IL192313A - Method and equaliser for detecting data symbol sequences from a received signal containing said sequences, transmitted via a time-variable transmission channel - Google Patents

Description

METHOD AND EQUALISER FOR DETECTING DATA SYMBOL SEQUENCES FROM A RECEIVED SIGNAL CONTAINING SAID SEQUENCES, TRANSMITTED VIA A TIME-VARIABLE TRANSMISSION CHANNEL □mie/ia, fin D'D*T VjiDn o^pa TUKYI υτη 'Dsn ■ΙΊΆ'Ι ιτχηι no«¾/ Eitan-Mehulal Law Group Advocates-Patent Attorneys P-10618-IL I, David Charlston, MMus, BA, MIL, MITI, Dipl. Trans., of 26 Castleford Rd, Ludlow, Shropshire, SY8 IDF hereby certify that to the best of my knowledge and belief the following is a true translation made by me of the full specification including drawings of PCT Application No. PCT/EP2006/011198 Dated this day of 1 Translation of PCT/EP2006/011198 Method and equaliser for the detection of data- symbol sequences transmitted via a time-variable transmission channel from a received signal containing the latter The invention relates to a method and an equaliser for the detection of data-symbol sequences transmitted via a time-variable transmission channel from a received data signal containing the latter.

Received signals in a real transmission channel are subject to many forms of disturbance. In addition to the superposition of interference signals - primarily noise -, the transmitted signal is particularly susceptible to interference. In a mobile telephone network, this interference can result from inter-symbol interference, from the superposition of different transmitted signals, which result from several mobile-telephone devices from adjacent cells transmitting in the same frequency band (same-channel interference) or from different frequency bands (adjacent-channel interference) , or can result from the superposition of identical transmitted signals, which are transmitted by a single user via different transmitters - transmitter-end diversity with space-time coding or diversity-generating delays.

The disturbed received signal, which is present after demodulation as a distorted and additively and/or multiplicatively disturbed data-symbol sequence, must be transferred in an equaliser into several data streams 2 corresponding to the individual, transmitted data-symbol sequences .

The prior art provides a plurality of detection and equalisation methods, from which the optimum detection or equalisation methods must be selected in each case dependent upon the available transmitted signal and the dominant sources of interference and distortion.

One important group of detection and/or equalisation methods is represented by the maximum- likelihood methods, according to which the disturbed, received data-symbol sequence is compared with all possible undisturbed data-symbol sequences from a data-symbol alphabet used in the modulation, and the undisturbed data-symbol sequence, which provides a minimal Euclidian distance relative to the disturbed, received data-symbol sequence, is selected as an estimate for the transmitted data-symbol sequence. The number of comparisons between the disturbed, received data symbol and all possible reference data symbols, which corresponds to the cardinality of the data-symbol alphabet of the modulation method used, can be extremely large in the case of relatively high-quality modulation methods, for example, even with 8-PSK, and, in particular, with 64-QAM, 128-QAM.

This complexity in estimation is additionally intensified by the fact that, because of the convolution of the transmitted data-symbol sequence with the impulse response of the transmission channel of a given impulse length, components of a data symbol of the transmitted data-symbol sequence are superposed over data symbols of the transmitted data-symbol sequence preceding them in time. These time couplings 3 between the individual data symbols of a data-symbol sequence, which represent a finite-state machine, can be modelled in their time sequence by means of a state diagram. One widely distributed state diagram, the trellis diagram, represents all possible states and state transitions for the impulse length of the impulse response of the transmission channel and for the data-symbol alphabet of the modulation method used.

Using the trellis diagram, the estimation of the data symbol transmitted at the respective timing point can be determined from the Euclidian distance between the disturbed data symbol received at the respective timing point and all reference data symbols corresponding to the possible states at the respective timing point. An estimation of the data symbol transmitted at each timing point is not possible in real time because of the plurality of states and the even-more-numerous possibilities for combinations of successive states in the high-quality modulation methods used at present . One practicable approach to this problem is provided by the Viterbi algorithm, which reduces the plurality of possible combinations in the trellis diagram by selecting only the transition between a state at the last timing point and all possible following states at the current timing point, which provides the minimum Euclidian distance between the disturbed data symbol received at the current timing point and the reference data symbols associated with all possible precursor states at the current timing point. In this manner, the estimation problem is reduced to the identification of the number of so-called "survival paths" in the trellis diagram corresponding to the number of states. 4 In minimising the Euclidian distance at each state transition, not only must the data symbol associated with the state to be selected at the current timing point be estimated, but the impulse response of the transmission channel at the current timing point must also be estimated as a result of the time variability of the transmission channel . Since the estimation of the impulse response of the transmission channel at the current timing point is dependent upon the data symbol transmitted at the current timing point and therefore upon the data symbol estimated at the current timing point, an estimate of the impulse response of the transmission channel is required for every state at the current timing point. With a symbol alphabet of the modulation methods used of cardinality M and a total of Ns states per timing point, a total of M - Ns estimates of the channel-impulse response must therefore be implemented.

This plurality of estimates of the impulse response of the transmission channel is reduced in the case of methods according to the prior art in that the number of states is reduced by "shortening the impulse length of the transmission channel" .

For the most general case, wherein different transmitted signals are transmitted from different transmitters in each case via different transmission channels and superposed on a received signal, the transmission signal illustrated in Figure 1 is obtained. A data-symbol sequence ∑d{l) (k)S(t - kT), ..,∑d{u) (k)S(t - kT), ..,∑d{U k)S(t - kT) is transmitted * k k respectively in several transmitters llf .. , lu, .. , lu, which each provide a transmitter-weighting function £ΤΊ( »··.£Λ(')>■■»ί?π/(0 · The data-symbol sequence weighted respectively with the transmitter-weighting function is supplied via a respective transmission channel 21# .. , 2U, .. , 2u with the respective time-variant weighting function gcwl(r,t),..,gCHu(r, ,..,ga/y(T> to a receiver 3, which is generally realised as a matched-filter with the weighting function gR(t) , to a sampling unit 4, a pre-filter 5 and a mixed channel-data estimator 6. This pre-filter 5 is realised as an impulse-shortening filter optionally combined with a whitening filter.

The realisation of an impulse-shortening filter of this kind in combination with a data-channel estimator, in which a joint-delayed-decision-feedback-estimation algorithm (JDDFSE) - a variation of the Viterbi algorithm with the memory of several parallel-transmitted data-symbol sequences per state of the trellis diagram - is implemented and which represents the prior art for the combined data-channel estimation in the case of a superposition of several transmitted symbol sequences in a received symbol sequence, is described by Detert, T. : "Fractional Spaced Channel Estimation and Shortening for Joint Delayed Decision Feedback Sequence Estimation". As an alternative, the detection and equalisation of several simultaneously-occurring, received symbol sequences can also be implemented with a joint-maximum likelihood sequence estimator (JMLSE) or a joint reduced-state sequence estimator (JRSSE) instead of the JDDFSE algorithm. 6 The disadvantage of all of these realisations is the comparatively-high computational cost for calculating the filter algorithm of the pre-filter.

Added to this is the fact that, in the practical use of the maximum-likelihood method for estimating the transmitted data-symbol sequences, a so-called block fading, wherein an estimate of the respective channel -impulse response is implemented only once per time slot or per data-symbol burst to be transmitted, is assumed for reasons relating to computational time, and the impulse response of the respective transmission channel is regarded as constant over the length of the time slot or respectively the data-symbol burst. With this approximation for the impulse response of the respective transmission channel, in the least favourable case, if the convolution of the data-symbol sequence r(k) received and pre-filtered with the matched filter is implemented with the impulse response gIS (k) at the end of the data-symbol burst - symbol "o" in Figure 2 -, the respective channel has changed and, as shown in Figure 2, pre-shooters occur; these do not occur in the more favourable case of the convolution of the data-symbol sequence r(k) received and pre-filtered with the matched filter with the impulse response gIS(k) in the middle of the data-symbol burst - symbol "x" in Figure 2. The reason is that gIS(k) results from an estimation of the respective channel by means of a training sequence. The further one moves away from the training sequence, the less gfS(k) shortens the changing channel in each case. As a result, in the unfavourable case, in spite of a good signal/noise 7 ratio, an undesirable error floor occurs in the received data-symbol sequence with the use of a matched filter.

The object of the invention is therefore to develop a method and a corresponding equaliser for the detection of several transmitted data-symbol sequences from the disturbed, received data-symbol sequence transmitted respectively via a time-variable transmission channel, which is associated with low computational costs and which at the same time generates no additional interference in the received data-symbol sequence with a given signal/noise ratio.

The object is achieved by a method for detection of several transmitted data-symbol sequences from a received signal transferred in each case via a time-variable transmission channel with the features of claim 1 and a corresponding equaliser with the features of claim 20. Advantageous further developments of the method according to the invention are -specified in the dependent claims.

With the method according to the invention, the metric for selecting the states in the individual "survival paths" at the current timing point - as estimates for the data symbol transmitted at the current timing point via the respective transmission channel - and also the estimates for the respective channel-impulse response at the current timing point are both calculated iteratively.

In this context, since the metrics associated with the individual states at the current timing point and also the estimates of the individual channel -impulse responses for every state at the current timing point depend upon the 8 estimation of the individual channel-impulse responses at the preceding timing points, with a total of Ns states at the preceding timing point, only Ns estimates of the respective channel-impulse responses are required in each case by contrast with the total of M-Ns estimates of the respective channel-impulse responses required when using the Viterbi algorithm.

As in the case of the Viterbi algorithm, those states in the trellis diagram, which provide a minimal path metric, are selected at the current timing point. In a first embodiment of the invention, only those states, which result from a common state at the preceding timing point, are taken into consideration by means of minimisation of the metric in the selection; while in a second embodiment of the invention, all states at the current timing point, which result from all states at the preceding timing point, are used in the selection of the states by minimisation of the metric.

The method according to the invention can search the trellis diagram not only initially "by width" for an optimal estimate for the respectively-transmitted data-symbol sequence ("breadth-first" method), as just presented, but, in a further embodiment of the invention, can also initially search through the trellis diagram "by depth" for an optimal estimate for the respectively-transmitted data-symbol sequence ( "depth-first" method) by analogy with the stack algorithm.

In the iterative calculation of the path metric of a state at the current timing point, the associated branch metric is 9 added to the path metric of the precursor state at the preceding timing point, which is obtained from the product of a first and second a-priori estimation error. In their turn, the first and respectively second a-priori estimation errors are obtained from the difference between the data-symbol sequence received in each case at the current timing point and the estimation of the estimate of the data-symbol sequence transmitted up to the current timing point respectively weighted with an impulse response of the respective transmission channel estimated at a first and respectively second timing point. In each case, the first and second timing point represents a different timing point before the current timing point.

Instead of the product of a first and second a-priori estimation error, the product of an a-priori estimation error and an a-posteriori estimation error can also be used. In this context, the a-priori estimation error is obtained from the difference between each data-symbol sequence received up to the current timing point and the estimation of the estimate of the data-symbol sequence transmitted in each case up to the current timing point weighted with an impulse response of the respective transmission channel estimated at the preceding timing point, and the a-posteriori estimation error is obtained from the difference between each data-symbol sequence received up to the current timing point and the estimate of the data-symbol sequence transmitted in each case up to the current timing point weighted with an impulse response of the respective transmission channel estimated at the current timing point.

In further embodiments of the invention, the products from the first and second a-priori estimation error or respectively the products from the a-priori estimation error and the a-posteriori estimation error can be subjected to a modulus-forming function, a real-component forming function or another function to simplify the calculation of the values consisting of complex numbers.

Previously-transmitted data symbols can be weighted less-strongly in the recursive calculation of the path metrics than data symbols transmitted at a later time by introducing a weighting factor.

Since, as a result of the convolution operation in the determination of the estimate of the respectively-received data-symbol sequence at future timing points, estimated values for respectively-transmitted data symbols and channel -impulse responses at the current timing point or respectively at preceding timing points, which are already determined at the current timing point, are included, these can be taken into consideration, in a further embodiment of the invention, within an extension term, which forms an extended path metric with the iteratively-calculated path metric. Since, future respectively received and transmitted data symbols are not yet known at the current timing point, the extended metric is determined at the current timing point as an expected value for the differences between the data symbols received in each case at future timing points and the data symbols of the data-symbol sequences transmitted respectively at future timing points weighted respectively with the impulse response of the respective transmission channel estimated at the current timing point, 11 wherein the number of future timing points corresponds to the impulse length of the respective channel-impulse response reduced by the factor 1.

In this manner, the full energy of the data symbol transmitted in each case at the current timing point is taken into consideration in the estimation of the respectively-received data-symbol sequence at the current timing point, and accordingly, the estimation error in the equalisation of a respectively-received data-symbol sequence, which is transmitted on each transmission channel with a channel-impulse response with an impulse length greater than 1, is minimised.

The iterative estimate of the channel-impulse response of each transmission channel can be implemented via an adaptive, recursive channel-estimation method, for example, via the recursive-least-squares algorithm. However, other adaptive, recursive channel-estimation methods can also be used as an alternative.

The channel-impulse response of the respective transmission channel need not be estimated at every timing point. In the case of a slowly-changing channel-impulse response of the respective transmission channel, an estimation within a larger time raster is entirely possible. If the channel-impulse response of the respective transmission, channel changes only to an insubstantial extent, it is sufficient to implement a channel estimation only at the beginning of the transmission. 12 The individual embodiments of the method according to the invention and the equaliser according to the invention for the detection of data-symbol sequences transmitted via a time-variable transmission channel from a received signal are explained in detail below with reference to the drawings. The drawings are as follows: Figure 1 shows a block-circuit diagram of the transmission system according to the prior art; Figure 2 shows a time-flow chart of the impulse response with a transmission system with a pre-filter according to the prior art; Figure 3 shows a trellis diagram for estimation of the data-symbol sequence according to the method of the invention; shows an overview diagram of relevant terms for the path-metric calculation at different timing points ; shows a block circuit diagram of the transmission system according to the invention; shows a flow chart of the method according to the invention; Figure 7 shows a presentation of the bit-error probability dependent upon the transmission power of two transmitters in the context of a 13 method according to the prior art and the method according to the invention.

Before presenting in greater detail with reference to Figure 6 the method according to the invention for the detection of several transmitted data-symbol sequences transferred respectively via a time-variable transmission channel from a received signal, the following paragraphs describe the mathematical basis required for an understanding of the method according to the invention: The starting point for the method according to the invention is a time-invariant or time-variant signal model of the transmission channels according to equation (1) : Dw-hik)+n (1) For the estimation of the impulse responses of the transmission channels, the transmission channels are excited in a first phase with a transmitted data-symbol training-sequence d of length I, . In order to estimate the impulse response of the respective transmission channel in the first Lt timing points, an adaptive channel -estimation algorithm can be used without taking into consideration the channel statistics (for example, a least-squares algorithm) , taking into consideration the unknown channel statistics (for example an MMSE channel-estimation methods) , taking into consideration the known channel statistics (for example, a maximum-likelihood estimation method or derivatives therefrom) or a blind or semi-blind first channel estimate. 14 Consequently, an estimation of the transmitted data symbols cannot be implemented in the first I( received data symbols r(k), 0≤k≤Ll - l, but can be implemented, at the earliest, at the timing point Lt . The vector r lc) of the received data symbols for the estimation of the respectively-transmitted data symbols at a random timing point k therefore begins according to equation (2) only from the timing point Lt . rw = [r(I,), r( +l), ... ,rWf (2) By analogy, the noise vector « according to equation (3] only begins from the timing point Lt . «w - [n(X,),«(A + l),... ,n(A:)f (3) According to equation (4), the vector h contains the impulse responses of the individual transmission channels: hw =[h .,L{k)T,.,huwT)T (4) In this context, the impulse response huw of the u"th transmission channel is obtained according to equation (5) . u{k)T ={Κ(θ)Α(^-Α(^-ψ (5) The Toeplitz matrix Du of the data symbols transmitted by the u"th transmitter is therefore obtained according to equation (6) : du(L.) du(L,-l) du{Lt-{Lh-\)) du(L,+l) du(Lt) du(L,-(Lh-2)) D k) = du(L,+2) du(L,+l) du(L,-(Lh-3)) (6) du{k) du{k-\) du(k-(Lh-l)) The Toeplitz matrix D in equation (1) is therefore composed according to equation (7) from the individual Toeplitz matrices defined for each transmitter according to equation (6) . (7) In order to estimate the data symbols transmitted at the timing point k respectively from a received data-symbol sequence r after a total of N timing points according to equation (8) , wherein N is a random timing point N extended by the impulse length Lh of the respective channel -impulse response, using the maximum-likelihood approach, the conditional probability is maximised. r = [r(0),r(l),...,r(N-l)]T where N = N + Lh-\ (8) The conditional probability from the received data-symbol sequence r can, according to equation (9) , be approximated by the conditional probability from the received data-symbol sequence (k) r up to the timing point k . 16 P{ W\r)»P{Dw\rm) (9) An identity between the two conditional probabilities in equation (1) is generally not present, since signal components of the respectively-transmitted data-symbol sequence duw can also be contained in the received data-symbol sequences { ^'' after the timing point k because of the convolution of the data-symbol sequence k) =[du(k),du(k-\),du(k-2),...,du(k-(Lh-l))]T transmitted, for example, by the u~th transmitter with the impulse response hu , for example, of the u"th transmission channel.

Equation (10) is obtained after the application of the Bayes rule and logging of the conditional probabilities in equation (9) : fp(rw\Dw)-P(Dw^ = ln P(r(k)) (10) Since all of the data- symbol sequences D are assumed to be equally probable, equation (11) applies. const. (11) The probability density function f w(r ) of a data-symbol (k) sequence r received up to the timing point k provides an identical characteristic for all possible data-symbol 17 sequences R received up to random timing points k and therefore does not influence the conditional probability p(Dik)\r).

For Gaussian-distributed noise, the probability density function k)(rw | Dk)) is obtained according to equation (12), wherein L^D(k),hik r{k)) denotes the log- likelihood function, Cn denotes the covariance matrix of the noise signal n , In denotes the unity matrix and N denotes the dimension of the received data- symbol sequence r according to equation (13) : / J^■<*>,„<-) (->" \ I -D ) = -^= e ' where C =σ„ -L (12) N = k-L,+l (13) Taking into consideration the mathematical relationships in equations (11) to (13) , the mathematical relationship for the Togged conditional probability ln.P(Z)w|r) can be transferred, starting from equation (10) , to equation (14) . ln( ( w| « ln ^(i) (rw|5(4)) = -L(D{k),hw,rw)-(k - L, +\)\ηπ -1ησ„2 (14) The log-likelihood function L(Dw,hw,rw) is obtained by analogy with Kammeyer, K. D. : "Message Transmission", 18 Teubner-Verlag, 1996, page 554-555, according to equation (15) : L(Dw,hw,rw)= (rik) - Dw ■ hw)" -(rw - Dw -hw) (15) Since the two last terms in equation (14) contain only parameters, they are not essential for the maximisation of the conditional probability P Dw \rJ* and can be ignored. The conditional probability P^DW |r is consequently maximised, wherein the log-likelihood function l(Dw,hw,rw) is minimised.

The mathematical relationship for the conditional probability P^D(k) \rj in equation (15) can be converted starting from Trager, J. : "Combined Channel Estimation and Decoding for Mobile Telephone Channels", ISBN 3 -8265-4336-X, Shaker-Verlag, Aachen, 1993, corresponding to equation (16). (16) ,(*) (*) In this context, an estimate of the channel -impulse response hw according to the RLS algorithm - reduced-least-squares algorithm - is used according to equation (17) . 19 =(DW"DW\ -DW" - rik) (17) It is very evident that the quadratic form of the first term 1 j 1 j-y minimises the log-likelihood function through the RLS algorithm used in this context.

Furthermore, since the third term r C~ r of the log-likelihood function provides · a dependence neither upon the channel-impulse response hw nor upon the Toeplitz matrix DW , only the quadratic form of the second term r k)HC DW (DW"C;1DW)~L DWHC;lrw of the log-likelihood function can be used in the estimation of the data symbol transmitted at the timing point k . For this purpose, the path metric M(k) according to (18) is maximised.

Mt» =r_w" .Dik).{D{k)HDw)1 -D{k)H -rw (is) By analogy with the Viterbi algorithm, the path metric M{k) according to equation (18) must be calculated in order to estimate the data symbols transmitted respectively at every timing point k for every state at every timing point k .

Since the calculation of every individual path metric M{le) is too complicated with regard to the method according to the invention for the detection of several transmitted data-symbol sequences transferred respectively via a time- variable transmission channel from a received signal, an iterative path metric Mk) for maximum-likelihood estimation of the data symbols transmitted respectively at the timing point k and an iterative maximum-likelihood estimated value (k) (i) /z, ,..,hu are derived in the paragraphs below for the individual channel-impulse responses at the timing point k .

In both cases, the iteration is implemented over every individual timing point k from data symbol to data symbol . In general, the Toeplitz matrix Dw must first be estimated iteratively at every timing point k, and, on the basis of the iteratively estimated Toeplitz matrix Dw , the channel- f (*) f (*) (*) , . impulse responses hx ,..,nu must be estimated iteratively, which are used once again for the iterative estimation of the Toeplitz matrix D(k+l) at the next timing point k + l . Alternatively, the iteration of the estimated values h ,.., u ,-,\υ of the channel-impulse responses can also be implemented over several data symbols.

In order to develop a respectively-independent iteration for (k) (t) the estimated values A, ,..,hu ,-.,Α^ of the channel-impulse responses h(k ,..,huw',-.,Λ^ and for the path metric M{k) taking into consideration the last iteratively-determined estimated values of the respectively other estimated value, in an intermediate stage for the calculation of the estimated values Λ, ,-, u ...,Α^ of the channel-impulse responses hiW >~>hulk) >->tlu k) according to equation (17) , the two auxiliary 21 parameters v(t) according to equation (19) and B(k) according to equation (20) are introduced. y(*> =Dlk)" -_rw (19) <*> = D_(k)H ■ D_(k) (20) The estimated values A, ,..,Λ„ of the channel-impulse responses A,i),.., uw,..,hyk) can therefore be determined taking into consideration the auxiliary parameters v(t) and D(A) according to equation (21) . (2i; The two auxiliary parameters - vector v(i) and matrix JD{k) -can each be calculated iteratively according to equation (22) and (23) : v(t|= -"+ . W (22) Dw = ik-l +dw' -ikf (23) The data-symbol sequence d(k) is obtained according to equation (24) from the data-symbol sequences ,..,du(k),,.,ά^ transmitted by the individual transmitters 1χ, .. , lu,■ . , lu in each case. d{k) ^{d^d^k-l) ...4(*-(Z -l)) ... du{k) du(k-l) .. du(k-(Lhu-\)) ... .... dv(k) dvik-V) .. du{h-(Lhu-\))) (24) 22 Since, under some circumstances, the data- symbol sequence d_{k) provides data symbols with a negative index, dependent upon the timing point k and upon the impulse length Lhl,..,Lhu,..,LhU of the' respective channel -impulse response h\k ~>huk ~>huk) > these are suitable for initialisation (e.g. dl(k),..,du(k)1..,d(/(.k) = 0 Vk<0).

Using the matrix- inversion lemma by analogy with Kammeyer, K.D. : "Message Transmission", Teubner-Verlag, 1996, page 729-730, the inverse matrix E>{k)~' of the matrix D(k) is obtained according to equation (25) using the Kalman amplification g(k) according to equation (26) : kr> = JD{k-)" - gw■dkf ■ JD{k-yl (25) gW = £(*-!)-' . . (1 + . ø(*-!)- . ( 2g ) Equation (25) can be mathematically transformed according to equation (27) , and equation (26) can be transformed taking into consideration equation (27) according to the equation (28) . (27) DW- .dw' =gw-(\ + d{k)T -≠k-iyi -dw')-gw -d}k)T -D(*-ir' -d(k)' (28) 23 From equation (28) , the mathematical relationship of the Kalman amplification g{k) is finally obtained according to equation (29) : gW = W' -dw' (29) The iterative calculation of the estimated values « (A) - (A) ~ (A) i > ~> ku -> h.u °f tne channel -impulse responses hi k --> huk)>">huk) is obtained, starting from equation (21) and taking into consideration equations (22) , (25) and (29) , according to equation (30) : h =h +g( ) -(r(k)-d -h ) (30) With the introduction of the a-priori estimation error e{k*~) between the received data symbol r(k) and the estimates - (kf (A-l) j (kf r (A-l) j W f (*-D _ · j j v, i ίίι -.ii >·■,_£_/ of tne received data-symbol sequences d^■ ,..,duWT ■ ,-,έα^ -h^ , which are obtained (A) (A) (A) from the weightings of the estimates rf, ,..,du ,-,ά_υ of the data- symbol sequences d k),..,du(k),..,dyk) transmitted up to the timing point k with the channel -impulse responses * (A-l) (A-l) » (A-l) j¾i ,..,/zu estimated at the previous timing point k-l, the iterative calculation formula for the estimated »(*) ik) value h of the channel -impulse response h can be transformed according to equation (30) , starting from equation (31) , into equation (32) . 24 e^ = r{k)-tT -tX) (3D = % »-e« (32) The iterative calculation of the path metric M(k) for maximum- likelihood estimation of the data symbols dl(k),.., du (k), .., du(k) transmitted at the timing point k is obtained starting from equation (18) taking into consideration the mathematical relationship for the auxiliary parameter v in equation (17) and the ->(*) mathematical relationship for the estimated value h of the channel -impulse response in equation (19) corresponding to equation (33) : M^=vW" (33) Equation (33) can be mathematically transformed, taking into consideration the iterative calculation formula for the auxiliary parameter v(t) in equation (22) and for the estimated value h of the channel-impulse response in equation (32), into equation (33'): (k-l)H k)T)(£ .(* *l*-i) ) (33') Equation (33') can be transformed into equation (33'') taking into consideration the mathematical relationship for the Kalman amplification factor gw in equation (26) and the iterative calculation formula for the auxiliary parameter vw in equation (22) . ΰ "t^ rik ' ^^^t'e^ (33 ~ ) The first term in equation (33'') corresponds to the path metric M(k~l) at the previous timing point k - l . The term v(k)HDw_1 in equation (33'') can be substituted according to equation (32) with the estimated value h of the channel-impulse response. Finally, the right-hand side of equation (33'') can be extended with the modulus squared of the received data-symbol sequence \r(k) and the modulus-identical negative term - r(k)' · r(k) . Accordingly, the iterative calculation formula for the path metric M(k) presented in equation (33''') is obtained.

Mw = M k~l) - r{k)'■ {r{k) - · ) + ■ '· e k]k~l) + \r(k)\2 (33'") Taking into consideration the a-priori estimation error e(*M) according to equation (31), equation (33''') can be transferred into equation (33''''). w = (*-" - {r{k)'- - ^-^ + \r(k)\2 (33 " " ) If the a-posteriori estimation error e( is introduced between the received data symbol r(k) and the estimates -Λι ,..,^u ·Λ„ - h of the received data-symbol sequences d -A *- ,..,^ -A^-0.--.^ """- which are obtained from the weightings of the data-symbol sequences 26 λ (*) » (*) ,.·,4λ_υ(*) d_x , .., du transmitted up to the timing point k with the channel -impulse responses h ,.., hu , .., hu estimated at the timing point k according to equation (34) , the iterative calculation formula for the path metric w of the maximum-likelihood estimate of the data symbol dl (k), .., du (k),.., du (k) transmitted at the timing point k can be represented mathematically according to equation (33''''') · e^ = r(k)-t)T (34) Mw = M(k~l) - e{m'■ eWk~l) + \r(k)f (33 ) Since the term |r(&)|2 in the iterative calculation formula for the path metric M{k) in equation (33''''') is not an estimated value and is therefore not significant for decision-making in the trellis diagram, it can be ignored and, it is therefore possible to transform equation (33''''') into equation (35) .

MW=M -ewr.ew-» (35) The inverse matrix Bw ' of the matrix JDW is described as a prediction-error-correlation matrix Kw . With the introduction of the prediction-error-correlation matrix Kw , equation (25) can be transformed into equation (36), and equation (26) can be transformed into equation (37) . (36) 27 g<*> = (*-■> . . (1 + ^*>r . ^(*-D . )-i ( 3 7 ) In view of the time variance of the transmission channel, data symbols transmitted at an earlier time have a lower significance in the equalisation results of the currently-received data symbol r(k) than data symbols transmitted currently. This circumstance is taken into consideration by a forgetting factor μ with a value range: 0 Accordingly, maximisation of the path metric Mk according to equation (40) can be transformed into a minimisation of the path metric M(k) according to equation (43) using a modulus-forming function, or according to equation (44) using a real -component forming function. (43) Mw=Re{ -M{k-l -em'-e^} (44) 29 A calculation formula for a path metric Mk) to be minimised, which is equivalent to equations (43) and respectively (44) is obtained by modulus formation of the term e'im■ eWk'l) and subsequent addition to the path metric M(k~l) calculated at the preceding timing point k-l according to equation (45) or by real -component formation of the term e'1*1*' ·β(* ) and subsequent addition to the path metric M{k~[) calculated at the preceding timing point k-l according to equation (46) . e(m* . e<* ) (45) w = μ■ M^ + Re(ew · e« } (46) For the calculation of the path metric Mw , instead of the product from the a-priori estimation error e(t|i_1) at the preceding timing point k-l and the a-posteriori estimation error e( at the current timing point k , as an alternative, a product from an a-priori estimation error and/or an a-posteriori estimation error e(k^~n) at the timing point n according to equation (47) and from an a-priori estimation error and/or an a-posteriori estimation error e k~m) at the timing point m can be used in the embodiments of equations (48) , (49) , (50) and (51) , wherein the timing points n and m are integer, positive values 0≤m,n, n,meN0. The timing points n and m should be selected dependent upon the time-variability of the transmission channel. In the case of a large time variability, relatively small values are appropriate for the timing points n and m . e(k\k-n) = r(k)-d h (47) M{k) = \μ■ Mk~l) - e^-r■ e^"" (48) (49) M{k) = μ■ M{k~x) + (50) w = μ■ M^x + Re[e^■ e^~m) } (51) The products from the a-priori and a-posteriori estimation errors in equations (43) to (46) and (48) to (51) for the calculation of the path metric M{k) represent the branch metrics between the respective states at the preceding timing point k-\ and at the current timing point k .

From the calculation formulae of the a-priori and the a-posteriori estimation error in equations (31) , (34) and (47] and the iterative calculation formula for the estimated (A) - (k) « (k) values A, ,.., AU ,..,h of the channel-impulse responses hik ">huW >->huk) ^n equation (32) , it is evident that, in order to calculate the path metric Mk) for the individual states S i = l,...,Ns at the timing point k , the estimated values hx ,..,hu ,-,hu at t^ie preceding timing point k-l « (k-n) (A-n) Λ (*-") and respectively A, ,..,hu at the timing point k-n are necessary.

While, in the case of a Viterbi algorithm with a cardinality M of the symbol alphabet of the modulation method used and 31 a total of Ns states, a total of M-Ns potential new states are analysed in each case at the current timing point and, for each potential new state, a total of U estimates of the channel -impulse responses h k) ,..,huw1,.-,Η^ at the current timing point is required, and accordingly, a total of U-M-Ns channel estimates are implemented, with the method according to the invention, for the analysis of the total of M-Ns potential new states at the current timing point only the U channel -impulse responses at the total of Ns precursor states at the preceding timing point k-l or respectively at an even earlier timing point k -2, k-3 etc. need to be estimated.

In view of the convolution of the data-symbol sequence rfw=[^..,£^...,^]r with the vector ,..,huw h k) of the impulse responses of the transmission channels in the time-invariant or respectively time-variant signal model of the transmission channel according to equation (1) , the log-likelihood function according to equation (16) and the path metric Mk) according to equation (18) at future timing points k also contain in the individual terms 4( AO ^(0A A(0 A ') data symbols 4( · ( >·· ( from current or respectively past timing points i≤ k , as is evident from the right-hand half of Figure 4. To ensure that the energy of these signal components is not lost in the iterative calculation of the path metric (i) and of the estimated values h{ ,..,hu ,..,h of the channel -impulse responses and therefore leads to an unsatisfactory estimate 32 of the data-symbol sequences ,.., du ,..,dv transmitted up to the timing point k and of the channel-impulse responses hi > -> hu >-->hu an extended path metric M is developed in the following paragraphs, which takes into consideration the signal components of these data-symbol sequences d{k) ,.., duw ,.., du(k) transmitted up to the timing point k included in the received data symbols r{,) at the future timing points i > k .

For this purpose, the time- invariant signal model of the transmission channel according to equation (1) is once again considered. With an impulse length LM,..,Lhu , ..,Lhu of the channel-impulse responses, signal components of data-symbol sequences d_^k , .., d_^k ..,d transmitted up to the timing point k can be contained in the received data symbol r{k) at a total of Lhl - l, .., Lhu - l,.., LhU -1 future timing points. The vector r{k) of the received data symbols from equation (2) is extended according to equation (52) into a vector k+Lh~x) . with r = [r((k + l), ..., r(k + Lh - l)] (52) The Toeplitz matrix Du of the data symbols from equation (6) transmitted via the u"th transmitter is extended according to equation (53) corresponding to a Toeplitz matrix n . 33 D, (*) (k+Lllu -\) _ du(k+l) du(k-(Lhu-\)) D (53) du(k+Lhu-V) du(k +Lhu-2) u(k) The Toeplitz matrix D^Lh~x) according to equation (54) is composed of the Toeplitz matrices DL{K^L'L .., DMLK+I*, ~L) , .., DULK+IW ~L) associated with the individual transmitters , lu/ .. lu according to equation (53) . (,k+Li,u D D (*+ *-t) -\ (54) ") The log-likelihood function Z( J(i),h(k),rw) from equation (15) is accordingly extended to provide an extended log-likelihood function L^Dik+L'~l) '^***-0j according to equation (55) : (55) The missing information regarding the data symbols {r(i)}k*^1 received at future timing points and regarding the data symbols {4(0,. (0,··Α(0}ί ,_1 with L» = max { Lh\ ·· 4. ■· hu) transmitted at future timing points is taken into consideration in equation (55) in comparison with the mathematical presentation of the log- likelihood function L (DW >htk) >rW) in equation (15) by the introduction of the expected-value function E{.} . Additionally, in equation 34 (55) , the impulse response h{w,..,huw,,.,Η^ of the transmission channel in equation (15) is replaced by the associated ?(*) -(*) .'(*) estimated value ¾ .

In determining the covariance matrix C , it must be taken into consideration that this is composed not only from the noise power ση2 of the noise signal according to equation (12) , but also from the signal power of the signal components ί/,( Λ ' -0»».^«( Λ " - >·Ά (»)·¾/(./ "0 OF THE DATA symbols dl(/),..,du (),··,d^i) with k + \≤i≤k + Lh-\ and Lh=max(LM, .., Lhu, .., LhU) transmitted in the future, which are contained in the received data symbol r(j) with i≤j≤k + Lh-\ - data symbols with "?" symbol in Figure 4 -and which falsify the estimate of the data-symbol sequences d^1 ..,d k ,~,d_yk) transmitted up to the timing point k using =(*) the extended path metric M , m spite of the fact that they are unknown at the timing point k . The signal power of a signal component dxi)- {j -i),~,du{i)-hu(j -i),..,du{i)-huj -i) of this kind is obtained, subject to the condition that the mean signal power of the transmitted data symbols dl (?'),..,i/u(i'),..,iiy( is assumed to be 1, from the modulus squared of the corresponding tap |Α,Ο"-Ο.·.Λ '-Ο.»ΑΟ"-ΟΙ of the estimated values Λ, ,..,hu ...,Α^ of the channel-impulse responses h k ->huk) >~>hj{k) · Accordingly, the covariance matrix C presented according to equation (56) .

Lt≤i≤k Cn = diag(a2(i)) with σ2(ί) = \ U ιηίιι(ί-(*+1)Α„-1) k + l AT"' + 5(k) (58) 36 A weighting of the extension term S(k) relative to the iteratively-calculated metric w can be achieved by introducing a weighting factor w , which is positive with an additive metric M(k) , and negative in the case of a subtractive metric w .

M =÷r + w5{k) (59) σ Figure 5 presents the transmission system for the use of the method according to the invention for the detection of data-symbol sequences received via a time-variable transmission channel from a received signal containing the latter, which, by comparison with the prior art shown in Figure 1, contains no pre-filter 5 and, instead of a common channel-data estimator 6, provides an iterative estimator 6' according to the invention with fully de-coupled estimation of the channel and of the transmitted data-symbol sequence.

The method according to the invention implemented in the iterative estimator 6' according to the invention for the detection of data-symbol sequences received via a time-variable transmission channel from a received signal containing the latter is illustrated in the flow chart of Figure 6.

In the first procedural stage S10, the channel-impulse responses h^k)',-,huw',..,huw of the transmission channels are determined in a first channel estimation. For this purpose, the transmission channels are supplied, either individually for themselves or in combination within the framework of a 37 joint channel estimation associated with the prior art, by preference with a known training data-symbol sequence of length Lt , and, from the received data symbol r(k) , using an adaptive channel-estimation algorithm, in each case, a first (0) (0) (0) channel-estimation value /J, , .., hu , -, hy of the channel-impulse responses Λ,(0),.., ι1(ί0)>..,Α£/(ο) at the timing point 0 or (-1) (-1) (-1) first channel-estimation values h{ , .., hu ...,Α^ , (-2) (-2) (-2) i , .., hu ,..,Ay of the transmission channels disposed further back in time is calculated. In this context, estimation algorithms without taking into consideration a noise-conditioned channel statistic, such as least-squares algorithms, estimation algorithms taking into consideration a noise-conditioned, unknown channel statistic, such as maximum-likelihood methods, or estimation algorithms taking into consideration a noise-conditioned, unknown channel statistic, such as the MMSE algorithm, can be used. A blind or semi-blind first channel estimation without the use of a training-data symbol sequence, which estimates the channels only from the received user-data symbol sequence, is also suitable for the first channel estimation.

In the next procedural stage S20, the scalar and vector variables and matrix variables used in the method according to the invention are initialised: Since, dependent upon the timing point k and the impulse length Lhl, ..,Lhu , ..,LhU of the channel-impulse responses hiW>">LW>">kuk) ' certain data symbols <¾( ·Α( ,·· (ζ') of the (k) (k) estimated data-symbol sequences d{ ,..,du ,..,d_v can be 38 disposed at negative timing points / , these must be predefined in advance, ideally with the value 0.

The elements of the prediction-error correlation matrix Kw , which represents the inverse auto-correlation matrix of the estimated data symbols d ,..,du ,-.,ά^ , can be defined either with constant values, for example, with the coarse Eh estimation value γ for the signal-noise ratio — in the respective transmission channel, weighted with the inverse impulse length Lhl~l,..,Lh ~ ..,LhU~x of the respective channel-impulse response ,..,huw,-.,Η^ , or can be calculated from the auto-correlation coefficients of the training-data symbol sequence determined in the first channel estimate or from the user-data symbol sequence used in the case of a blind first channel estimate.

Following this, the iterative loop of the method according to the invention begins in procedural stage S30. In procedural stage S30, the a-priori estimation error e^'^ is calculated using channel-impulse response A, ,..,hu estimated at the timing point k-l according to equation (31) , and the a-posteriori estimation error e(m is calculated using a channel-impulse response ,..,hu ,..,hy estimated at the timing point k according to equation (31) . Alternatively, every further a-priori estimation error e*""' can be calculated using the channel -impulse response 39 » (k-n) (k-n) ~ (k-n) h{ ,..,hu ,.;hy estimated at an earlier timing point k n according to equation (47) .

In the case of a first implementation of procedural stage S30, the data symbol r(0) received at the timing point 0, (0) the vector of the estimated data-symbol sequence d predefined in procedural stage S20 and the estimated values Λ (0) . (0) (0) ~ (-1) (-1) j. (-1) - (-2) r (-2) (-2) hi >->hu >->hu > i >~>hu >~>hu > i >■·>«_ ,-,hu etc- of the channel -impulse responses at the timing points 0, -1 , -2 etc. determined in the first channel estimate according to procedural stage S10, are used.

In the case of an iteration, which has already been run through several times, the data symbol r(k) received at the timing point k , the data symbols d{{k -V),..,du{k - X),..,du k-Ϊ) , dl(k-2),. u(k-2),. u(k-2) , d,{k- ),. u{k-l>),. u{k- ) etc. of the data- symbol sequence dxw,..,duw,..,d_y k) transmitted up to the timing point k-l and estimated respectively in procedural stage S60 at the individual timing points k-l , k-2 , £-3 etc. for the timing point k , respectively every data symbol d(k) contained in the data-symbol alphabet of the modulation * (k-l) (k-l) * (k-l) method used and the estimated values hx ,..,hu ,-,hu > (k-2) j. (k-2) (k-2) f (k-l) j. (ft-3) r (k-l) /J, ,..,hu ,.-,hu ' hi >->hu >~>hu etc. of the channel-impulse responses Α1(*\..,λ1((*),..,λ£ *) determined in procedural stage S70 at the timing point k-l or at earlier timing points k-2 , k-3 etc., are used for this purpose. 40 In the next procedural stage S40, the metric (0) at the timing point 0 in the case of a first run of the iteration and the metric Mw at the timing point k in the case of an iteration, which has already been run through several times, are calculated from the initialised metric ) in the case of a first run of the iteration and from the metric M{k~) determined iteratively at the preceding timing point k-l with the addition of the branch metric determined respectively for every possible data symbol d(k) of the data- symbol alphabet at the timing point k , which can be determined from the product ew_1) · e{m of the a-priori estimation error eikVc~l and the a-posteriori estimation error eW) calculated in procedural stage S30.

In this context, the iterative calculation formula for the path metric w of equation (35) , the iterative calculation formula for the path metric Mw of equation (40) using the forgetting factor μ for branch metrics disposed further back in time, the iterative calculation formula for the path metric M{k) according to equation (43) with final modulus formation of the calculated path metric Mw , the iterative calculation formula for the path metric Mw according to equation (44) with final real -component formation of the calculated path metric Mw , the iterative calculation formula for the path metric w according to equation (45) with a modulus formation of the branch metric determined in the respective iterative step for each data symbol d(k) of the data- symbol alphabet and the iterative calculation formula for the path metric w according to equation (46) 41 with a real -component formation of the branch metric determined in the respective iterative step for every data symbol d(k) of the data- symbol alphabet, can be used.

Alternatively, the path metric w can be calculated in each case after one of the iterative calculation formulae according to equations (48) to (51) , in which the respective branch metrics are calculated from a-priori estimation errors e(i|t"" and et|*"m) at earlier timing points k - n and k - m .

In the next procedural stage S50, according to equation (57) and (58) , the extension term S(k) and, building upon the =(*) latter, the extended metric M are calculated. Using a weighting factor w according to equation (59) , a different weighting between the iteratively-determined metric Mw and the extension term S(k) can be realised in the calculation ==(*) ' of the extended metric M In the next procedural stage S60, the respective, minimal, =(*) extended metrics M are determined from the respectively- =(*) calculated extended metric M by means of a depth-first or a breadth- first method, for every data symbol d{k) of the data-symbol alphabet of the modulation method used at the timing point k , and accordingly, the data symbol di (k),.., du (k), .., du (k) at the timing point k is estimated in the individual "survival paths" . 42 In this context, when using a breadth-first method, by-analogy with the Viterbi algorithm, starting from the state St selected at the preceding timing point k - \ for the respective "survival path", the subsequent state St at the timing point k and, associated with this, the estimated data symbol dl(k), .., du (k),.., du(k) at the timing point k characterising this state Sl , which provides the smallest branch metric, can be selected. In this manner, an individual state Sl at the timing point k is once again selected in each case from every individual state S, selected at the timing point k - \ and continued in the respective "survival path" at the timing point k .

Alternatively, however, states St , which provide the smallest path metrics, can be selected in each case, as shown in Figure 3. In this manner, from a state St selected at the timing point k - l , either several states Ss , a single state St or no state S1, can be selected at the timing point k . In both variants, the number of states S, selected at the timing point k can be reduced by comparison with the states Si selected at the timing point k - \ , if several "survival paths" disposed respectively at the timing point k - \ in a different state St are combined in a single state Sj at the timing point k .

In the case of a depth-first method, the trellis diagram is first analysed "by depth" , in that one "survival path" is pursued iteratively over so many timing points k until the - =(*) respective path metric w or M exceeds a predetermined 43 threshold value. In the event of an overshooting of the threshold value by the respective path metric - m =(A) M( ' or M , the system moves back by so many timing points k on the "survival path" until a branching path is found, of which the branched metric leads to a path metric - (k =w M ' or M , which is disposed below the predetermined threshold value. This branching path is once again pursued until the respective path metric My ' or M once again exceeds the predetermined threshold value, and another branching path is found, once again, by moving back within the selected "survival path", which leads to a path metric M - tk\' or M==(*) disposed below a predetermined threshold value. This procedure is continued until the trellis diagram has been run through with a found "survival path" up to a predetermined timing point k .

In the next procedural stage S70, the Kalman amplification g{k according to equation (37) or according to equation (42) is calculated using the forgetting factor μ for the lower weighting of data symbols d{k),..,du(k),..,du(k) transmitted relatively earlier than currently-transmitted data symbols dl(k),..)du(k),..,du(k) . For this purpose, the estimates di(k)>">i.u(k>"> u(k determined for the respective "survival path" of the data symbol sequences dk ..,d k),..,dyk) transmitted up to the timing point k are used with the data symbols ^(k),..,^^),..,^^) estimated in the preceding procedural stage S60 for the respective "survival path" at the timing point k and the prediction-error correlation 44 matrix K^k~l) at the preceding timing point k - l . In the first run of the iteration, this prediction-error correlation matrix Kw provides the values initialised in procedural stage S20 and, in the case of an iteration which has already been run several times, provides the values determined iteratively in the last iteration in procedural stage S70 of the correlation matrix K{k~[) at the timing point k - l .

The prediction-error correlation matrix K(k) at the timing point k is also calculated iteratively in procedural stage S70 with the Kalman amplification g(k) determined in this manner at the timing point k and the prediction-error correlation matrix K{k'l) at the timing point k - \ .

Finally, with the Kalman amplification g{k) just determined in procedural stage S70 and the a-priori estimation error calculated in procedural stage S30, on the basis of * (t-l) « « (t-l) the estimated values ht ,.., hu ,.., hu of the channel-impulse responses hw at the timing point k - l , the estimated value h of the channel-impulse responses & , .., hu , .., hjj at the timing point k is calculated iteratively. The estimated value f[ ) of the channel- impulse responses h k .., h^k) ,.., hy k) at the timing point k - \ is obtained in a first run of the Λ (-1) (-1) ~ (-1) iteration from the estimated values h , .., hu , .., hy of the channel-impulse responses hi k --, uw , .., hy k) at the timing point -1 determined in the first-channel estimate in procedural stage S10, and, in the case of an iteration, which has already been run several times, from the estimated values 45 ft, of the channel-impulse responses i ~>!luk)'--> u k) at tne timing point k - l determined iteratively in the last iteration in procedural stage S70.

Procedural stage S80 determines whether the estimation of the data-symbol sequences d k),-,duw,..,dyk) has been completed.

This is the case, if all available "survival paths" are finally combined after a given number of iterations into one state Sl of the trellis diagram at a given timing point k to form a single "survival path", and the method according to the invention is therefore concluded.

If this event has not yet occurred, the next timing point k + \ is waited for in procedural stage S90, and the next iteration is begun with procedural stage S30 .

Curve 1 in Figure 7 presents the bit-error rate - BER as a function of the mean power of the first and second transmitter (U=2) of a JDDFSE (Joint Delayed Decision Feedback Sequence Estimation) method with symbolically-operating pre-filter, which represents a method for simultaneous estimation of several time-variable transmission channels and of the data-symbol sequences dik --,d k),.., uw transmitted respectively via one of the transmission channels according to the prior art, and curve 2 in Figure 7 presents the bit error rate BER as a function of the mean power of the first and second transmitter of a method according to the invention for detection of several transmitted data-symbol sequences transferred respectively 46 via one time-variable transmission channel from a received signal without pre-filter.

In both cases, an un-coded 8-PSK modulated transmission signal according to the GSM/EDGE standard, which is transmitted from two transmitters (U=2) , a signal-noise £ ratio — of 30 dB, an urban environment TU (typical urban) N and a receiver velocity of 0 km/h are provided. In the case of the JDDFSE method, 64 states are provided; with the method according to the invention, 24 states are provided.

The relatively lower bit-error rate of the method according to the invention by comparison with the method according to the prior art (JDDFSE) is clearly evident, especially with relatively lower transmission powers of the two transmitters 1 and 2.

The invention is not restricted to the embodiments presented. As adaptive channel-estimation methods, other recursive channel -estimation methods, such as Kalman algorithms or affine projection algorithms, for instance, the NLMS (normalised-least-mean-square) algorithm, are covered by the invention, in particular, as alternatives to the RLS algorithm.

Claims (1)

1. 47 Method for the detection of several transmitted data- symbol sequences ( d^,..,du(k),,.,ά^ ) transferred in each case via a time-variable transmission channel from a received data-symbol sequence (r ), wherein the impulse response ( ) of the respective transmission channel and the respective, currently- transmitted data symbol {d{k)i..,d1{k),..,du{k)) is estimated in alternation for each timing point [k) , and the number of combinations of data-symbol sequences ( d_ k ..,d_^k),,.,ά^ ) to be taken into consideration for the estimate of the currently- transmitted data symbol ( d^k),..^^),..^^) ) is reduced by comparison with the maximum-possible number of combinations of data-symbol sequences ( Λ {k) d (k) d {k) ) characterised in that for each state ( S( ) in the state diagram selected at the current timing point (k), only one channel- (4) * (t) - (t) estimation hypothesis {hx ,..,hu ,..,h ) of the respective transmission channel, which is obtained from a channel-estimation hypothesis f. (t-l) (t-l) Λ (k-l) ~ (*-2) - (t-2) f {k-l) ( «i >··Α >-> u < i >-> u >~>hu f (*-3) f (A-3) - (i-3) , , A, ,..,«„ ,··>¾/ ,..) of the respective transmission channel at one of the preceding timing points {k-\ , k-l . k-3 , .. ) , is used. 48 Method for detection according to claim 1, characterised in that for the. selection of the data symbol {dl(k),..,d2(k),..,du(k)) transmitted respectively at the current timing point {k) , those states ( S. ), of which - m =(*) the path metrics ( , M ) are minimal, are selected at the current timing point (k ) . Method for detection according to claim 1, characterised in that for the estimation of the data-symbol sequence ( 4-\k -->d_uk),..,d_uk ) transmitted respectively up to the current timing point {k) , a path is selected successively from successive states (£,.), so long as ~ m ==(*) the path metric (M( , M ) of the last-selected state (_?,) is below a threshold value, and otherwise, the path is continued iteratively in one of the previously-selected states (S() with an alternative state (S(.) or respectively its successive states (S,) , - ,,. =(*) if their path metrics ( w , M ) are below the threshold value . Method for detection according to claim 2 or 3, characterised in that the path metric ( w) of a state {Si ) at the current timing point (k) is calculated iteratively from the path metric ( (t-1)) of the respectively-preceding state (S(. ) with the addition of a branch metric between the respectively-preceding state (5,) at the preceding timing point {k-l) and the state (S, ) at the current timing point (&). Method for detection according to claim 4, characterised in that the branch metric between the respectively-preceding state (S,) at the preceding timing point (k-l) and the state ( 5( ) at the current timing point ( k ) takes into consideration a function of a product ( e(*l*-"> . e(*l*-* ) from a first a-priori estimation error ( £(*!*-«)) and second a-priori estimation error ( e{kVc'm) ) respectively between the data-symbol sequence {r ) received up to the current timing point (k) and the * (*)r ~ (*) λ (*)Γ λ (*) λ (*)Γ λ (*) estimate ( rf, -A, +.. + du -hu +.. + dv -h ) of the data-symbol sequence [r{k)) received up to the current timing point {k) . Method for detection according to claim 5, characterised in that the function is a modulus-forming function. Method for detection according to claim 5, characterised in that the function is a real -component forming function. Method for detection according to any one of claims 5 to 7, 50 characterised in that the estimate (kf (k-n) (k)T T (k-n) (kf 7 (k-n) (dt ·Λ, + + ·/?„ + -Ay wr ? <*_l) j wr r rf, -A, +.. + ^u ·Α„ +- + έυ -hu - ( f (k-m) * (kf ? (k-m) (fc-m) of, +·· +≤_„ ■¾„ +- + ^t -hu ) of the data-symbol sequence ( rw ) of the first a-priori estimation error ( g(*1*"n) , ) received up to the current timing point (it) and of the second a-priori estimation error (,··Α ,»>hu > i >-->h» '-'hu ; i »··>«. ,~, u ) of the respective transmission channel estimated at a first and respectively second timing point (k-n , k-l ; k-m ) . Method for detection according to claim 8, characterised in that the first timing point (k-n , k-l ) of the first a-priori estimation error ( e^""' , e^"1' ) is a timing point (k-n ) preceding the current timing point (k ) by n timing points, and the second timing point (k-m ) of the second a-priori estimation error ( e(kVc~m) ) is a timing point (k-m ) preceding the current timing point ( k ) by m timing points. Method for detection according to claim 8, characterised in that the first timing point (k-n, k-l) of the first a-priori estimation error ( e(kVc~n) , e(*M)) is the preceding timing point (k-l), and the second a-priori estimation error (e{kVc~m)) is substituted with an a-posteriori estimation error ( ) between the data-symbol sequence (r ) received up to the current - (4) - (-> (k) (t) (*) (A, ,-,hu ,--,hy ) of the respective transmission channel estimated at the current timing point ( k ) . Method for detection according to any one of claims 4 to 10, characterised in that, in the case of the iteratively-calculated path metric (M{k)) , data symbols ( dl(k),..,d2(k),..,du(k) ) transmitted earlier are weighted less strongly than data symbols ( dl(k),..,d2(k),..,du(k) ) transmitted later. Method for detection according to any one of claims 4 to 11, characterised in that the iteratively-calculated path metric is extended by an extension term (S(k)) to form an =(*) extended metric [M ) , wherein the extension term (S(k) ) is obtained from the difference between the data symbols ( r(k + l) , r(k + 2) , r(k+3), . . ) received at future timing points (k+l , k+2 , k+3 , . . ) and the -> (*) - (*) - (*) estimates {d_x ,--,du ,-,4_υ ) of the data-symbol sequence ( d k) ,..,d^k) ,..,d, k) ) transmitted respectively up to the current timing point ( k ) weighted with the impulse , f (*) .« (*) response ( x ,..,hu ,.-,Λ^ ) of the respective transmission channel estimated at the current timing point (k ) . Method for detection according to claim 2, characterised in that those states ( St ) , which, among all states (S,) , ~