WO2004034663A1

WO2004034663A1 - Channel estimation for ofdm systems

Info

Publication number: WO2004034663A1
Application number: PCT/IB2002/004609
Authority: WO
Inventors: Stefan Mueller-Weinfurtner; Peter Schramm; Jörn Thielecke; Udo Wachsmann
Original assignee: Telefonaktiebolaget Lm Ericsson
Priority date: 2002-10-08
Filing date: 2002-10-08
Publication date: 2004-04-22
Also published as: AU2002347422A1

Abstract

The present invention concerns a method for channel estimation for OFDM-based communications. According to the invention, a coarse channel estimate is first obtained from the received signal, after which a single filter is being applied to all available coarse channel estimates. The present invention also concerns a method for channel estimation for OFDM-based communications, which includes obtaining a coarse estimate of the channel transfer factor by removing known pilot subchannel amplitudes from a Fourier- transformed pilot sequence; according to the invention, said pilot sequence is obtained by averaging over at least two repeatedly received preamble OFDM symbols. Application to devices and apparatus implementing these methods.

Description

CHANNEL ESTIMATION FOR OFDM SYSTEMS

The present invention concerns a method and a device for channel estimation in communications systems using Orthogonal Frequency-Division Multiplexing (OFDM).

In wireless digital communications, one usually deals with multipath channels: due to reflections on obstacles, the transmitted signal reaches the receiver after having followed a plurality of paths. Hence the received signal results from the superposition of a plurality of replica of the transmitted signal, each one associated (in the equivalent complex baseband representation) with a specific delay and attenuation. This received signal is therefore equal to the convolution of the transmitted signal with a so-called Channel Impulse Response (CIR) h(f) (where denotes time). Equivalent^, implementing a Fourier transform, this time-dispersive characteristic of a channel may be represented in the "frequency domain" by means of a "channel transfer function" /-/( ); at any given frequency, the value of this function is called the "Channel Transfer Factor" (CTF). The CIR is non-zero only in an interval 0 < t < τ, where τ is the so-called excess delay of the channel, viz., the maximum possible delay between the various paths. The data symbols to be transmitted are modulated, and the receiver demodulates the corresponding received signal in order to recover those symbols. Clearly, knowledge of the CIR allows one to conduct this demodulation more accurately.

Furthermore, in many modern digital communications systems, for example telephone systems or mobile radio systems, the demodulation process is "coherent". This requires that the system provides a means for "channel estimation", viz., for computing an estimate of some channel characteristics of interest (such as the channel impulse response) using a reference portion of the received signal. For example, in so-called pilot-assisted channel estimation, one transmits a "pilot signal" based on symbols which are a priori known by the receiver. As another example, in so-called decision-directed channel estimation, the receiver uses as a reference some received symbols whose value has been determined by means of a tentative decision process.

Coherent demodulation is often implemented, for example, in communications systems using OFDM. OFDM is a multiple-channel modulation scheme. It is especially appropriate for highly frequency-selective channels such as typical channels for mobile communications, or for high-rate wireline transmission over copper lines. Such channels are characterised by impulse responses which are substantially longer than one sample interval. This means that each received sample in the digital baseband domain is a superposition of multiple transmitted samples weighted by the appropriate channel coefficients. In order to resolve such "intersample interference", some kind of equalisation needs to be performed.

The way OFDM combats intersample interference is by dividing the total channel bandwidth into a number D of substantially smaller portions, called subchannels. One OFDM channel comprises one parallel use of all subchannels. The data to be transmitted is collected into so-called OFDM symbols, and each OFDM symbol is transmitted in parallel on a number D_u (0 < D_u < D) of these subchannels. The transmitted subchannel signals are orthogonal to each other. Since the duration of one OFDM symbol is much longer than the sample interval, the problem of intersymbol interference is strongly reduced.

To get totally rid of intersymbol interference, a guard interval between two symbols is usually introduced during OFDM transmission. If the length of the guard interval exceeds the length of the channel impulse response, there is no residual intersymbol interference. Furthermore, if the guard interval is used in the form of a cyclic prefix, as is usually the case for OFDM transmission, one may implement a very simple equalisation of the frequency-selective channel in the frequency domain.

The wireless Local Area Networks (WLAN) systems are examples of radio communications systems which use OFDM. ETSI (European Telecommunication Standard) BRAN (Broadband Radio Access Network) has developed a short-range high-data-rate communications system called "HIPERLAN type 2" (HIPERLAN/2). HIPERLAN/2 may be used to transport Internet Protocol (IP) packets, and will also be capable to act as a wireless Asynchronous Transfer Mode (ATM) system, as well as a public access system, e.g. with an interface to the Universal Mobile Telecommunications System (UMTS). The physical layer of HIPERLAN/2 is based on OFDM, with a guard interval in the form of a cyclic prefix. Other WLAN systems based on OFDM have been standardised by ARIB in Japan (MMAC and its extensions), and IEEE in the US (IEEE802.11a and its extensions).

In pilot-assisted channel estimation schemes for OFDM, known symbols are transmitted on given subchannels and time instants for training purposes; for example, in systems according to the HIPERLAN/2 or to the IEEE802.11a standard, there are two full OFDM pilot symbols preceding every burst of data-carrying OFDM symbols. The principle of decision-directed approaches for OFDM is quite similar: before channel estimation, some data symbols are being decided; these decided symbols are then treated in the same way as pilot symbols.

The simplest channel estimation method consists in comparing a transmitted pilot symbol with the received value in the respective subchannel. The ratio between these two quantities then yields an estimated subchannel transfer factor. This method is known as the "least-squares estimation".

But a realistic channel always suffers from random noise, which adds up to the ideally-noiseless received signal. Therefore, if channel estimation is purely based on reference symbols, one only obtains a coarse channel estimate, so that the coherent demodulation process based on this estimate will offer sub-optimal performance. In order to improve over such coarse estimates, it is often necessary to take into account known statistical properties of the channel and/or the noise process. For example, channel variations over time or over frequency have typically a smaller bandwidth than the noise process, so that the amount of noise afflicting the estimates can be reduced by using a filter; such a filter is called a Channel Estimation Filter (CEF). The present invention is concerned with how to design a CEF requiring a small amount of computations in the receiver, while providing nonetheless a channel estimation of good quality, compared with the prior art. A CEF ideally adapted to the statistics of a time-dispersive channel should be based on the so-called power delay spectrum of the CIR, which describes the expected channel output power for given delays. The major parameter of the power delay spectrum regarding the CEF is the above- mentioned excess delay of the channel, which represents the effective CIR length; namely, the expected power for delays greater than the excess delay is negligibly small.

In the paper by Peter Hoeher called "TCM on Frequency-Selective Land-Mobile Fading Channels" (Proc. of the 5^th Tirrenia Int. Workshop on Digital Communications, pages 317-328, Tirrenia, Italy, 1992), it is argued that Wiener filters are optimal for estimating dispersive and time-variant channels. Since the OFDM signal is a function of time and of (subchannel) frequency, the Wiener filter designed for this approach, called "Minimum Mean-Squared Error" estimation, is a priori two-dimensional. However, implementing such filtering would be prohibitive due to computational complexity and high storage requirements for the complex coefficients, especially if the number of subchannels is large. It is therefore recommended in that paper to replace this two-dimensional filter by two, serially applied, one-dimensional filters, one filter working in the frequency-domain and the other in the time-domain.

Another Wiener-based channel estimation method was proposed in the paper by Ove Edfors, Magnus Sandell, Jan-Jaap van de Beek, Sarah Kate Wilson, and Per Ola Bδrjesson, titled "Analysis of DFT-Based Channel Estimators for OFDM" (Research Report, Div. of Signal Processing, Lulea University of Technology, Sweden, 1996). The authors of that paper derive an expression for the frequency-domain filter matrix, and disclose a method for getting a, simpler to implement, approximation of this matrix (so-called rank- reduction). This approach requires that all available OFDM subchannels are "active" (viz., actually used to transmit data) and carry pilot signals: this, however, is generally not the case in practice. Yet another Wiener-based method was proposed in the paper by V.K. Jones and Gregory G. Raleigh titled "Channel Estimation for Wireless OFDM Systems", in Proceedings of the Global Telecommunications Conference (GLOBECOM'98), pages 980-985, Sydney, Australia, November 1998. According to this method, received pilot amplitudes are converted into the time-domain, and the channel estimates obtained from them are filtered with a Wiener filter along the time axis. Finally, the smoothed time-domain channel estimate is transformed back into the frequency-domain. This approach requires that the OFDM subchannels carrying pilot signals are equally spaced by D_e, where D_e is the excess delay of the CIR expressed in units of the sampling time; therefore, in this approach, one must assume that the total number D of subchannels is a multiple of D_e: this too is generally not the case in practice.

A channel estimation method using decision-directed coherent demodulation is disclosed in the paper by V. Mignone and A. Morello titled "CD3-OFDM: A Novel Demodulation Scheme for Fixed and Mobile Receivers" (IEEE Trans. Comm., vol. 44, No. 9, pp. 1144-1151 , Sep. 1996). This method is based on feeding back received signals after they have been corrected by means of a channel coding scheme (which needs to be fairly powerful in order to ensure stability). Two types of appropriate filters are discussed: the first one has a pre-set bandwidth which is flat in the time-domain (and is of the order of the guard interval): such a filter is therefore not matched to the actual channel excess delay as it optimally should. The second one has a bandwidth which is adaptively determined after the receiver has calculated the CIR by Fourier- transforming the CTF: but this conversion from the frequency-domain to the time-domain is computationally expensive.

By exploiting correlations inside the channel transfer function, either in the frequency- or in the time-domain, or both, one can achieve noise suppression in channel estimation by linear means. Assuming, for simplicity, that only correlations in the frequency-domain shall be exploited, the characteristics of the channel transfer function over frequency can be regarded as a "band-limited" process. Band-limited means here that the transformation of the channel transfer function into the time-domain yields a CIR of limited length, i.e. the CIR length is substantially smaller than the OFDM symbol length. This usually holds for OFDM transmission systems.

In the paper by Ye (Geoffrey) Li, Leonard J. Cimini Jr., and Nelson R. Sollenberger, titled "Robust Channel Estimation for OFDM Systems with Rapid Dispersive Fading Channels" (IEEE Trans, on Commun., vol. 466, No. 7, pages 902-915, 1998), the focus is on the design of a frequency-domain MMSE filter to exploit the correlations between subchannels, both in the frequency- domain and in the time-domain. To achieve the sought-for rank reduction, the matrix with the optimal estimator coefficients is eigendecomposed into the matrix product of the Hermitian transpose of a unitary matrix, a diagonal matrix with eigenvalues, and the unitary matrix. This unitary, time-invariant matrix is related to the frequency-domain correlations, and the few time-variant, dominating eigenvalues are treated with a MMSE time-domain filter. A structurally similar decomposition for the case of a static channel has been proposed by Ove Edfors, Magnus Sandell, Jan-Jaap van de Beek, Sarah Kate Wilson, and Per Ola Bόrjesson, in the paper titled "OFDM Channel Estimation by Singular Value Decomposition" (IEEE Trans. On Commun., vol. 46, No. 7, pages 931-939, 1998), where tracking the singular values is not required due to the static nature of the channel.

These last two methods for rank-reduction use back-and-forth conversions between the frequency-domain and the time-domain, and are therefore computationally expensive.

Another method exploiting correlations inside the channel transfer function for estimating excess delays can be found in the paper by T. Onizawa et al. titled "A Simple Adaptive Channel Estimation Scheme for OFDM Systems", in Proceedings of the 50^th IEEE Vehicular Technology Conference (VTC 1999-Fall), pages 279-283, Amsterdam, The Netherlands, September 1999. In this paper, a local channel variation metric is used to select the appropriate CEF for a given portion of the entire bandwidth. For that purpose, the length of the difference vector between adjacent subchannels in the preamble is exploited to classify the frequency-local channel variation into three classes, each class being associated with a respective CEF. This method for exploiting the magnitude of difference signals, however, is derived only in a heuristic fashion, so that the level of performance of this approach is not reliable. None of the above-described prior art methods is thus able to provide channel estimation which is simultaneously of good quality and reliable in all circumstances without requiring complex computations in the receiver.

In order to solve this problem, according to a first aspect, the invention concerns a method for channel estimation for OFDM-based communications, said method being remarkable in that a single filter is being applied to all available coarse channel estimates.

By "available" channel estimates, we mean the ones which are fed to the filter input. An example of such channel estimates is provided by the coarse channel estimates corresponding to the active subchannels. Another example is provided by the coarse channel estimate corresponding to a "virtual" subchannel (viz., not carrying any modulation) and which is obtained, according to an embodiment of the invention described in detail below, by assigning to this virtual subchannel the value of the coarse channel estimate corresponding to a neighbouring subchannel. Indeed, it was discovered by the authors of the present invention that, surprisingly, one can achieve excellent noise suppression for all the CTF's corresponding to the D_u active subchannels, even though only one filter is being used for this purpose. Thus, the single-filter estimation method according to the invention has the advantage of avoiding multiplication by a D_u x D_u filter matrix for "smoothing" the coarse CTF's.

Naturally, the efficiency of the method according to the invention can be further increased by a wise choice of the coefficients of the single filter provided for in the receiver.

In a preferred embodiment, designed to optimise noise removal, said filter is determined by designing a filter suitable for a specific subchannel located in the middle of the OFDM multiplex. Indeed, as shown below, it turns out that this choice provides an excellent global quality to the filtering, as can be verified by measuring the respective Signal-to-Noise Ratio (SNR) of each of the filtered CTF's corresponding to the active subchannels. According to a second aspect, the invention provides for various ways to improve the quality of channel estimation during signal reception.

Firstly, said filter may be applied sequentially to each of the available coarse channel estimates, first in one frequency direction, then in the other frequency direction, after which one averages over the results of these two filtering operations.

This method provides for better accuracy than filtering in only one frequency direction, but of course at the price of some additional computations.

Secondly, one may assign to at least one subchannel a value for its coarse channel estimate equal to the value corresponding to a neighbouring subchannel. The subchannel, to which such a value is being assigned, will then be included in what we called the "available" subchannels.

Implementing this method will advantageously reduce filter transients appearing, for example, close to an edge of the OFDM multiplex or in the proximity of a virtual subchannel. As explained above, a convenient way to obtain a coarse estimate of the CTF's is by means of the so-called least-squares estimation method.

Thus, the invention also concerns a method for channel estimation for OFDM-based communications, the method including obtaining a coarse estimate of the channel transfer factor by removing known subchannel pilot amplitudes from a Fourier-transformed pilot sequence, said method being remarkable in that said pilot sequence is obtained by averaging in the time domain over at least two repeatedly received preamble OFDM symbols.

This improvement over the known least-squares estimation method advantageously reduces the amount of noise present in the least-squares estimate of the CTF's. Note that a frequency-domain averaging, i.e., performed after Fourier-transforming the received pilot sequences, would be equivalent in terms of noise-reduction, but implementationally more expensive since a plurality of Fourier transformations would be needed.

According to another improvement -- designed to further reduce complexity -- over the known least-squares estimation method, the invention concerns a method for channel estimation for OFDM-based communications, the method including obtaining a coarse estimate of the channel transfer factor by removing known pilot subchannel amplitudes from a Fourier-transformed pilot sequence, said method being remarkable in that an adequate number of time-domain samples are circularly shifted within each OFDM symbol so that the power delay profile of the channel becomes circularly symmetric around the starting time of said OFDM symbol.

As explained in detail below, the response of the CEF along the time-axis can in this case be designed to be symmetric around zero, which leads to real-valued filter coefficients. This reduces considerably the amount of computation required by the filtering operations, compared with using a filter having complex coefficients.

According to a third aspect, the invention concerns various devices.

It thus concerns, firstly, a channel estimation device for OFDM-based communications, including a filtering unit capable of applying a single filter to all available coarse channel estimates.

The invention concerns, secondly, a channel estimation device for OFDM-based communications, including a replacing unit capable of assigning to at least one subchannel a value for its coarse channel estimate equal to the value corresponding to a neighbouring subchannel. The invention concerns, thirdly, a channel estimation device for

OFDM-based communications, including:

- a DFT unit for transforming a time-domain pilot sequence into a frequency-domain signal, and

- a pilot-removal unit for removing known pilot subchannel amplitudes from said frequency-domain signal, said device being remarkable in that it also includes an averaging unit capable of averaging over at least two repeatedly received preamble OFDM symbols in order to yield said pilot sequence.

The invention concerns, fourthly, a channel estimation device for OFDM-based communications, including:

- a pilot-removal unit for removing known pilot subchannel amplitudes from said frequency-domain signal, said device being remarkable in that it also includes a shifting unit capable of performing a circular time-shift within each OFDM symbol, in order to yield said pilot sequence.

The invention also relates to:

- a modulated-signal reception apparatus including at least one device as succinctly described above,

- a telecommunications network including at least one reception apparatus as succinctly described above,

- a data storage means containing computer program code instructions for executing steps of anyone method as succinctly described above, and - a computer program containing instructions such that, when said program controls a programmable data processing device, said instructions mean that said data processing device implements anyone method as succinctly described above.

The advantages offered by these devices, apparatus, telecommunications networks, data storage means and computer programs are essentially the same as those offered by the methods according to the invention.

Other aspects and advantages of the invention will emerge from a reading of the detailed description, which will be found below, of preferred embodiments given by way of non-limitative example. This description refers to the accompanying drawings, in which: - Figure 1 is a diagram illustrating the standard time-domain structure of an OFDM preamble,

- Figure 2 shows, for two specific subchannels, analytical results for the SNR in the CTF estimates after filtering, versus the number of non-zero filter coefficients, if averaging in the time-domain according to the invention is being used,

- Figures 3a and 3b are diagrams illustrating schematically a cyclic shift of the OFDM symbols and an effect of this shift, according to a preferred embodiment of the invention, - Figures 4a and 4b illustrate schematically how one can assign a value for a coarse CTF corresponding to a subchannel devoid of pilot signals, according to a preferred embodiment to the invention,

- Figure 5 shows the SNR for the CTF estimate for all OFDM subchannels, after filtering using the single-filter method according to the invention, and

- Figure 6 depicts schematically a device for channel estimation according to a preferred embodiment of the invention.

For introduction, consider the transmission of one single OFDM symbol generated with a D-dimensional Inverse Discrete Fourier Transform (IDFT). Each of the D subchannels is modulated by a complex-valued amplitude A_μ[υ], where v is the subchannel number (O ≤ tx D ) representing subchannel frequency, and μ indicates the OFDM symbol number representing transmission time. The data are mapped on the subchannel amplitudes A [υ].

The OFDM symbol is equipped with a guard interval of D_g samples. The discrete-time complex baseband OFDM transmitted signal a_μ for OFDM symbol number μ, when written out as a vector over discretised time p, with: - D_g ≤ p < D, has the following components:

1 =;1 _r -, +j— υp , D υ=0 which can be generated by an IDFT of dimension D. Using s to denote expectation value, the average signal power is

where E_s is the average energy per channel symbol and T is the modulation interval.

For convenient notation, the symbol index μ will be suppressed in the following.

We assume transmission over a multipath channel, whose CIR will be modelled, during the transmission of each OFDM symbol, by means of a discrete-time vector h having components h[p] (p = 0,... , D-1). The fact that the continuous-time CIR is non-zero only up to the excess delay τ is equivalent to having only the components h[p] with p = 0 D_e-1 (where D_e is the discretised excess delay of the CIR) being non-zero.

As discussed in the introduction, the noiseless received signal is given by y = a * h , where * denotes circular convolution.

For convenient notation, without loss of generality, perfect frequency synchronisation will be assumed in the receiver. At the receiver input, samples n[p] of Additive White Gaussian Noise (AWGN) corrupt the noiseless signal samples y[p] to yield the actually-received samples y[p] = y[p] + ].

The noise power is

^ = ^s {|^«H|²)= ^ ^{, (1)} where N₀ is the "one-sided power spectral density" of the white noise. The channel Signal-to-Νoise power Ratio (SΝR) at the receiver input is thus ζ ≡E_s /N₀ = _σ ² /_σ ².

Implementing a Discrete Fourier Transform (DFT), one defines the discrete Channel Transfer Factor (CTF) at subchannel υ as

The OFDM receiver yields the noisy subchannel amplitudes via DFT processing as

= Ϋ[υ] + N[υ] , where

Ϋ[o] ≡ A[υ] H[υ] (3) is the noiseless received subchannel amplitude, and N[υ] is the resulting noise sample on subchannel v. Here we assumed that the guard interval D_g is sufficiently large so that the linear convolution of the transmitted OFDM signal and the CIR is equal to their circular convolution in the time interval of interest. It is obvious from Equation (3) that for data recovery from y[υ] , an estimate of H[υ] is required.

We shall now describe, as an example of a method which can be implemented in the receiver to obtain a coarse estimate of H[υ] within the framework of the present invention, the known "least-squares" estimation method.

The active subchannel positions will be referred to by the subchannel indices v which belong to a set U containing the D_u indices of these positions. The remaining (D - D_u) subchannels, namely the ones in which the modulation amplitude is set to zero, are usually called "virtual" subchannels. Since the signal power is concentrated in the active subchannels, it is useful to consider the "subchannel signal-to-noise power ratio" ζ_u = (DID_U) ζ.

We shall assume that, for so-called training purposes, a preamble symbol containing known subchannel amplitudes covering the entire active frequency-domain is provided; we will collect these amplitudes in a vector A_p of length D_u.

The transmitted time-domain preamble (or pilot) OFDM symbol is depicted in the upper part of Figure 1. The repeatedly transmitted time-domain sequence of length D is obtained by the IDFT

where we introduced the D_u x D partial DFT matrix

and ^f denotes the conjugate transpose of a matrix. The sample sequence resulting from the convolution of the transmitted preamble sample sequence with the CIR h is disturbed by additive noise. Since the guard interval and the repeated preamble, which are assumed to be of sufficient size, are both cyclic, the linear convolution is equal to the circular convolution for these signal segments which are of interest for final demodulation. Thus, the noiseless received sequence y_p, of length D is equal to the circular convolution of a_p and h.

In the lower part of Figure 1 , the temporal structure of the received signal is indicated. Perfect channel frequency synchronisation has been assumed. The successive received sequences y-i, y₂, and so on, are made of the repeated noiseless sequence y_p disturbed respectively by the (statistically independent) successive D-dimensional noise vectors riι, n₂, and so on.

Implementing a DFT, we find:

Ϋ_{p ≡} D_u a_p }- D_u h = diag { A_P } H = A H , (6)

where we collected the D_u channel transfer factors H[υ] (v e U) in the column vector

H ≡ D_u h , (7) and we collected the transmitted pilot subchannel amplitudes in the D_u x D_u diagonal matrix

A ≡ diag { A_p } . (8) According to one aspect of the present invention, prior to signal processing for channel estimation, the received signal sequences are combined as follows:

where _{n ≡} _(n_{1 +}n₂) . (₁₀)

Indeed, this combination of the received signals in the time-domain allows for a 3 dB reduction in noise power, as can be readily seen from the expression of the noise covariance matrix:

where ϊ_DxD denotes the unit matrix of dimension D.

The combined received signal y_p is transformed into frequency domain via the DFT

Y_{p ≡} A H + N , (12)

where we used Equations (6) and (9), and we introduced the D_u -dimensional frequency-domain noise vector N.

Finally, the "least-squares estimate" H_LS of the Channel Transfer Factors vector ("CTF vector") is obtained by dividing out the frequency-domain received signal by the pilot subchannel amplitudes:

H_Ls = A^"1 Y_P = H + A-¹ N . (13)

This operation, which can be seen as extracting or removing the influence of the transmitted pilot amplitudes from the received signal, will be referred to below as "removing pilot amplitudes".

The least-squares estimation method just described is only one possible way to obtain a coarse estimate of the CTF vector. Once a coarse estimate H_coarse has been obtained, filtering of H_coarse by the CEF yields the filtered estimate H_F of the CTF vector. The filters used in the framework of the present invention are assumed to be normalised in such a way that there is neither an amplification nor an attenuation in the passband; in other words, one tries, when designing a filter, to have the parts in the filter input signal which belong to the filter passband be equal to the corresponding parts in the filter output signal, up to signal distortions introduced by the filter itself. Then, a "good" filter is a filter which, besides introducing negligible distortions, is characterised by a passband which is well-adjusted to the noiseless signal characteristics.

This filtering can be expressed by means of a filter matrix F as:

H_F = FH_LS . (14)

Each row of F contains the filter coefficients needed, during signal reception, for good-quality estimation of the CTF associated with the corresponding specific subchannel.

It will be assumed here that some suitable filter matrix has been chosen one way or another. In the case of a non-adaptive system, the filter coefficients are determined at the level of receiver design for a chosen estimation method, based on model expectations concerning what the channel statistics and the possible sources of noise will be when this receiver will be put to use. In the case of an adaptive system, the filter bandwidth (through the filter coefficients) can be matched to the actual channel excess delay during operation of the receiver, on the basis of some suitable predetermined method, so as to optimise the efficiency of the filter. For example, as discussed in the introduction, a known method for determining such a filter matrix is based on Wiener "optimal" filtering, which yields a so-called Minimum Mean-Squared Error value FM SE for this filter matrix. Assuming the use, in the receiver, of a least-squares estimation method with averaging according to Equation (9), one derives, using Equations (1) and (10), that this optimal filter matrix is:

where

is the CTF correlation matrix, which describes the statistical properties of the frequency-domain channel gains. This matrix depends via Equation (7) on the Power Delay Profile (PDP) of the channel, viz. the power dispersion of the channel in the time-domain. One can thus calculate FMM_SE on the basis of a model of the channel.

The invention, however, does not depend on which method has been used to compute suitable filter coefficients. Furthermore, in the method presented above as an example, the filter has a Finite Impulse Response (FIR), but it is also possible to use an Infinite Impulse Response (IIR) filter within the framework of the present invention. Particularly attractive are filters whose gain is approximately flat in the passband and zero elsewhere, and having linear phase; such filters are not optimised for specific channel statistics.

Indeed, as explained in the introduction, one goal of the present invention is to find a way to reduce the complexity which would result from using a two-dimensional (D_u x D_u) complex-valued filtering matrix for a CEF.

In order to appreciate how the invention solves this problem, it will be illuminating to study Figure 2, which shows analytic results for the Signal-to- Noise power Ratio (SNR) ζ_v (viz., the ratio of signal power to noise power in subchannel number v) for two specific components (v = 12 and v = 26) of the CTF vector estimate after filtering, versus the number of non-zero filter coefficients ("filter taps") of a Wiener matrix filter (see Equation (15)). In this numerical example, the number of OFDM subchannels D is equal to 64, out of which subchannel numbers 1 to 26, and 38 to 63 are actually being used; hence D_u is equal to 52. A uniform PDP has been assumed, with an excess delay D_e equal to 8.

The horizontal lines show a channel SNR ζ equal to 10 dB. The subchannel SNR ζ_u is about 11 dB, since D/D_u ~ 1.1. Thanks to the signal averaging according to this embodiment of the invention, we get already with one tap (equivalent to having no filter at all) an estimation SNR ζ_v of approximately 14 dB, viz., a further 3 dB gain. When one increases the number of filter coefficients, this SNR increases, and finally saturates, with a considerable difference in estimation quality between subchannels in the middle of the frequency multiplex (v = 12) and the ones on the edge (v = 26). For all subchannels, only a small number of filter coefficients is required to achieve the largest portion of the maximum gain. For v = 12 for example, a gain of about 6 dB (compared to a gain at saturation of 8.5 dB) is obtained with only five filter taps. It should be emphasised that the requirements on the model describing the statistics of the channel are not very stringent. In particular, a uniform PDP is often sufficient to obtain a good filter. Indeed, the filter may be simply designed as a conventional low-pass filter, with a filter bandwidth matching the excess delay of the channel. Now, according to the invention, a single filter will be used instead of a matrix filter, since the latter is too expensive to implement. This amounts to choosing a specific row in the filter matrix F, and replacing all the other rows by this chosen row. Based on the study just carried, it appears that the coefficients for this single filter should preferably be determined by optimising them for a subchannel in the middle of the multiplex.

It is also apparent that only a small number of filter taps are actually needed to obtain a very good quality of filtering, and hence of channel estimation.

One may simply choose to apply this single filter sequentially in one frequency direction to each of the available components of the coarse CTF vector. As a variant, for better accuracy, one may implement the filtering twice, going in one, then in the other frequency direction, and finally average the two results.

Within the framework of the single-filter method according to the invention, the coefficients of this filter could well be complex-valued, but, compared to real-valued coefficients, this requires up to three times more multiplications and twice the number of additions for filter processing. According to a preferred embodiment of the invention, in order to obtain an estimation filter having real-valued coefficients, the PDP of the channel model used to design the filter is shifted in such a way that the PDP becomes circularly symmetric around time-index zero. Thanks to this shifting, the spectrum of the CEF can be designed to be symmetric around zero: this leads to real-valued filter taps, which further reduces the amount of computation required during the estimation procedure. Due to this reason, it is advantageous to use an odd number of taps in the filter design for a uniform PDP.

The above-described shift of the PDP creates an "equivalent channel" derived from the one really seen by the preamble and data symbols, and whose effect amounts to a circular convolution of a shifted received signal with a shifted CIR. We shall now present, by way of example, two different ways of building such an equivalent channel.

According to a first method, one does not shift the OFDM symbols. Instead, since the shift of the PDP corresponds to a delay in the time domain, the finally obtained frequency-domain CTF's (after filtering) are appropriately phase-rotated.

A second, more elegant and complexity-efficient method consists in cyclically shifting all received OFDM symbols, whether they belong to the preamble or to the data. To be more specific, after removing the cyclic prefix (CP), the samples a^, a₂, ..., aw within one OFDM symbol are rearranged. If the PDP is shifted by L samples to the left, where L = (D_e-1)/2, the rearrangement is conducted in such a way that L samples from the end of each OFDM symbol are shifted to the beginning of this symbol: the samples are then reordered as a_/v-i+₁, ■■•, a/v, &\ &N-L- This shifting of samples is illustrated in Figure 3a, and the resulting shift of the PDP is illustrated in Figure 3b.

In the above derivation of the least-squares estimation method, it was assumed that there exists a pilot signal for each active subchannel. However, it is perfectly possible to implement the present invention in communications systems where pilot signals are assigned on some only, predetermined subchannels in the OFDM multiplex. Taking again the least- squares method as an example of a method for channel estimation, the above computations will then only involve the pilot-transmitting subchannels rather than all active subchannels, while the least-squares estimates of the CTF's associated with the subchannels devoid of pilot signals will be assigned a zero value. In this embodiment, the set of "available" channel estimates thus consists of the channel estimates corresponding to the pilot-transmitting subchannels, plus zero values for the other subchannels.

Alternatively, all subchannels may be included if one obtains coarse channel estimates by means of a decision-directed method. As only one filter is used for the estimation of all the CTF's corresponding to active subchannels, the estimates close to an edge of the multiplex or in the proximity of subchannels devoid of pilot signals will suffer from filter transients. According to an embodiment of the present invention, in order to lessen this adverse effect, we simply replace at least one component of H_coarse (whether measured or assigned a zero value) corresponding to such a subchannel, with the value corresponding to a neighbouring, preferably the nearest, active subchannel. This procedure is illustrated schematically in Figures 4a and 4b for a multiple-channel communications system having several virtual subchannels (represented by means of open circles), and several active, pilot-transmitting subchannels (represented by means of dots); Figure 4b shows how some of the virtual subchannels have been "filled-up" using the value of the component of H_coarse corresponding to an adjacent, active subchannel.

This method amounts to a filter input sample repetition, up to some given number of samples. In this way, the filter performs interpolation. In principle, it is possible to "fill-up" all subchannels close to an edge of the multiplex or devoid of pilot signals. But for simplicity and efficiency sake, it is recommended for each series of such subchannels to fill-up only as many successive subchannels as necessary to cover a frequency range equal to the group delay of the CEF; in the example illustrated in Figures 4a and 4b, a CEF group delay corresponding to 2 subchannels was assumed, and therefore only 2 instead of all 4 concerned subchannels were filled-up in each series.

We now show the results of implementing the invention. The various above-mentioned embodiments will be simultaneously taken advantage of in the following. In the present example, the single FIR filter according to the invention was given 11 taps, and was optimised for v = 12. The transfer function of the IIR filter according to the invention had degree 1 in the numerator, and degree 3 in the denominator.

Figure 5 shows the resulting SNR ζ_v of the CTF estimate, versus the index v of the subchannel under estimation, for FIR filtering as well as for IIR (Infinite Impulse Response) filtering, the latter being performed in a single (from left to right) direction, or in both directions. In this numerical example, the number of OFDM subchannels D is equal to 64, out of which subchannel numbers 1 to 26, and 38 to 63 are actually being used (number 0 corresponds to the so-called DC subchannel). A uniform PDP has been assumed, with an excess delay D_e equal to 9. Also, perfect frame alignment is assumed.

The channel SNR is at 10 dB. The circles show the SNR of the least-squares estimate, and we clearly recognise the virtual subchannels with a SNR equal to 1 (0 dB). The crosses indicate the SNR achieved by filling-up a maximum number of two virtual positions with pilot amplitudes from the nearest active pilot position. These modified subchannel amplitudes are input to the CEF.

As the IIR filtering in single direction is performed from left to right, we find the IIR results to be worse than FIR on outer left edges and to be better on outer right edges. A minor improvement is achieved by implementing the second direction of filtering.

The efficiency of the method according to the invention is measured by a SNR of about 20 dB. This value holds practically over the whole range of used subchannels.

An exemplary device (100) for channel estimation according to the invention is schematically depicted in Figure 6. By way of example, one uses here the least-squares method in order to obtain a coarse estimate of the CTF's.

One first combines, according to Equation (9), two received pilot sequences yi and y₂ in an averaging unit (101). Next, shifting unit (102) performs a circular time-shift on the resulting signal. DFT unit (103) then transforms this shifted time-domain signal into the frequency-domain by a DFT, preferably implemented as a Fast Fourier Transform (FFT), according to Equation (12). Next, "removal of pilot amplitudes" in pilot-removal unit (104), according to Equation (13), yields a least-squares estimate of the CTF vector. Replacement, by value repetition, of the null entries of this CTF vector is then performed in replacing unit (105). Finally, the filtered estimate of the CTF vector is obtained in filtering unit (106) by using, according to the invention, a single filter for all (frequency-domain) available components of the CTF vector.

Claims

1. A method for channel estimation for OFDM-based communications, characterised in that a single filter is being applied to all available coarse channel estimates.

2. A method according to Claim 1 , characterised in that said filter is determined by designing a filter suitable for a specific subchannel located in the middle of the OFDM multiplex.

3. A method according to Claim 1 or Claim 2, characterised in that said filter is applied sequentially to each of the available coarse channel estimates, first in one frequency direction, then in the other frequency direction, after which one averages over the results of these two filtering operations.

4. A method according to any one of Claims 1 to 3, characterised in that one assigns to at least one subchannel a value for its coarse channel estimate equal to the value corresponding to a neighbouring subchannel.

5. A method for channel estimation for OFDM-based communications, the method including obtaining a coarse estimate of the channel transfer factor by removing known subchannel pilot amplitudes from a Fourier-transformed pilot sequence, characterised in that said pilot sequence is obtained by averaging in the time domain over at least two repeatedly received preamble OFDM symbols.

6. A method for channel estimation for OFDM-based communications, the method including obtaining a coarse estimate of the channel transfer factor by removing known pilot subchannel amplitudes from a Fourier-transformed pilot sequence, characterised in that an adequate number of time-domain samples are circularly shifted within each OFDM symbol so that the power delay profile of the channel becomes circularly symmetric around the starting time of said OFDM symbol.

7. A method according to Claims 1 and 5, or to Claims 1 and 6, or to

Claims 5 and 6, or to Claims 1 , 5 and 6.

8. A channel estimation device for OFDM-based communications, including a filtering unit (106) capable of applying a single filter to all available coarse channel estimates.

9. A channel estimation device for OFDM-based communications, including a replacing unit (105) capable of assigning to at least one subchannel a value for its coarse channel estimate equal to the value corresponding to a neighbouring subchannel.

10. A channel estimation device for OFDM-based communications, including: - a DFT unit (103) for transforming a time-domain pilot sequence into a frequency-domain signal, and

- a pilot-removal unit (104) for removing known pilot subchannel amplitudes from said frequency-domain signal, characterised in that it also includes an averaging unit (101) capable of averaging over at least two repeatedly received preamble OFDM symbols in order to yield said pilot sequence.

11. A channel estimation device for OFDM-based communications, including:

- a DFT unit (103) for transforming a time-domain pilot sequence into a frequency-domain signal, and

- a pilot-removal unit (104) for removing known pilot subchannel amplitudes from said frequency-domain signal, characterised in that it also includes a shifting unit (102) capable of performing a circular time-shift within each OFDM symbol, in order to yield said pilot sequence.

12. A modulated-signal reception apparatus, characterised in that it includes a device according to anyone of Claims 8 to 1.

13. A telecommunications network, characterised in that it includes at least one reception apparatus according to Claim 12.

14. A data storage means, characterised in that it contains computer program code instructions for executing steps of a method according to any one of Claims 1 to 7.

15. A data storage means according to Claim 14, characterised in that it is partially or totally removable.

16. A computer program, characterised in that it contains instructions such that, when said program controls a programmable data processing device, said instructions mean that said data processing device implements a method according to any one of Claims 1 to 7.