Abstract:
Wireless communication systems are provided with an adaptive subcarrier loading function for a mobile receiver in a wireless communication system based on Orthogonal Frequency Division Multiplexing (OFDM) that can advantageously be applied to predict the channel transfer function of a multipath propagation channel being severely impaired by frequency-selective fading and an extremely time-variant behavior by detecting the position and/or movement of zero points of the transfer function, thereby reducing the probability of incorrect assignment of the modulation scheme for each subcarrier caused by mobile terminals moving at high velocity. The zero points of the estimated channel transfer function are determined by detecting the position of deep notches on the associated amplitude response of the measured channel transfer function caused by frequency-selective fading whose depths are larger than a predefined threshold.

Description:
BACKGROUND OF THE INVENTION 
     The underlying invention generally relates to the field of wireless communication systems with high-speed mobile access, especially to Orthogonal Frequency Division Multiplexing (OFDM) systems considering channel estimation and/or channel tracking. More particularly, the invention provides an adaptive subcarrier loading function for a mobile receiver in a wireless communication system based on OFDM that can advantageously be applied to predict the channel transfer function H(j·ω,t) of a multipath propagation channel being severely impaired by frequency-selective fading and an extremely time-variant behavior by detecting the position and/or movement of zero points of said transfer function H(j·ω,t), thereby reducing the probability of an incorrect assignment of the modulation scheme for each subcarrier, that is caused by mobile terminals moving at high velocity. 
     The development of wireless communication systems for high bit-rate data transmission and high-quality information exchange between terminals in indoor and outdoor environments is becoming the new research challenge in telecommunication area. Possible applications are mobile cellular systems, the Wireless Local Area Network (WLAN), the Wireless Local Loop (WLL), and others. In this connection, the underlying research activity aims at the performance evaluation of an adaptive multi-carrier modulation scheme (Adaptive Orthogonal Frequency Division Multiplexing, AOFDM) for wireless broadband indoor modems. The framework of AOFDM is the European project “WIND-FLEX” that aims to design and demonstrate a high-bit-rate flexible and configurable modem architecture, that provides wireless access to the Internet in an indoor environment where slow mobility is required (about 1 m/s). The system scenario is the one typical for domestic environments with a short range (within 20 meters). This scenario could be characterized by a set of terminals that needs to exchange data and to communicate with the external world. The requested modem platform has then to support different kinds of services, voice, data or video, with the possibility of transmitting both in a synchronous (for real-time applications) and an asynchronous way. A modem requirement is the capability of supporting variable bit rates in the range of 64 kBit/s to 100 MBit/s of payload, in order to create a multi-technological platform, available for different applications. 
     The frequency band around 2.4 GHz and 5 GHz have already been used by other wireless transmission standards, such as IEEE-802.11 and HiperLAN/2 and are close to saturation. For the WIND-FLEX system, the expectation of the 17 GHz unlicensed frequency band seems to be a promising and challenging solution. The whole available spectrum (17.1 to 17.3 GHz) will be divided into four 50 MHz-width channels, which are not simultaneously selectable. The considered AOFDM modulation scheme has been designed to efficiently transmit in one of these channels. 
     Before examining the applied transmission systems according to the state of the art, it is necessary to briefly describe the characteristics of the channel distortions mobile communication is faced with. Wireless environments are characterized by a variety of factors that severely impede reliable communication over a mobile radio channel. In general, the sources of degradation can be grouped into two categories: channel impairments and noise sources. On the one hand, a broadband radio channel, as needed for the transmission of high data rates, is characterized by severe attenuation fades (frequency-selective fading) caused by multipath propagation of the transmitted mobile radio signals. On the other hand, it exhibits a time-variant behavior due to the mobility of the receiver, which possibly requires a continuous adaptation of the transmission system to said behavior. Thereby, despite a plurality of differences, most wireless links share two common characteristics, time dispersion and time variability, which shall briefly be described in the following sections. 
     Wireless links can be described by the presence of multiple signal paths between the transmitter and the receiver. These multipath components are generated whenever signals are reflected by objects in the environment such as buildings, walls, ceilings, mountains, cars, people, etc. Differences in reflected path lengths cause impulsive signal transmissions to arrive at the receiver with a finite temporal scattering, which is called the root mean square (RMS) delay spread Δ of the multipath propagation channel. With the aid of Δ, the approximate duration of the channel “echoes” resulting from multipath arrivals can be measured. 
     Time-dispersive channels generate at least two potentially deleterious effects at the receiver, namely frequency-selective amplitude, phase variations and intersymbol interference (ISI). Frequency-dependent variations are caused by (randomly) delayed signal components adding out of phase at the receiver. Since the spectral location of fades is strongly dependent on the signal phase, the overall channel impulse response is highly sensitive to changes in the location and orientation of the receiver. Meanwhile, ISI occurs whenever delayed arrivals from one symbol interval “spill over” into subsequent symbol intervals. Thereby, ISI impedes the ability of the receiver to distinguish the desired signal from the echoes of previously transmitted symbols. The impact of both channel selectivity and ISI primarily depends on whether the system uses narrowband or wideband signaling. 
     Wireless channels, like other communication mediums, are subject to time-varying behavior. One of the distinguishing features of wireless links is the magnitude and rate at which these variations occur. An important measure of variability for a wireless channel is the coherence time T coh —the interval during which the impulse response of the multipath propagation channel remains correlated. The coherence time T coh  can be approximated by the reciprocal value of the Doppler spread B D  using a generalized channel model that explicitly incorporates the channel&#39;s time dependence: 
     
       
         
           
             
               
                 
                   T 
                   coh 
                 
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                         B 
                         D 
                       
                     
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             wherein f D  denotes the Doppler shift of the channel. 
           
         
       
    
     Thereby, T coh  provides a measure of the rate at which variations in the wireless link occur. Channels are described as “fast fading” or “slow fading” depending on the length of the coherence time T coh  relative to a single symbol interval: A slowly changing channel has a large coherence time T coh  or, equivalently, a small Doppler spread B D , and vice versa. As can be expected, the channel coherence time T coh  is strongly dependent on the rate of motion for the transmitter, receiver, and other objects in the environment. For narrowband signals, the fading rate directly affects the responsitivity and dynamic range requirements of the receiver. For wideband systems, the fading rate primarily impacts the required convergence rate for adaptive receiver algorithms. Wireless designs often guarantee adequate performance under “worst-case” conditions, by limiting the achievable performance under more favorable conditions. One solution would be to exploit time-varying channel knowledge to provide optimized time-varying performance. This approach requires both channel estimation and adaptive receiver implementation, but offers the promise of substantial performance gains. Of course, the larger and faster the link variations, the more difficult (and computationally intensive) the tasks of estimation and adaptation become. Hence, the receiver consumes more energy. Because channel modeling is an active area of wireless research, a wide variety of models—both empirical and statistical—have been developed to characterize the channel impairments described above. 
     In an indoor wireless channel, the dominant impairment is the fading, which is connected with a multipath propagation environment. Thereby, the electromagnetic waves are perturbed by structures, walls and furniture inside the building in such a way that the modulated signal propagates along several paths that connect the transmitter with the receiver. According to the diffuse multipath model, the received signal y(t) can be viewed as the composition of a continuum of signal replicas: When a narrowband signal
 
 x ( t )= Re {{tilde over (x)} ( t )· e   j·2π·f     c     ·t }
 
having the complex envelope {tilde over (x)}(t) and the center frequency f c  is transmitted, the received narrowband signal
 
 y ( t )= Re {{tilde over (y)} ( t )· e   j·2π·f     c     ·t }
 
has a complex envelope {tilde over (y)}(t) which can be expressed by means of the following convolution integral:
 
                   y   ~     ⁡     (   t   )       =           x   ~     ⁡     (   t   )       *     h   ⁡     (     τ   ,   t     )         =       ∫     -   ∞       +   ∞       ⁢         h   ⁡     (     τ   ,   t     )       ·       x   ~     ⁡     (     t   -   τ     )         ⁢     ⅆ   τ             ,         
wherein
         h(τ,t) denotes the time-varying complex baseband impulse response of the underlying multipath propagation channel,   τrepresents the time delay, and   t represents the observation instant.       
     It has been shown that the diffuse multipath model can be represented in baseband as a tapped-delay line (TDL) with time-varying complex coefficients and a fixed tap spacing 1/B, where B is the passband signal bandwidth. For practical reasons, the number of taps in the TDL is kept finite, and it is related to the delay spread of the fading channel. The tap gains are scaled according to the Power Delay Profile 
     
       
         
           
             
               
                 
                   
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             (using Z*Z=Re{z} 2 +Im{z} 2 =|z| 2 ∀z εC)
 
wherein
 
             Δt represents the difference in the observation instant t, 
             “*” denotes the complex conjugate operation, and 
             E{·} denotes the expectation over the time t.
 
Thereby, the delay cross-power spectral density φ h (τ, Δt) is defined as follows:
 
           
         
       
    
                   φ   h     ⁡     (     τ   ,     Δ   ⁢           ⁢   t       )       ≡         1   2     ·   E     ⁢     {         h   ′     ⁡     (     τ   ,   t     )       ·     h   ⁡     (     τ   ,     t   +     Δ   ⁢           ⁢   t         )         }         =       lim     T   →   ∞       ⁢       1     2   ·   T       ·       ∫       -   T     /   2       T   /   2       ⁢           h   ′     ⁡     (     τ   ,   t     )       ·     h   ⁡     (     τ   ,     t   +     Δ   ⁢           ⁢   t         )         ⁢       ⅆ   t     .                   
The Power Delay Profile R c (τ) characterizes the fading channel and measures the mean signal power relative to its dispersion across time. Several forms have been suggested for a decaying Power Delay Profile that models different fading channels. For a wide range of a frequencies and environments, including the 17 GHz indoor radio channel, the decaying Power Delay Profile could reasonable be described by an exponential distribution. Therefore, the considered Power Delay Profile is given by
 
                 R   c     ⁡     (   τ   )       =     {               1   τ     ·     ⅇ       -   t     /     τ   _                   for   ⁢           ⁢   τ     ≥   0             0       otherwise         ,             
wherein  τ  denotes the mean delay. In general,  τ  is determined by the physical environments, and it is assumed to be about 50 ns for an indoor link at 17 GHz frequency band. The length of the TDL is determined by the delay spread Δ, which is defined as the range of τ for which the delay profile R c (τ) is essentially non-zero. The length is therefore given by the nearest integer of Δ·B+1, wherein B is the passband signal bandwidth and Δ can reasonably assumed to be about 200 ns. The tap gains are independent complex Gaussian processes, whose variances are determined according to the Power Delay Profile R c (τ).
 
     Since the preferred embodiment of the underlying invention is directed to a pilot-assisted multi-carrier transmission system wherein Adaptive Orthogonal Frequency Division Multiplex (AOFDM) is applied, the basic aspects and principles of OFDM and adaptive loading techniques shall briefly be summarized in the following sections. 
     Conventional single-carrier modulation methods for the transmission at high symbol rates experience a severe limitation in time-dispersive and frequency-selective channels due to their sensitivity to ISI. To handle ISI, usually the entire bandwidth of the single-carrier signal has to be (adaptively) equalized by quite complex time-domain channel equalizers, e.g. Viterbi equalizers. Thereby, the complexity of a channel equalizer increases with the amount of ISI which has to be eliminated. If a high data rate of about 10 7  modulation symbols per second is transmitted over a radio channel having a maximum delay τ max  of 10 μs, ISI extending over 100 modulation symbols might arise. For this reason, such an equalizer might be too expensive for an implementation. 
     If a conventional single-carrier transmission system is applied in an environment with severe transmission conditions, the channel equalization, which is supposed to eliminate the influence of the radio channel as far as possible, can be very extensive. The choice of an appropriate modulation technique for wireless data communication is therefore a critical issue due to the adverse influence of the dispersive and mostly time-variant mobile radio channel. In recent years, the interest in multi-carrier modulation for wireless transmission has been revived, whereas in former times the practicality of this concept appeared to be limited. 
     A promising approach to multi-carrier modulation which can easily be realized is Orthogonal Frequency Division Multiplexing (OFDM). OFDM offers advantages in transmission over severe multipath channels, so that there is an increased interest in applying OFDM in high-rate mobile or portable data transmission today. OFDM is a powerful technique that can advantageously be employed in communication systems suffering from frequency-selective distortion. Combined with multiple antennas at the transmitter and receiver as well as adaptive modulation, OFDM proves to be robust against channel delay spread. Furthermore, it leads to significant data rates with improved bit error performance over links having only a single antenna at both the transmitter and the receiver. 
     The main advantage of OFDM is that each sub-channel is relatively narrowband and is assumed to have flat fading. However, it is possible that a given sub-channel has a low power, which results in a large bit error ratio (BER). Thus, it is desirable to take advantage of sub-channels having relatively good performance, which is the motivation for adaptive modulation. In the context of time-varying channels, there is a decorrelation time associated with each frequency-selective channel instance. Thus, a new adaptation must be implemented each time the channel decorrelates. Since the channel is slowly time-varying, the receiver can provide reliable channel state information to its transmitter using a robust feedback channel. For this reason, loading modulation schemes according to the channel response of each subcarrier seems to be an interesting approach for increasing the capacity usage of the channel. 
     On the assumption that the transmitter knows the instantaneous channel transfer functions of all users simultaneously participating in different mobile communication sessions, many authors have demonstrated that significant performance improvement can be achieved if adaptive modulation is used together with OFDM. Thereby, adaptive modulation is an important technique that yields increased data rates over non-adaptive uncoded schemes. In general, subcarriers with large channel gains employ higher-order modulation to carry more bits per OFDM symbol, while subcarriers in deep fades carry one or even zero bits per symbol. Integrated design of forward error correction (FEC) and adaptive modulation using the Bose-Chadhuri-Hocquenghem (BCH) code and Trellis-Coded Modulation (TCM) has also been studied. Although both coding techniques consider only time-varying flat fading channels, the same coded adaptive modulation design can easily be applied to OFDM systems. As different subcarriers experience different fades and transmit different numbers of bits, the power level of the transmitted RF signal has to be changed accordingly. 
     When OFDM with adaptive modulation is applied in a frequency-selective fading channel, a significant portion of the subcarriers may not be used. These are typically subcarriers which experience deep fade and are not power-efficient to carry any information bits. In multiuser systems using static Time Division Multiple Access (TDMA) or Frequency Division Multiple Access (FDMA) as multi-access schemes, each user is allocated a pre-determined time slot or frequency band, respectively, to apply OFDM with adaptive modulation. Consequently, these unused subcarriers (as a result of adaptive modulation) within the allocated time slot or frequency band of the respective user are wasted and can not be used by other users. However, those subcarriers which appear in deep fades to one user may not be in deep fade for other users. In fact, it is quite unlikely that a subcarrier will be in deep fade for all users, as the fading parameters for different users are mutually independent. This motivates to consider a so-called adaptive multiuser subcarrier allocation scheme. Thereby, subcarriers are assigned to the users based on instantaneous channel information. This approach will allow all subcarriers to be used more efficiently as subcarriers will only be left unused if they appear to be in deep fade to all users. 
     The main object of an adaptive subcarrier loading function is to assign the modulation scheme of each subcarrier according to the channel impulse response which can be determined by frequency-selective channel distortion. Thereby, for subcarriers around deep distortions, a lower modulation scheme such as BPSK is assigned, whereas for subcarriers without any severe distortion, a higher modulation scheme—e.g. Quadrature Amplitude Modulation (QAM) with a 16- or 64-point signal constellation—is assigned. For example, the communication system between an access point  401  (AP) and a mobile terminal  405  (MT) capable of executing this function comprises the following steps:
         measurement of the channel transfer function H(j·ω,t),   creation of a modulation scheme assignment plan for each subcarrier according to the result of the respective channel impulse response measurement and negotiation between the AP  401  and the MT  405 ,   transmission of a signal by the AP  401  according to the applied modulation scheme assignment plan.       

     In case an MT  405  is moving at high velocity, the channel transfer function H(j·ω,t) is changing fast. Compared to the changing of H(j·ω,t), the time duration between the timing of its measurement and the timing of a transmission according to a new modulation scheme assignment plan should be longer to guarantee a correct assignment. Otherwise, an incorrect assignment of the employed modulation scheme for said subcarriers might occur. 
     BRIEF DESCRIPTION OF THE STATE OF THE ART 
     According to the state of the art, there are different solutions to the problem of pilot-pattern-based channel estimation and/or channel tracking available, each of them being optimized to a specific application environment given by the transmission channel. Since the underlying invention is basically dedicated to pilot-assisted multi-carrier systems such as OFDM, it is necessary to briefly describe the main principles and techniques of conventional OFDM systems according to the state of the art. 
     OFDM techniques are used in several wireless communication systems, e.g. in Wireless Local Area Networks (LANs) such as HiperLAN/2 and IEEE 801.11a. In order to explain the principle of OFDM, the spectrum of an OFDM symbol and the applied modulation schemes for its subcarriers are shown in  FIG. 1 . In frequency domain, an OFDM symbol  101  is split up into several subcarriers  102 . In case of HIPERLAN/2, their number is 52 (with the exception of the component at 0 Hz). Thereby, each subcarrier is modulated by means of a digital modulation technique. There are several modulation schemes that can be applied to each subcarrier of an OFDM symbol, e.g. low-order modulation schemes such as BPSK (M=2) and QPSK (M=4), or high-order modulation schemes like 16-QAM (M=16) and 64-QAM (M=64) as shown in diagrams  201 ,  202 ,  203 , and  204 , which are depicted in  FIG. 2 . 16-QAM and 64-QAM are able to carry 
             b   =         log   2     ⁡     (   M   )       =     {           4   ⁢           ⁢   Bit           (     16   -   QAM     )               6   ⁢           ⁢   Bit           (     64   -   QAM     )                     
at once, respectively. Thereby, M represents the number of signal points. However, if the signal power is limited, the distance between neighboring signal points on the constellation planes  201 ,  202 ,  203 , and  204  is reduced. For this reason, compared to low-order modulation schemes, the bit error rate (BER) becomes higher on the same noise or distortion condition (linear or non-linear).
 
     A block diagram for a mobile transmission and reception system supporting wireless communication over a multipath propagation channel  320  with the aid of a pilot-assisted wireless multi-carrier system (here: an OFDM system) comprising means for a channel estimation according to the state of the art is shown in  FIG. 3 . Thereby, the user data is fed to a channel encoder  303 . After that, by using a serial-to-parallel converter  304 , the output data of said channel encoder is converted from serial to parallel according to the number of bits per subcarrier in one OFDM symbol. The output of said serial-to-parallel converter  304  is then modulated by a modulator  305 , converted from frequency domain to time domain by an Inverse Fast Fourier Transform (IFFT,  306 ), and then submitted to a digital-to-analog conversion by a digital-to-analog converter (DAC,  307 ). The output of said DAC  307  is then up-converted to the passband by using an RF block  308 , supplied to a transmitting (TX) antenna  309  and radiated to the air. 
     The radiated signal propagates through several paths (here: the paths  403  and  404 ), which are modeled as a multipath fading channel  320  that causes frequency-selective distortion. 
     At an OFDM receiver  310 , the received signal is amplified, down-converted to the baseband by another RF block  312  and supplied to an analog-to-digital converter (ADC,  313 ). The output of said ADC  313  is then transformed from time domain to frequency domain by a Fast Fourier Transform (FFT,  314 ). Using the output data of said FFT  314 , a channel estimator  318  estimates the current channel transfer function H(j·ω,t) of said multipath fading channel  320 . 
     At a demodulator  315 , the output data of said FFT  314  along with the frequency-selective distortion caused by said channel  320  is compensated by using an estimated channel transfer function Ĥ(j·ω,t) and supplied to a parallel-to-serial converter  316 . The output of said parallel-to-serial converter  316  is then fed to a channel decoder  317 , and the user data is derived. 
     In the following sections, the mechanism of using frequency-selective fading for a prediction of the channel transfer function H(j·ω,t) shall be explained on the basis of the scenario depicted in  FIG. 4 , which shows a typical example of a propagation model with one access point  401  (AP) and one moving mobile terminal  405  (MT). Thereby, the transmitted RF signal x(t) is radiated from an antenna  402  of the AP  401 . The signal propagates via several paths (here designated with  403  and  404 ) caused by reflection at mountains, trees, buildings or other objects. At a receiver side—e.g. at an MT  405  in a car which is driving at high speed—, signals coming via said paths  403  and  404  are received and summed at an antenna  406  of the receiver  405 . This channel is called a “multipath fading channel”  320 . Since the delay time τ i  of each propagation path i is different, frequency-selective distortion might occur at the MT  405 . 
     The channel impulse response h(τ,t) of this multipath fading channel  320  is given by 
                 h   ⁡     (     τ   ,   t     )       =         a   0     ·     δ   ⁡     (   τ   )         +       ∑     i   =   1       n   -   1       ⁢         a   1     ⁡     (   t   )       ·     δ   ⁡     (     τ   -       T   i     ⁡     (   t   )         )               ,         
wherein
         i represents the path number (i =0, 1, 2, . . . , n−1) between the transmitter and the receiver,   a i (t) denotes the complex amplitude of the i-th path,   τ i (t) denotes the delay time of the i-th path, and   δ(t) is Dirac&#39;s delta function in time domain.       
     By applying the Laplace transform            {·} on h(τ,t), the channel transfer function H(s,t) is derived as follows:
                 H   ⁡     (     s   ,   t     )       =       ℒ   ⁢     {     h   ⁡     (     τ   ,   t     )       }     ⁢       ∫   0     +   ∞       ⁢         h   ⁡     (     τ   ,   t     )       ·     ⅇ       -   s     ·   τ         ⁢     ⅆ   τ           =       a   0     +       ∑     i   =   1       n   -   1       ⁢         a   1     ⁡     (   t   )       ·     ⅇ       -   s     ·       τ   i     ⁡     (   t   )                     ,         
thereby using
 
                 ℒ   ⁢     {     δ   ⁡     (   τ   )       }       =   1     ,       ℒ   ⁢     {     c   ·     f   ⁡     (   τ   )         }       =         c   ·   ℒ     ⁢     {     f   ⁡     (   τ   )       }     ⁢     ∀     c   ∈     ℝ   ⁢           ⁢   and   ⁢           ⁢   ℒ   ⁢     {     f   ⁡     (     τ   -     τ   0       )       }             =         ⅇ       -   s     ·     τ   0         ·   ℒ     ⁢     {     f   ⁡     (   τ   )       }     ⁢     ∀       τ   0     ∈   ℝ             ,         
wherein
 
     
       
         
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 s := σ + j · ω 
                 denotes the complex observation frequency, 
               
               
                   
                 ω = 2π · f 
                 denotes the angular observation frequency, 
               
               
                   
                 f 
                 denotes the observation frequency, 
               
               
                   
                 j := √{square root over (−1)} 
                 is the imaginary unit, and 
               
               
                   
                 e ≈ 2.718281828 
                 represents Euler&#39;s constant. 
               
               
                   
                   
               
             
          
         
       
     
     The exponential terms e -s·τ     i    (for i=i,2, 3, . . . , n−1) can be expanded by using the following Taylor series: 
     
       
         
           
             
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     By applying said Taylor series, the channel transfer function H(s,t) can be described by using a polynomial of m-th order: 
                 H   ⁡     (     s   ,   t     )       =         ∑     i   =   0       m   -   1       ⁢         b   i     ⁡     (   t   )       ·     s   i         =     A   ·       ∏     i   =   0       m   -   1       ⁢     (     1   -     s       T   i     ⁡     (   t   )           )             ,         
wherein
         A is a complex amplitude factor, derived by transformation of the equation,   b i (t) denotes the complex coefficient of the i-th path, derived by transformation of the equation, and   T i (t) denotes the position of the i-th zero point of the channel transfer function H(s,t).       
     Thereby, m is determined according to the power delay profile R c (τ) of the underlying mobile radio channel. 
     This means, the amplitude response |H(j·ω,t)| of the channel in frequency domain can be expressed by using the positions T i (t) of the zero points: 
     
       
         
           
             
               
                 
                   
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                               j 
                               · 
                               ω 
                             
                             
                               
                                 T 
                                 i 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                          
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                        
                       A 
                        
                     
                     · 
                     
                       
                         ∏ 
                         
                           i 
                           = 
                           0 
                         
                         
                           m 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             Δ 
                             i 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         
                           
                             T 
                             i 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
         
         
           
             with Δ i (t):=|T i (t)−j·ω| for i ε {0, 1, 2, . . . , m−1}. 
           
         
       
    
     This formula expresses the distance between the observation frequency ω on the ω-axis and the positions T i (t) of the zero points. Therefore, the amplitude response of the channel in frequency domain can be calculated by multiplying the distances between the observation frequency ω and the positions T i (t) of these zero points. Accordingly, the frequency response 
     
       
         
           
             
               ∠ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 H 
                 ⁡ 
                 
                   ( 
                   
                     
                       j 
                       · 
                       ω 
                     
                     , 
                     t 
                   
                   ) 
                 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         arc 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           tan 
                           ⁡ 
                           
                             ( 
                             
                               Im 
                               ⁢ 
                               
                                 
                                   { 
                                   H 
                                   } 
                                 
                                 / 
                                 Re 
                               
                               ⁢ 
                               
                                 { 
                                 H 
                                 } 
                               
                             
                             ) 
                           
                         
                       
                       , 
                     
                   
                   
                     
                       
                         Re 
                         ⁢ 
                         
                           { 
                           H 
                           } 
                         
                       
                       &gt; 
                       
                         0 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         and 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Im 
                         ⁢ 
                         
                           { 
                           H 
                           } 
                         
                       
                       &gt; 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         
                           360 
                           ⁢ 
                           ° 
                         
                         + 
                         
                           arc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
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                             ⁡ 
                             
                               ( 
                               
                                 Im 
                                 ⁢ 
                                 
                                   
                                     { 
                                     H 
                                     } 
                                   
                                   / 
                                   Re 
                                 
                                 ⁢ 
                                 
                                   { 
                                   H 
                                   } 
                                 
                               
                               ) 
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       
                         Re 
                         ⁢ 
                         
                           { 
                           H 
                           } 
                         
                       
                       &gt; 
                       
                         0 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         and 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Im 
                         ⁢ 
                         
                           { 
                           H 
                           } 
                         
                       
                       &lt; 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         
                           180 
                           ⁢ 
                           ° 
                         
                         + 
                         
                           arc 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 Im 
                                 ⁢ 
                                 
                                   
                                     { 
                                     H 
                                     } 
                                   
                                   / 
                                   Re 
                                 
                                 ⁢ 
                                 
                                   { 
                                   H 
                                   } 
                                 
                               
                               ) 
                             
                           
                         
                       
                       , 
                     
                   
                   
                     
                       
                         Re 
                         ⁢ 
                         
                           { 
                           H 
                           } 
                         
                       
                       &lt; 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         0 
                         ⁢ 
                         ° 
                       
                       , 
                     
                   
                   
                     
                       
                         
                           Re 
                           ⁢ 
                           
                             { 
                             H 
                             } 
                           
                         
                         &gt; 
                         
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Im 
                           ⁢ 
                           
                             { 
                             H 
                             } 
                           
                         
                       
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         90 
                         ⁢ 
                         ° 
                       
                       , 
                     
                   
                   
                     
                       
                         Re 
                         ⁢ 
                         
                           { 
                           H 
                           } 
                         
                       
                       = 
                       
                         
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Im 
                           ⁢ 
                           
                             { 
                             H 
                             } 
                           
                         
                         &gt; 
                         0 
                       
                     
                   
                 
                 
                   
                     
                       
                         180 
                         ⁢ 
                         ° 
                       
                       , 
                     
                   
                   
                     
                       
                         
                           Re 
                           ⁢ 
                           
                             { 
                             H 
                             } 
                           
                         
                         &lt; 
                         
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Im 
                           ⁢ 
                           
                             { 
                             H 
                             } 
                           
                         
                       
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         270 
                         ⁢ 
                         ° 
                       
                       , 
                     
                   
                   
                     
                       
                         Re 
                         ⁢ 
                         
                           { 
                           H 
                           } 
                         
                       
                       = 
                       
                         
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Im 
                           ⁢ 
                           
                             { 
                             H 
                             } 
                           
                         
                         &lt; 
                         0 
                       
                     
                   
                 
               
             
           
         
       
         
         
           
             for H≡H(j·ω,t) and ∠H(j·ω,t) ε[0°;360°[(thereby assuming that |H(j·ω,t)|≠0)
 
can be determined with the aid of the zero points T i (t) of the channel transfer function H(j·ω,t):
 
           
         
       
    
     
       
         
           
             
               ∠ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 H 
                 ⁡ 
                 
                   ( 
                   
                     
                       j 
                       · 
                       ω 
                     
                     , 
                     t 
                   
                   ) 
                 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   m 
                   - 
                   1 
                 
               
               ⁢ 
               
                 
                   φ 
                   i 
                 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
             
           
         
       
         
         
           
             with φ i (t):=∠(j·ω−T i (t)) for i ε{0, 1, 2, . . . , m−1}. 
           
         
       
    
     For example, if these zero points T i (t) are located near the ω-axis, the frequency-selective distortion becomes severe as notches appear on the amplitude response |H(j·ω,t)| near the observation frequency ω as depicted in  FIG. 5 . 
     Likewise, the characteristics of the frequency-selective fading will change if the MT  405  (receiver) is moved. Therefore, the receiver must be able to instantaneously estimate the actual channel transfer function H(j·ω,t). 
     In the following sections, the mechanism of the channel estimation according to the state of the art shall briefly be described. In  FIG. 7 , the frame structure of HiperLAN/2 is illustrated. Thereby, three preamble sections  701 ,  702 , and  703  (A, B, and C) are added in front of the data block  704 . These preambles  701 ,  702 , and  703  are modulated by a known scrambling sequence SC consisting of 53 scrambling elements SC n  ε {−1, 0, +1}. For example, the sequence of preamble C in frequency domain is given by 
     
       
         
           
             
               
                 
                   SC 
                   = 
                     
                   ⁢ 
                   
                     { 
                     
                       
                         SC 
                         n 
                       
                       | 
                       
                         
                           - 
                           26 
                         
                         ≤ 
                         n 
                         ≤ 
                         
                           + 
                           26 
                         
                       
                     
                     } 
                   
                 
               
             
             
               
                 
                   := 
                     
                   ⁢ 
                   
                     { 
                     
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         - 
                         1 
                       
                       , 
                       
                         - 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         - 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         - 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                     
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     
                       + 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     0 
                     , 
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     
                       + 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       + 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                     
                       - 
                       1 
                     
                     , 
                   
                 
               
             
             
               
                 
                   
                       
                     ⁢ 
                     
                       
                         - 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         - 
                         1 
                       
                       , 
                       
                         - 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         - 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         - 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                       , 
                       
                         + 
                         1 
                       
                     
                     } 
                   
                   . 
                 
               
             
           
         
       
     
     The received preamble C in frequency domain can be expressed by the equation
 
 R   SC ( j·ω,t )= H ( j·ω,t )· T   SC ( j ·ω),
 
wherein
     R SC (j·ω,t) denotes the spectrum of the received preamble C, and   T SC (j·ω) is the spectrum of the transmitted preamble C.   

     The relationship between T SC (j·ω) and R SC (j·ω) is given by the following equation:
 
 T   SC ( j ·ω)= A   T   ·SC   n ·δ(ω− n·ω   s −ω c ),
 
wherein
 
     
       
         
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 A T   
                 is the amplitude determined by the gain of the 
               
               
                   
                   
                 transmitter amplifier and the performance of the 
               
               
                   
                   
                 antenna, 
               
               
                   
                 δ(ω) 
                 is Dirac&#39;s delta function in frequency 
               
               
                   
                   
                 domain, 
               
               
                   
                 f c   
                 represents the carrier frequency, 
               
               
                   
                 f s   
                 represents the frequency interval between two 
               
               
                   
                   
                 different subcarriers, 
               
               
                   
                 n 
                 is the number of the current scrambling element 
               
               
                   
                   
                 sc n , 
               
               
                   
                 ω c  = 2π · f c   
                 denotes the associated angular frequency of the 
               
               
                   
                   
                 carrier frequency f c . 
               
               
                   
                 ω s  = 2π · f s   
                 denotes the associated angular frequency of the 
               
               
                   
                   
                 frequency interval f s , and 
               
               
                   
                   
               
             
          
         
       
     
     Therefore, the estimated channel transfer function Ĥ(j·ω,t) can be calculated by means of the following formula: 
     
       
         
           
             
               
                 H 
                 ^ 
               
               ⁡ 
               
                 ( 
                 
                   
                     j 
                     · 
                     ω 
                   
                   , 
                   t 
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     R 
                     sc 
                   
                   ⁡ 
                   
                     ( 
                     
                       
                         j 
                         · 
                         ω 
                       
                       , 
                       t 
                     
                     ) 
                   
                 
                 
                   
                     T 
                     sc 
                   
                   ⁡ 
                   
                     ( 
                     
                       j 
                       · 
                       ω 
                     
                     ) 
                   
                 
               
               . 
             
           
         
       
     
     As can be taken from  FIG. 3 , the demodulator  315  compensates the received signal R(j·ω,t) of the data part as depicted in  FIG. 7  with frequency-selective fading, thereby using the estimated channel transfer function Ĥ(j·ω,t) as follows: 
                 X   ⁡     (       j   ·   ω     ,   t     )       =         R   ⁡     (       j   ·   ω     ,   t     )           H   ^     ⁡     (       j   ·   ω     ,   t     )         =         H   ⁡     (       j   ·   ω     ,   t     )           H   ^     ⁡     (       j   ·   ω     ,   t     )         ·     T   ⁡     (     j   ·   ω     )             ,         
wherein
 
     
       
         
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 R(j · ω, t) 
                 denotes the received data part in 
               
               
                   
                   
                 frequency domain, 
               
               
                   
                 T(j · ω) 
                 denotes the transmitted data part in 
               
               
                   
                   
                 frequency domain, and 
               
               
                   
                 X(j · ω, t) 
                 represents the compensation of R(j · ω, t). 
               
               
                   
                   
               
             
          
         
       
     
     As an extension of OFDM, conventional AOFDM systems according to the state of the art employ adaptive subcarrier loading techniques. Thereby, the modulation scheme of each subcarrier is determined according to the SNR of each subcarrier, which improves data transfer speed and reduces BER. In this connection,  FIG. 6  presents a block diagram  600  for a mobile transmission and reception system supporting wireless communication over a multipath propagation channel  620  by means of a pilot-assisted wireless multi-carrier system (here: an OFDM system) comprising means  618  for a channel estimation, which can be used for an adaptive subcarrier loading. 
     In the following sections, the adaptive subcarrier loading technique shall be explained by means of diagrams  1001  and  1002  depicted in  FIG. 10  and the sequence chart  800  depicted in  FIG. 8 . 
     Due to the multipath fading channel, frequency-selective distortion is caused as illustrated in  FIG. 10 . Around the deep notch of |H(j·ω,t)|, the distortion is severer, and therefore lower-order modulation schemes such as BPSK (M=2) and QPSK (M=4) are more appropriate than higher-order modulation schemes like 16-QAM (M=16) or 64-QAM (M=64), since the distance between neighboring signal points on the constellation planes  201 ,  202 ,  203 , and  204  decreases with the number M of said signal points, thereby increasing the BER. 
     When an adaptive subcarrier loading technique is used, lower-order modulation schemes such as BPSK and QPSK are applied to subcarriers around deep notches of |H(j·ω,t)|, and high-order modulation schemes like 16-QAM and 64-QAM are applied to subcarriers around less severe fades as depicted in  FIG. 10 . Accordingly, the BER can be reduced. 
     A sequence chart of a conventional subcarrier loading technique showing the data transfer between the access point  401  (AP) and the mobile terminal  405  (MT) according to the state of the art is depicted in  FIG. 8 . The underlying OFDM system is based on a Time Division Duplex (TDD) system, in which the same frequency is used for the uplink signal and the downlink signal. At first, the MT  405  receives the downlink signal of the AP  401 , and estimates the transfer function of the channel. After that, the MT  405  makes the proposal of a modulation scheme according to the channel estimation, and sends the proposal to the AP  401 . The AP  401  receives the proposal and evaluates it. If it is acceptable, the AP  401  sends an acknowledgment message for the proposal, sets up the modulation scheme for the downlink signal according to said proposal, and sends the downlink signal. The MT  405  receives the acknowledgment message for the proposal, sets up the modulation scheme according to the proposal, and receives the downlink signal. 
     In the U.S. Pat. No. 6,175,550, a scaleable OFDM system and a method for providing OFDM signals are disclosed that support increased flexibility and adaptability in various communication environments by providing a dynamic scaling of specific operating parameters and/or characteristics of the OFDM system, including symbol duration, guard time interval, number of the OFDM carriers, and number of bits per symbol and OFDM carrier. For example, by dynamically scaling the bit rate, widely varying signal bandwidths, delay spread tolerances and signal-to-noise ratio (SNR) requirements can be achieved. As such, a scaleable OFDM system is particularly suitable for applications in wireless communication devices which support a plurality of services in a variety of environments (both indoor and outdoor) and in radio channels with differing bandwidths. 
     In the article “Performance of the BRAIN Air Interface: Simulation Results and Proposed System Optimization for the Standardization Process” (BRAIN Deliverable 3.2 Document IST-1999-10050/BRAIN, 2001), an adaptive subcarrier modulation for an enhanced HiperLAN/2 link level performance is disclosed. Thereby, adapting the transmission scheme in HiperLAN/2 systems is possible by choosing an appropriate combination of modulation level and code rate in the link adaptation process. In the OFDM transmission technique, however, there is even the flexibility to individually adapt the modulation scheme for each OFDM subcarrier depending on the specific signal-to-noise ratio (SNR) on a sub-channel. This principle is usually referred to as “adaptive modulation”. The actual bit (and power) allocation is performed by so-called loading algorithms, which mainly differ in their optimization criteria and computational load. It is well-known that this technique can drastically reduce the bit error rate in the uncoded case and is thus an interesting technique to meet the requirement of increasing the spectral efficiency. Adaptive (subcarrier-specific) modulation has already been incorporated into standards for OFDM-based wired transmission (e.g. Asymmetric Digital Subscriber Line, ADSL). This technology is effective in static- or slow-mobility environments to increase the throughput at a given SNR or to decrease the required SNR (and therefore to increase the range and capacity for a given throughput). 
     In case conventional adaptive subcarrier loading techniques according to the state of the art are applied, which do not comprise any prediction function, an incorrect assignment of the modulation schemes for said subcarriers could possibly occur since the channel transfer function H(j·ω,t) is extremely time-variant and might change between the time when the channel distortion is measured and the time when the signal according to a new modulation scheme assignment is transmitted. On the other hand, the negotiation of the modulation scheme between an MT  405  and an AP  401  always needs some time. 
     SUMMARY OF THE INVENTION 
     In view of the explanations mentioned above, it is the object of the invention to propose a new adaptation technique for a pilot-assisted wireless multi-carrier system which allows to reduce the probability of an incorrect assignment of different modulation schemes to the applied subcarriers caused by MTs moving at high velocity. 
     This object is achieved by means of the features of the independent claims. Advantageous features are defined in the dependent claims. 
     The underlying invention is basically dedicated to the idea of supporting wireless communication systems based on OFDM by providing an adaptive subcarrier loading function which can advantageously be applied to predict the transfer function H(j·ω,t) of a multipath propagation channel being severely impaired by attenuation fades (frequency-selective fading) and a time-variant behavior by estimating the position and movement of zero points of the channel transfer function H(s,t) on an s-plane, where s represents the complex observation frequency (s:=σ+j·ω), in order to assign the modulation scheme of each subcarrier according to the estimated channel transfer function Ĥ(j·ω,t), determined by an evaluation of the distortion caused by frequency-selective fading. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Further advantages and possible applications of the underlying invention result from the subordinate claims as well as from the following description of two preferred embodiments of the invention which are depicted in the following drawings. 
         FIG. 1  presents a diagram showing the spectrum of an OFDM symbol and the modulation schemes for its subcarriers, 
         FIG. 2  exhibits four diagrams showing the modulation schemes that can be applied to each subcarrier, 
         FIG. 3  shows a block diagram for a mobile transmission and reception system supporting wireless communication over a multipath propagation channel with the aid of a pilot-assisted wireless multi-carrier system (here: an OFDM system) comprising means for a channel estimation according to the state of the art, 
         FIG. 4  presents a diagram showing a typical example for a propagation model with one access point (AP) and one moving mobile terminal (MT), 
         FIG. 5  presents five diagrams giving an overview of channel distortion caused by a severe frequency-selective fading and the time-variant behavior of the underlying multipath propagation channel, 
         FIG. 6  presents a block diagram for a mobile transmission and reception system supporting wireless communication over a multipath propagation channel by means of a pilot-assisted wireless multi-carrier system (here: an OFDM system) comprising means for a channel estimation, which can be used for an adaptive subcarrier loading, 
         FIG. 7  shows an example of a downlink signal burst with three preambles (A, B, and C), 
         FIG. 8  exhibits a sequence chart showing the data transfer between the access point (AP) and the mobile terminal (MT) according to the state of the art, 
         FIG. 9  exhibits a sequence chart showing the data transfer between the access point  401  (AP) and the mobile terminal  405  (MT) according to the underlying invention, 
         FIG. 10  presents two diagrams giving an overview of the adaptive subcarrier loading according to the underlying invention, 
         FIG. 11  shows a flowchart of a modulation scheme planning, 
         FIG. 12  shows a timing chart according to the underlying invention which is applied to calculate the movement of zero points of the extremely time-variant channel transfer function H(j·ω,t), and 
         FIG. 13  presents a block diagram for a mobile transmission and reception system supporting wireless communication over a multipath propagation channel by means of a pilot-assisted wireless multi-carrier system (here: an OFDM system) comprising means for a channel estimation according to the underlying invention, which can be used for an adaptive subcarrier loading. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following, the functions of the structures in an embodiment of the underlying invention as depicted in  FIGS. 9 to 13  are explained in detail. The meaning of the employed symbols designated with reference signs in  FIGS. 1 to 13  can be taken from the appended table of reference signs. 
     The invention provides an adaptive subcarrier loading function for a mobile receiver  1310  in a wireless communication system  1300  based on OFDM that can advantageously be applied to predict the channel transfer function H(j·ω,t) of a multipath propagation channel  1320  being severely impaired by frequency-selective fading and an extremely time-variant behavior by detecting the position and/or movement of zero points (A, B, C) of said transfer function H(j·ω,t). The position of said zero points (A, B, C) changes continuously if there is no shadowing phenomenon. By observing the position and movement of said zero points (A, B, C), the frequency response H(j·ω,t) of the multipath propagation channel  1320  can be expected. Thereby, the probability of an incorrect assignment of different modulation schemes for the applied subcarriers  102 , that is caused by mobile terminals  405  (MTs) moving at high velocity, can significantly be reduced. 
     A sequence chart  900  for the adaptive subcarrier loading according to the underlying invention is depicted in  FIG. 9 . In the depicted case, the employed OFDM system is a Time Division Duplex (TDD) system, wherein the same frequency is used for uplink and downlink. At first, the MT  405  receives the downlink signal of the AP  401  and estimates the transfer function H(j·ω,t) of the multipath propagation channel  1320 . Then, the MT  405  estimates the position of zero points (A, B) and predicts the position of zero points (C) for succeeding downlink signal bursts  700 . After that, the MT  405  makes a proposal for a modulation scheme according to said prediction, and sends this proposal to the AP  401 . The AP  401  receives the proposal and evaluates it, and—if it is acceptable—sends an acknowledgment message for the proposal, sets up the modulation scheme of the downlink signal according to the proposal, and sends the downlink signal. The MT  405  receives the acknowledgment message for the proposal, sets up the modulation scheme according to the proposal, and receives the downlink signal (emphasis added). 
     A detailed explanation of the function to estimate and predict the position and movement of zero points (A, B, C) is depicted in  FIG. 11 . At first, the receiver  1310  estimates the channel response for the preamble  703 . In  FIG. 7 , the frame structure of HiperLAN/2 is illustrated. Thereby, said preamble  703  is modulated by a known scrambling sequence. Reference symbols transmitted by means of said pilot patterns are scrambled by means of a pseudo-noise scrambling sequence generated by a generator polynomial, which is known to the mobile transmitter  1301  and the mobile receiver  1310 , in order to randomize the reference symbols to be transmitted. 
     In the following, the channel transfer function H(s,t) shall be approximated by a polynomial G(s,t) of M-th order (wherein M&lt;m): 
                 G   ⁡     (     s   ,   t     )       =         ∑     i   =   0       M   -   1       ⁢         b   i     ⁡     (   t   )       ·     s   i         =     A   ·       ∏     i   =   0       M   -   1       ⁢     (     1   -     s       T   i     ⁡     (   t   )           )             ,         
wherein
         A is a complex amplitude factor, derived by transformation of the equation,   b i (t) denotes the complex coefficient of the i-th path, derived by reformation of the equation, and   T i (t) denotes the position of the i-th zero point point of the channel transfer function G(s,t).       
     Therefore, to obtain an approximation Ĥ(j·ω,t) of the channel transfer function H(j·ω,t), the values of A and T i (t) are determined to minimize the energy γ(t) of the difference
 
 Ĥ ( j·ω,t )− G ( j·ω,t ),
 
which is defined as follows:
 
     
       
         
           
             
               γ 
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             := 
             
               
                 
                   ∫ 
                   
                     - 
                     ∞ 
                   
                   
                     + 
                     ∞ 
                   
                 
                 ⁢ 
                 
                   
                     
                        
                       
                         
                           
                             H 
                             ^ 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 j 
                                 · 
                                 ω 
                               
                               , 
                               t 
                             
                             ) 
                           
                         
                         - 
                         
                           G 
                           ⁡ 
                           
                             ( 
                             
                               
                                 j 
                                 · 
                                 ω 
                               
                               , 
                               t 
                             
                             ) 
                           
                         
                       
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     Accordingly, the positions of the zero points T i (t) are derived, and the movement of the zero points can be calculated as depicted in  FIG. 12 . Thereby, the zero point T i,j−1 , of burst j−1 is calculated by the position of the zero point estimator  1206 , and the zero point T i,j  of the succeeding burst j is calculated by the position of the zero point estimator  1207 . The movement ΔT of said zero points can be obtained from the difference
 
 ΔT:=T   i,j   −T   i,j−1 .
 
     Therefore, the predicted zero point position at burst j+1 can be calculated as
 
 T   i,j+1   =T   i,j   +ΔT.  
 
     To make a proposal for a new modulation scheme, the position and movement of zero points (A, B, and C) is considered. In  FIG. 5 , the position and movement of said zero points on an s-plane is illustrated. If a zero point is located at A as depicted in diagram  501 , the amplitude of the transfer function H(j·ω,t) has a notch at A. If zero points are located at B and C as depicted in diagram  502 , the function H(j·ω,t) has a notch at B and C, respectively. The position of the zero point at B is located nearby the ω-axis; therefore, the notch at B is deeper. In this case, the frequency-selective fading becomes severer. 
     If the current position of a zero point is A and the prediction of said zero point is B, a higher modulation scheme can not be assigned around the frequency of B, even if currently there is no notch around the frequency of B. If the current position of the zero point is B and the position of the prediction for said zero point is C, a higher modulation scheme can be assigned around the frequency of B, even if currently there is a deep notch around the frequency of B. 
     A block diagram  1300  for a mobile transmission and reception system supporting wireless communication over a multipath propagation channel  1320  by means of a pilot-assisted wireless multi-carrier system (here: an OFDM system) according to the underlying invention, which comprises means for a channel estimation  318  and an adaptive subcarrier loading is given by  FIG. 13 . Thereby, the user data is fed to a channel encoder  1303 . Then, by using a serial-to-parallel converter  1304 , the output data of said channel encoder is converted from serial to parallel according to the number of bits per subcarrier in one OFDM symbol. After that, the output data of said serial-to-parallel converter  1304  is modulated by means of a modulator  1305  and converted from frequency domain to time domain by using an Inverse Fast Fourier Transform  1306  (IFFT), and then submitted to a digital-to-analog conversion performed by a digital-to-analog converter  1307  (DAC). The output of said DAC  1307  is then up-converted to the passband by means of an RF block  1308 , and is finally supplied to a transmitting antenna  1309  and radiated to the air. 
     The radiated RF signal propagates through several paths, which are modeled as a multipath fading channel  1320 , which causes frequency-selective distortion. 
     At an OFDM receiver  1310 , the signal from said multipath fading channel  1320  is amplified and down-converted to the base-band by another RF block  1312 , and supplied to an analog-to-digital converter  1313  (ADC). The output of said ADC  1313  is then transformed from time domain to frequency domain by a Fast Fourier Transform  1314  (FFT). Finally, by using the output of the FFT  1314 , a channel estimator  1318  estimates the channel transfer function Ĥ(j·ω,t) of said channel  1320 . 
     At a demodulator  1315 , the output of said FFT  1314 , which includes frequency-selective distortion caused by said channel  1320 , is then compensated with the aid of the estimated channel transfer function Ĥ(j·ω,t), and supplied to a parallel-to-serial converter  1316 . The output of said parallel-to-serial converter  1316  is finally fed to the channel decoder  1317 , and the user data is derived. 
     Using the output of the channel estimator  1318 , the so-called zero estimator  1321  estimates the position and movement of zero points (A, B, C), and supplies them to the central processing unit  1319  (CPU), which makes the modulation assignment plan for each subcarrier. 
     The main advantageous differences between the underlying invention and the state of the art consist in the prediction of the channel transfer function Ĥ(j·ω,t), which is determined on the basis of frequency-selective fading. Thereby, based on the principle of the propagation model, the channel distortion caused by frequency-selective fading is predicted. When the proposed approach according to the underlying invention is employed, the BER of OFDM systems using an adaptive subcarrier loading technique can significantly be reduced. Furthermore, the probability of an incorrect assignment of the applied modulation scheme for the subcarriers can be reduced by using said prediction method. 
     Table: Depicted Features and Their Corresponding Reference Signs 
     
       
         
               
               
             
           
               
                   
               
               
                 No. 
                 Feature 
               
               
                   
               
             
             
               
                  100 
                 diagram showing the spectrum of an OFDM symbol 101 and the 
               
               
                   
                 modulation schemes for its subcarriers 102 
               
               
                  101 
                 OFDM symbol consisting of 52 subcarriers 
               
               
                  102 
                 subcarriers of said OFDM symbol 101 
               
               
                  200 
                 four diagrams 201, 202, 203, and 204 showing the modulation 
               
               
                   
                 schemes that can be applied to each subcarrier 
               
               
                  201 
                 1 st  modulation scheme: Binary Phase Shift Keying (BPSK) 
               
               
                  202 
                 2 nd  modulation scheme: Quaternary Phase Shift Keying with a 
               
               
                   
                 phase shift of φ k  = k · π/4 for k ε {1, 3, 5, 7} (π/4-QPSK) 
               
               
                  203 
                 3 rd  modulation scheme: Quadrature Amplitude Modulation for 
               
               
                   
                 a 16-point signal constellation (16-QAM) 
               
               
                  204 
                 4 th  modulation scheme: Quadrature Amplitude Modulation for 
               
               
                   
                 a 64-point signal constellation (64-QAM) 
               
               
                  300 
                 block diagram for a mobile transmission and reception sys- 
               
               
                   
                 tem supporting wireless communication over a multipath 
               
               
                   
                 propagation channel 320 by means of a pilot-assisted wire- 
               
               
                   
                 less multi-carrier system (here: an OFDM system) comprising 
               
               
                   
                 means for a channel estimation 318 according to the state 
               
               
                   
                 of the art 
               
               
                  301 
                 OFDM transmitter 
               
               
                  303 
                 channel encoder 
               
               
                  304 
                 serial-to-parallel (S/P) converter 
               
               
                  305 
                 OFDM modulator 
               
               
                  306 
                 digital signal processor performing an Inverse Fast Fourier 
               
               
                   
                 Transform (IFFT) 
               
               
                  307 
                 digital-to-analog (D/A) converter 
               
               
                  308 
                 RF block performing a signal up-conversion from the base- 
               
               
                   
                 band to the passband 
               
               
                  309 
                 transmitting (TX) antenna 
               
               
                  310 
                 OFDM receiver 
               
               
                  311 
                 receiving (RX) antenna 
               
               
                  312 
                 RF block performing a signal down-conversion from the pass- 
               
               
                   
                 band to the baseband 
               
               
                  313 
                 analog-to-digital (A/D) converter 
               
               
                  314 
                 digital signal processor performing a Fast Fourier Trans- 
               
               
                   
                 form (FFT) 
               
               
                  315 
                 OFDM demodulator 
               
               
                  316 
                 parallel-to-serial (P/S) converter 
               
               
                  317 
                 channel decoder 
               
               
                  318 
                 channel estimator 
               
               
                  320 
                 multipath propagation channel, characterized by a severe 
               
               
                   
                 frequency-selective fading and a time-variant behavior 
               
               
                  400 
                 diagram showing a typical example for a propagation model 
               
               
                  401 
                 access point (AP) 
               
               
                  402 
                 RX/TX antenna of said access point 401 
               
               
                  403 
                 1 st  path of the radiated RF signal from the transmitter to 
               
               
                   
                 the receiver, characterized by reflection at buildings and 
               
               
                   
                 other objects 
               
               
                  404 
                 2 nd  path of the radiated RF signal from the transmitter to 
               
               
                   
                 the receiver, characterized by reflection at buildings and 
               
               
                   
                 other objects 
               
               
                  405 
                 mobile terminal (MT) in a moving receiver (e.g. a car which 
               
               
                   
                 drives at high speed) 
               
               
                  406 
                 receiving (RX) antenna of said mobile terminal (MT) 
               
               
                  500 
                 five diagrams giving an overview of channel distortion 
               
               
                   
                 caused by a severe frequency-selective fading and the time- 
               
               
                   
                 variant behavior of the underlying multipath propagation 
               
               
                   
                 channel 320 
               
               
                  501 
                 diagram showing the movement of zero points (A, B, and C) 
               
               
                   
                 of the channel transfer function H(s, t) on an s-plane, 
               
               
                   
                 where s is the complex observation frequency (s = σ + j · ω) 
               
               
                  502 
                 diagram showing the amplitude response |H(j · ω, t)| of the 
               
               
                   
                 channel transfer function H(j · ω, t) according to the current 
               
               
                   
                 position of its notches (A, B, and C) 
               
               
                  503 
                 diagram showing a conventional spectrum of an OFDM signal, 
               
               
                   
                 in which each subcarrier is modulated by a fixed modulation 
               
               
                   
                 scheme (202, 203, or 204) 
               
               
                  504 
                 diagram showing a first spectrum of a transmitted OFDM sig- 
               
               
                   
                 nal between the positions of the zero points A and B ac- 
               
               
                   
                 cording to the underlying invention 
               
               
                  505 
                 diagram showing a second spectrum of a transmitted OFDM 
               
               
                   
                 signal between the positions of the zero points B and C ac- 
               
               
                   
                 cording to the underlying invention 
               
               
                  600 
                 block diagram for a mobile transmission and reception sys- 
               
               
                   
                 tem supporting wireless communication over a multipath 
               
               
                   
                 propagation channel 620 by means of a pilot-assisted wire- 
               
               
                   
                 less multi-carrier system (here: an OFDM system) comprising 
               
               
                   
                 means for a channel estimation 618, which can be used for 
               
               
                   
                 an adaptive subcarrier loading 
               
               
                  601 
                 OFDM transmitter 
               
               
                  603 
                 channel encoder 
               
               
                  604 
                 serial-to-parallel (S/P) converter 
               
               
                  605 
                 OFDM modulator 
               
               
                  606 
                 digital signal processor performing an Inverse Fast Fourier 
               
               
                   
                 Transform (IFFT) 
               
               
                  607 
                 digital-to-analog (D/A) converter 
               
               
                  608 
                 radio frequency (RF) block 
               
               
                  609 
                 transmitting (TX) antenna 
               
               
                  610 
                 OFDM receiver 
               
               
                  611 
                 receiving (RX) antenna 
               
               
                  612 
                 radio frequency (RF) block 
               
               
                  613 
                 analog-to-digital (A/D) converter 
               
               
                  614 
                 digital signal processor performing a Fast Fourier Trans- 
               
               
                   
                 form (FFT) 
               
               
                  615 
                 OFDM demodulator 
               
               
                  616 
                 parallel-to-serial (P/S) converter 
               
               
                  617 
                 channel decoder 
               
               
                  618 
                 channel estimator 
               
               
                  619 
                 central processing unit (CPU) 
               
               
                  620 
                 multipath propagation channel, characterized by a severe 
               
               
                   
                 frequency-selective fading and a time-variant behavior 
               
               
                  700 
                 example of a downlink signal burst with three preambles 
               
               
                   
                 (A, B, and C) according to the HiperLAN/2 standard 
               
               
                  701 
                 1 st  preamble frame (A) of the downlink signal burst 700 
               
               
                  702 
                 2 nd  preamble frame (B) of the downlink signal burst 700 
               
               
                  703 
                 3 rd  preamble frame (C) of the downlink signal burst 700 
               
               
                  704 
                 data frame of the downlink signal burst 700 
               
               
                  800 
                 sequence chart showing the data transfer between the access 
               
               
                   
                 point 401 (AP) and the mobile terminal 405 (MT) according 
               
               
                   
                 to the state of the art 
               
               
                  801 
                 downlink signal transmission 
               
               
                  802 
                 channel estimation 
               
               
                  803 
                 proposal for the execution of a modulation scheme according 
               
               
                   
                 to the state of the art 
               
               
                  803′ 
                 proposal for the execution of a modulation scheme using the 
               
               
                   
                 position and movement of zero points of the channel trans- 
               
               
                   
                 fer function H(j · ω, t) according to the underlying invention 
               
               
                  804 
                 evaluation of the proposal 803 for the execution of a modu- 
               
               
                   
                 lation scheme 
               
               
                  805 
                 set-up of a modulation scheme 
               
               
                  806 
                 estimation of the position of zero points of the channel 
               
               
                   
                 transfer function H(j · ω, t) 
               
               
                  807 
                 prediction of the position of said zero points for the pre- 
               
               
                   
                 amble C of next downlink signal burst j 
               
               
                  808 
                 estimation of the movement of zero points of the channel 
               
               
                   
                 transfer function H(j · ω, t) using the results of the current 
               
               
                   
                 downlink signal burst j − 1 and the next downlink signal 
               
               
                   
                 burst j 
               
               
                  900 
                 sequence chart showing the data transfer between the access 
               
               
                   
                 point 401 (AP) and the mobile terminal 405 (MT) according 
               
               
                   
                 to the underlying invention 
               
               
                 1000 
                 two diagrams giving an overview of the adaptive subcarrier 
               
               
                   
                 loading according to the underlying invention 
               
               
                 1001 
                 diagram showing the amplitude response |H(j · ω, t)| of the 
               
               
                   
                 channel transfer function H(j · ω, t) 
               
               
                 1002 
                 diagram showing the spectrum of a transmitted OFDM signal 
               
               
                   
                 and the modulation schemes of its subcarriers 102 
               
               
                 1100 
                 flowchart of a modulation scheme planning 
               
               
                 1200 
                 timing chart according to the underlying invention which is 
               
               
                   
                 applied to calculate the movement of zero points of the 
               
               
                   
                 channel transfer function H(j · ω, t) 
               
               
                 1201 
                 downlink signal burst j − 1 with the preambles A, B, and C 
               
               
                 1202 
                 preamble C of the (j − 1)-th downlink signal burst 1201 
               
               
                 1203 
                 downlink signal burst j with the preambles A, B, and C 
               
               
                 1204 
                 preamble C of the j-th downlink signal burst 1203 
               
               
                 1205 
                 unit applied to calculate the movement of zero points of 
               
               
                   
                 the channel transfer function H(j · ω, t) 
               
               
                 1206 
                 1 st  unit applied to estimate the position of zero points of 
               
               
                   
                 the channel transfer function H(j · ω, t) based on the pream- 
               
               
                   
                 ble C of the (j − 1)-th downlink signal burst 1201 
               
               
                 1207 
                 2 nd  unit applied to estimate the position of zero points of 
               
               
                   
                 the channel transfer function H(j · ω, t) based on the pream- 
               
               
                   
                 ble C of the j-th downlink signal burst 1203 
               
               
                 1208 
                 downlink signal burst j + 1 with the preambles A, B, and C 
               
               
                 1300 
                 block diagram for a mobile transmission and reception sys- 
               
               
                   
                 tem supporting wireless communication over a multipath 
               
               
                   
                 propagation channel 1320 by means of a pilot-assisted wire- 
               
               
                   
                 less multi-carrier system (here: an OFDM system) comprising 
               
               
                   
                 means for a channel estimation 1318 according to the under- 
               
               
                   
                 lying invention, which can be used for an adaptive subcar- 
               
               
                   
                 rier loading 
               
               
                 1301 
                 OFDM transmitter 
               
               
                 1303 
                 channel encoder 
               
               
                 1304 
                 serial-to-parallel (S/P) converter 
               
               
                 1305 
                 OFDM modulator 
               
               
                 1306 
                 digital signal processor performing an Inverse Fast Fourier 
               
               
                   
                 Transform (IFFT) 
               
               
                 1307 
                 digital-to-analog (D/A) converter 
               
               
                 1308 
                 radio freguency (RF) block 
               
               
                 1309 
                 transmitting (TX) antenna 
               
               
                 1310 
                 OFDM receiver 
               
               
                 1311 
                 receiving (RX) antenna 
               
               
                 1312 
                 radio freguency (RF) block 
               
               
                 1313 
                 analog-to-digital (A/D) converter 
               
               
                 1314 
                 digital signal processor performing a Fast Fourier Trans- 
               
               
                   
                 form (FFT) 
               
               
                 1315 
                 OFDM demodulator 
               
               
                 1316 
                 parallel-to-serial (P/S) converter 
               
               
                 1317 
                 channel decoder 
               
               
                 1318 
                 channel estimator 
               
               
                 1319 
                 central processing unit (CPU) 
               
               
                 1320 
                 multipath propagation channel, characterized by a severe 
               
               
                   
                 freguency-selective fading and a time-variant behavior 
               
               
                 1321 
                 zero estimator 
               
               
                 A 
                 position of the i-th zero point T i,j−1  of the channel trans- 
               
               
                   
                 fer function H(s, t) on an s-plane obtained for the (j − 1)-th 
               
               
                   
                 downlink signal burst, which corresponds to a certain notch 
               
               
                   
                 on the amplitude response |H(j · ω, t)| of the channel transfer 
               
               
                   
                 function H(j · ω, t) at the discrete time j − 1 
               
               
                 B 
                 position of the i-th zero point T i,j  of the channel transfer 
               
               
                   
                 function H(s, t) on an s-plane obtained for the j-th down- 
               
               
                   
                 link signal burst, which corresponds to a certain notch on 
               
               
                   
                 the amplitude response |H(j · ω, t)| of the channel transfer 
               
               
                   
                 function H(j · ω, t) at the discrete time j 
               
               
                 C 
                 position of the i-th zero point T i,j+1  of the channel trans- 
               
               
                   
                 fer function H(s, t) on an s-plane obtained for the (j + 1)-th 
               
               
                   
                 downlink signal burst, which corresponds to a certain notch 
               
               
                   
                 on the amplitude response |H(j · ω, t)| of the channel transfer 
               
               
                   
                 function H(j · ω, t) at the discrete time j + 1