WO2017157453A1

WO2017157453A1 - A receiver and a method for estimating the carrier frequency offset in a multicarrier modulation signal

Info

Publication number: WO2017157453A1
Application number: PCT/EP2016/055916
Authority: WO
Inventors: Fredrik RUSEK
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2016-03-18
Filing date: 2016-03-18
Publication date: 2017-09-21

Abstract

The invention relates to a receiver (101) for receiving a multicarrier modulation signal over a communication channel (120), wherein the multicarrier modulation signal comprises at least one training signal. The receiver (101) comprises an estimator (103) configured to estimate a fractional frequency offset ε of the multicarrier modulation signal on the basis of the at least one training signal, wherein the estimator (103) is configured to estimate the fractional frequency offset ε on the basis of an approximation (A) of a log-likelihood function λ(ε), wherein the approximation (A) of the log-likelihood function λ(ε) is based on the following equation: (I), wherein (B) denotes a set of weighting coefficients, φ _κ (ε) denotes a set of basis functions and Κ is an odd number equal to or larger than 3 and wherein the set of basis functions is based on the following equations: (II) for odd κ and (III) for even κ, wherein (C) denotes an adjustment factor, which is smaller than one and decreases with increasing Κ; and an adjuster (105) configured to adjust the multicarrier modulation signal on the basis of the estimated fractional frequency offset ε.

Description

DESCRIPTION

A receiver and a method for receiving a multicarrier modulation signal TECHNICAL FIELD

In general, the present invention relates to the field of telecommunications. More specifically, the present invention relates to a receiver and a method for receiving a multicarrier modulation signal implementing a mechanism for estimating and

compensating a frequency offset between a transmitter and a receiver in a

telecommunication system.

BACKGROUND Orthogonal Frequency Division Multiplexing (OFDM) is the dominant modulation technique in contemporary systems such as 3^rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) and Wireless Fidelity (WIFI). OFDM is a Frequency-Division Multiplexing (FDM) scheme used as a digital Multicarrier Modulation (MCM) method for encoding digital data on multiple carrier frequencies. In OFDM, a large number of closely spaced orthogonal subcarriers are used to carry data.

A common and severe problem of OFDM is the frequency offset between the transmitting part and the receiving part. This is herein referred to as Carrier Frequency Offset (CFO). A CFO implies that the transmitter and the receiver are misaligned with each other and a consequence of this is that orthogonality among the OFDM subcarriers is lost. As the orthogonality among the OFDM subcarriers is the crucial point of OFDM, this situation is unacceptable and solutions have to be found. If the CFO is known to the receiver, then it can compensate for the CFO by a frequency shift, and orthogonality can be assured. Therefore, mitigating CFOs is equivalent to the problem of estimating the CFO from the received data.

The CFO can be broken up into two parts, the integer frequency offset e_Int and the fractional frequency offset ε:

where ε_Ιηί is an integer multiplied by the subcarrier spacing and ε is limited in magnitude to half subcarrier spacing. The CFO is usually expressed in the physical unit Hz.

The degradation of the system performance for a given OFDM system and a given CFO depends on the ratio between the CFO and the subcarrier spacing. Therefore, it is common and convenient to normalize the CFO by the subcarrier spacing in order to obtain a dimensionless quantity, so that e_Int e {... , -3, -2, -1,0,1,2,3, ... ) and ε e [-1/2,1/2].

During an initial synchronization phase, the precise value of the integer frequency offset e_Int can be obtained. Therefore, the remaining problem is to estimate the fractional frequency offset ε, which can be done on the basis of a training or pilot signal. For instance, the fractional frequency offset ε can be estimated on the basis of a received signal, which comprises two OFDM symbols with training symbols, also known as pilot symbols.

Different approaches for estimating the CFO are known in the prior art. A method of particular importance, due to its excellent performance, is the maximum-likelihood estimator (MLE). The MLE comes at the price of high complexity. However, some techniques to closely approximate the MLE with low complexity are known.

In an exemplary scenario, where a single OFDM symbol has been received by a receiver, the OFDM symbol comprises known training symbols at all subcarriers. This scenario can be easily modified to a OFDM symbol having only a partial pilot allocation. Assuming that a cyclic prefix has been perfectly removed, the time signal representing the OFDM symbol can be expressed as: s

wherein s denotes the received signal vector of dimension Nx1 , N denotes the Fast- Fourier-Transform (FFT) size, p denotes an Nx1 vector with known training symbols, Q denotes the NxN Inverse-FFT (I FFT) matrix, h^circ denotes an NxN cyclic convolutional matrix representing the unknown communication channel, Ο(ε) denotes an NxN diagonal matrix representing the effect of the CFO having

) as k-t diagonal element and n denotes a vector of dimension Nx1 representing the zero mean complex Gaussian noise with a covariance matrix N₀. Although the properties of the communication channel are unknown, it can be assumed that its second order statistics are known to the receiver. For instance, the power delay profile of the channel is given by:

wherein h[n] denotes the n-th tap of the channel impulse response (this is the n-th element in the first column of the matrix

Once the signal s .including the known training symbols, has been received, the log- likelihood of ε can be estimated on the basis of the following equation:

wherein P denotes an NxN diagonal matrix with p along its main diagonal, wherein the superscript "H" denotes the Hermitian transpose, while the superscript "-H" denotes the inverse and Hermitian transpose and wherein the matrix Λ is given by the following equation:

i.e. the matrix Λ is an NxN diagonal matrix with its n-th element equal to∑_n.

On the basis of the definitions above the MLE for estimating the fractional frequency offset ε can be formulated as follows:

Although the MLE has an excellent performance, in practice it is used very seldom, because the evaluation of λ(ε) is computationally extremely expensive.

Conventional approaches for improving the computational efficiency of the evaluation of λ(ε) rely on the approximation of the log-likelihood function in a low dimensional space. In particular, it is common to make use of the following approximation in order to estimate the fractional frequency offset ε:

wherein K is an odd number representing the number of dimensions in the expansion, denote a set of expansion coefficients and denote basis functions.

In the prior art, basis functions ) of the following form have been suggested:

In order to find the expansion coefficients

exact log-likelihoods

are computed at pre-determined values Then, a linear relation is

assumed between

namely:

Now, the expansion coefficients can be determined using a least squares approach:

Once the expansion coefficients have been determined, an approximate solution to the CFO estimation problem can be found, making use of the following relation:

Since each evaluation

( ) is relatively cheap, the computational complexity in estimating the fractional frequency offset ε is reduced.

Although the above conventional solutions for estimating the fractional frequency offset using an approximation of the log-likelihood function in a low dimensional space already provide some improvements, there is still room for further improvements. Thus, there is a need for improved devices and methods for estimating the fractional frequency offset using an approximation of the log-likelihood function in a low dimensional space. SUMMARY

It is an object of the invention to provide improved devices and methods for estimating the fractional frequency offset using an approximation of the log-likelihood function in a low dimensional space.

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 receiver for receiving a multicarrier modulation signal, in particular an OFDM signal, over a communication channel, wherein the multicarrier modulation signal comprises at least one training signal. The receiver comprises an estimator configured to estimate a fractional frequency offset ε of the multicarrier modulation signal on the basis of the at least one training signal, wherein the estimator is configured to estimate the fractional frequency offset ε on the basis of an approximation of a log-likelihood function λ έ) associated with the likelihood of the

fractional frequency offset ε given the multicarrier modulation signal comprising the at least one training signal. The approximation of the log-likelihood function λ(ε) is

based on the following equation:

wherein a_k denotes a set of weighting coefficients (also referred to as expansion coefficients denotes a set of basis functions and K is an odd number equal to or

larger than 3 and wherein the set of basis functions is defined by the following equation:

wherein denotes an adjustment factor, which is smaller than one and decreases with increasing K. Furthermore, the receiver comprises an adjuster configured to adjust the frequency of the multicarrier modulation signal on the basis of the estimated fractional frequency offset.

Thus, an improved receiver is provided allowing for a computationally more efficient estimation of the fractional frequency offset using an approximation of the log-likelihood function in a low dimensional space. More specifically, the receiver according to the first aspect allows estimating the fractional frequency offset using, for instance, much less complex computations than conventional receivers. In a first possible implementation form of the receiver according to the first aspect as such, the estimator is configured to set the adjustment factor ξ_κ for K=3 to a value in the range from 0.56 to 0.58, in particular to a value of 0.57, for K=5 to a value in the range from 0.375 to 0.395, in particular to a value of 0.385, for K=7 to a value in the range from 0.274 to 0.294, in particular to a value of 0.284 and/or for K=9 to a value in the range from 0.213 to 0.233, in particular to a value of 0.223.

In a second possible implementation form of the receiver according to the first aspect as such or the first implementation form thereof, the estimator is configured to choose the value of K on the basis of a signal to noise ratio.

In a third possible implementation form of the receiver according to the first aspect as such or the first or second implementation form thereof, the estimator is configured to choose the value of K on the basis of a look-up table, wherein the look-up table assigns different values of K to different ranges of signal to noise ratios.

In a fourth possible implementation form of the receiver according to the first aspect as such or any one of the first to third implementation form thereof, the estimator is configured to estimate the fractional frequency offset ε on the basis of the approximation λ έ) of the log-likelihood function by finding a fractional frequency offset estimate, for which the approximation λ έ) of the log-likelihood function is larger than a log-likelihood threshold, in particular equal to a log-likelihood maximum.

In a fifth possible implementation form of the receiver according to the first aspect as such or any one of the first to fourth implementation form thereof, the estimator is configured to estimate the set of weighting coefficients a_k on the basis of a plurality of values of the log- likelihood function at a plurality of predetermined fractional frequency offsets

In a sixth possible implementation form of the receiver according to the fifth

implementation form of the first aspect, the estimator is configured to estimate the set of weighting coefficients a_k on the basis of a plurality of values of the

log-likelihood function

at the plurality of predetermined fractional frequency offsets on the basis of the following equation:

In a seventh possible implementation form of the receiver according to the fifth implementation form of the first aspect, the estimator is configured to estimate the set of weighting coefficients

on the basis of a plurality of values of the

log-likelihood function at the plurality of predetermined fractional frequency offsets

on the basis of the following equation:

wherein the estimator is configured to determine the matrix A by minimizing a measure of error between the log-likelihood function

) and the approximation ) of the log-

likelihood function.

In an eighth possible implementation form of the receiver according to the seventh implementation form of the first aspect, the estimator is configured to determine the matrix A by minimizing the measure of error e between the log-likelihood function

and the approximation (ε) of the log-likelihood function defined by the following equation:

wherein ] denotes the expectation value and e(s) denotes the difference between the log-likelihood function λ(ε) and the approximation (ε) of the log-likelihood function as a function of the fractional frequency offset. In a ninth possible implementation form of the receiver according to the seventh or eighth implementation form of the first aspect, the matrix A is given by the following equation:

wherein Z₀ and Z are given by the following equations:

wherein denotes a vector comprising the set of basis functions

and wherein R is the covariance of the log-likelihood function λ(ε) .

In a tenth possible implementation form of the receiver according to the first aspect as such or any one of the first to ninth implementation form thereof, the log-likelihood function λ(ε) of the fractional frequency offset ε is defined by the following equation:

wherein s denotes a vector representing the received multicarrier modulation signal, D denotes a diagonal matrix representing the frequency offset, Q denotes a matrix representing an IFFT, P denotes a diagonal matrix with the components of a vector p along its diagonal, p denotes a vector representing the at least one training signal and Λ denotes a diagonal matrix with its n-th element being given by

∑_n = £ [| /i[n] | ²] , wherein E[... ] denotes the expecation value and h[n] denotes the n-th tap of the impulse response vector of the communication channel.

According to a second aspect the invention relates to a method of receiving a multicarrier modulation signal, in particular an OFDM signal, over a communication channel, wherein the multicarrier modulation signal comprises at least one training signal. The method comprises the step of estimating a fractional frequency offset ε of the multicarrier modulation signal on the basis of the at least one training signal using an approximation λ(ε) of a log-likelihood function λ(ε) associated with the likelihood of the fractional frequency offset ε given the multicarrier modulation signal comprising the at least one training signal. The approximation

of the log-likelihood function λ(ε) is based on the following equation:

wherein a_k denotes a set of weighting coefficients (also referred to as expansion coefficients),

denotes a set of basis functions and K is an odd number equal to or larger than 3 and wherein the set of basis functions is based on the following equation:

wherein ξ_κ denotes an adjustment factor, which is smaller than one and decreases with increasing K. The method comprises the further step of adjusting the frequency of the multicarrier modulation signal on the basis of the estimated fractional frequency offset ε.

The method according to the second aspect of the invention can be performed by the receiver 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 receiver according to the first aspect of the invention and its different implementation forms.

According to a third aspect the invention relates to a computer program comprising program code for performing the method according to the second aspect 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 communication system including a user equipment with a receiver according to an embodiment; Fig. 2 shows a schematic diagram illustrating a method according to an embodiment; and

Fig. 3 shows a schematic diagram of a receiver according to an embodiment. In the various figures, identical reference signs will be used for identical or at least functionally equivalent features.

DETAILED DESCRIPTION OF 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 will be appreciated 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 by the appended claims.

For instance, it will be appreciated 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.

Moreover, in the following detailed description as well as in the claims embodiments with different functional blocks or processing units are described, which are connected with each other or exchange signals. It will be appreciated that the present invention covers embodiments as well, which include additional functional blocks or processing units that are arranged between the functional blocks or processing units of the embodiments described below.

Finally, it is understood that the features of the various exemplary aspects described herein may be combined with each other, unless specifically noted otherwise.

Figure 1 shows a schematic diagram of an exemplary communication system comprising a transmitter in the form of a base station 1 10, a communication channel 120 and a user equipment 100 comprising a receiver 101 according to an embodiment. The receiver 101 of the user equipment 100 is configured to receive a multicarrier modulation signal, in particular an OFDM signal, from the base station 1 10 over the communication channel 120, wherein the multicarrier modulation signal comprises at least one training or pilot signal.

The receiver 101 comprises an estimator 103 configured to estimate a fractional frequency offset ε and an adjuster 105 configured to adjust the frequency of the multicarrier modulation signal on the basis of the estimated fractional frequency offset ε. The estimator 103 of the receiver 101 is configured to estimate the fractional frequency offset ε of the multicarrier modulation signal on the basis of the at least one training signal by using an approximation Α(ε) of a log-likelihood function λ(ε) associated with the likelihood of the fractional frequency offset ε given the multicarrier modulation signal comprising the at least one training signal. The approximation of the log-likelihood

function λ(ε) is based on the following equation:

wherein a_k denotes a set of weighting or expansion coefficients, <¾(ε) denotes a set of basis functions and K is an odd number equal to or larger than 3, corresponding to the number of dimensions in the approximation. The set of basis functions is based on the following equation:

wherein ξ_κ denotes an adjustment factor, which is smaller than one and decreases with increasing K.

Figure 2 shows a schematic diagram of a method 200 of receiving a multicarrier modulation signal, in particular an OFDM signal, over the communication channel 120, wherein the multicarrier modulation signal comprises at least one training signal. The method 200 comprises the step 201 of estimating a fractional frequency offset ε of the multicarrier modulation signal on the basis of the at least one training signal using an approximation Α(ε) of a log-likelihood function λ(ε) associated with the likelihood of the fractional frequency offset ε given the multicarrier modulation signal comprising the at least one training signal. The approximation of the log-likelihood function λ(ε) is

based on the following equation:

wherein a_k denotes a set of weighting coefficients (also referred to as expansion coefficients), denotes a set of basis functions and K is an odd number equal to or

larger than 3 and wherein the set of basis functions is based on the following equation:

wherein ξ_κ denotes an adjustment factor, which is smaller than one and decreases with increasing K. The method 200 comprises the further step 203 of adjusting the frequency of the multicarrier modulation signal on the basis of the estimated fractional frequency offset ε.

Preferred values for the adjustment factor ξ_κ as a function of K are given in the following table:

Thus, in an embodiment, the estimator 103 is configured to set the adjustment factor ξ_κ for K=3 to a value in the range from 0.56 to 0.58, in particular to a value of 0.57, for K=5 to a value in the range from 0.375 to 0.395, in particular to a value of 0.385, for K=7 to a value in the range from 0.274 to 0.294, in particular to a value of 0.284 and/or for K=9 to a value in the range from 0.213 to 0.233, in particular to a value of 0.223.

The expansion coefficients are determined making use of the following relation:

In an embodiment, the matrix A is optimized relative to corresponding matrices used in prior art solutions. The cost function to be optimized over 4 is the total approximation error. The approximation error as a function of the CFO is defined as:

Thus, the total average approximation error can be written as:

wherein denotes the expectation value (or expectation value operator) and the

average is over the statistics of the received signal s. From this, the following optimization problem results:

where the total error e is a function of the matrix A through the expansion coefficients. This optimization problem can be solved on the basis of the covariance of the log- likelihood function, which should be known in advance and which is denoted as i.e.:

The function R (ε₁₍ ε₂) is based on the same parameters as the channel estimation, namely the power delay profile of the channel and the Signal-to-Noise-Ratio (SNR). In an embodiment, the power delay profile and the SNR can be classified into different categories. For each category, the function can be computed or estimated offline

and the optimal matrix can then be found and stored. In an embodiment, the same

can be done with the channel parameters, i.e. the channel parameters can first be estimated and classified as belonging to one of these different categories. The matrix

can then be taken directly from a look-up table of matrices corresponding to that category.

Furthermore, the value K is another design parameter. In an embodiment, the value of K increases as the SNR increases. Therefore, once the SNR (e.g. of the received OFDM signal) has been estimated and classified, the corresponding value of K can directly be read from a look-up table.

Once the function has been determined, the error e can be estimated as follows:

Once all the above defined quantities are available at the receiver 101 , the frequency offset of the received signal can be estimated and corrected.

Figure 3 shows a schematic diagram illustrating different submodules as well as different steps performed by these submodules of the estimator 103 and the adjuster 105 of a receiver 101 according to a further embodiment. As can be taken from figure 3, at the wake up of the receiver 101 a set of OFDM signals is received and the integer part of the frequency offset of the CFO is estimated by the estimator submodule 103a by performing an initial acquisition. In an embodiment, at least some of the below additional processing steps implemented in the receiver 101 shown in figure 3 can be executed repeatedly over time.

In an embodiment, the integer frequency offset e_Int is corrected in the adjuster submodule 105a on the basis of the set of received OFDM signals.

In an embodiment, the current channel parameters are classified as belonging to one category of a plurality of predetermined values by the estimator submodule 103b-1 . In an embodiment, the parameters are the SNR and the power delay profile. In an embodiment, based on the previous classification, the values of K, A_opt and ξ_κ are taken from a database or look-up table by the estimator submodule 103b-2. In an embodiment, the estimator submodule 103b-3 computes K values of the true-likelihood function

In an embodiment, the estimator submodule 103b-5 is configured to recover the weighting or expansion coefficients a , ... a_k by multiplying the values of the true-likelihood function with the optimized matrix A_opt.

In an embodiment, the function can be maximized using any

standard method in the estimator submodule 103b-5 for providing the value of the fractional frequency offset ε, which can be used for correcting the fractional frequency offset ε of the received OFDM signals.

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 receiver (101 ) for receiving a multicarrier modulation signal over a

communication channel (120), the multicarrier modulation signal comprising at least one training signal, the receiver (101 ) comprising: an estimator (103) configured to estimate a fractional frequency offset ε of the multicarrier modulation signal on the basis of the at least one training signal, wherein the estimator (103) is configured to estimate the fractional frequency offset ε on the basis of an approximation of a log-likelihood function wherein the approximation of the

log-likelihood function λ(ε) is based on the following equation:

wherein a_k denotes a set of weighting coefficients,

wherein ξ_κ denotes an adjustment factor, which is smaller than one and decreases with increasing K; and an adjuster (105) configured to adjust the multicarrier modulation signal on the basis of the estimated fractional frequency offset ε.

2. The receiver (101 ) of claim 1 , wherein the estimator (103) is configured to set the adjustment factor ξ_κ for K=3 to a value in the range from 0.56 to 0.58, in particular to a value of 0.57, for K=5 to a value in the range from 0.375 to 0.395, in particular to a value of 0.385, for K=7 to a value in the range from 0.274 to 0.294, in particular to a value of 0.284 and/or for K=9 to a value in the range from 0.213 to 0.233, in particular to a value of 0.223.

3. The receiver (101 ) of claim 1 or 2, wherein the estimator (103) is configured to choose the value of K on the basis of a signal to noise ratio.

4. The receiver (101 ) of any one of claims 1 to 3, wherein the estimator (103) is configured to choose the value of K on the basis of a look-up table, wherein the look-up table assigns different values of K to different ranges of signal to noise ratios.

5. The receiver (101 ) of any one of the preceding claims, wherein the estimator (103) is configured to estimate the fractional frequency offset ε on the basis of the

approximation

of the log-likelihood function by finding a fractional frequency offset estimate, for which the approximation

of the log-likelihood function is larger than a log-likelihood threshold, in particular equal to a log-likelihood maximum.

6. The receiver (101 ) of any one of the preceding claims, wherein the estimator (103) is configured to estimate the set of weighting coefficients on the basis of a plurality of

values of the log-likelihood function at a plurality of predetermined fractional

frequency offsets

7. The receiver (101 ) of claim 6, wherein the estimator (103) is configured to estimate the set of weighting coefficients a_k on the basis of a plurality of values

of the log-likelihood function λ(ε) at the plurality of predetermined fractional frequency offsets on the basis of the following equation:

8. The receiver (101 ) of claim 6, wherein the estimator (103) is configured to estimate the set of weighting coefficients a_k on the basis of a plurality of values

of the log-likelihood function

at the plurality of predetermined fractional

frequency offsets on the basis of the following equation:

wherein the estimator (103) is configured to determine the matrix A by minimizing a measure of error between the log-likelihood function λ(ε) and the approximation of

the log-likelihood function.

9. The receiver (101 ) of claim 8, wherein the estimator (103) is configured to determine the matrix A by minimizing the measure of error e between the log-likelihood function λ(ε) and the approximation of the log-likelihood function defined by the

following equation:

wherein

denotes the expectation value and

denotes the difference between the log-likelihood function and the approximation of the log-likelihood function as a

function of the fractional frequency offset.

10. The receiver (101 ) of claim 8 or 9, wherein the matrix A is based on the following equation:

wherein

are based on the following equations:

wherein denotes a vector comprising the set of basis functions

and wherein R is the covariance of the log-likelihood function λ(ε) .

1 1 . The receiver (101 ) of any one of the preceding claims, wherein the log-likelihood function λ(ε) of the fractional frequency offset ε is based on the following equation:

wherein s denotes a vector representing the received multicarrier modulation signal, D denotes a diagonal matrix representing the frequency offset, Q denotes a matrix representing an IFFT, P denotes a diagonal matrix with the components of a vector p along its diagonal, p denotes a vector representing the at least one training signal and Λ denotes a diagonal matrix with its n-th element being given by wherein

denotes the expecation value and h[n] denotes the n-th tap of the impulse response

vector of the communication channel (120).

12. A method (200) of receiving a multicarrier modulation signal over a communication channel (120), the multicarrier modulation signal comprising at least one training signal, the method (200) comprising: estimating (201 ) a fractional frequency offset ε of the multicarrier modulation signal on the basis of the at least one training signal by using an approximation

of a log-likelihood function λ έ), wherein the approximation

of the log-likelihood function λ έ) is based on the following equation:

wherein a_k denotes a set of weighting coefficients, denotes a set of basis functions

and K is an odd number equal to or larger than 3 and wherein the set of basis functions is based on the following equation:

wherein ξ_κ denotes an adjustment factor, which is smaller than one and decreases with increasing K; and adjusting (203) the multicarrier modulation signal on the basis of the estimated fractional frequency offset ε.

13. A computer program comprising program code for performing the method (200) of claim 12 when executed on a computer.