in embodiments of the present invention. As can be taken from figure 15, typical convergence numbers are 460 iterations for the conventional algorithm disclosed in reference [3] in comparison to 20 iterations for the conventional iterative algorithm 200 disclosed in reference [4] and the algorithm implemented in embodiments of the present invention. It is noted that typical lengths of the TEQ filter are 1 12 taps for the conventional algorithm disclosed in reference [3] and the conventional iterative algorithm 200 disclosed in reference [4] in comparison to 600 taps for the algorithm implemented in embodiments of the present invention. In summary, embodiments of the invention provide a reduction of the complexity to a factor of about 2/3 with respect to the conventional algorithm disclosed in reference [3], which is the best of the state-of-the-art in term of low complexity, and to a factor of about 1/15 with respect to the conventional iterative algorithm disclosed in reference [4]. This significant reduction of complexity is due to the fact that during each iteration the conventional algorithm disclosed in reference [3] requires four FFT computations, each of which, in turn, requires N_FFT log(N_FFT) computations. The conventional iterative algorithm disclosed in reference [4] needs to inverse the matrix Aj__{1 ;} which requires ^ ³ computations. By contrast, the algorithm implemented in the embodiments of the present invention only uses element-wise operations during each iteration and one matrix inversion for the final step. Moreover, the matrix that has to be inverted C = H^rH in the algorithm implemented in the embodiments of the invention is a M x M Toeplitz matrix since H itself is a Toeplitz matrix. Therefore, inverting the matrix C only requires 3 ² MACs instead of - ³.

3

While a particular feature or aspect of the disclosure may have been disclosed with respect to only one of several implementations or embodiments, such feature or aspect may be combined with one or more other features or aspects of the other implementations or embodiments as may be desired and advantageous for any given or particular application. Furthermore, to the extent that the terms "include", "have", "with", or other variants thereof are used in either the detailed description or the claims, such terms are intended to be inclusive in a manner similar to the term "comprise". Also, the terms "exemplary", "for example" and "e.g." are merely meant as an example, rather than the best or optimal. The terms "coupled" and "connected", along with derivatives may have been used. It should be understood that these terms may have been used to indicate that two elements cooperate or interact with each other regardless whether they are in direct physical or electrical contact, or they are not in direct contact with each other.

Although specific aspects have been illustrated and described herein, it will be

appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations may be substituted for the specific aspects shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific aspects discussed herein. Although the elements in the following claims are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence.

Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teachings. Of course, those skilled in the art readily recognize that there are numerous applications of the invention beyond those described herein. While the present invention has been described with reference to one or more particular embodiments, those skilled in the art recognize that many changes may be made thereto without departing from the scope of the present invention. It is therefore to be understood that within the scope of the appended claims and their equivalents, the invention may be practiced otherwise than as specifically described herein.

Claims

1 . A communication apparatus (400) for receiving a multicarrier modulation signal (401 ) over a communication channel, the communication channel being associated with a channel impulse response vector h, the communication apparatus (400) comprising: a time domain filter (403) configured to filter the multicarrier modulation signal (401 ) on the basis of a plurality of filter coefficients w configured to reduce the delay spread of the multicarrier modulation signal caused by the communication channel; and a determiner (405) configured to determine the plurality of filter coefficients w on the basis of an effective channel impulse response vector b_{i ;} wherein the determiner (405) is configured to determine the effective channel impulse response vector b_; by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector of the (i - l)-th iteration on the basis of an adjustment vector d^, wherein each iterative adjustment of the effective channel impulse response vector of the (i - l)-th iteration on the basis of the adjustment vector comprises an element-wise division or multiplication operation of the effective channel impulse response vector b_i_₁ of the (i - l)-th iteration with the adjustment vector d^.

2. The communication apparatus (400) of claim 1 , wherein the elements of the adjustment vector d^ are defined as the squared distances between a plurality of taps of the effective channel impulse response vector b^ of the (i - l)-th iteration and a reference time of the (£ - l)-th iteration associated with the effective channel impulse response vector of the (i - l)-th iteration.

3. The communication apparatus (400) of claim 2, wherein the determiner (405) is configured to determine the adjustment vector d^ of the (i - l)-th iteration on the basis of the following equation: di__! = v(/c_i_₁) O v(/c_i_₁), wherein Θ denotes the element-wise product, denotes the reference time associated with the effective channel impulse response vector b^ of the (i - l)-th iteration and vC/q.i) denotes a vector defined by the following equation:

with L_b = M + K - 1, wherein M denotes the number of filter coefficients w and K denotes the size of the channel impulse response vector h.

4. The communication apparatus (400) of claim 3, wherein the determiner (405) is configured to modify the adjustment vector d_i_₁ of the (i - l)-th iteration by setting

= 1 for any n = 0, ... , L_b - 1, for which = 0.

5. The communication apparatus (400) of any one of claims 2 to 4, wherein the determiner (405) is configured to determine the reference time k_i_₁ associated with the effective channel impulse response vector of the (i - l)-th iteration as the center-of- mass of the plurality of taps of the effective channel impulse response vector of the (i - l)-th iteration.

6. The communication apparatus (400) of any one of claims 2 to 4, wherein the determiner (405) is configured to determine the reference time associated with the effective channel impulse response vector b^ of the (i - l)-th iteration by selecting a tap from a window S covering a plurality of taps of the effective channel impulse response vector b^ of the (i - l)-th iteration, wherein the window S has the size L of a cyclic prefix of the multicarrier modulation signal (401 ) and for which the sum of the powers of the taps covered by the window 5 is a maximum.

7. The communication apparatus (400) of claim 6, wherein the determiner (405) is configured to determine the reference time k_i_₁ associated with the effective channel impulse response vector b^ of the (i - l)-th iteration by selecting the tap from the window S that has the largest power of the taps covered by the window S.

8. The communication apparatus (400) of any one of the preceding claims, wherein the determiner (405) is configured to determine the effective channel impulse response vector b; by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b^ of the (i - l)-th iteration on the basis of the adjustment vector on the basis of the following equation: hi = b^_! 0 d^i, wherein 0 denotes the element-wise division of the effective channel impulse response vector b_;._! of the (i - l)-th iteration by the adjustment vector d^ and wherein the effective channel impulse response vector of length L_b of the first iteration b₀ is initialized to the channel impulse response vector h, i.e. b₀ = [h^T, 0, ... ,0]^T.

9. The communication apparatus (400) of any one of claims 1 to 7, wherein the adjustment vector is chosen to be invariant over iterations and wherein the determiner (405) is configured to determine the effective channel impulse response vector b; by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b_i_₁ of the (i - l)-th iteration on the basis of the adjustment vector = d₀ on the basis of the following equation : hi = b_i_₁ 0 d_o , wherein 0 denotes the element-wise division of the effective channel impulse response vector b_;._! of the (i - l)-th iteration by the adjustment vector d₀ and wherein the effective channel impulse response vector of the first iteration b₀ is equal to the channel impulse response vector h.

1 0. The communication apparatus (400) of any one of claims 1 to 7, wherein the determiner (405) is configured to determine the effective channel impulse response vector b; by starting from the channel impulse response vector h and using a single iteration of adjusting the effective channel impulse response vector b₀ of the first iteration on the basis of the adjustment vector d₀ on the basis of the following equation: b_; = b₀ 0 d°\ wherein 0 denotes the element-wise division of the effective channel impulse response vector b₀ of the first iteration by the adjustment vector d®¹ that is the adjustment vector d₀ to the element-wise power i and wherein the effective channel impulse response vector of the first iteration b₀ is equal to the channel impulse response vector h.

1 1 . The communication apparatus (400) of any one of the preceding claims, wherein the determiner (405) is configured to determine the plurality of filter coefficients w on the basis of the effective channel impulse response vector b_; of the i-th iteration on the basis of the following equation : w = C^H^bi, wherein C ¹ denotes the inverse of a matrix C, which is defined as C = H^rH, H^7* denotes the transpose of the matrix H, wherein H denotes the Toeplitz matrix of size ( + K - 1) x M with the first column being [h₀, h_x, ... , h_K__lt 0, ... ,0]^T and the first row being

12. The communication apparatus (400) of any one of the preceding claims, wherein the determiner (405) is configured to determine the effective channel impulse response vector b; by iteratively adjusting the channel impulse response vector h on the basis of the adjustment vector d^, as long as a variation measure between the effective channel impulse response b_; of the i-th iteration and the effective channel impulse response b^ of the (i - l)-th iteration is larger than or equal to a variation measure threshold.

13. The communication apparatus (400) of any one of the preceding claims, wherein the communication apparatus (400) is configured to deactivate the time domain filter (403), in case the SNR of the multicarrier modulation signal (401 ) is smaller than a predefined SNR threshold or in case the transmission distance is shorter than a transmission distance threshold.

14. A method (500) for receiving a multicarrier modulation signal (401 ) over a communication channel, the communication channel being associated with a channel impulse response vector h, the method (500) comprising: determining a plurality of filter coefficients w on the basis of an effective channel impulse response vector b_{i ;} wherein the effective channel impulse response vector b_; is determined by starting from the channel impulse response vector h and iteratively adjusting the effective channel impulse response vector b^ of the (i - l)-th iteration on the basis of an adjustment vector d^, wherein each iterative adjustment of the effective channel impulse response vector of the (i - l)-th iteration on the basis of the adjustment vector comprises an element-wise division or multiplication operation of the effective channel impulse response vector of the (i - l)-th iteration with the adjustment vector d^; and filtering the multicarrier modulation signal (401 ) on the basis of the plurality of filter coefficients w configured to reduce the delay spread of the multicarrier modulation signal (401 ) caused by the communication channel.

15. A computer program comprising program code for performing the method of claim 14 when executed on a computer.