IL201489A - Method and equalizer for detecting data symbol sequences transmitted via a time-variable transmission channel - Google Patents

Abstract

The invention relates to a method and an equalizer for detecting at least one data symbol sequence (d

Description

IVIETHOD AND EQUALIZER FOR DETECTING DATA f SYMBOL SEQUENCES TRANSMITTED VIA A TlfVIE-VARSABLE TRANSMISSION CHANNEL mnun in' y yj-u pmsran yr'K. ,Lmo ^ y D«DXI M^ *? |τκηι no'ty Eitan-MehuiaS Law Group Advocates-Patent Attorneys P-10982-IL 201489/2 Translation International Patent Application No. PCT/EP2008/002489 Method and equaliser for the detection of data-symbol sequences transmitted via a time-variable transmission channel The invention relates to a method and an equaliser for the detection of data-symbol sequences transmitted via a time-variable transmission channel with reduced signal-processing costs.

Interference in received signals in a real transmission channel - for example, in a mobile-telephone network - can result, inter alia, from inter-symbol interference, through the superposition of different transmitted signals, which originate from several transmitting mobile-telephone devices from neighbouring cells within the same frequency band (same-channel interference) or from different frequency bands (adjacent-channel interference), or through the superposition of identical transmitted signals, which are transmitted from a single user via different transmitters - transmitter-end diversity with space-time coding or diversity -generating delay.

A disturbed, received signal, which is present after demodulation as a distorted data-symbol sequence, must be transferred in an equaliser into several data streams corresponding to the individual transmitted data-symbol sequences . One important group of detection or equalisation methods is represented by the maximum-likelihood methods, in which the disturbed, received data-symbol sequence is compared with all possible undisturbed 2 201489/2 data-symbol sequences from a data-symbol alphabet used in the modulation, and the undisturbed data- symbol sequence, which provides a minimal Euclidean distance from the disturbed, received data-symbol sequence, is selected as an estimate for the transmitted data- symbol sequence.

The complexity of the estimation of the individual data-symbol sequences in the equaliser is dependent upon the power of the symbol alphabet used and the extent of the interference. The diversity of combinations of possible data- symbol sequences is presented in a state diagram -preferably a trellis diagram - by means of states to be selected in the estimation. Selection of the sequence from successive states is optimised in the conventionally-used Viterbi algorithm by selecting one or more so-called survival paths.

Because of the time-variability of the transmission channel, in minimising the Euclidean distance at every state transition, not only the data symbol associated with the state to be selected at the current timing point, but also the impulse response of the transmission channel at the current timing point must be estimated, which additionally increases the complexity of the estimation.

The path metric to be minimised for the selection of states in the individual survival paths at the current timing point for an estimation of the data symbols transmitted at the current timing point via the individual transmission channels and also the estimation of the channel - impulse responses associated with the individual transmission channels at the current timing point is determined iteratively in patent publication No. DE 10 2006 029 464 Al .

Since, in view of the convolution operation in determining the estimate of each received data-symbol sequence at future timing points, estimated values, which are already determined at the current timing point, are used for respectively-transmitted data symbols and channel-impulse responses at the current or at respectively preceding timing points, these can be taken into consideration within an expansion term, which forms an expanded path metric together with the iteratively-calculated path metric .

Since data symbols received and transmitted in future are not yet known at the current timing point, the expanded metric at the current timing point is determined as an anticipated value of the differences between the data symbols received at future timing points and the data symbols of the data-symbol sequences transmitted at future timing points weighted with the impulse response of the respective transmission channel estimated at the current timing point, 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 at the current timing point is taken into consideration in the estimate of the received data-symbol sequence at the current timing point, and accordingly, the estimation error is minimised in the equalisation of a received data-symbol sequence, which is transmitted on a respective transmission channel with a channel-impulse response with an impulse length greater than 1. 4 201489/2 The disadvantage with the introduction and calculation of an expanded path metric in the estimation of the individual data- symbol sequences is the comparatively-high numerical signal -processing cost.

SUMMARY OF THE INVENTION According to a first aspect of the invention there is provided a method for detecting at least one transmitted data-symbol sequence ( , . ,, ά^ , ,., ά^ ) associated in eac case with one signal transmitted via respectively one time-variable transmission channel from a received data-symbol sequence associated with a single received signal, in which the impulse response ( h^k) , .., h^k) , .., hy k) ) of the respective transmission channel and the respective, currently- transmitted data symbol estimated in alternation for every timing point (it), wherein for the estimation of the data symbol { d{k ..,du{lc ..,d 'l<'> ) transmitted in each case at the current timing point ( k ) , those states ( S, ) in the state diagram are selected, ={ of which the iteratively- calculated expanded metrics [M ) consisting respectively of a path metric { M(k} } and an expansion term { 5{k) ) are minimal, wherein the numerator of the expansion term { S(k) ) is obtained solely from the difference between the data symbols { r(k + l) , r(k + 2) , r(k+ 3) , . . ) received at future timing points ( k + \ , k + 2, k + 3,..) and the estimates (dt ,-.,d_u ,..,d_u ) °f t&e data-symbol sequence (a, ,..,«„ ,·■,<¾/ ) transmitted in each case up to the current timing point { k ) weighted with the impulse response ( ?, ,..,«„ ) of the respective transmission channel estimated at the current timing point ( k ) . 201489/2 According to a second aspect of the invention there is provided an equaliser for the detection of at least one transmitted data-symbol sequence ( d_^k ..,d_^k) ,..,d associated in each case with one signal transmitted via respectively one time- ariable transmission channel from a received data- symbol sequence { r ) associated with a single received signal, in which, the impulse response of the respective transmission channel and the respective, currently- transmitted data symbol {dl(k),..,d1(k),..,du(k)) is estimated for every timing point (k) in alternation, wherein for the estimation of the data symbol ( dt (k),..t d2(k), ,.,dfj (k) ) transmitted at the current timing point ( k ) , those states ( S,. ) in the state diagram are selected, of which the iteratively-calculated expanded metrics ( ) consisting in each case of a path metric { w ) and an expansion term ( According to a fourth aspect of the invention there is provided a computer program with program-code means, in order to implement all of the stages according to the first aspect of the invention, when the program is run on a computer or a digital signal processo .

DESCRIPTION OF THE II BNTION The object of the invention is therefore to develop further, with low signal-processing costs, a method for equalisation and an equaliser in such a manner that a combined data symbol and channel - impulse response estimation is implemented by means of iteration at each timing point.

The object is achieved by a method according to the invention for the detection of data- symbol sequences transmitted via a time-variable transmission channel with reduced signal-processing costs and an associated equaliser .

With the method according to the invention and with the equaliser according to the invention, in determining the expanded path, metric, zero values are set instead of anticipated values for the data symbols transmitted at future timing points. In this manner, the mathematical relationship to be calculated for the expanded path metric 5b 201489/1 is reduced by the term Consequently, at each timing point, a signal-processing cost reduced, in comparison with the technical doctrine of the patent publication No. DE 10 2006 029 464A1, by the calculation of this mathematical term is implemented.

The following advantageous extensions of the method according to the invention and of the device according to the invention are provided: 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 in the selection by means of minimisation of the expanded path metric, 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 means of minimisation of the expanded path metric .

The method according to the invention can search the trellis diagram not only, as just presented, "by breadth" first according to an optimal estimation for the respectively transmitted data-symbol sequence ("breadth first" method), but, in a further embodiment of the invention, can search the trellis diagram "by depth" first according to an optimal estimation for the respectively 5c 201489/1 transmitted data- symbol sequence ( "depth- first" method) with reference to the stack algorithm.

In the iterative calculation of the expanded path metric of a state at the current timing point, the associated branch metric is added to the expanded 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. The first or respectively second a-priori estimation error in its turn is obtained from the 6 difference between the data-symbol sequence received up to the current timing point and the estimation of the estimate of the data-symbol sequence transmitted up to the current timing point weighted with an impulse response of the respective transmission channel estimated at a first or respectively second timing point. In each case, the first and second timing point is 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 the data-symbol sequence received up to the current timing point and the estimation of the estimate of the data-symbol sequence transmitted 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 from the difference between the data-symbol sequence received up to the current timing point and the estimation of the estimate of the data-symbol sequence transmitted 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 for the 7 simplification of the calculations of the values consisting of complex numbers.

Through the introduction of a weighting factor in the recursive calculation of the expanded path metrics, data symbols transmitted earlier can be weighted more weakly than data symbols transmitted later.

An additional reduction of the signal-processing costs can be achieved in the case of signals, which provide significantly-different signal powers, transmitted in each case via several transmission channels. Since, in this case, the data-symbol hypotheses of the lower-power signals are negligably small by comparison with the data-symbol hypotheses of the higher-power signals, all data-symbol hypotheses of the lower-power signals in relation to each data-symbol hypothesis of each higher-power signal are approximately equivalent with regard to a metric minimisation. If only the estimation of the data symbols of higher-power signals is relevant, these equivalent data-symbol hypotheses of the lower-power signals lead to several equivalent states in the trellis diagram and accordingly to a pursuit of several equivalent "survival paths". In order to reduce the number of survival paths in a case of this kind, not every data symbol hypothesis, but only a reduced number of data-symbol hypotheses are taken into consideration for each lower-power signal. The greater the ratio of the signal power of the higher-power signal is to the signal power of the lower-power signals, the lower the reduced number of data-symbol hypotheses to be taken into consideration for each lower-power signal must be set. 8 The estimation of the channel-impulse response of each transmission channel need not be implemented at every timing point. In the case of a slowly-changing channel-impulse response of the respective transmission channel, an estimation in a larger time raster is entirely possible. If the channel-impulse response of the respective transmission channel changes only to an insignificant extent, a channel estimation only at the start of the transmission is adequate.

The individual embodiments of the method according to the invention and of the equaliser according to the invention for the detection of data-symbol sequences transmitted via a time-variable transmission channel with reduced signal-processing costs are explained in detail below with reference to the drawings. The drawings are as follows: Figure 1 shows a first trellis diagram for the estimation of the data-symbol sequence according to the method of the invention; Figure 2 shows a second trellis diagram for the estimation of the data-symbol sequence according to the method of the invention; Figure 3 shows an overview presentation of relevant terms for the path metric calculation at various timing points; Figure 4 shows a block diagram of the transmission system according to the invention; Figure 5 shows a flow chart of the method according to the invention; and 9 Figure 6 shows a presentation of the bit-error probability dependent upon the transmission power of two transmitters in the case of a method according to the prior art and the method according to the invention.

Before the method according to the invention for the detection of several data-symbol sequences transmitted and transferred respectively via a time-variable transmission channel from a received signal is presented in detail with reference to Figures 4 and 5, the following section describes the mathematical basis necessary 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): In order to estimate the impulse responses of the transmission channels, the transmission channels are excited in the first phase with a transmitted data-symbol training sequence d of length Lt . For the estimation of the impulse response of the respective transmission channel at the first Li timing points, an adaptive channel-estimation algorithm without consideration of the channel statistics (for example, a least-squares algorithm) , with consideration of the unknown channel statistics (for example, an MMSE channel-estimation method) , with consideration of the known channel statistics (for example, a maximum-likelihood estimation method or its derivatives) or a blind or semi-blind first channel estimation can be used.

Consequently, an estimation of the transmitted data symbols cannot be implemented in the first Lt received data symbols r{k), Q≤k≤Lt-l, but, at the earliest, at the fit) timing point L, . The vector r of the received data symbols for estimation of the respective transmitted data symbols at an arbitrary timing point k therefore begins according to equation (2) only from the timing point Lt .

By analogy, the noise vector r according to equation also begins only rom the timing point Lt . «w =[«(4X«( + i)--5 ^)f ( According to equation (4), the vector h contains the impulse responses of the individual transmission channel In this context, the impulse response h ^ of the u-th transmission channel is obtained according to equation (5) .

The Toeplitz matrix Du(i) of the data symbols transmitted by the u-th transmitter is therefore obtained according to equation ( 6) : 1 1 du(Lt) du(L,-l) du(Lt+l) du(Lt) D du(Ll+2) du(Ll+l) d.(k) du(k-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) .

For the estimation according to equation (8) of the data symbols transmitted respectively at the timing point k from a received data-symbol sequence r after a total of N timing points, wherein N is an arbitrary timing point N extended by the impulse length Lh of the respective channel-impulse response, the conditional probability P{i^k) \z) is maximised by the use of the maximum-likelihood approach. r = [r(Q r(l),...,r(N-l)]T with N = N + LM-l The conditional probability from the received data-symbol sequence r can be approximated according t equation (9) by the conditional probability (k) from the received data-symbol sequence r up to the timing point k . 12 PiDw\L)*p(Dm\rw) (9) An identity between the two conditional probabilities in equation (9} is not generally present, because, as a result of the convolution of the data-symbol sequence .«W =[d!l(k\d![k-\ du(k~~2),...,d!i(k-{Lh -l)) transmitted, for example, by the u-th transmitter with the impulse response hu, for example, of the u-th transmission channel, signal components of the respectively-transmitted data-symbol sequence duw can also be contained within the received data-symbol sequences { ^+'' after the timing point k .

Equation (10) is obtained after the application of the Bayes rule and logging of the conditional probabilities in equation (9) : Since all data-symbol sequences Z> are assumed to be equally probable, equation (11) applies.

P(DW)= const. (11) The probability density function f^ rm of a data-symbol sequence r(k} received up to the timing point k provides an identical characteristic for all possible data-symbol sequences Rik) received up to arbitrary timing points k , and does not therefore influence the conditional probability 13 For Gaussian-distributed noise, the probability-density function fR^DW((k) \D )) according to equation (12) is obtained, wherein is the log-likelihood function, Cn denotes the covariance matrix of the noise signal n , /„ denotes the unity matrix and N denotes the dimension of the received data-symbol sequence r according to equation (13) : (12) N = k-Ls +1 (13) Taking into consideration the mathematical relationships in equations (11) to (13), the mathematical relationship for the log conditional probability can be transferred starting from equation (10) to equation (14) ΗΡ&'Ίύν^/^ν' 'Ί = -L(D(k),hik , *>) - (* - L, + 1)Inπ ~ Inσ„2 (14) The log-likelihood function is obtained with reference to Kammayer. K.D.: ^'Message transmission", Teubner Verlag, 1996, pages 554-555, according to equation (15) : (15) ur 14 Since the two last terms in equation (14) contain only parameters, they are not significant for the maximisation of the conditional probability and can be ignored. The conditional probability P^D^lllj is therefore maximised, wherein the log-likelihood function is minimised.

The mathematical relationship for the conditional probability P^Dk)\L) 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) . -r{kHC;'Dik) (D(k)HC;lD{k)YD{k)HC;lr(k} + In this context, an estimation of the channel-impulse response hw according to the RLS algorithm - reduced-least squares algorithm - is used as shown in equation (16) . s can be readily be recognised, the quadratic form of the first term of the log-likelihood function L^D(k hik rik)^j is minimised by the RLS algorithm used in this context.

Furthermore, since the third term r(k)H C~lr(k of the log-likelihood function provides a dependence neither upon the channel-impulse response hm nor upon the Toeplitz matrix D(k) , only the quadratic form of the second term k)H&tfk (DWH Dk)f DWFFC;lrik) of the log-likelihood function L^k),h(k), k)^ can be used for the estimation of the data symbol transmitted at the timing point k . For this purpose, the path metric (ir) is maximised according to equation (18) .

With reference to the Viterbi algorithm, the path metric Mik) according to equation (18) for estimating the data symbols transmitted in each case at every timing point k must be calculated for every state at every timing point k . Since the calculation of every individual path metric M{k) is too complex, with regard to the method according to the invention for the detection of several data-symbol sequences from one received signal transmitted and transferred via respectively one time-variable transmission channel, an iterative path metric w for the maximum-likelihood estimation of the data symbols transmitted in each case at the timing point k and an iterative maximum-likelihood estimated value hx ,■·>¾/ for the individual channel-impulse responses at the timing point k is derived in the following section- 16 In both cases, the iteration is implemented over every individual timing point k from data symbol to data symbol. In general, at every timing point k , the Toeplitz matrix w must first be estimated iteratively and the channel-impulse responses must be estimated on the basis of the iteratively estimated Toeplitz matrix Dm , which is used in turn for the iterative estimation of the Toeplitz matrix D at the next timing point k + \ . Alternatively, the iteration of the estimated values Λ (A) Λ (A) Λ (*) hy , .., h„ s»,^y °f the channel-impulse responses can also be implemented over several data symbols.

In order to develop in each case an independent iteration (k) " (k) (k) for the estimated values h , .,, hu , -, h.u °f tne channel-impulse responses ^k .., h„k) ,,., ίΐ; ^ and for the path metric M{k) taking into consideration the last, iteratively-determined estimated values of the respectively other (A) estimated parameter, the two auxiliary values v according to equation (19) and D{k) according to equation (20) are introduced in an intermediate stage for the (k) k) (A) calculation of the estimated values hx , -, hu of the channel-impulse responses hlik .., hllw , .., h(fk'> according to equation (17 ) . v(t) = D(t) TW (19) m {k) = D ■ D (20) 17 The estimated values z, ,..,?„ ,··>.¾/ of the channel-impulse responses ,..,huk ..,hu{k) can therefore be determined taking into consideration the auxiliary values v(t) and according to equation (21) . ^w' ' (21) The two auxiliary values - vector vm and matrix D(k) - can be calculated in each case iteratively according to equation (22) and (23) : v(k) = -l) +d(k)' -r(k) (22) The data-symbol sequence r is obtained according to equation (24) from the data-symbol sequences d_ k),..,d^,.,,ά^ transmitted respectively by the individu transmitters lx, .. , lu, .. , 1σ. r=(W,(*-i) - ... u(k) du(k~i) .. du(k~(Lhu-i)) ... .... dv(k) d^k-l) .. d^k-iL^-l))) (24) Since the data-symbol sequence d dependent upon the timing point k and upon the impulse length Lhl,..,Lhu,,.,Lhu of the respective channel-impulse response may under some circumstances provide data symbols with negative index, these are appropriate for initialisation (for example, d](k),..,du(k),..,du(k) - 0 V£<0) . 18 Using the matrix-inversion lemma with reference to Kammayer, K.D.: "Message Transmission", Teubner-Verlag, 1996, pages 729-730, the inverse matrix D(/t) of the matrix E>{k) corresponding to equation (25) is obtained using the Kalman amplification gw according to equation (26) : gW = £){ ~iyi . dm' - (1 + d(kf■ ®wl -dw'rl (26) Equation (25} can be mathematically converted according to equation (27) and, taking into consideration equation (27), equation (26) can be mathematically converted according equation (28). (28) The mathematical relationship of the Kalman amplification g(k) according to equation (29) is finally obtained from equation (28) : The iterative calculation of the estimated values hi >">hu i->ku °f the channel-impulse responses \k ~ikuk' ->huk) is obtained starting from equation (21) taking into consideration equation (22), (25) and (29) according to equation (30) : 19 A =h + g[;i) -(r{k)-d -h ) (30) Inserting the a-priori estimation error e(klk~i} between the received data symbol r(k) and the estimates (if (i (A-l) (if Λ (Jfc-l) ;-, jj -hjj of the received data-symbol sequences d^k) •Η^'^,,.,ά^ • ^k~v^,..,dj k) -hyk~X , which is obtained from the weightings of the estimates » (*) - W 5 (t) _ _ , , , _ ,(i) , (k) , (i) a, «y of the data-symbol sequences d ,~,du ,.., f/ transmitted up to the timing point k with the channel- ~ (Jt~l) « (t-l) « (A-I) impulse responses hx ,..,hu ,»,hu estimated at the preceding timing point k-l, the iterative calculation formula for the estimated value h of the channel-impulse response A according to equation (30) can be converted starting from equation (31) according to equation {32} . e^=r(k)~ f- l) ( 3 D =tl)+g(k)-eWk-1' (32) The iterative calculation of the path metric M{k) for the maximum-likelihood estimates of the data symbols dl(k)f..;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 value v(lc} in equation (17) and the mathematical relationship for the estimated value h of the channel-impulse response in equation (19) corresponding to equation (33) : (33 Equation (33) can be transformed taking into consideration the iterative calculation formula for the auxiliary value v in equation (22) and for the estimated value h of the channel-impulse response in equation (32) according to equation { 33' ) : j&W = (∑(*-»* r{k)* T)[ilk"V/V^) (33' ) Equation (33' ) can be transformed taking into consideration the mathematical relationship for the Kalman amplification factor g(k) in equation (26) and the iterative calculation formula for the auxiliary value v in equation (22) according to equation (33'').

M^^x)H ^r{kr T l) + )HJ^ ^ (33 ' * ) The first term in equation (33'') corresponds to the path metric M{k~l) at the preceding timing point k-l . The term vW Dw_1 in equation (33'') can be replaced according to equation (32) by the estimated value h of the channel-impulse response. Finally, the right-hand side of the equation (33'') can be expanded by the modulus-squared of the received data-symbol sequence |r(£)|2 and by the negative term -r(k)*-r(k) equal to the modulus. Accordingly, the iterative calculation formula presented in equation (33''') is obtained for the path metric (i) . (33" ' ) 21 Taking into consideration the a-priori estimation error e{klk~1} according to equation (31), equation (33''') can be transferred according to equation (33'''')· M{k) = M{k~l) - (r(k)* - h(k)■ fT)■ eW-l) + \r(kf (33""} If the a-posteriori estimation error e(i,li) is inserted between the received data symbol r{k) and the estimates Λ (kf (kf (k~l) » (kf ^ (k-1) 4\ ' hi > ~> dv - hu , ~, 4u ■ ' u °^ the received data-symbol sequences which are obtained from the weightings of the data-symbol sequences - (kf {kf - (kf 4.1 >~>4u > - -> 4u transmitted up to the timing point k with {k) « (k) « (k) the channel-impulse responses h{ ,-, hu ,..,hv estimated at the timing point k according to equation (34), the iterative calculation formula for the path metric M{k} for the maximum-likelihood estimate of the data-symbols dl (k)f ..,du(k)>..,dc (k) transmitted at timing point k can be represented mathematically according to equation (33' " " ) . eWk^ r(k)-i(k)r- (34) Since the term \r(k) in the iterative calculation formula for the path metric in equation (33''''') is not an estimated value, and is therefore not significant for decision-making in the trellis diagram, it can be ignored, so that it is possible to transfer from equation (33''''') to equation (35). 22 The inverse matrix ' of the matrix JD^ is described as a prediction-error correlation matrix K(k^ . With the insertion of the prediction-error correlation matrix K{le equation (25) can be transferred into equation (36) and equation (26) can be transferred into equation (37).

As a result of the time-variance of the transmission channel, data symbols transmitted earlier have a lower significance on the equalisation result of the currently-received data symbol r(k) than currently-transmitted data symbols. This circumstance is taken into consideration by the introduction of a forgetting factor μ with a value range 0 < < 1 . The iteration formulae for the two auxiliary values - vector v(k) and matrix E>{k - in equations (22) and (23) can be transferred taking into consideration the forgetting factor μ into the corresponding equations (38) and (39) . vw =p.v(k-l)+dlk)' Finally, equation (37) for the iterative calculation of the Kalman amplification g(/t) is transferred into equation (42) taking into consideration the forgetting factor μ . gm = Kw . ^" .{μ + f .gv-i . )-i (42) If the channel-impulse response changes only slightly from the preceding timing point k-\ to the current timing point k , the a-priori estimation error e(*l*~i) ancj .j-^g a-posteriori estimation error e^k) is approximately identical. The term 'im -em't} is therefore a positive real value, and the path metric (A) in equation (40) is correspondingly a negative real value, since the maximal path metric w made up of all real-value negative path metrics corresponds to the minimal path metric M(k) made up of all real-value positive path metrics M(k) , provided that the modulus Mik) of the mutually-corresponding positive and negative path metrics M{k) is of the same magnitude. Accordingly, the maximisation of the path metric w according to equation (40) can be transferred into a minimisation of the path metric according to equation (43) using a modulus- 24 forming function or equation (44) using a real-component forming function.

M{k =Κβ{μ- M(k~l) - e(m*■ eWk~»} (4 ) A calculation formula equivalent to equation (43) or respectively (44) for a path metric M{k) to be minimised is obtained through modulus formation of the term e·<*!*> ig(*i*-o ancj subseque t addition to the path metric (A-I) calculated at the preceding timing point k-l according to equation (45) or through real-component formation of the term e'i -em'l) and subsequent addition to the path metric M{k"l calculated at the preceding timing point k-l according to equation (46) e(k\k)* , e(kk-\) M(k) =μ-Μ[Ιί-χ) + 45' Mm = μ-Μ^ +Re{e(m* -e(k^} (46) For the calculation of the path metric Mm , instead of the product of the a-priori estimation error at the preceding timing point k-l and the a-posteriori estimation error at the current timing point k , a product from an a-priori estimation error or an a-posteriori estimation error e(i¾t~fl) at the timing point n according to equation (47) and from an a-priori estimation error or an a-posteriori estimation error e(*"w) at the timing point m can be used as an alternative in the embodiments of the equations (48), (49), (50) and (51), wherein the timing points n and m are integer, positive values 0≤m,n, n,meWQ. The timing points n and m should be selected dependent upon the time-variability of the transmission channel. With a high time-variability, relatively small values for the timing points n and m are suitable. e(k I k - n) = r(k) - d_ h (47) Mk =Re{ -M^-e{k^-e(k^m)} (49) Mk) =μ-Μ^ +Re{eWk-r -ew~ffi)} (51) The products of the a-priori and a-posteriori estimation errors in the equations (43) to (46) and (48) to (51) for the calculation of the path metric 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 a~ posteriori estimation error in the equations (31), (34) and (47) and from the iterative calculation formulae for r (A) - (*) ,* (*) „ , , , . the estimated values hx ,..,hu ,-·,¾/ of the channel-impulse responses ^k),..,h^k),,.,Η^ in equation (32), it is evident (k-\) (k-l) (k-l) that the estimated values x ,..,hu ,·.,¾, at the preceding timing point k-l or respectively (Jfc-„) (i-fl) , , , , , «, ,:,nu , > ·> υ at the timing point k-n are required 26 for the calculation of the path metric M{k) for the individual states S i = l, ...,Ns at the timing point k .

While, in the case of a Viterbi algorithm with a power M of the symbol alphabet of the modulation method used and a total of Ns states, in each case, a total of M - Ns potential new states at the current timing point are analysed and, for each potential new state, a total U estimates of the channel-impulse responses at the current timing point is required, and accordingly, a total of U -M - Ns channel estimations are implemented, in the case of 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.

Because of the convolution of the data-symbol sequence k) = \dtl*f f with the vector h^^h^^h^ 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 (i) according to equation (18) at future timing points k in the individual terms dl {i) - hi {j),..,du {i) - hu{j),..,du{i) ' hv (j) also contains data symbols dl(i),..,du(i),..:,du(i) from current or respectively past timing points i < k as can be seen from the right-hand half of Figure 2. To ensure that the energy of these signal components in the case of the iterative calculation of the 27 path metric M( ' and the estimated values h ,.->hu ,.,,hv of the channel-impulse responses is not lost and leads to an unsatisfactory estimation of the data-symbol sequences transmitted up to the timing point k and of « (k) (k) (k) the channel-impulse responses hx ,..,hu ,-, v , an expanded path metric is developed in the following section, which takes into consideration the signal components going into the received data symbols r(,) at future timing points i>k of these data-symbol sequences d^k),..,d^k),..,d -k) transmitted up to the timing point k .

For this purpose, the time-invariant signal model of the transmission channel according to equation (1) is considered again. With an impulse length Lhl,..,Lhu,..,Lhu of the channel-impulse responses, signal components of data-symbol sequences d^k),..,d k ..idui'k) transmitted up to the timing point k can be contained in the received data symbol r(k) at a total of Lhl -l,..,Lhu -\,..,Lhu -1 future timing points.

The vector rm of the received data symbols from equation (2} is expanded according to equation {52} to provide a vector r . = [r((* + l),..., r(A + - l)f (52; The Toeplitz matrix Du of the data symbols transmitted from the u- transmitter from equation (6) is expanded 28 corresponding to a Toeplitz matrix Du according to equation (53) : The data symbols {dl(i),..}dtl(i),..,du(}^*,"' witn IA = max(lM .. Ite .. LhU) transmitted at future timing points are unknown and therefore represent random variables with a discrete probability distribution, which are in each case mutually un-correlated - E^d (i)-du,(j)} = S(i-j)-S(u-u) and in each case mean-value-free E du(i) = Q - and each provide a mean signal power of one.

Accordingly, in the signal model of equation (1), they therefore provide the signal property of a noise signal superposed on the transmission channel and not that of the data-symbol sequence Dk) to be transmitted.

Consequently, the data symbols {dx (),..,da (ζ), -·> du(} ·^Ί ' transmitted at future timing points are [ determined ] by zeroing the corresponding elements in the Toeplitz matrix Duw and, as will be shown below, through additive expansion of the noise power ση2 of the noise signal in the covariance matrix Cn of the noise signal according to equation (12) by the signal power of the signal components ^ι(0 Ο'- - (ΛΟ'~0»·- (Λ '- of data symbols d1(i),..,dll(i),..,du(i) with k + \≤i≤k + Lh-\ transmitted in the future. This, once again, results from the multiplication of the mean signal power of the transmitted data symbols 29 ^(i),..,^^'),..,^^) of one by the modulus squared of the sponding tap A, 0" - 0» - A J ~ 0»■·> ^ 0' " of the estimated (it) (Jt) * (i) values /¾ ,..,¾, of the channel-impulse responses thilm>">hHu{k) > ··'ίhίυ{k) The Toeplitz matrix £)(m* l) according to equation (54) is composed of the Toeplitz matrices associated with the individual transmitters li, .. , lu, .. lu corresponding to equation (53) The log-likelihood function I^ ^./z^.r^ J from equation (15) is therefore expanded to form an expanded log- likelihood function L^D{k÷L"'l) }^ ^ι"~ι^ according to equation (55) (55) Additionally, in equation (55) , the impulse response h\ k) ->hu k)>~>huk) of the transmission channel in equation (15) is replaced by its estimated value In the determination of the covariance matrix C„ , it must be taken into consideration that this is composed not only of the noise power ση2 of the noise signal according to equation (12), but also from the signal power of the signal components d(i)-hi(j- i))..,du (i)-hu(j-i),..,du(i)-hu(j~~ i) of the data symbols dl(i),..,du(i),..,du(i) with k + \≤i≤k + Lh-\ and Lh=max(Lhl, .., Lhu, .., LhU) transmitted in future, which are contained in the received data symbol r(j) with i≤j≤k + Lh-l - data symbols with "?" symbol in Figure 3 -and in spite of their not being known at the timing point k , falsify the estimation of the data-symbol sequences d\k),.,,d^k),..,dyk) transmitted up to the timing point k with =(*) the assistance of the expanded path metric M . The signal power of a signal component of this kind -~i)>-;du(i)-hu(j -ϊ),..^υ(ϊ)·Ηυ^ -) is obtained, subject to the condition that the mean signal power of the data symbols dx{i),..,du{i),.r,du(i) transmitted is assumed to be one, from the modulus squared of the corresponding tap -i),-,hu{j-i),..,hv j-i) of the estimated values /¾ ,..,¾, of the channel-impulse responses hr{k ..,h^k)^,,.,Η^ .

Accordingly, the covariance matrix Cn can be presented according to equation (56) .

C„ = diag(a2()) with (56) The minimisation of the expanded log-likelihood function accorcjj_ng to equation (55) leads to the expanded path metric M corresponding to equation (57) : 31 r(^ + l) ~∑ ∑ du(k-n)-hu(i +n) =1 n=0 M = ·+ (57; σ ί=1 =(*> The expanded metric M is therefore obtained from the addition of the metric M{k) calculated iteratively according to one of the equations (43) to (46) or respectively (48) to (51), weighted with the inverse noise power σ2 and an expansion term S(k) , which corresponds to the bracketed expression in equation (57) and takes into consideration the signal components contained in the data symbols {r(i)}^^ received in future from the data-symbol sequences d_^k ..,dyk),..,dyk) transmitted up to the current timing point k . As is evident from equation (57), the =(*) expansion term d(k) of the expanded metric M of the method according to the invention does not provide the term contained in the expansion term 5(k) of =(*) the expanded metric M of the patent application DE 10 2006 029 464.5. The calculation of the expansion metric M is therefore associated in the method according to the invention with a lower signal-processing cost.

The expansion metric M can be presented in abbreviated form according to equation (58) .

A weighting of the expansion term S(k) for the iteratively-calculated metric can be achieved by 32 introducing a weighting factor , which is positive with an additive metric M{k) and negative with a subtractive metric M{k) , according to equation (59).

Figure 4 shows the transmission system for the use of the method according to the invention for detection of data-symbol sequences transmitted via a time-variable transmission channel with reduced signal-processing costs In each case, a data-symbol sequence T d(1 (k)S(t - kT),.,,∑ d{u) (k)S(t - kT), ..,∑ d(U (k)S(t - kT) is k k k transmitted in several transmitters li, .. , lu, .. , lur which each provide a transmitter-weighting function The data-symbol sequence weighted in each case with the respective transmitter weighting function is supplied via a respective transmission channel 2l f .. , 2U .. , 2σ with the respective, time-variant weighting function gcm fa t-igcH fa i-t gcHvfa to a recei er 3, which is generally realised as a matched-filter with the weighting function gR(t) , to a sampling unit 4 and a mixed-channel-data estimator 5. The method according to the invention implemented in the iterative estimator 5 according to the invention for the detection of data-symbol sequences received via a time-variable transmission channel with reduced signal-processing costs is shown from the flow chart of Figure 5.

In the first procedural stage S10, the channel-impulse responses h k --,h^k -->hu k of the transmission channels are 33 determined in a first-channel estimation. For this purpose, the transmission channels are supplied either individually for themselves or jointly within the framework of a joint-channel estimation, preferably with a known training-data-symbol sequence of the length Lt , and in each case, a first-channel estimation value (0) (0) (0) j¾i ,-,hu ,..,zy of the channel-impulse responses hx^' ">hu° "'hu'1) at the timing point 0, or first-channel " C-I) - (-1) - (-1) f (-2) - (-2) (-2) estimation values hx ,..,hu ,··,&/ , ¾ ,··,«„ >··>¾/ °f t e transmission channels disposed further back, are calculated from the received data symbol r(k) using an adaptive channel-estimation algorithm. In this context, estimation algorithms without taking into consideration a noise-conditioned channel statistic, such as least-squares algorithms, estimation algorithms with consideration of a noise-conditioned, unknown channel statistic, such as maximum-likelihood methods, or estimation algorithms with consideration of 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 exclusively from the received useful data-symbol sequence, is also suitable for the first-channel estimation .

In the next procedural stage S20, the scalar and vectorial variables and matrix variables used in the method according to the invention are initialised: Since given data symbols dl(i),..,d!1(i\..}du(i) of the estimated (jfc) (jfc) ^ (ft) data-symbol sequence d ,..,du >»> The elements of the prediction-error correlation matrix K{k) , which represents the inverse auto-correlation matrix (k) Λ (k) - (k) of the estimated data symbols d_x ,..,du ,..,άυ , can be defined either with constant values, for example, with the EL coarse estimated value r for the signal/noise ratio —~ m N0 the respective transmission channel, weighted with the inverse impulse length ,..,Z¾B~! > .., LhU~x of the respective channel-impulse response ,..,h^k),.,,Κ^'^ , or calculated from the auto-correlation coefficients of the training-data symbol sequence determined in the first-channel estimation, or the useful-data symbol sequence used in the case of a blind first-channel estimation.

The iterative loop of the method according to the invention then begins in procedural stage S30. In procedural stage S30, the a-priori estimation error e*"11 is calculated using a channel-impulse response «I ,·.,«„ ,->n.u estimated at the timing point k - l according to equation (31) , and the a-posteriori estimation error ekVc) using a channel-impulse response (i) (jfc) h\ > -> u >"> u estimated at the timing point k according to equation (31) . Alternatively, every other a-priori estimation error e(^~n) can also be calculated using a (k-n) (k-n) (k-n) channel-impulse response hx ,-;hu ,»,hu 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 timing point 0, the vector of the estimated data-symbol sequence d predefined in procedural stage S20 and of the estimated Λ (0) - (0) (0) (-1) (-1) Λ (-2) Λ (-2) (-2) values A, ,..,¾„ ,..,Ay , A, ,..,h , , ,..,hu ,.., Ηυ etc. of the channel-impulse responses at the timing points 0, -1, —2 etc. determined in the first-channel estimation according to procedure S10 are used for this purpose.

In the case of an iteration already run through several times, the data symbol r(k) received at the timing point k , the data symbols dl{k -\),..,du{k -l ..,du{k -\) , ί¾(Α-2),..,¾(*-2)...(¾(*-2) , ^(&-3),..,ί¾(£~3),.., ( --3) etc. of the data-symbol sequence transmitted up to the timing point k - \ estimated in procedural stage S60 respectively at the timing points k - \ , k - 2 , k - 3 etc., every data symbol d(k) contained in the data-symbol alphabet of the modulation method used in each case for the timing point k and the estimated values A, ,..,AW , A, ,..,A„ ,..,Ay , A, ,..,«„ etc. of the channel-impulse responses ^k .., h^k) ,.^Η^ determined in procedural stage S70 at the timing point k - l or respectively at earlier timing points k - 2 , k - 3 etc. are used for this purpose.

In the subsequent procedural stage S40, in the case of a first run through the iteration, the metric <0} at the timing point 0, and the metric M{k at the timing point k , in the case of an iteration after several runs through is calculated from the initialised metric M{~^ in the case of a first run through of the iteration and from the metric 36 (i_1) determined iteratively at the preceding timing point k~\ , with the addition of the branch metric determined respectively for every possible data symbol (k) of the data symbol alphabet at the timing point k , which can be determined from the product of the a-priori estimation error eWk~l) calculated in procedural stage 30 and the a-posteriori estimation error eWk) .

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

Alternatively, the path metric (/° can be calculated respectively according to one of the iterative calculation formulae as shown in equations (48) to (51), in which the respective branch metrics are calculated from a-priori 37 estimation errors eWk'"^ and eift~w) at relatively earlier timing points k - n and k - m .

In the next procedural stage S50, according to equation (57) and (58), the expansion term S(k) is calculated, and building upon this, the expanded metric M . With the use of a weighting factor w according to equation (59), a different weighting between the iteratively-determined metric (< and the expansion term S(k) can be realised in =(*) the calculation of the expanded metric M In the subsequent procedural stage S60, the respective, =.(*) minimal expanded metrics M are determined from the ==(*) expanded metric M calculated respectively for every data symbol d(k) of the data-symbol alphabet used in the modulation method at the timing point k , by means of a depth-first or a breadth-first method and, accordingly, the data symbol dl(k),..,du(k),..,du(k) at the timing point k in the individual "survival paths" is estimated.

In 'this context, when using a breadth first method, starting from the state St selected at the preceding timing point k - l , for the respective "survival path", with reference to the Viterbi algorithm, the state St following at the timing point k and accordingly the estimated data symbol dl(k),..,du(k),..,du(k) at the timing point k ' characterising this state St , which provides the smallest branch metric, can be selected. In this manner, from every individual state S, selected at the timing point k - l , once again, in each case, a single state Ss at 38 the timing point k is selected and continued in the respective "survival path" at the timing point k .

Alternatively, however, as presented in Figure 1, states St can be selected, which provide the smallest path metrics in each case. In this manner, from a state S(. selected at the timing point k-\, either several states S[ , a single state Ss or no state S,. at the timing point k can be selected. With both variants, the number of selected states Sl at the timing point k can be reduced by comparison with the states S( selected at the timing point k-l, if several "survival paths" disposed at the timing point k— l in each case in a different state St are combined in a single state St at the timing point k .

In the case of a depth-first method, the trellis diagram is first analysed "by depth" by following a "survival path" iteratively over so many timing points k until the ===(*) respective path metric M exceeds a predetermined threshold value. Upon exceeding the threshold value by the =(*) respective path metric M , the method moves back by so many timing points k on the "survival path" until a branching path is found, of which the branch metric leads to a path metric M , which is disposed below the predetermined threshold value. This branching path is once =<*) again followed until the respective path metric M once again exceeds the predetermined threshold value, and, once again, by moving back along the selected "survival path", a further branching path is found, which leads to a path =<*) metric M relatively smaller by comparison with the predetermined threshold value. This procedure is followed until the trellis diagram has been run through up to a 39 predetermined timing point k with one found "survival path" .

In the case that at least one signal provides a significantly-higher signal power than the other signal or respectively the other signals, the number M' of data-symbol hypotheses, reduced by comparison with the power M of the symbol alphabet, which is taken into consideration in the estimation of the data symbol within the data-symbol sequences of lower-power signals, is specified on the basis of the previously-determined relationships of the signal powers of the highest power signal or respectively of the highest power signals relative to the signal powers of the lower-power signal or respectively of the lower-power signals. The determination of the ratio of the signal powers of the highest-power signal or the highest-power signals relative to the signal powers of the lower-power signal or the lower-power signals - so-called carrier-to-interference ratio (CIR) -is determined by measuring the signal power of the channel-impulse response of the transmission channel transmitting the respective low-power or high-power signal. The reduced number M' of data-symbol hypotheses to be taken into consideration in the case of lower-power signals should be specified to be indirectly proportional to the determined carrier-to-interference ratio value. In the trellis diagram, in the case of the signal equalisation at the respective timing point k , only those states Si are selected, which are associated with a number M' of data-symbol hypotheses with the respectively smallest Euclidean distances relative to the received data symbol dr(k),..,du(k\,.,du(k) for each lower-power signal. From the trellis diagram in Figure 2 , with a high-power signal 40 d{ and the two lower-power signals d2 and d3 , all of which are modulated in a modulation method with the power M = 4 , for example, QPSK, it is evident that, at the timing point k, in each case, the data-symbol hypothesis of the high-power signal d_ with the minimal metric - in k = L, : data-symbol hypothesis d1 = 01 ; in k = L,+l: data-symbol hypothesis ^ = 00 - and the M'—2 data-symbol hypotheses with the minimal metric for each low-power signal d2 and d2 ™ in k = Lt : data-symbol hypothesis d2 = 00 and d2=Ql or respectively d3 ~ 00 and j = l l in k = Lt +\ : data-symbol hypothesis d2 = 0\ and d2=\\ or respectively £¾ = 00 and In the next procedural stage S70, the Kalman amplification g(i) is calculated according to equation (37) or respectively according to equation (42) with the use of the forgetting factor μ for the smaller weighting of data symbols dl(k),..,du(k),..)du(k) transmitted earlier by comparison with currently-transmitted data symbols dl(k),..,du(k),..,du(k) . For this purpose, the estimates £ transmitted up to the timing point k determined for the respective "survival path" are used with the data symbols d^k^.^d^kX^d^k) at the timing point k estimated in the preceding procedural stage S60 for the respective "survival path" and the prediction-error correlation matrix K^k~X) at the previous timing point k-\. In the first run through of the iteration, this prediction-error correlation matrix K^k"^ provides the values initialised in procedural stage S20, and, in the case of several runs through of the iteration, 41 the values of the correlation matrix K^~l at the timing point k - l determined iteratively in the last iteration in procedural stage S70.

In procedural stage S70, the prediction-error correlation matrix at the timing point k is also calculated iteratively with the Kalman amplification g(k determined in this manner at the timing point k and the prediction-error correlation matrix Κ^~1) at the timing point k - l .

Finally, in procedural stage S70, with the Kalman amplification t determined and the a-priori estimation err calculated in procedural stage S30, on the basis of the estimated values hx ,..,hu of the channel-impulse responses at the timing point k - l , the estimated value h of the channel-impulse responses at the timing point k is calculated k-\) iteratively. The estimated values h of the channel-impulse responses h^' ->h^k: -,h( k') at the timing point k - l is obtained, in the case of a first run through of the iteration from the estimated values °f the channel-impulse responses ^k ..,ht k ..,hu(k) determined in the first-channel estimation in procedural stage S10 at the timing point —1 , and, in the case of several runs through of the iteration already, from the estimated values h ,··,«£/ of the channel-impulse responses k --> u{k --> u^ at the timing point k - l determined iteratively in the last iteration in procedural stage S70. 42 In procedural stage S80, it is determined whether the estimates of the data-symbol sequences are completed. This is the case, if, after a given number of iterations, all "survival■ paths" present have finally combined in one state S, of the trellis diagram at a given timing point k to form a single "survival path", and the method according to the invention is completed.

If this event has not yet occurred, in procedural stage S90, the next timing point k + 1 is waited for, and the next iteration is started with procedural stage S30.

Curve 1 of Figure 6 presents the bit-error rate - BER (bit error rate) - 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 presents a method for the simultaneous estimation of several time-variable transmission channels and the data-symbol sequences d_i k ..,d^k ..,du k) transmitted in each case via one of the transmission channels according to the prior art, and curve 2 of Figure 6 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 the detection of several transmitted data-symbol sequences transmitted respectively via a time-variable transmission channel from a received signal without pre-filter.

In this context, both cases provide an un-coded 8-PS -modulated transmission signal according to the GSM/EDGE standard, which is transmitted from two transmitters E (U=2) , a signal/noise ratio — of 30 dB, an urban N0

Claims (1)

1. 44 Claims Method for detecting at least one transmitted data- symbol sequence ( d_\ k ->d^k),..,d_( k) ) associated in each case with one signal transmitted via respectively one time-variable transmission channel from a received data-symbol sequence {r ) associated with a single received signal, in which the impulse response of the respective transmission channel and the respective, currently- transmitted data symbol {d k ..,d1 k ..,du(k)) is estimated in alternation for every timing point (k ), wherein for the estimation of the data symbol ( ,..,dtllk),..,d k) ) transmitted in each case at the current timing point (k), those states ( S, ) in the state diagram are selected, of which the =(*) iteratively-calculated expanded metrics ( M ) consisting respectively of a path metric ( Mik) } and an expansion term (S(k)) are minimal, wherein the numerator of the expansion term ( S(k) ) is obtained solely from the difference between the data symbols {r(k + V), r(k + 2) , r(£+3),..) received at future timing points {k+[r k + 2, k+3,..) and the estimates ( d\ vj-5_y ) °f the data-symbol sequence ( d k),..,d}k),,.,ά^ ) transmitted in each case up to the current timing point [k] weighted with the impulse - (*) - (*) - (*) response ( n, ,..,«;/ ) of the respective transmission channel estimated at the current timing point ( k ) . 45 Method for detection according to claim 1, characterised in that the metric ( M{k) ) of a state ( ) at the current timing point (k) is calculated iteratively from the expanded path metric ( M{k'X) ) of the respectively-preceding state {Sj) with the addition of a branch metric between the respectively-preceding state ( Sl ) at the preceding timing point (k-\ ) and the state (S,) at the current timing point ( k ) . Method for detection according to claim 2, characterised in that the branch metric between the respectively-preceding state (St) at the preceding timing point (k-\) and the state ( St ) at the current timing point (k) takes into consideration a function of a product from a firgt a_priori estimation error (e k~"]) and a second a-priori estimation error (eWk~m)) or an a-posteriori estimation error (eWk)), wherein the first a-priori estimation error ( e(*'*"n) ) , the second a-priori estimation error (e{kk'm)) and the a-posteriori estimation error ( eWk) ) is determined in each case between the data-symbol sequence (r ) received up to the current timing point (k) and the estimate ( \ 't\ +~ + du -hu +.. + d; -ha ) of the data-symbol sequence (r ) received up to the current timing point ( k ) . Method for detection according to claim 3, 46 characterised in that the function is a modulus-forming function. Method for detection according to claim 3, characterised in that the function is a real-component forming function. Method for detection according to any one of claims 3 to 5 , characterised in that the estimate - (*)r r (k-n) * ; (A) -> (*-«) - (kf 7 (k-n) ( · -i >->du ) of the data-symbol sequence ( ik "> u k) >->duk) ) transmitted up to the current timing point (A) weighted with an impulse response ,.·,_¾, ,..,/¾, , A, ,..,hu ,..,hu » (k-m) « (k-m) - (k-m) - <*) - (*) (t) «, ,->nu !··)£.(/ ' _?i V5»,, ?·■)¾/ ) of the respective transmission channel estimated at a first and respectively second timing point [k-n , k-\ ; k - m ; k ) . Method for detection according to claim 6, characterised in that 47 the first timing point (k-n, k-\ ) of the first a-priori estimation error ( e estimation hypothesis (A, ,..,AH ,.., (, ), an a-priori estimation error ( e(/f|*_l) ) between the data-symbol sequence [r ) received up to the current timing -point {k) and the estimate ( d^ ,-,du ,-,du ) of the data-symbol sequence ( ,,.,ά^,..,άυ{Ιί) ) transmitted up to the current timing point {k) weighted with the « - (k-\) p (k-\) impulse response (A, ,..,h„ ,-,ίίυ ) °* transmission channel estimated at the preceding timing point (k-l) for the respectively preceding state {Sj) is determined for every state ( Sj ) selected at the current timing point ( k ) . Method for detection according to any one of claims 1 to 16, characterised in that p (*) - (*) <*) the channel estimation hypothesis (A, ,..,A„ ) at the current timing point (k) is determined via an adaptive channel-estimation method from the most recently past channel-estimation hypothesis » (k-n) « (k-n) {k-n) ( >"}flu i->ku ) °f all or tne channel-estimation (k-n) [k-n) p (k-n) p (k-2n) - (k-Zn) p (k-2n) hypotheses (A, ,..,hu ,..,hv , A, ,..,AH ,..,/¾, p (k-ln) p (k~3n) » (*-3«) Aj ,..,«„ ,··>«