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WO2006018034A1 - Dispositif de filtre et procede de filtrage de domaine frequentiel - Google Patents

Dispositif de filtre et procede de filtrage de domaine frequentiel Download PDF

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Publication number
WO2006018034A1
WO2006018034A1 PCT/EP2004/009372 EP2004009372W WO2006018034A1 WO 2006018034 A1 WO2006018034 A1 WO 2006018034A1 EP 2004009372 W EP2004009372 W EP 2004009372W WO 2006018034 A1 WO2006018034 A1 WO 2006018034A1
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WO
WIPO (PCT)
Prior art keywords
signal
filter
pass
channel
low
Prior art date
Application number
PCT/EP2004/009372
Other languages
English (en)
Inventor
Günther Auer
Original Assignee
Ntt Docomo, Inc.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Ntt Docomo, Inc. filed Critical Ntt Docomo, Inc.
Priority to PCT/EP2004/009372 priority Critical patent/WO2006018034A1/fr
Publication of WO2006018034A1 publication Critical patent/WO2006018034A1/fr

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Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0224—Channel estimation using sounding signals
    • H04L25/0228—Channel estimation using sounding signals with direct estimation from sounding signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0224—Channel estimation using sounding signals
    • H04L25/0228—Channel estimation using sounding signals with direct estimation from sounding signals
    • H04L25/023—Channel estimation using sounding signals with direct estimation from sounding signals with extension to other symbols
    • H04L25/0232—Channel estimation using sounding signals with direct estimation from sounding signals with extension to other symbols by interpolation between sounding signals
    • H04L25/0234—Channel estimation using sounding signals with direct estimation from sounding signals with extension to other symbols by interpolation between sounding signals by non-linear interpolation

Definitions

  • the present invention is in the field of digital signal processing and, in particular, in the field of digital fil- tering in frequency domain.
  • Multi-carrier modulation in particular orthogonal fre ⁇ quency division multiplexing (OFDM) has been successfully applied to transmitting information in a plurality of digi- tal communication systems.
  • OFDM orthogonal fre ⁇ quency division multiplexing
  • QAM Quadrature Amplitude Modulation
  • the number of complex values are further processed using e.g. an Inverse Fourier Transform (IFT) . Therefore, the number of complex values representing the plurality of data values is considered as being a frequency domain signal since each complex value is associated with a sub-carrier appointed to a certain frequency point.
  • IFT Inverse Fourier Transform
  • Fig. 13 shows a block diagram of an OFDM receiver utilizing a Fast Fourier Transform (FFT) for time-frequency trans ⁇ forming.
  • FFT Fast Fourier Transform
  • the received, so called time domain signal is transformed into a transformed signal in the so- called frequency domain by the means of e.g. the Fast Fou ⁇ rier Transform.
  • the transformed signal represents a re- ceived version of the number of complex values obtained from mapping data values onto signal space constellation points.
  • the transformed signal represents a one-sided spectrum of the received time domain OFDM signal.
  • the transformed signal being a received ver ⁇ sion of the number of complex values comprises at least partly the transmitted information. Therefore, the trans- formed signal in the so-called frequency domain is a signal having a certain spectrum. If, for example, a Fourier Transform is applied for transforming the transformed sig ⁇ nal, then a spectrum of the transformed signal obtained from the Fourier Transform is, due to Fourier Transform rules, closely related to the received time domain signal.
  • a channel transfer function In frequency domain, an influence of the communication channel can be described by a channel transfer function, which, generally, is complex.
  • Fig. 14 by the way of ex- ample only, a phase of a channel transfer function and a magnitude of the channel transfer function are shown.
  • Fig. 15 shows a corresponding spectrum of the channel transfer function of Fig. 14, wherein the corresponding spectrum is the time domain channel impulse response being only non-zero within the range left [0, ⁇ ma ⁇ ] , where ⁇ max de ⁇ notes the maximum delay of the channel. From this point of view, the spectrum of the channel transfer function is one sided and has a band-pass characteristic.
  • proc ⁇ essing signals in the so-called "frequency domain” is often associated with complex signal processing structures, like for example complex filters, in order to e.g. equalize the received OFDM signal, corresponding to the transformed sig ⁇ nal mentioned above, in frequency domain.
  • filter ⁇ ing complex valued signals using complex filters having complex valued coefficients is associated with a high com ⁇ putational complexity since complex convolution operations need to be performed.
  • the channel transfer function is to be estimated.
  • known pilot symbols are used in the transmitter for modulating sub- carriers, wherein, in a receiver, the corresponding re ⁇ ceived sub-carriers are de-modulated using the (known) pi- lot symbols in order to obtain sub-carrier values compris ⁇ ing information on the channel transfer function at fre ⁇ quency points being associated with sub-carriers being modulated by pilot symbols.
  • the sub-carrier values already comprise an estimate of the channel transfer func ⁇ tion for the modulated sub-carriers, a further estimate of the channel transfer function with a better accuracy can be obtained when e.g. filtering the channel transfer estimate using e.g. Wiener filters.
  • Fig. 16 shows a block diagram of an OFDM receiver wherein, after FFT, the sub-carriers being modulated by pilot sym ⁇ bols are de-multiplexed (DMUX pilot) and provided to a channel estimation unit being configured for estimating the channel transfer function on a basis of the de-multiplexed sub-carriers.
  • the estimator of the channel transfer func ⁇ tion is then provided to a means for extracting information (DET) , the means for extracting information being config- ured e.g. for equalizing the frequency domain signal using the estimate of the channel transfer function.
  • DET means for extracting information
  • the estimate of the channel transfer function does not comprise any information on channel transfer coefficients at frequency points associ ⁇ ated with sub-carriers, which are not used for pilot symbol transmission.
  • the estimate of the channel transfer function can be interpolated using e.g. interpolation filters. How ⁇ ever, this operation is associated with an increased com ⁇ plexity since the interpolation filter are complex in order to interpolate between complex values of a signal having a band-pass characteristic.
  • the present invention is based on the finding that complex ⁇ ity reduced frequency domain filtering can be achieved when using filters having real valued coefficients only, pro ⁇ vided that a spectrum of a frequency received signal is shifted towards a pass-band of the filter.
  • the present invention exploits the fact that a spectrum of a real valued filter response is two-sided and symmetric.
  • the transformed signal resulting from time-frequency transforming a time domain signal either the time domain signal is pre-processed in time domain, or the transformed signal is post-processed in frequency do ⁇ main, or the time domain signal is pre-processed in time domain and the transformed signal is post-processed in fre ⁇ quency domain.
  • the time domain signal is de ⁇ layed in time domain, for example cyclically delayed, so that a phase shift is introduced to the transformed signal resulting from time-frequency transforming the time domain signal after pre-processing.
  • a phase of the transformed signal may be post-processed in order to di ⁇ rectly introduce a phase shift to the transformed signal for influencing its spectrum. It is an advantage of the present invention that, in fre ⁇ quency domain, real valued filter can be used for filter ⁇ ing, which significantly reduces e.g. a receiver's complex- ity.
  • a width of a pass-band of the frequency domain filter may be chosen, e.g. by approximating a rectangular shape, such that a width of the pass-band optimally matches a spectral range occupied by the transformed signal to be filtered or even coincides with the spectral range so that an accurate frequency domain filtering can be performed.
  • Fig. 1 shows a block diagram of a filter apparatus for frequency domain filtering in accordance with an embodiment 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 o'f 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
  • Fig. 16 shows a channel estimation approach.
  • Fig. 1 shows a block diagram of a filter apparatus for fre ⁇ quency domain filtering in accordance with an embodiment of the present invention.
  • the filter apparatus comprises a transformer 101, the transformer 101 having an input 103 and an output 105, the output 105 of the transformer 101 being coupled to a low- pass filter 107, the low-pass filter 107 having an output 109.
  • the transformer 101 is configured for time-frequency trans ⁇ forming a time domain signal being provided to the trans ⁇ former 101 via the input 103 into a transformed signal into frequency domain, the transformed signal being provided via the output 105 of the transformer 101 to the low-pass fil- ter 107.
  • the low-pass fil ⁇ ter 107 comprises only real-valued filter coefficients rep ⁇ resenting the real part of a filter response, wherein fil- ter coefficients representing an imaginary part of the fil ⁇ ter response are set to zero.
  • the filter has a filter response, which is only real valued.
  • the transformer is configured for pre-processing the signal before time- frequency transforming, i.e. for pre-processing the time domain signal, or for post-processing the transformed sig ⁇ nal before filtering, the transformed signal 'resulting from time-frequency transforming the time domain signal in order to introduce a phase shift to the transformed signal for shifting a spectrum of the transformed signal towards a pass-band of the low-pass filter.
  • Fig. 1 fur- ther shows a magnitude M of a transformed signal 111 pro ⁇ vided by the transformer 105 after pre- or post-processing
  • the transformed signal being provided by the transformer 101 has a spectrum 113, which spectrum is two-sided and symmetric with respect to an origin of an axis f' .
  • a spectrum 115 of a transformed signal prior to pre- or post-processing is shifted in the shift direction as depicted by the arrow towards a pass-band 117 of the low-pass filter 107, wherein the pass-band 117 is symmetric and two-sided with respect to the origin of the axis f , wherein M' denotes a magnitude in the f' region.
  • the transformer 101 is configured for pre-processing the time domain signal and/or for post ⁇ processing the transformed signal after time-frequency transform in order to manipulate the spectrum of the re ⁇ sulting transformed signal in the frequency domain f .
  • the transformed signal may be considered as a set of values, wherein each value of the transformed signal is as ⁇ sociated with a frequency point. Nevertheless, the set of values represents a signal which can be filtered using a convolution operation. Since the filter coefficients are real valued only, a complex convolution operation can be avoided.
  • the transformer 101 is configured for pre ⁇ processing the time domain signal or for post-processing the transformed signal in order to shift the spectrum of the transformed signal by a spectrum distance of half the width of the pass-band of the low-pass filter 107, the pass-band being symmetric with respect to an origin in the f region.
  • the transformer 101 may be configured for pre-processing the time domain signal or for post ⁇ processing the transformed signal in order to shift the spectrum of the unprocessed transformed signal by a spec ⁇ trum distance of half the band width of the transformed signal.
  • the transformer is configured for shifting the spectrum of the transformed signal such that a resulting spectrum is symmetric with respect to the origin, so that the spectrum of the resulting transformed signal coincides with the pass-band of the low-pass filter 107 or, at least, overlaps with the pass-band.
  • the time domain signal is a received version of a transmit signal, the transmit signal being transmitted through a communication channel from a transmitting point to a receiving point, the receiving point comprising the inventive apparatus for frequency domain filtering.
  • the transmit signal is a time domain transmit sig ⁇ nal resulting from frequency-time transforming a multi- carrier signal in frequency domain for multi-carrier trans ⁇ mission, for example, for multi-carrier wireless transmis ⁇ sion.
  • a width of the pass-band of the low-pass filter 107 may be determined by a maximum channel delay associated with the communication channel through which the transmit signal is to be transmitted or by a length of a power delay profile associated with that channel.
  • the width of the pass-band of the low-pass filter 107 may be determined by a channel delay of a certain communi ⁇ cation channel, the certain communication channel having a maximum channel delay among a plurality of communication channels to be considered when receiving the transmit sig ⁇ nal.
  • each communication channel may be repre- sented by a certain type of communication channel being as ⁇ sociated with a certain type of environment in case of wireless transmission or associated with a certain cable length in a case of a wired transmission.
  • a plurality of commu- nication channels is possible for the different kinds of environment like e.g. urban areas or hilly terrains.
  • the width of the pass-band may be determined by a maximum expectable channel delay or, in other words, by a longest power delay profile specifying an attenuation of signal components over time.
  • the width of the pass-band of the low-pass filter 107 is equal to or smaller than the maximum channel delay plus an additional delay introduced by a slope of a filter response in order to take a finite slope duration of the filter response into account.
  • the pass-band of the filter 107 may be uniformly shaped and have, for exam ⁇ ple, an approximately rectangular shape.
  • the pass- band of the low-pass filter 107 may have any shape provided that the pass-band is symmetric with respect to an origin of a spectral region (e.g. to an origin of the f axis de- picted in Fig. 1) .
  • the transformer is configured for pre-processing the time do- main signal in time domain and/or for post-processing the transformed signal in frequency domain so that a phase shift is introduced into the transformed signal.
  • the transformer may be configured for delaying the time domain signal in time domain, the phase shift in fre ⁇ quency domain introducing a shift of the spectrum of the transformed signal, e.g. along the f axis.
  • the transformer 101 may be configured for cy ⁇ tunally delaying or for cyclically shifting the time do ⁇ main signal.
  • the transformer 101 may comprise a cyclic shift element for pre-processing the time domain signal, the cyclic shift element being configured for cyclically shifting the time domain signal by a number of values in order to introduce a phase shift to the transformed signal in frequency domain.
  • the number of values may be dependent on a width of the pass-band of the low-pass filter 107 in order to shift the spectrum of the trans ⁇ formed signal in dependence on the pass-band width of the low-pass filter.
  • Cyclically shifting the time domain signal means that val ⁇ ues of the time domain signal are shifted such that, in the case of a right shift, a last value of the time domain sig ⁇ nal is placed before a first value of the time domain sig- nal or, in the case of a left shift, that the first value of the time domain signal is attached at the end of the time domain signal and that the second value of the time domain signal becomes a first value of the time domain sig ⁇ nal.
  • the number of values may be equal to or smaller than half the width of the pass-band in order to, for example, shift the spectrum of the transformed signal by the previ- ously mentioned spectrum distance of half the width of the pass-band of the low-pass filter 107.
  • the number of values the time domain signal is to be shifted by is equal to half the difference between the width of the pass-band and an additional delay introduced by a slope of a filter response, when the slope of the fil ⁇ ter response has e.g. a finite duration.
  • the transformer 101 may comprise a shift register, the shift register having an input and an output, wherein the output is coupled back to the input for cyclically shifting the time domain signal.
  • the shift register may be controllable by the transformer in dependence on a currently adjusted pass-band width of the low-pass filter 107.
  • the transformer 101 may comprise a Fourier trans ⁇ former, the Fourier transformer being configured for per ⁇ forming e.g. a Fast Fourier Transform (FFT) .
  • FFT Fast Fourier Transform
  • the output of the cyclic shift element is coupled to the Fourier transformer, wherein the Fourier transformer per ⁇ forms e.g. a serial to parallel conversion and the Fourier Transform, wherein, after having performed the Fourier Transform, a set of values representing the transformed signal is provided to the filter 107 for filtering.
  • the transformer 101 may be configured for post ⁇ processing the transformed signal in order to directly in ⁇ troduce the phase shift to the transformed signal for shifting its spectrum.
  • the transformer 101 may be configured for time-frequency transforming the time do ⁇ main signal without pre-processing the time domain signal, so that the phase shift is introduced only in frequency do ⁇ main.
  • the transformer may be configured for performing both: pre-processing in time domain and post-processing in frequency domain for an accurate spectrum shift.
  • the transformer 101 may be configured for cyclically shifting the time domain signal in order to introduce a coarse phase shift, an for post-processing the resulting transformed signal in frequency domain for introducing a fine phase shift so that the spectrum of the resulting transformed signal may accurately be positioned within the pass-band of the low-pass filter 107.
  • the transformer 101 may be configured for chang ⁇ ing a phase of the transformed signal by e.g. multiplying each value of the transformed signal by a complex factor introducing the phase shift.
  • the trans ⁇ former 101 may comprise a phase compensator being config ⁇ ured for phase shifting the transformed signal.
  • the phase shift may be dependent on half the width of the pass-band of the low-pass filter 107 in order to "fit" the spectrum of the transformed signal into the pass-band.
  • an output of the phase compensator is connected to an input of the filter 107.
  • the outputs of the Fourier transformer may be connected to an input or to a plurality of inputs of the phase compensator for post-processing.
  • the inventive apparatus for frequency domain filter ⁇ ing may be used in a receiver, preferably in a multi- carrier receiver, in order to process the time domain sig ⁇ nal, which is for example, a received version of a transmit signal being transmitted through a communication channel.
  • the low-pass filter 107 may be configured for channel estimation, i.e. for providing an estimate of the channel transfer function from the transformed signal.
  • the transformed signal may comprise a set of received versions of sub-carrier values resulting from modulating sub-carrier values by pilot symbols for channel estimation, wherein the pilot symbols are known in the transmitter and in the receiver.
  • the trans ⁇ former 101 may be configured for de-modulating the received versions of sub-carrier values using the pilot symbols in order to provide a set of values to the low-pass filter for channel estimation, the set of values representing the transformed signal.
  • the transformer 101 may be configured for dividing each received version of sub-carrier values by an associated pilot symbol or by multi ⁇ plying each received version of sub-carrier values by a complex conjugate version of an associated pilot symbol.
  • the received versions of sub-carrier values may be considered as being a coarse (or, in other words, a first) estimate of the channel transfer function, so that the transformed signal, i.e. the set of values, comprises a first estimate of the channel transfer function.
  • the low-pass filter 107 may be configured for further estimating the channel, i.e. the channel transfer function, on a basis of the set of values in order to ob ⁇ tain a better estimate of the channel transfer function.
  • the low-pass filter 107 is configured for de ⁇ modulating the received versions of sub-carrier values us ⁇ ing the pilot symbols in order to obtain the set of values as a coarse estimate of the channel transfer function, and for further estimating the channel on the basis of the set of values in order to provide a better, i.e. a more accu ⁇ rate estimate of the channel.
  • the low-pass filter 107 comprises a Wiener filter for performing the channel estimation.
  • the low-pass filter comprises real valued coefficients be ⁇ ing obtained from solving a Wiener-Hopf equation. This is ⁇ sue will be addressed later in detail.
  • the low-pass filter 107 my comprise an interpolation filter.
  • the interpolation filter is configured for performing an interpolation between two subsequent val- ues of an estimate of the channel transfer function in or ⁇ der to obtain interpolated values of the channel transfer function, when e.g. only certain sub-carriers were modu ⁇ lated by pilot symbols, so that sub-carriers between modu- lated sub-carriers cannot be exploited for estimating coef ⁇ ficients of the channel transfer function at the corre ⁇ sponding frequency points.
  • the low-pass filter 107 may be configured for interpolating between values in the set of values in order to obtain an estimate of the channel transfer function for all sub-carriers.
  • the apparatus for frequency domain filtering may fur ⁇ ther comprise means for determining filter coefficients.
  • the means for determining filter coefficients is configured for determining the filter coefficients in dependence on a uniform power delay profile of the communi- cation channel.
  • the means for determining fil ⁇ ter coefficients is configured for receiving a control sig ⁇ nal from a means for providing channel information, the control signal indicating a maximum channel delay or a length of a power delay profile associated with a communi- cation channel. Based on this information, the means for determining filter coefficients may be configured for de ⁇ termining the filter coefficients such that the resulting pass-band has a width being e.g.
  • the means for determining filter coefficients is configured for matching the width of the pass-band of the low-pass filter to the channel delay for an efficient low-complexity chan ⁇ nel estimation. For example, if only certain sub-carriers are modulated by pilot symbols for channel estimation so that the sub- carriers are spaced apart by a number of sub-carriers, which are not modulated by pilot symbols, then the means for determining may be configured for determining the fil ⁇ ter coefficients from the following equations:
  • i is an index countin pilots only and i is a sub- carrier index for data and pilots, wherein
  • T denotes a sample interval
  • Tw denotes a delay be ⁇ ing equal to or greater than a maximum channel delay
  • Rgg ⁇ denotes an inverse of an autocorrelation ma ⁇ trix of the set of values, i.e. the autocorrelation matrix of an estimate of the channel transfer function.
  • the low-pass filter 107 is an interpolation filter for performing e.g. a linear or polynomial interpolation
  • the means for determining filter coefficients may be configured for determining the filter coefficients in de ⁇ pendence on a number of values, for which the estimate of the channel transfer function is to be interpolated. This issue will be addressed later in detail.
  • the means for determining filter coefficients may be configured for determining a control signal indicating a width of the pass-band being associated with the determined filter coefficients.
  • the transformer 101 may be configured, in response to the con ⁇ trol signal, for pre-processing the time domain signal as has been described above or for post-processing the trans- formed signal as has been described above for shifting the spectrum of the transformed signal into the pass-band of the low-pass filter in order to take a possible change of the pass-band into account, when new filter coefficients are determined.
  • the present invention further provides a multi-carrier re ⁇ ceiver comprising the filter apparatus as described above, the filter apparatus being configured for transforming a received time domain multi-carrier signal into a trans ⁇ formed signal representing a spectrum of the received time domain multi-carrier signal, and for filtering the spectrum of the received time domain multi-carrier signal, i.e. the transformed signal, in order to obtain a received frequency domain multi-carrier signal.
  • the multi-carrier receiver comprises means for extracting information from the received frequency domain multi-carrier signal.
  • the means for extracting information is con- figured for equalizing the transformed signal using an es ⁇ timate of the channel transfer function provided by the low-pass filter, when the low-pass filter is configured for channel estimation.
  • the functionality of the inventive filter ap ⁇ paratus for frequency domain filtering may be used for re ⁇ ducing a phase drift affecting the transformed signal, wherein the phase drift may result when a frame synchroni ⁇ zation error in time domain occurs.
  • the means for extracting information may com ⁇ prise a detector for detecting the phase drift in the transformed signal and for controlling the transformer in order to control the pre-processing or post-processing for introducing a correction phase drift to the transformed signal for at least partly compensating the phase drift.
  • the received signal will have unknown amplitude and phase variations.
  • CTF channel transfer func- tion
  • phase drift 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.
  • phase drift E[A ⁇ 1 ] if the timing offset, T off , does not exceed the guard interval length, T GI , minus the maximum delay of the chan ⁇ nel ⁇ n , so T nff ⁇ T rr - r v , there will be no loss in or- thogonality of the OFDM signal.
  • T off ⁇ 0 will re- suit in a different phase drift S[A ⁇ 1 ], as is described in M. Hsieh and C.
  • 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 ⁇ sponding time domain snapshot of a channel impulse response (CIR) .
  • the non-zero phase drift E[A ⁇ d ] 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.
  • CIR channel impulse response
  • the CIR which generates the CTF in Fig. 14 is shown in Fig. 15.
  • the CIR is only non-zero within the range [ ⁇ , r max ], where ⁇ max denotes the maximum delay of the channel.
  • 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.
  • 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.
  • an OFDM transmitter may introduce so-called pilot symbols be- ing known in the receiver for channel estimation.
  • the pilot symbols are used for modulating sub-carriers of a OFDM signal to be transmitted.
  • 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.
  • a block diagram of pilot symbol based channel estimation for OFDM is depicted.
  • FFT Fast Fourier Transform
  • a transformed signal is obtained having values associated with sub-carriers, wherein only certain sub-carriers are modulated by pilot symbols for channel estimation.
  • 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.
  • DMUX de ⁇ multiplex
  • 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.
  • 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.
  • a detection unit In order to detect information con ⁇ tained by the transformed signal bypassed by the de- multiplexer, a detection unit (DT) is used.
  • 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.
  • a phase compensation can be performed, as is described e.g. in M. Hsieh and C.
  • the channel transfer functions of data carriers are interpolated using linear or higher order interpola- tions.
  • 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.
  • Fig. 2a shows an OFDM receiver with phase compensation af ⁇ ter Fourier Transform
  • 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) .
  • FFT Fast Fourier Transform
  • 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.
  • 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.
  • the detector may be configured for controlling the phase com- pensator 209 and the cyclic shift element 301.
  • 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.
  • Cy ⁇ tract 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. Dammann and S. Kaiser, "Standard Conformable Antenna Diversity Techniques for OFDM and its Application to the DVB-T System,” in Proc.
  • 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.
  • 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 — ⁇ samples, a phase compensation of ⁇ cyc degree per sub-carrier requires one multiplication by e j cyc ⁇ 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. It should be noted however, that the phase compensation as shown in Fig. 2 has not yet been proposed for all applications described in the remainder of this section.
  • 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[Aq) 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.
  • DCT discrete cosine trans ⁇ form
  • 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.
  • [Ai] L ⁇ M&M ⁇ I . e - ⁇ ( 4 , ⁇ tT a ⁇ .l
  • 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.
  • T w r max -fA w , where A w accounts for a roll-off delay, which may be inserted to non-perfect slope of the filter response.
  • T a T GI .
  • the WIF matched to the uniform power delay pro ⁇ file is also real valued. This means that the computational cost is cut by half.
  • any FIR low pass interpo ⁇ lation filter benefits from the proposed cyclic shift.
  • the filter is matched to a passband of the filter will be real valued.
  • 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.
  • 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 ⁇ cyc .
  • Fig. 6 shows an OFDM receiver with cyclic shift before the FFT.
  • the OFDM re ⁇ DCVER 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 ⁇ tun 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.
  • the cyclic shift may be chosen to compensate the phase drift of (1) , that is
  • OFDM systems with differential modulation or space- frequency coded OFDM systems will have an improved perform ⁇ ance if E[A(P 1 ] is estimated sufficiently well.
  • ap ⁇ pears attractive as shown in Fig. 5.
  • this solu ⁇ tion can be implemented as shown in Fig. 6.
  • the cyclic shift, ⁇ cyc may be set to a default value within the range [ ⁇ , T ⁇ I /2].
  • ⁇ cyc 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.
  • the system parameters of the OFDM system and of the channel model are shown in Fig. 7.
  • the total transmit power of the system is fixed, such that the total transmit power of a N 7 .
  • antenna system is equivalent to a single antenna sys ⁇ tem. No outer channel coding has been employed.
  • the BER floor can be somewhat reduced by optimizing the cyclic shift ⁇ cyc .
  • the optimum cyclic shift is about 44T spI , which result in the best performance. It can also be seen that the accuracy of ⁇ cyc does not need to be high.
  • a performance of a polynomial interpolator can significantly be optimized.
  • 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.
  • the benefit of inserting a cyclic shift, ⁇ will be described for a linear interpolator. The results are applicable for higher order polynomial interpolators as well.
  • a performance of a polynomial interpolator can significantly be optimised.
  • two successive pilot sub-carriers are used to determine the channel response for sub-carrier located in between these two pilots.
  • sub-carrier i the channel estimate is given by
  • 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.
  • a performance of the inventive approach for some polynomial interpolation algorithms will be de ⁇ scribed.
  • 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.
  • Possible applications of the proposed cyclic shift at the OFDM receiver are e.g.:
  • the signal stream is divided into N c parallel sub-streams, typically for any multi-carrier modulation scheme.
  • An inverse DFT with N FFT points is performed on each block, and subsequently the guard interval having N GI sam ⁇ ples is inserted to obtain x trD .
  • the signal x(t) is transmitted over a mobile radio channel with response h(t, ⁇ ) .
  • n(t) represents additive white Gaussian noise
  • 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 Y l ⁇ .
  • the received signal after OFDM de ⁇ modulation is given by
  • X l ⁇ and H t ⁇ denotes the transmitted information sym ⁇ bol and the channel transfer function (CTF) at sub-carrier i of the I th OFDM symbol, respectively.
  • CTF channel transfer function
  • N ⁇ ri ac ⁇ counts for additive white Gaussian noise (AWGN) with zero mean and variance N 0 . It is assumed that the transmitted signal consists of Jr OFDM symbols, each having N c sub- carriers. We focus on channel estimation in frequency direction (sub- carrier index i) . Thus, the index denoting the OFDM symbol, £, will be dropped in the following.
  • the channel transfer function (CTF) of (11), is the Fourier Transform of the CIR h (A) (r) .
  • the guard interval is longer than the maximum delay of the channel, i.e. T GI ⁇ ⁇ max , the orthogonality at the re- ceiver after OFDM demodulation is maintained, and the re ⁇ ceived signal of (11) is obtained.
  • the FFT translates a cyclic delay into phase shifts.
  • the effective CTF of the cyclic receiver is described by
  • pilot-symbol aided channel estimation PACE
  • known symbols pilots
  • pilots pilots
  • PACE pilot-symbol aided channel estimation
  • pilot sequence is trans ⁇ mitted at a D f times lower rate i in frequency di ⁇ rection.
  • G is the subset of the OFDM frame containing the pi ⁇ lots.
  • 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
  • the channel estimator uses the demodulated pilots H- from (17) to yield the channel estimate
  • the FIR filter W [W 0 , •••, W M ⁇ 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 H x and the observation, i.e. the received pilot symbols. This means that knowledge about the channel statistics is required.
  • low-pass interpolation filters and polynomial interpolators do not assume any knowledge of the channel statistics.
  • the observed channel is typically correlated in two dimensions, frequency and time. Moreover, the extension to PACE in two dimensions is possible.
  • the Wiener interpolation filter (WIF) is implemented by a FIR filter with M f taps, according to (18) .
  • the ' WIF, W is obtained by solving the Wiener-Hopf equation
  • the m th entry of the cross-correlation vector can be expressed as
  • 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 T w fulfils this requirement.
  • This assumption provides the frequency correlation function of the mismatched esti- mator, 2?j ⁇ c) [ ⁇ i], from (6) .
  • the mismatched estimator is de ⁇ termined by substituting i ⁇ yc) [ ⁇ i] from (6) into (21) and (23) . Then the Wiener-Hopf equation (19) needs to be deter ⁇ mined only once.
  • the filter coefficients can be pre-computed and stored.
  • 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.
  • the average SNR at the filter input, ⁇ w which is used to generate the filter coefficients, should be equal or larger than actual average SNR, so ⁇ w ⁇ ⁇ c .
  • ⁇ a F w , and ⁇ w are required. If the maximum delay of the channel ⁇ max is not known it can be upper bounded by the guard interval dura ⁇ tion T 31 . Since the filter should also satisfy the sampling theorem, the filter pass-band can be chosen within the range
  • phase drift £[ ⁇ pJ, specifies the average change in phase between two adjacent sub-carriers, as defined in (1) .
  • One possibility to estimate the phase drift is
  • the CTF H 1 is not available at the receiver. Instead a noisy estimate of H 1 can easily be generated by H 1 « Y ⁇ /Xi i where X 1 is a hard decision of X 1 . The accuracy of (25) will degrade due to noise and decision feedback ef ⁇ fects. Fortunately, A ⁇ 1 does not need to be particularly accurate.
  • phase drift may be estimated by
  • Fig. 12 shows a further embodiment of an OFDM receiver in accordance with the present invention.
  • 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.
  • 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.
  • the means 1209 for extracting information is configured for determining an in ⁇ formation amount comprised by a signal provided by the de ⁇ multiplexer 1201.
  • the apparatus 1203 for reducing the phase drift 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.
  • the present invention provides concepts for fil ⁇ tering and interpolation for OFDM.
  • the frequency response of the received signal after OFDM demodulation has a one-sided spectrum.
  • the one-sided spectrum can be trans ⁇ formed into a symmetric two-sided spectrum.
  • the performance of standard interpolation algorithms such as linear or spline interpolation can be improved if the cy-rod shift is appropriately chosen.
  • the per ⁇ formance of space frequency codes and differential modula ⁇ tion can also be improved.
  • 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.
  • 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.
  • 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.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Digital Transmission Methods That Use Modulated Carrier Waves (AREA)

Abstract

L'invention concerne un dispositif de filtrage du domaine fréquentiel, qui comprend un transformateur (101) servant à transformer un signal du domaine temporel en un signal du domaine fréquentiel; et un filtre passe-bas (107) pour filtrer le signal du domaine fréquentiel, ledit filtre (107) comportant des coefficients à valeur réelle. Le transformateur (101) est conçu pour prétraiter le signal du domaine temporel ou pour traiter le signal du domaine fréquentiel afin d'introduire un décalage de phase dans le signal transformé, de manière à décaler le spectre de ce dernier vers la bande passante du filtre passe-bas (107). L'invention permet de mettre en oeuvre un filtrage de faible complexité dans le domaine fréquentiel.
PCT/EP2004/009372 2004-08-20 2004-08-20 Dispositif de filtre et procede de filtrage de domaine frequentiel WO2006018034A1 (fr)

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WO2012134677A3 (fr) * 2011-03-29 2012-11-22 Intel Corporation Symétrisation d'une réponse impulsionnelle de canal
EP2685686A1 (fr) * 2012-07-09 2014-01-15 MIMOON GmbH Procédé et appareil d'estimation de canal basée sur une autocorrélation estimée
CN111385230A (zh) * 2018-12-29 2020-07-07 中兴通讯股份有限公司 一种基于维纳自适应的信道估计的方法及系统
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Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101394383B (zh) * 2007-09-18 2011-07-20 华为技术有限公司 时频域信号转换方法及装置
WO2012134677A3 (fr) * 2011-03-29 2012-11-22 Intel Corporation Symétrisation d'une réponse impulsionnelle de canal
EP2685686A1 (fr) * 2012-07-09 2014-01-15 MIMOON GmbH Procédé et appareil d'estimation de canal basée sur une autocorrélation estimée
CN111385230A (zh) * 2018-12-29 2020-07-07 中兴通讯股份有限公司 一种基于维纳自适应的信道估计的方法及系统
CN111385230B (zh) * 2018-12-29 2023-03-14 中兴通讯股份有限公司 一种基于维纳自适应的信道估计的方法及系统
CN114024802A (zh) * 2021-11-02 2022-02-08 杭州红岭通信息科技有限公司 一种低复杂度的信道估计方法
CN114024802B (zh) * 2021-11-02 2023-09-22 杭州红岭通信息科技有限公司 一种低复杂度的信道估计方法

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