The present invention is in the field of telecommunications and, in particular, in the field of digital signal process- ing.

Multi-carrier modulation, in particular, orthogonal fre¬ quency division multiplexing (OFDM) has been successfully applied for transmission in a wide variety of digital com- munication systems. In an OFDM transmitter, an OFDM symbol to be transmitted, the OFDM symbol comprising a number of complex values resulting from mapping a group of data val¬ ues onto signal space constellation points being associated with a chosen mapping scheme, e.g. QAM (QAM = Quadrature Amplitude Modulation) , is transformed into so-called time domain transmit signal using e.g. an inverse Fourier Trans¬ form to obtain a transmit signal to be transmitted. In or¬ der to eliminate inter-symbol interferences (ISI) and to preserve orthogonality of a received signal at a receiver, cyclic prefix is inserted into a guard interval (GI) of the transmit signal, the guard interval being preferably longer than a maximum delay of the communication channel through which the transmit signal is to be transmitted.

Fig. 13 shows, by the way of example, a block diagram of a conventional OFDM receiver. Firstly, the guard interval is removed from a signal received by an antenna. After a se¬ rial to parallel conversion (S/P) , a Fourier Transform, for example a Fast Fourier Transform (FFT) is performed in or- der to obtain a received version of the multi-carrier sig¬ nal in frequency domain.

When transmitting an OFDM modulated signal over a multi- path fading channel, the received signal will have unknown amplitude and phase variations. After OFDM demodulation the channel response is described by the channel transfer func¬ tion (CTF) for sub-carrier i, H1 = u{f = IfT)1 where 1/T de¬ notes the sub-carrier spacing. A snapshot of the magnitude and phase of the observed CTF is shown in Fig. 24 illus¬ trating that the phase of the CTF, φi = arg(Hj), experiences a phase drift, defined by

where Aφd = argji^fl*^} accounts for the phase between sub- carriers i-1 and i. The phase drift defines the average change of phase between two adjacent sub-carriers. For many applications this phase drift should be as small as possi¬ ble.

Phase drift in frequency domain results e.g. from frame synchronization errors, i.e. from timing errors introducing a phase shift in spectral domain, the phase shift increas¬ ing e.g. linearly over frequency.

It should be noted that non-perfect timing synchronization will also result in a change of the phase drift .E[A^] . In fact, if the timing offset, Toff, does not exceed the guard interval length, TGI, minus the maximum delay of the chan- nel τmax> so Toff ≤ TGI ~ τma*' there will be no loss in or¬ thogonality of the OFDM signal. However, Toff ≠ 0 will re¬ sult in a different phase drift E[Ap1], as is described in M. Hsieh and C. Wei, "Channel Estimation for OFDM Systems Based on Comb-Type Pilot Arrangement in Frequency Selective Fading Channels," IEEE Transactions on Consumer Electron¬ ics, vol. 44, pp. 217-225, Feb. 1998.

The phase drift may degrade the performance if space fre¬ quency codes or differential modulation is used. Further¬ more, the phase drift also degrades the performance of polynomial interpolation algorithms, e.g. linear or spline interpolation.

Fig. 14 shows a phase and a magnitude of a snapshot of a channel transfer function (CTF) . Fig. 15 shows a corre- spending time domain snapshot of a channel impulse response (CIR) .

The non-zero phase drift E[Aφd] is typical for any OFDM system. It is due to the structure of the channel impulse response (CIR) , which is the inverse Fourier Transform of the CTF. The CIR which generates the CTF in Fig. 14 is shown in Fig. 15. As a general property, the CIR is only non-zero within the range fθ,r, 1, where τma denotes the maximum delay of the channel, or TOff being a frame offset.

Since the CIR is related to the CTF by a Fourier Transform it may be viewed as the spectrum of the CTF.

A non-zero phase drift can degrade a performance of an OFDM system, for example in a case of a differential phase cod¬ ing. This is due to the fact that a phase drift introduces an additional phase term leading to phase errors when per- forming a differential phase demodulation, so that informa¬ tion detection errors occur.

Furthermore, the phase drift can introduce channel estima¬ tion errors when estimating the communication channel, for example when estimating the channel transfer function, in order to e.g. equalize the received multi-carrier signal in frequency domain.

In order to estimate e.g. the channel transfer function, an OFDM transmitter may introduce so-called pilot symbols be¬ ing known in the receiver for channel estimation. Usually, the pilot symbols are used for modulating sub-carriers of a OFDM signal to be transmitted. At a receiver, the pilot symbols are removed from the modulated sub-carriers by the means of demodulation, e.g. by dividing the modulated sub- carriers by corresponding pilot symbols in order to obtain sub-carrier values comprising information with respect to the channel transfer function. In Fig. 16, a block diagram of pilot symbol based channel estimation for OFDM is depicted. After transforming the re¬ ceived signal to frequency domain by the means of the Fast Fourier Transform (FFT) a transformed signal is obtained having values associated with sub-carriers, wherein only certain sub-carriers are modulated by pilot symbols for channel estimation. In order to extract the modulated sub- carriers, a de-multiplexer can be used in order to de- multiplex (DMUX) the modulated sub-carriers, which are, subsequently, provided to a channel estimator being config¬ ured for channel estimation. The channel estimator may per¬ form the pilot demodulation mentioned above in order to ex¬ tract the sub-carrier values, wherein, after having per- formed the de-modulation, the sub-carrier values are esti¬ mates of the channel transfer function at frequency points associated with sub-carriers modulated by the pilot sym¬ bols. In order to obtain a channel estimate for all sub- carriers, the channel estimator may, for example, be con- figured for performing an interpolation in order to provide channel estimates for all sub-carriers by means of interpo¬ lating between two subsequent channel estimates obtained from the modulated sub-carriers being spaced apart by a number of sub-carriers. In order to detect information con- tained by the transformed signal bypassed by the de¬ multiplexer, a detection unit (DT) is used. For example, the detection unit is configured for receiving the channel estimates in order to equalize the transformed signal. How¬ ever, if a phase drift occurs, then the channel estimates are erroneous due to an additional phase term. This leads to a performance degradation while detecting the informa¬ tion comprised by the transform signal after having equal¬ ized the transformed signal using the erroneous channel es¬ timates.

In order to reduce the phase drift, a phase compensation can be performed, as is described e.g. in M. Hsieh and C. Wei, "Channel Estimation for OFDM Systems Based on Comb- Type Pilot Arrangement in Frequency Selective Fading Chan¬ nels," IEEE Transactions on Consumer Electronics, vol. 44, pp. 217-225, Feb. 1998, for the case of channel estimation. In particular, after a DFT and after a subsequent pilot signal extraction, a least squares estimate of pilot sig¬ nals is performed in order to provide an estimated channel transfer function. In a next step, a change in phase caused by frame error is determined from subsequent values of the channel transfer function. In a next step, the estimated change in phase is removed from the estimated channel transfer function and the resulting channel transfer func¬ tion is provided to a minimum mean squared error estimator for further channel estimation. After the MMSE channel es¬ timation, the channel transfer functions of data carriers are interpolated using linear or higher order interpola¬ tions. In a next step, a phase post-compensation is per¬ formed where the previously removed phase change is re¬ stored in order to provide an interpolated channel transfer function comprising the change in phase.

For differentially modulated signals, S. M. Weinfurtner, "Frequency-Domain Frame Synchronization for Optimum Fre¬ quency-Differential De-modulation of OFDM," in Proc. IEEE Global Telecommunications Conference (GLOBECOM '99), Rio de Janeiro, Brazil, pages 857-862, 1999 discloses applying a phase correction coefficient in the differential demodula¬ tion process in order to perform a phase rotation on sub- carrier amplitudes in frequency domain for compensating frame synchronization errors.

It is the object of the present invention to provide a con¬ cept for an efficient phase drift reduction.

This object is obtained by an apparatus for reducing a phase drift according to claim 1, or by a multi-carrier re¬ ceiver according to claim 19, or by a method for reducing a phase drift according to claim 27, or by a method for re- ceiving multi-carrier signals according to claim 28, or by a computer program according to claim 29.

The present invention is based on the finding that the phase drift can efficiently be reduced when a feed-back loop phase drift reduction structure is used. More specifi¬ cally, the phase drift can efficiently be reduced when a detector for detecting the phase drift in a signal is ar¬ ranged after a phase drift compensating entity in order to detect the phase drift or a remaining phase drift in the signal provided by the phase drift compensating entity and in order to control the phase drift compensating entity in dependence on a phase drift detected in the signal via a 'feed-back loop so that e.g. in each compensation step a further phase drift reduction can be achieved.

In accordance with the present invention, the functionality of the phase drift compensating entity is comprised by a transformer for time-frequency transforming a time domain signal into a transformed signal in frequency domain. For example, the time domain signal may be a received version of a multi-carrier signal, the received version suffering from e.g. frame synchronization error. Therefore, the transformed signal representing the spectrum of the time domain signal suffers from the phase drift influencing a phase of each sub-carrier.

The detector may be configured for directly detecting the phase drift in frequency domain in the transformed signal provided by the transformer.

Alternatively, the detector may be configured for detecting the phase drift indirectly in time domain from a pre- processed time-domain signal. For example, the detector may be configured for detecting a delay resulting from a frame synchronisation error, and for calculating the phase drift resulting from the delay sing e.g. a Fourier transform. The transformed signal is provided to a detector connected to an output of the transformer for detecting the phase drift in the transformed signal, wherein the detection of the phase drift is preferably performed in frequency do- main. In accordance with the present invention, the detec¬ tor is configured for generating a control signal indicat¬ ing the phase drift upon detecting the phase drift. The control signal is then fed-back to the transformer which is configured, in response to the control signal, for pre- processing the time-domain signal in time-domain before time-frequency transforming in order to introduce a correc¬ tion phase drift to the transformed signal in frequency do¬ main, or for post-processing the transformed signal after time-frequency transforming the time domain signal in order to directly introduce the correction phase drift to the transformed signal, the correction phase drift, in both cases, at least partly compensating the phase drift so that the phase drift is reduced.

In accordance with the present invention, the transformed signal obtained from time-frequency transforming the time domain signal, e.g. obtained from applying a Fourier Trans¬ form to the time-domain signal, may be post-processed in frequency domain by e.g. manipulating the phase of the transformed signal so that a correction phase drift is in¬ troduced in frequency domain to the transformed signal, i.e. so that a correction phase is introduced to the phase of the transformed signal in order to reduce the phase drift.

In addition, the inventive transformer has the ability of pre-processing the time domain signal in the time domain in order to indirectly introduce the correction phase drift to the transformed signal resulting from transforming the time domain signal into frequency domain after pre-processing. In this case, the time delay-phase shift correspondence of a time-frequency transform, for example of a Fourier Trans¬ form, is exploited since e.g. a time delay always intro- duces an additional phase shift in a spectrum of a time de¬ layed signal.

As mentioned above, the detector is configured for detect- ing the phase drift in the transformed signal, the trans¬ formed signal resulting from transforming the time domain signal into frequency domain signal after pre-processing the time domain signal or resulting from transforming the time domain signal into frequency domain. Therefore, the phase drift can also adaptively be reduced, wherein, in a plurality of reduction steps, a phase drift remaining after a previous compensation step may be detected and reduced.

For example, in a first step, the detector receives the transformed signal comprising the uncompensated phase drift. Then, the detector determines, on the basis of the unprocessed transformed signal, the phase drift comprised by the transformed signal and generates a control signal, which is provided to the transformer for controlling the pre-processing or post-processing or both. In response to the control signal comprising e.g. information on the de¬ tected phase drift, the transformer is configured for pre¬ processing or post-processing or pre- and/or post¬ processing the transformed signal in order to reduce the phase drift. In a next step, the detector receives the processed transformed signal comprising reduced phase drift. In a next step, the detector detects the remaining phase drift comprised by the (processed) transformed signal provided by the transformer, generates a further control signal indicating the remaining phase drift and feeds the control signal back to the transformer for further reduc¬ tion of the remaining phase drift and so forth.

In addition, the phase drift can effectively be reduced when the transformer applies all inventive processing func¬ tionalities for phase drift reduction. For example, the transformer may be configured for coarsely reducing the phase drift by the means of pre-processing the time domain signal before time frequency transforming, for transforming the time domain signal after pre-processing and for post¬ processing the resulting transformed signal in frequency- domain for obtaining a fine phase drift reduction, or vice versa.

Further embodiments of the present invention will be de¬ scribed with respect to the following figures, in which:

Fig. 1 shows a block diagram of an apparatus for reduc¬ ing a phase drift in accordance with an embodi¬ ment of the present invention.

Fig. 2a shows the inventive post-processing approach;

Fig. 2b shows the inventive pre-processing approach;

Fig. 3a shows a phase of a channel transfer function;

Fig. 3b shows a magnitude of a channel transfer function;

Fig. 4 shows a corresponding spectrum of the channel transfer function of Figs. 3a and 3b;

Fig. 5 shows a block diagram of an apparatus for reduc¬ ing a phase drift in accordance with a further embodiment of the present invention;

Fig. 6 shows a block diagram of an apparatus for reduc- ing a phase drift in accordance with a further embodiment of the present invention;

Fig. 7 shows OFDM system parameters;

Fig. 8 shows a power delay profile of a channel;

Fig. 9 demonstrates a performance of the inventive ap¬ proach; Fig. 10 shows an effective channel impulse response re¬ sulting when cyclically shifting a received sig¬ nal in time domain;

Fig. 11 demonstrates the performance of the inventive ap¬ proach;

Fig. 12 shows a block diagram of the inventive apparatus for reducing a phase shift in accordance with a further embodiment of the present invention;

Fig. 13 shows a block diagram of an OFDM receiver;

Fig. 14 shows a phase and a magnitude of a channel trans¬ form functions;

Fig. 15 shows a corresponding time domain channel impulse response; and

Fig. 16 shows a channel estimation approach.

Fig. 1 shows a block diagram of the inventive apparatus for reducing a phase drift in accordance with an embodiment of the present invention.

The apparatus shown in Fig. 1 comprises a transformer 101, the transformer 101 having an input 103, a control input 105 and a plurality of outputs 107 connected to a plurality of inputs of a detector 109. The detector 109 comprises a plurality of outputs 111 and a control output 113, the con¬ trol output 113 being coupled to the control input 105 of the transformer 101.

The transformer 101 is configured for receiving a time- domain signal via the input 103. If, for example, during frame synchronization being performed in order to obtain the time-domain signal an error occurs, then a spectrum of the time-domain signal comprises a phase drift superimpos¬ ing the phase of the spectrum of the time-domain signal. For example, the phase drift may be described as a linearly increasing phase ramp superimposing the phase of the spec- trum of the time domain signal. In this case, the phase change between two subsequent spectral values is constant.

In order to reduce the phase drift affecting the spectrum of the time-domain signal, which can be a received version of a transmit signal, the transformer is configured for transforming the time-domain signal into a transformed sig¬ nal in frequency domain, the transformed signal represent¬ ing a spectrum of the time-domain signal.

The transformed signal in frequency domain comprises a num¬ ber of spectral coefficients which are provided via the plurality of outputs 107 to the detector 109 for detecting the phase drift in the transformed signal. The detector 109 is configured for detecting the phase drift in the trans- formed signal, for generating a control signal indicating the phase drift and to providing the control signal via the control output 113 to the transformer 101. In response to the control signal, the transformer 101 is configured for pre-processing the time domain signal before time-frequency transforming or for post-processing the transformed signal after time-frequency transforming the time domain signal in order to introduce a correction phase drift to the trans¬ formed signal, the correction phase drift at least partly compensating the phase drift for phase drift reduction.

In order to pre-process the time-domain signal for achiev¬ ing the effect of introducing the correction phase drift to the transformed signal after time-frequency transforming the (pre-processed) time domain signal, the transformer may comprise a delay element for delaying the time-domain sig¬ nal so that, upon exploiting the time delay/frequency shift correspondence the correction phase shift is introduced. In accordance with a preferred embodiment of the present invention, the transformer comprises, as a delay element, a cyclic shift element for pre-processing the time-domain signal, wherein the cyclic shift element is configured for receiving the control signal from the detector 109 and, in response to the control signal, for cyclically shifting the time domain signal in order to introduce the correction phase drift to the transformed signal.

For example, the cyclic shift element is configured for cy¬ clically shifting the time-domain signal by a number of values, wherein the number of values depends on the phase drift detected by the detector. For example, the detector 109 is configured for determining the number of values the time-domain signal is to be shifted by using the detected phase drift and exploiting the cyclic shift/frequency shift property of a time-frequency transform, for example of a Fourier Transform. The control signal provided to the transformer may in this case comprise the information on the number of values the time domain signal is to be shifted by.

In accordance with a further embodiment of the present in¬ vention, the detector is configured for detecting the phase shift from the transformed signal and for providing infor¬ mation on the detected phase drift to the transformer. The transformer, in response to the received information on the phase drift, may be configured for determining the number of values the time-domain signal is to be shifted by in ex- actly the same way as described above in connection with the detector 109.

Preferably, the transformer comprises a Fourier transformer coupled to an output of the delay elements, e.g. to an out- put of the cyclic shift element, for transforming the time- domain signal provided by the cyclic shift element into the transformed signal. In this case, the plurality of outputs 107 comprised by the transformer 101 corresponds to a plurality of outputs of the Fourier transformer, the Fourier transformer outputting the transformed signal comprising a number of spectral val- ues, wherein a number of the outputs 107 corresponds to the number of spectral values. In this case, the plurality of inputs of the detector is coupled to the plurality of out¬ puts of the Fourier transformer. For example, the plurality of outputs of the Fourier transformer is directly connected with the plurality of inputs of the detector 109. In order to control the pre-processing of the time-domain signal, the control output 113 of the detector 109 may be connected to a control input comprised by the cyclic shift element, so that the detector 109 directly controls the pre- processing of the time-domain signal.

As has been described above, either the detector 109 or the transformer 101 may be configured for determining the num¬ ber of values the time-domain signal is to be shifted by. For example, the number of values is determined based on an expectation value for a phase drift, which expectation value is calculated in frequency domain by, for example, averaging over a phase change between two subsequent sub- carriers. In order to obtain the number of values the time domain signal is to be shifted by, the expectation value for the phase drift may be multiplied by a number of values comprised by the transformed signal and divided by a factor of 2π , wherein the number of values of the transformed signal corresponds for example to a number of sub-carriers associated with a multi-carrier transmission scheme.

For example, the cyclic shift element is configured for performing a left shift or a right shift in dependence on a sign of the phase drift. For example, the cyclic shift ele- ment is configured for performing a left shift in order to introduce a positive correction phase drift to the trans¬ formed signal for compensating a negative phase drift, or for performing a right shift in order to introduce a nega- tive correction phase drift to the transformed signal for compensating a positive phase drift.

In order to cyclically shift the time-domain input signal, the cyclic shift element may comprise a shift register, the shift register having an input for receiving the time- domain signal and an output coupled to the input, so that a cyclic shift can be performed.

As has been mentioned above, the transformer may be config¬ ured for post-processing the transformed signal in order to introduce the correction phase drift directly in the fre¬ quency domain for compensating the phase drift. For exam¬ ple, the transformer comprises a phase compensator for post-processing the transformed signal in frequency domain, the phase compensator being configured for changing a phase of the transformed signal in frequency domain in order to introduce the correction phase drift. For example, the phase compensator is configured for multiplying each trans- formed signal value by a complex value for phase shifting the transformed signal values in frequency domain.

In accordance with an embodiment of the present invention, the transformer 101 comprises either the cyclic shift ele- ment for pre-processing the time domain signal or the phase compensator for post-processing the transformed signal. In the latter case, the transformer may comprise a Fourier transformer for time-frequency transforming the time domain signal, wherein the phase compensator is connected to an output or to a plurality of outputs of the Fourier trans¬ former, wherein the detector 109 is connected to an output or to a plurality of outputs of the phase compensator, so that the detector 109 only receives the transformed signal provided by the phase compensator, wherein . the phase com- pensator is configured for receiving the control signal generated by the detector 109 upon detecting a phase drift in the transformed signal. In order to receive the control signal, the phase compensator may comprise a control input for receiving the control signal from the detector 109. For example, the control input of the phase compensator is di¬ rectly connected to the control input 105 of the trans¬ former 101.

The compensator may be configured for adding the correction phase drift to a phase of the transformed signal for com¬ pensating a negative phase drift, or for subtracting the correction phase drift from the phase of the transformed signal for compensating a positive phase drift.

In accordance with an embodiment of the present invention, the correction phase drift to be introduced by the phase compensator may be determined by the detector 109 upon de- tecting the phase drift. Furthermore, the correction phase drift may be determined by the transformer 109 in response to information on the phase drift provided by the detector 109. For example, the correction phase drift to be intro¬ duced by the phase compensator corresponds to the phase drift detected by the detector 109, except for the sign. In accordance with a further aspect of the present invention, the transformer may comprise both: the cyclic shift element for pre-processing the time domain signal and the phase compensator for post-processing the transformed signal for two-stage reduction of the phase drift. For example, the cyclic shift element cyclically shifts the time domain sig¬ nal in order to coarsely reduce the phase drift. The time domain signal provided by the cyclic shift element is then transformed into frequency domain by e.g. a Fourier trans- former coupled to the cyclic shift element in order to ob¬ tain the transformed signal. The phase compensator is cou¬ pled to an output or to a plurality of outputs of a Fourier transformer for post-processing the transformed signal, wherein an output or a plurality of outputs of the phase compensator is coupled to the detector 109 for detecting the phase drift. Preferably, the detector 109 simultane¬ ously controls the cyclic shift element and the phase com¬ pensator for phase drift reduction. For example, the cyclic shift element is configured for re¬ ceiving the control signal from the detector, wherein the control signal indicates a number of values the time domain signal is to be shifted by in order to introduce a correc¬ tion phase drift to the transformed signal for coarsely compensating the phase drift. In response to the control signal, the cyclic shift element may be configured for cy¬ clically shifting the time domain signal by the number of values in order to coarsely compensate the phase drift.

Accordingly, the phase compensator may be configured for receiving a further control signal from the detector 109, the further control signal indicating a further correction phase drift to be introduced to a phase of the transformed signal for a fine compensation of the phase drift. In re¬ sponse to the further control signal, the phase compensator may be configured for introducing the further correction phase drift to the phase of the transformed signal.

It is to be noted that the control signal and the further control signal may be comprised by a common control signal generated by the detector 109 upon detecting phase drifts affecting the transformed signal.

As has been mentioned above, the number of values the time domain signal is to be shifted by or the correction phase drift to be added to a phase of the transformed signal may be determined by the detector 109 upon detecting the phase drift or by the transformer 101 upon receiving a control signal indicating a detected phase drift.

In order to detect the phase drift, the detector 109 may be configured for determining an average change in phase be- tween two subsequent values of the transformed signal, wherein the average change in phase represents the phase drift. For example, the transformed signal may comprise all spec¬ tral values resulting from transforming the time domain signal into frequency domain. In accordance with a further aspect of the present invention, the transformed signal may be composed of a set of spectral values associated with sub-carriers being, in a transmitter, modulated by pilot symbols for channel estimation purposes. For example, two subsequent sub-carriers being modulated by pilot symbols may be spaced apart by a number of sub-carriers being used e.g. for information transmission. In this case, the detec¬ tor is operative for detecting the phase drift from the spectral values associated with sub-carriers being modu¬ lated by the pilot symbols. In order to extract the modu¬ lated sub-carriers, the transformer may further comprise a selector, the selector being configured for selecting the sub-carriers modulated by the pilot symbols from spectral values obtained from time-frequency transforming the time- domain signal. In this case, the set of spectral values representing the sub-carriers modulated by the pilot sym- bols constitutes the transformed signal. In order to de¬ modulate the modulated sub-carriers, the transformer may further be configured for demodulating the set of spectral values constituting the transformed signal using pilot sym¬ bols wherein, by way of example only, each spectral value may be divided by an associated pilot symbol. Alterna¬ tively, each spectral value may be multiplied by a conju¬ gate complex version of the associated pilot symbol.

In order to determine the phase drift, the detector 109 may be configured for determining an average value of a product between two subsequent values of the transformed signal, wherein one of these values may complex conjugated. For ex¬ ample, the detector 109 may be configured for determining an average value of a product between a value associated with a certain sub-carrier and a complex conjugate version of a value associated with a sub-carrier preceding the sub- carrier. In order to determine the phase drift, the detector 109 may be configured for determining a phase of the average value, the phase of the average value representing the phase drift. In the case that the transformed signal comprises a set of values associated with sub-carriers being spaced apart, the phase of the average value is preferably defined by a spacing, the spacing indicating a number of sub- carriers separating two subsequent sub-carriers used for pilot symbol transmission.

In accordance with a further aspect of the present inven¬ tion, the detector may be configured for determining an av¬ erage phase change between two values of the transformed signal, the two values being spaced apart by a number of values, and for dividing the average phase change by the number of values in order to detect the phase shift for each value of the transformed signal. This case may, for example, correspond to the above-mentioned case when only certain sub-carriers are used for pilot symbol transmis- sion, and, unlike in the above embodiment, the transformer does not comprise any selector. However, the phase drift may be also derived from spectral values of the transformed signal, which are not associated with sub-carriers being used for pilot symbol transmission. In any case, a complex- ity reduction can be introduced since only a certain subset of values of the transformed signal will be used for de¬ tecting the phase drift.

The present invention further provides a multi-carrier re- ceiver comprising the apparatus for reducing a phase drift as has been described above.

Preferably, the apparatus for reducing the phase drift is configured for reducing the phase drift in a receivable multi-carrier signal in time domain and for providing a transformed signal representing a receivable multi-carrier signal in frequency domain, the transformed signal having reduced phase drift. In other words, the inventive appara- tus for reducing the phase drift is utilized for transform¬ ing the receivable multi-carrier signal in time domain into frequency domain in accordance with a multi-carrier receiv¬ ing scheme, for example OFDM, and simultaneously, for re- ducing a phase drift.

In addition, the multi-carrier receiver may comprise means for extracting information comprised by the transformed signal.

In accordance with a further aspect of the present inven¬ tion, the multi-carrier receiver may comprise a synchro¬ nizer for performing a frame synchronization in time do¬ main, wherein the phase drift results from a frame synchro- nization error due to an erroneous sample time instant be¬ ing considered the time instant determining a beginning of a frame in time domain.

In order to reduce the frame synchronization error, the de- tector 109 comprised by the apparatus for reducing the phase drift may be configured for generating a frame syn¬ chronization control signal indicating the phase drift, and providing the frame synchronization control signal to the synchronizer. The synchronizer may be configured, in re- sponse to the frame synchronization control signal, for ad¬ justing a sample time instant in order to reduce the frame synchronization error. Therefore, the detector may also control the operation of the synchronizer so that frame synchronization errors are reduced in dependence on a de- tected phase drift, wherein the synchronizer is arranged before the inventive transformer for performing a frame synchronization in time domain.

In order to reduce the remaining phase drift in frequency domain, the functionality of the apparatus for reducing the phase drift can be exploited. In accordance with a further aspect of the present inven¬ tion, the means for extracting information may comprise a differential de-modulator for differentially de-modulating the transformed signal in order to extract information from a phase change between two subsequent values of the trans¬ formed signal.

In accordance with a further aspect of the present inven¬ tion, the means for extracting information may comprise a low-pass filter for filtering the transformed signal in frequency domain. Preferably, the low-pass filter comprises real valued coefficients representing a real part of a fil¬ ter response, wherein filter coefficients representing the imaginary part of the filter response are set to zero. In this case, the transformer is further configured for pre¬ processing the receivable multi-carrier signal in time do¬ main or for post-processing the transformed signal in order to introduce a phase shift to the transformed signal for shifting a spectrum of the transformed signal towards the passband of the low-pass filter.

Therefore, frequency domain filtering using real valued filters having symmetrical two-sided filter transfer func¬ tion can be performed which further reduces a receiver's complexity.

In accordance with a further aspect of the present inven¬ tion, the low-pass filter comprised by the means for ex¬ tracting information may be configured for channel estima- tion in order to extract channel information from, for ex¬ ample, the receivable multi-carrier signal in time domain is a receivable version of a transmit signal being trans¬ mitted through a communication channel. For example, the low-pass filter is a Wiener filter for channel estimation.

In accordance with a further aspect of the present inven¬ tion, the low-pass filter is an interpolation filter for interpolating between estimated values of the channel transfer function, when the estimated values of the channel transfer function in frequency domain are associated with sub-carriers which are spaced apart by a number of sub- carriers. Tn this case, the interpolation process is per- formed in order to obtain estimates of intermediate values of the channel transfer function.

In accordance with a further aspect of the present inven¬ tion, the means for extracting information comprises a space frequency block decoder for space-frequency block de¬ coding the transformed signal in frequency domain when, in a receiver, space-frequency block coding is employed.

In the following, further embodiments of the present inven- tion will be described with respect to Figs. 2 to 12.

Fig. 2a shows an OFDM receiver with phase compensation af¬ ter Fourier Transform, wherein the receiver comprises an antenna 201 coupled to a means 203 for removing guard in- terval, the means 103 for removing the guard interval being coupled to a serial to parallel converter 205 (S/P) . The serial to parallel converter 205 has a plurality of outputs coupled to a plurality of inputs of a Fourier transformer 207, the Fourier transformer 207 being configured for per- forming a Fast Fourier Transform (FFT) . The Fourier trans¬ former 207 has a plurality of outputs coupled to a phase compensator 209, the phase compensator 209 having a plural¬ ity of inputs being coupled to a detector not shown in Fig. 2a. It is to be noted that the Fourier transformer 207 and the phase compensator 209 are comprised by the inventive transformer mentioned above.

Fig. 2b shows a block diagram of an OFDM receiver having cyclic shift before performing the Fourier Transform by the Fourier transformer 207. The cyclic shift is performed by a cyclic shift element 301 coupled between the means 203 for removing the guard interval and the serial to parallel con¬ verter 205. In this embodiment, the cyclic shift element 301, the serial to parallel converter 205 and the Fourier transformer 207 constitute the inventive transformer, wherein the plurality of outputs of the transformer 207 is coupled to the detector, which is not shown in Fig. 2b. Furthermore, it is not shown in Figs. 2a and 2b that the detector may be configured for controlling the phase com¬ pensator 209 and the cyclic shift element 301.

As is depicted in Figs. 2a and 2b, the solutions shown therein are applicable to a wide range of OFDM receivers due to the OFDM standard conform structure. Moreover, if the phase compensation is applied according to the embodi¬ ment of Fig. 2a, there is no need to compensate the induced phase shift after channel estimation and interpolation, contrary to the prior art approaches mentioned above.

In particular, the negative effects of a non-zero phase drift from (1) can be compensated by a phase compensation unit after the FFT at the OFDM receiver, as is shown in Figs. 2a and 2b.

Another possibility to solve the problem related to the one-sided spectrum of the frequency response is to match the filter response to the observed characteristics of the OFDM signal. This is indicated in Fig. 5, where the pass- band of the channel estimation filter is chosen within the range [θ, tmax]. However, this will always result in complex valued filter coefficients.

In order to obtain a channel estimate with a filter having real valued coefficients, the inventive approach described above can be applied, wherein cyclic shift at the receiver or phase compensation at the receiver can be applied. Cy¬ clic shifts in the receiver are known from M. I. Rahman, K. Witrisal, D. Prasad, O. Olsen, and R. Prasad, "Performance Comparison between MRC Receiver Diversity and Cyclic Delay Diversity in OFDM WLAN Systems, "in Proc. Int. Symposium on Wireless Personal Multimedia Communications (WPMC'03), Yo- kosuka, Japan, Oct. 2003 and from A. Damrtiann and S. Kaiser, "Standard Conformable Antenna Diversity Techniques for OFDM and its Application to the DVB-T System," in Proc. IEEE Global Telecommunications Conference (GLOBECOM 2001) , San Antonio, TX, USA, pages 3100-3105, Nov. 2001, wherein cy¬ clic shift is applied on the receiver side in order to ex¬ ploit spatial diversity. In accordance with the present in¬ vention, however, cyclic delays are not inserted in order to exploit spatial diversity, but in order to reduce phase drift or to obtain filter having real valued filter coeffi¬ cients.

We propose to cyclically shift the received signal before the FFT, as shown in Fig. 2b. Cyclically shifting the re- ceived signal by - δcyc samples before the FFT results in the following phase shift after the FFT:

θcyc = 2πδcyc/NFFT (2 )

Fig. 3a shows a phase of a channel transfer function (CTF) after cyclically shifting a time domain signal before FFT. Fig. 3b shows a corresponding magnitude of the channel transfer function.

The effect of the cyclic shift to the received signal is Y1 = Ydej9cycl . If δcyc is chosen according to (2), the effect to the received signal is identical, regardless whether a phase compensation after the FFT (Fig. 2a) or a cyclic shift before the FFT (Fig. 2b) is chosen.

In contrast to the cyclic shift operation as proposed in Fig. 2b, a phase shift according to Fig. 2a is more compu¬ tationally complex. While a cyclic shift can be performed very efficiently using a shift register of — Scyc samples, a phase compensation of θcyc degree per sub-carrier requires one multiplication by ejθcyai per sub-carrier. On the other hand, given the overall complexity of an OFDM receiver, one additional multiplication per sub-carrier may not be that significant.

Note, the cyclic shift only changes the phase of the CTF, the magnitude remains unaffected. This can be checked by comparing the CTF of an OFDM signal without and with cyclic shift shown in Figs. 14, 3a and 3b. Since the effects of the frequency selective channel are compensated by the channel estimator anyway, no other operations are neces- sary.

A snapshot of the magnitude and phase of the CTF and the corresponding CIR after cyclically shifting the received signal is shown in Figs. 3a, 3b and Fig. 4, respectively. While there are still strong variations in amplitude and phase due to frequency selective fading, the phase drift E[A^1] is compensated. The effective CIR of Fig. 4 is shifted towards negative delays. Instead of a one-sided spectrum, the received signal now has a two-sided spectrum.

The cyclic shift at the receiver side can also be applied to channel estimation based on the discrete cosine trans¬ form (DCT) . Since the DCT operates on a two-sided spectrum, the cyclic shift before OFDM demodulation may be very bene- ficial.

For pilot-symbol aided channel estimation (PACE) known sym¬ bols (pilots) are inserted, with an equidistant spacing of Df sub-carriers. In order to reconstruct the signal, fil- tering and interpolation between the pilots is necessary. For channel estimation the received signal After OFDM de¬ modulation at the pilot positions, H1 = Hi~D + N~D , with i are used. An FIR filter with dimension Mf can be written in the general form

If the symmetries of the spectrum of W1n are such that the real and imaginary parts are an even and odd function, re¬ spectively, the coefficients of FIR interpolation and/or smoothing filters will be real valued. In general a real valued filter will only have half the computational cost of a complex valued filter.

In P. Hδher et al, ,,Pilot-Symbol-Aided Channel Estimation in Time and Frequency", in Proc. Communication Theory Mini- Conference (CTMC) within IEEE Global Telecommunications Converence (Globecom 97), Phoenix, AZ, USA, pp.90-96, 1997, PACE by Wiener filtering was proposed.

In accordance with a further aspect of the present inven- tion, if a Wiener interpolation filter (WIF) with model mismatch is chosen, the filter W = ψi/ '" /WM j is designed such that it covers a great variety of power delay pro¬ files. Accordingly, a rectangular shaped power delay pro¬ file with maximum delay Tw fulfils this requirement. The Fourier Transform of a uniform power delay profile, which is non-zero within the range [0, Tff], yields the frequency correlation

} = T sin(πTw Ai/τ) ^^ (4}

Due to the complex phase term in f?OT[Δi] the corresponding Wiener filter will also have complex coefficients.

However, a complexity of a filtering operation or of a channel estimation operation when using filter having com¬ plex valued coefficients is insignificantly increased when compared with filtering or channel estimation using filters having real valued coefficients only.

Suppose the CIR without cyclic shift is within the range [O5T1113x] then a cyclic shift of - δcyc, denoting a left shift, will result in an effective CIR which is non-zero within the range [- δcyc, τmax - Scyc] , If the cyclic shift is chosen such that

*«. - 3 ( 5 )

the effective CIR will now be non-zero only within the passband of the channel estimation filter. Given a filter with low-pass characteristics, having a symmetric two-sided passband within the range the effective CIR of the cyclically shifted signal will pass through the filter undistorted, as illustrated in Fig. 4. If the maximum delay of the channel τmax can be estimated, Tw could be chosen according to Tw =rmax+Aw, where Aw accounts for a roll-off delay, which may be inserted to non-perfect slope of the filter response. On the other hand, if rmax is not known it can be upper bounded by TGI , so Tw = TGJ .

Now we can use a real valued frequency correlation function to generate the filter coefficients

^][Ai] = T Sin^ Ai^ (6) πTwAi

Therefore, the WIF matched to the uniform power delay pro¬ file [-Tw/2,Tw/2] is also real valued. This means that the computational cost is cut by half.

Alternatively to a mismatched WIF any FIR low pass interpo- lation filter benefits from the proposed cyclic shift. As long as the filter is matched to a passband of the filter will be real valued. For such a filter, the per¬ formance will be optimum if the signal to be filtered passes through the filter unchanged.

Fig. 5 shows an OFDM receiver with phase compensation after the FFT in accordance with a further embodiment of the pre¬ sent invention. Unlike the embodiment of Fig. 2a, the OFDM receiver shown in Fig. 5 comprises a phase compensator 501 having a plu¬ rality of outputs coupled to a detector 503, the detector 503 having a control output 505 coupled back to a control input of the phase compensator for providing information on the detected phase drift Θcyc-

Fig. 6 shows an OFDM receiver with cyclic shift before the FFT. Unlike the embodiment shown in Fig. 2b, the OFDM re¬ ceiver shown in Fig. 6 comprises a cyclic shift element 601 coupled between the means 203 for removing guard interval and the serial to parallel converter 205, and a detector 603 coupled to the plurality of outputs of the Fourier transformer 207, wherein the detector 603 comprises a con¬ trol output 605 coupled back to a control input of the cy¬ clic shift element 601 for providing information on the number of values the time domain signal provided by the means 203 for removing the guard interval is to be shifted by.

Dependent on the application the cyclic shift may be chosen to compensate the phase drift of (1) , that is

Scyc = E[AΨi] • ^ ( 7 )

OFDM systems with differential modulation or space- frequency coded OFDM systems will have an improved perform- ance if E[Δ^] is estimated sufficiently well.

In order to integrate this phase drift compensation in the proposed receiver structure, an adaptive implementation ap¬ pears attractive, as shown in Fig. 5. For the proposed re- ceiver performing a cyclic shift before the FFT, this solu¬ tion can be implemented as shown in Fig. 6. Initially, the cyclic shift, δcyc may be set to a default value within the range [θ, TGI/2] . Then, δcyc can be estimated and fed back to the cyclic shifting unit. Note, the phase drift is expected to change only on a long term basis, so no frequent updates are necessary.

In the following, a performance of the inventive approach for space-frequency block codes (SFBC) will be described.

In order to generate BER curves, an OFDM system using a space-frequency block code (SFBC) with Nτ = 2 transmit an- tennas has been implemented. An OFDM system with Nτ = 2 transmit and NR = 1 receive antennas is used. The system parameters of the OFDM system and of the channel model are shown in Fig. 7. The channel is modelled by a tap delay line model with Q0 = 12 taps, a tap spacing of Δr = 16 • Tspl , with an exponential decaying power delay pro¬ file, illustrated in Fig. 8. The total transmit power of the system is fixed, such that the total transmit power of a Nτ antenna system is equivalent to a single antenna sys¬ tem. No outer channel coding has been employed.

It is seen that for the considered system the BER floor can be somewhat reduced by optimizing the cyclic shift δcyc . For the considered parameters the optimum cyclic shift is about 44Tspi, which result in the best performance. It can also be seen that the accuracy of 6cyc does not need to be high.

In accordance with the present invention, a performance of a polynomial interpolator can significantly be optimized. For PACE interpolation in frequency and time direction is necessary. While in time direction the Doppler power spec¬ trum has in general a symmetric two-sided and real valued profile (at least approximately) , the power delay profile is real valued but one-sided. In the following, the benefit of inserting a cyclic shift, S^0 will be described for a linear interpolator. The results are applicable for higher order polynomial interpolators as well. Fig. 9 shows BER vs Eb/N0 for Nτ = 2, and various cyclic shifts δcyc .

In accordance with the present invention, a performance of a polynomial interpolator can significantly be optimised. For linear interpolation, two successive pilot sub-carriers are used to determine the channel response for sub-carrier located in between these two pilots. For sub-carrier i, the channel estimate is given by

It is instructive to describe linear interpolation by a FIR filter from (3) . A linear interpolator can be described by the filter response

Inserting W^11"^ into FIR filter equation from (3) will ac¬ complish linear interpolation. The distortion imposed by the linear interpolator can be assessed by considering the spectrum of (8), i.e. the inverse Fourier Transform of wlUn], given by

W'"%)=^DffI^ssiinn(f(2π^τ/2f)lJ (9)

The spectrum of the linear interpolator is plotted in Fig. 10. First of all, a higher over-sampling rate compared to an ideal low-pass filter will be required. Second, for the best performance the spectrum of the signal to be in¬ terpolated should be concentrated around τ = 0 Since, the CIR is zero only within the range [CVrΛax], a cyclic shift of δcyc = according to (7), will improve the interpo¬ lation performance.

Fig. 10 shows a time domain channel impulse response snap shot after cyclically shifting the signal before the FFT. In Fig. 10, also a frequency response of a linear interpo¬ lator is shown.

Fig. 11 shows MSE vs SNR for polynomial interpolation algo- rithms with a cyclic shift of 3cyc=0 (dashed lines) and <5^c=44 (solid lines) .

In the following, a performance of the inventive approach for some polynomial interpolation algorithms will be de¬ scribed. In Figure 13 the MSE is plotted against the SNR for various polynomial interpolation algorithms. It is seen that the linear interpolator with cyclic shift has a sig¬ nificantly lower error floor. The same is true for the spline interpolator, which gets close to the optimum Wiener filter if a cyclic shift is inserted.

In the following, further advantages associated with the inventive concept will be indicated.

Possible applications of the proposed cyclic shift at the OFDM receiver are e.g.:

• Providing real valued filter coefficients for PACE. This will cut the number of required multiplication per channel estimate by a factor of two, with identi¬ cal performance.

• Improving the performance of polynomial interpolation algorithms. The error floor caused by the interpola¬ tion error of polynomial interpolation algorithms can be improved significantly. • Improving performance of differentially modulated sig¬ nals and space frequency codes.

Compared to inserting a phase shift, which requires one complex multiplication per sub-carrier, a cyclic shift op¬ eration is significantly easier to implement. Furthermore, no post-processing after channel estimation and/or demodu¬ lation is required. For instance, the solution proposed in M. Hsieh and C. Wei, "Channel Estimation for OFDM Systems Based on Comb-Type Pilot Arrangement in Frequency Selective Fading Channels," IEEE Transactions on Consumer Electron¬ ics, vol. 44, pp. 217-225, Feb. 1998.requires an additional multiplication per sub-carrier after interpolation.

In the following, orthogonal frequency division multiplex¬ ing (OFDM) will be described.

For OFDM the signal stream is divided into Nc parallel sub-streams, typically for any multi-carrier modulation scheme. The ith sub-stream, commonly termed sub-carrier, of the 2th symbol block, named OFDM symbol, is denoted by XlΛ . An inverse DFT with N FFT points is performed on each block, and subsequently the guard interval having NGI sam¬ ples is inserted to obtain xlrn . After D/A conversion, the signal x(t) is transmitted over a mobile radio channel with response h(t, τ) . Assuming perfect synchronization, the re¬ ceived signal of the equivalent baseband system at sampling instants t = [n + £Nsym}rspl is in the form

Yt,n = y(fr + *WsymJrβpI) = £ h(t, τ) • x(t - τ)dτ + n(t) \t=[n+eNsyaKl ( 10 )

where n(t) represents additive white Gaussian noise, and Nsym = NFFT + NGI accounts for the number of samples per OFDM symbol. At the receiver, the guard interval is removed and the information is recovered by performing a DFT on the re¬ ceived block of signal samples, to obtain the output of the OFDM demodulation Yt/i . The received signal after OFDM de¬ modulation is given by

where XlΛ and H11 denotes the transmitted information sym¬ bol and the channel transfer function (CTF) at sub-carrier i of the £th OFDM symbol, respectively. The term N(ti ac¬ counts for additive white Gaussian noise (AWGN) with zero mean and variance W0. It is assumed that the transmitted signal consists of L OFDM symbols, each having Nc sub- carriers.

We focus on channel estimation in frequency direction (sub- carrier index i) . Thus, the index denoting the OFDM symbol, I1 will be dropped in the following.

We consider a time-variant frequency selective fading chan¬ nel, modeled by a tapped delay line with Q0 non-zero taps. It is generally assumed that the channel is time limited by the maximum delay τmax . Then the channel impulse response (CIR) h(t,τ) is zero outside the range [θ, τmax]. It is com¬ monly assumed that the channel impulse response (CIR) is approximately constant during one OFDM symbol, so the time dependency of the CIR within one OFDM symbol can be dropped, i.e. h(t, τ) « h(τ) .

The channel transfer function (CTF) of (11) , is the Fourier Transform of the CIR h{μ)(τ). Sampling the result at fre- quency f = i/T , the CTF at sub-carrier i is defined by E1 = H(f = i/T), where H(f) accounts for the analog CTF, and Tsym NFFTTspl represents the OFDM sym¬ bol duration with and without the guard interval, respec¬ tively.

If the guard interval is longer than the maximum delay of the channel, i.e. TGI > τmax, the orthogonality at the re- ceiver after OFDM demodulation is maintained, and the re¬ ceived signal of (11) is obtained.

In the following, an OFDM receiver with a cyclic shift at the receiver side will be described.

In this section the effective channel model after the cy¬ clic shift operation before the FFT. After the cyclic pre¬ fix is removed the received signal from (10) is cyclically delayed by - Scyc samples

= £ h(t + δcycTspl - T) • x(τ)dτ + π(t + δcycTspl) \t=nTspl ( 12 )

It is instructive to define an effective CIR, which de¬ scribes the equivalent CIR of the cyclically shifted signal

= h(τ + £cycrspI) ( 13 )

While the maximum delay of the channel τmax is not changed, the effective CIR, 2itcyol(τ) , is now non-zero within the range

The FFT translates a cyclic delay into phase shifts. The effective CTF of the cyclic receiver is described by

Jjfcyc] — JJ e32πlδcyc/NFFT ( 14 )

Now the cyclically shifted received signal after OFDM de¬ modulation can be expressed as

Y. = X.Hl°yc] + N . = Z.Hiej2)ri^c/N"r + N1 ( 15 )

In the following, the principles of pilot-symbol aided channel estimation for OFDM will be described For pilot-symbol aided channel estimation (PACE) , known symbols (pilots) are multiplexed into the data stream, which are used as side information to estimate the channel. PACE was first introduced for single carrier systems and required a flat-fading channel. To describe pilot symbol- assisted channel estimation it is useful to define a subset of the received signal sequence containing only the pilots, {χ[μ)} = {x[μ)}r with i = ΪDf. So, the pilot sequence is trans¬ mitted at a Df times lower rate i = in frequency di- rection. (As a general convention, variables describing pi¬ lot symbols will be marked with a ~ in the following. ) It is assumed that the pilots X1 are chosen from a PSK con¬ stellation, so X1 = 1.

After OFDM demodulation, the received signal Y1 of (11) is obtained. For channel estimation the received signal at the pilot positions are de-multiplexed from the data stream, to obtain the received pilot sequence

Y. = XιHχ~ + N- = X1H1 + N1, with {i} e G ( 16 )

where G is the subset of the OFDM frame containing the pi¬ lots.

In the following, OFDM channel estimation by FIR filtering will be described.

The first step in the channel estimation process is to re¬ move the modulation of the pilot symbols, which provides an initial estimate of the CTF at pilot positions

H- = X1-Y1- = H1- + X1~*N~ (17)

The channel estimator uses the demodulated pilots H1 from (17) to yield the channel estimate

where Mf denotes the filter order, i.e. the number of co¬ efficients of the FIR filter W1n .

The FIR filter W = [W0, ••• r WM ^1J may be implemented as e.g. low-pass interpolation filters, polynomial interpolators, or Wiener interpolation filters. The Wiener interpolation filter minimizes the mean squared error (MSE) between the desired response H1 and the observation, i.e. the received pilot symbols. This means that knowledge about the channel statistics is required. In contrast, low-pass interpolation filters and polynomial interpolators do not assume any knowledge of the channel statistics.

For multi-carrier systems the observed channel is typically correlated in two dimensions, frequency and time. Moreover, the extension to PACE in two dimensions is possible.

In the following, Wiener filtering will be described.

The Wiener interpolation filter (WIF) is implemented by a FIR filter with Mf taps, according to (18) . The WIF, W'[Ai] , is obtained by solving the Wiener-Hopf equation

In order to generate WIF, knowledge of the auto-correlation matrix and the cross-correlation vector are required

RS'B = ΦHH] = RM' + N0I e c"'"*' R^1 [Ai] = E(H1H11] = RH'S[Ai] e C^

The entry of the mth row and nth column of the auto¬ correlation matrix of the CTF at pilot positions is given by KHL,Π - ΦiJU = 4v«>>A--)J = SLEK" - nM (21 )

Provided the channel can be described by a tap delay line, the frequency correlation, Rm' [(m ~ n)DA between sub- carriers spaced Af = Ai/T Hz apart becomes

RH'H[M] L RW' (M/T) = ∑ σje-^' Δi/r ( 22 ) g=l

The mth entry of the cross-correlation vector -Ffø[ΔiJ = E[H.HH] can be expressed as

In the following, the inventive mismatched estimator will be described

For the WIF the auto and cross-correlation functions need to he estimated at the receiver. It may be prohibitive to estimate the filter coefficients during operation in real time. Alternatively, a robust estimator with a model mis- match may be chosen. The filter W is designed such that it covers a great variety of power delay profiles. For exam¬ ple, a rectangular shaped power delay profile with maximum delay Tw fulfils this requirement. This assumption provides the frequency correlation function of the mismatched esti- mator, E^yc)[Δi], from (6) . The mismatched estimator is de¬ termined by substituting from (6) into (21) and (23) . Then the Wiener-Hopf equation (19) needs to be deter¬ mined only once. By using a mismatched estimator the filter coefficients can be pre-computed and stored.

It is important to note that the parameters of the robust estimator should always be equal or larger than the worst case channel conditions, i.e. largest propagation delays and maximum expected velocity of the mobile user. Further¬ more, the average SNR at the filter input, γw , which is used to generate the filter coefficients, should be equal or larger than actual average SNR, so γn ≥ γc . In order to determine the channel estimator only Tn , FN , and γw are required. If the maximum delay of the channel τmax is not known it can be upper bounded by the guard interval dura¬ tion TGI . Since the filter should also satisfy the sampling theorem, the filter pass-bands can be chosen within the range

T^max <— T-1W —< T-1GI —< TxIlDuf (K2^-4^)J

In the following, estimating the phase drift will be de- scribed

The phase drift, specifies the average change in phase between two adjacent sub-carriers, as defined in (1) . One possibility to estimate the phase drift is

f 1 w 1 Δ& = argj- - ∑ HJtx A * E[A(P1] (25 ) L-W "~ -L i=2 J

which provides a sufficiently accurate estimate. More so¬ phisticated algorithms to estimate E[Aq)1] are described in S. Kay, "A Fast and Accurate Single Frequency Estimator", IEEE Transactions in Acoustics, Speech and Signal Process¬ ing", vol. 37, pp. 1987-1990, December 1989.

Obviously, the CTF H1 is not available at the receiver. Instead a noisy estimate of H1 can easily be generated by H1 « , where X1 is a hard decision of X1. The accuracy of (25) will degrade due to noise and decision feedback ef¬ fects. Fortunately, Aq)1 does not need to be particularly accurate.

If pilot symbols are transmitted, e.g. for channel estima¬ tion, the phase drift may be estimated by

where Hj was defined in (17) . The division through Df be¬ comes necessary, since the pilots are spaced Df sub- carriers apart, i.e. Df times the phase drift is esti¬ mated.

Fig. 12 shows a further embodiment of an OFDM receiver in accordance with the present invention.

Unlike the embodiment of Fig. 2a, the OFDM receiver shown in Fig. 12 comprises a de-multiplexer 1201 for de- multiplexing sub-carriers being modulated by pilot symbols for channel estimation. Optionally, the de-multiplexer 1201 (DMUX pilots) is configured for demodulating the sub- carriers being modulated by the pilot symbols. The de¬ multiplexer has an output coupled to the inventive appara- tus 1203 for reducing the phase drift. The apparatus 1203 for reducing the phase drift is coupled to a channel esti¬ mator 1205 being configured for estimating the channel transfer function in frequency domain. The channel estima¬ tor is coupled to means 1207 being configured for introduc- ing back the compensated phase shift so that all channel influences may be taken into account. The means 1207 for phase post-compensation is coupled to a means 1209 for ex¬ tracting information comprised by a transformed signal pro¬ vided by the FFT 207. In other words, the means 1209 for extracting information is configured for determining an in¬ formation amount comprised by a signal provided by the de¬ multiplexer 1201.

In accordance with a further aspect of the present inven- tion, the apparatus 1203 for reducing the phase drift (phase drift compensator) may be configured for providing a signal containing information on the phase drift to the means 1207 for phase post-compensation, so that in response to the signal provided by the apparatus 1203, phase post- compensation can be performed.

Moreover, the present invention provides concepts for fil- tering and interpolation for OFDM. Generally, the frequency response of the received signal after OFDM demodulation has a one-sided spectrum. By cyclically shifting the received signal before the FFT, the one-sided spectrum can be trans¬ formed into a symmetric two-sided spectrum. In general, the performance of standard interpolation algorithms such as linear or spline interpolation can be improved if the cy¬ clic shift is appropriately chosen. Furthermore, the per¬ formance of space frequency codes and differential modula¬ tion can also be improved. If the symmetries of the two- sided spectrum are such that the real and imaginary parts are an even and odd function, respectively, the coeffi¬ cients of FIR interpolation and/or smoothing filters become real valued, which cuts the computational cost by half.

Moreover, depending on certain implementation requirements of the inventive methods, the inventive methods can be im¬ plemented in hardware or in software. The implementation can be performed using a digital storage medium, in par¬ ticular a disk or a CD having electronically readable con- trol signals stored thereon, which can cooperate with a programmable computer system such that the inventive meth¬ ods are performed. Generally, the present invention is, therefore, a computer program product with a program code stored on a machine-readable carrier, the program code be- ing configured for performing at least one of the inventive methods, when the computer program products runs on a com¬ puter. In other words, the inventive methods are, there¬ fore, a computer program having a program code for perform¬ ing the inventive methods, when the computer program runs on a computer.