The present invention relates to an adaptive equalization method and an adaptive equalizer for use, for example, in mobile communications to reduce the influence of fading.
In a mobile communications environment signals transmitted from mobile stations arrive at a base station from various directions under the influence of surrounding buildings, trees and so forth. The influence of intersymbol interference, which results from the arrival of paths of large delay time differences in such a multipath channel, poses a serious problem for mobile communications. A known technique for lessening the influence of a signal waveform distortion by the intersymbol interference is an equalization technique that estimates the characteristic of the channel and performs equalization of delayed paths based on the estimated characteristic. One of equalization algorithms used in the equalization technique is a turbo-coding-technique-applied iterative equalization algorithm that achieves a very excellent error rate characteristic in low SNR. The turbo coding method implements, with practical coding-decoding complexity, an error rate characteristic that is almost a ceiling value obtainable with a channel coding method; only the presence of such an error rate is merely suggested in information theory. With the turbo coding method, the transmitting side transmits coded information sequence and its rearranged or interleaved version, and the receiving side repeatedly decodes them alternately with each other. Since the process of generating a coded sequence of convolution codes in the turbo coding is equivalent to the process of generation of the intersymbol interference in multipath channel, the decoding process of the turbo coding technique can be applied to the equalization of delayed paths.
In Eq. (1) the first term, λ1[b(i)], is extrinsic or external information derived by subtracting a priori information λ2[b(i)], by a subtractor 26, from the log-likelihood ratio Λ1[b(i)] provided from the SISO equalizer 21. The second term, λ2[b(i)], is the a priori information that is a rearranged or interleaved version, by an interleaver 25, of λ2[b(n)] obtained by subtracting λ1[b(n)], by a subtractor 24, from a log-likelihood ratio Λ2[b(n)] provided from a SISO decoder 23 in the previous iteration. The initial value of λ2[b(n)] is zero. The a priori information λ2[b(i)] is used as an a priori LLR value of a coded bit string {b(i)}. The extrinsic information is restored by a de-interleaver 22 to λ1[b(i)], which is input as a posteriori information to the SISO decoder 23. The SISO decoder 23 uses the a posteriori information to derive a posteriori LLR value Λ2 of the coded bit string {b(i)} by the following equation (2).
Λ2[b(n)]=λ2[b(n)]+λ1[b(n)] (2)
In the second and subsequent iterations, λ1[b(n)] is subtracted by the subtractor 24 from the a posteriori LLR value Λ2 derived by the SISO decoder 23 to obtain extrinsic information λ2[b(n)], which is provided as a priori information λ2[b(i)] via an interleaver 25 to the SISO equalizer 21. Such iterations of equalization and decoding update the LLR value, providing a more probable LLR value. That is, the first log-likelihood ratio Λ1 is calculated by the first adaptive equalization of the received digital signal, and the first log-likelihood ratio Λ1 is decoded to obtain the second log-likelihood ratio Λ2, which is used to perform the second adaptive equalization of the received digital signal to obtain the first log-likelihood ratio Λ1, which is then decoded, and the decoded value is output.
In the iterative equalization the SISO equalizer and the SISO decoder use a MAP (Maximum A-posteriori Probability) algorithm, Log-MAP algorithm based on the MAP algorithm, or Max-Log-MAP algorithm that has reduced the computational complexity of equalization and decoding through use of approximate calculation. Still another algorithm is SOVA (Soft-Output Viterbi Algorithm) that provides bit reliability information while performing optimum decoding on a sequence-wise basis. In the case of using any of these algorithms for equalization by the equalizer, however, the complexity of the algorithm exponentially increases with respect to the maximum number of delayed symbols to be considered in the equalizer, resulting in very high computational complexity. For example, when BPSK is used as the modulation system, assuming that the storage capacity of one receiving channel is 10 symbols (the maximum number of delayed symbols to be considered in the equalizer being 10 symbols), the number of states becomes as large as 210=1024, exceeding practical computational complexity. The computational complexity could be reduced by using a linear equalizer for the iterative equalization.
When such a linear equalizer is used for the above-described iterative equalization, it is necessary to derive a soft decision value as the equalizer output. In the afore-mentioned literature by Daryl Reynolds and Xiaodong Wang, there is set forth a scheme in which, by deriving the soft decision value through the use of the linear equalizer, the iterative equalization can be achieved with less computational complexity than in the case of using the conventional algorithm such as MAP, SOVA or the like. In the literature a description is given of the application of the linear equalizer assuming the following discrete-time model as a channel model. A received signal sample r(n) is expressed as follows:
v(n)=[v0(n)v1(n) . . . vM−1(n)]T (4)
h(n;j)=[H0(n;j)h1(n;j) . . . hM−1(n;j)]T (5)
In the above, M is the number of channel outputs and r(n)=[r0(n)r1(n) . . . rM−1(n)]T is a vector representing a received sample value in each channel at time n, where T indicates a transposed matrix. For example, in the case of using a plurality of antennas, M corresponds to the number of antennas. B(n) represents a coded bit, and v(n) in Eq. (4) is a complex vector of an average 0, representing noise. In Eq. (5), h(n;j) is a vector representing the tap weighting coefficient of the channel, and J is the channel ISI length. Now, a received signal vector R(n), a noise vector V(n), a coded bit vector B(n) and a channel matrix Hm(n) are defined as follows:
The vectors R(n) and V(n) given by Eqs. (6) and (7) are column vectors of a matrix with MJ rows and one column, that is, MJ-dimensional column vectors. B(n) is a (2J−1)-dimensional column vector, H(n) is a matrix with M rows and J columns, and Hm(n) is a matrix with MJ rows and (2J−1) columns. From the above, Eq. (3) becomes as follows:
R(n)=Hm(n)B(n)+σV(n) (11)
Next, the likelihood of the code bit string is defined by the following equation using the a priori LLR value λ2[b(k)] of the code bit string b(i).
b′(k)=tanh[λ2[b(k)]/2], n−(J−1)≦k≦n+(J−1) (12)
Eq. (12) has the property that it rapidly approaches 1 or −1 upon deviation of a variable x of a hyperbolic function tanhx from 0, and the likelihood b′(k) represents an estimated value of b(k). Further, that estimated value vector of the code bit in the received signal vector R(n) which affects, as intersymbol interference, code bit b(n) at time n is given by the following equation.
B′(n)=[b′(n+(J−1))b′(n+(J−2)) . . . b′(n+1)0b′(n−1) . . . b′(n−(J−1))]T (13)
In Eq. (13), since B′(n) is an estimated value vector that is used to subtract from the received signal vector R(n) the intersymbol interference component for the code bit b(n) at time n, the element corresponding to b(n) of the vector B′(n) is set to zero. A difference vector Rc(n) by subtracting an intersymbol interference component replica from the received signal vector R(n) is defined by the following equation using the estimated intersymbol interference code vector B′(n).
Rc(n)=R(n)−Hm(n)B′(n)=Hm(n)[B(n)−B′(n)]+σv(n) (14)
The difference vector Rc(n) is subjected to filtering expressed by the following equation through the use of a linear filter of tap coefficient G(n).
Z(n)=G(n)HRc(n) (15)
where H is a conjugate transposed matrix. The tap coefficient G(n) is so chosen as to minimize the mean square error between the code bit B(n) and the filter output Z(n) as expressed by the following equation.
G(n)=arg min E{∥b(n)−G(n)HRc(n)∥2}=arg min G(n)HE{Rc(n)Rc(n)H}G(n)−2 G(n)HE{b(n)Rc(n)} (16)
where arg min E { } represents that one of all J-dimensional vectors G whose content of { } is minimum.
Expansion of first and second terms in Eq. (16) gives
E{Rc(n)Rc(n)H{=Hn(n)Λ(n)Hm(n)H+σ2I (17)
E{b(n)Rc(n)}=Hm(n)ej (18)
where I is a unit matrix and
In the above, Cov represents a covariance matrix and diag represents a diagonal matrix. ej is a vector of a length 2J−1, a J-th element being 1 and other elements being 0s. By solving the normal equation with the gradient vector on the right-hand side of Eq. (16) to 0 and substituting Eqs. (17) and (18), the optimum tap coefficient G(n) is given as follows:
G(n)=[Hm(n)Λ(n)Hm(n)H+σ2I]−1Hm(n)ej (20)
Substitution of the thus derived tap coefficient G(n) into Eq. (15) gives
Z(n)=eJTHm(n)H[Hm(n)Λ(n)Hm(n)H+σ2I]−1[R(n)−Hm(n)B(n)] (21)
In this case, since it is necessary that Hm(n) be a full column rank, the antenna number M needs to be at least 2 or more.
Assuming that the filter output can be approximated by a Gaussian distribution, Z(n) by Eq. (21) can be described as follows (see V. Poor and S. Verdu, “Probability of Error in MMSE Multiuser Detection,” IEEE Trans. Information Theory., vol. IT-43, No. 3, pp. 858–871, May 1997).
Z(n)=μ(n)b(n)+η(n) (22)
where μ(n) is an equivalent amplitude of the output signal and η(n) represents a Gaussian distribution of an average 0 and the variance v2(n). Therefore, μ(n) and v(n) can be expressed as follows:
where [ ]j,j indicates the element at the intersection of the J-th row and the J-th column of the matrix.
V2=var{Z(n)}=μ(n)−μ2(n) (24)
From the above, the extrinsic information derived by the linear equalizer can be deduced from the following equation.
To obtain the optimum tap coefficient G(n) with the above-described method, however, it is necessary that the inverse matrix calculation expressed by the following equation be conducted in Eq. (20) for each point in time; hence, much time is required for calculation.
Φ(n)=[Hm(n)Λ(n)Hm(n)H+σ2I]−1 (26)
With the conventional method for iterative equalization by the linear equalizer, the inverse matrix calculation needs to be conducted for each point in time to update the tap coefficient—this gives rise to the problem of high computational complexity.
It is therefore an object of the present invention to provide an adaptive equalization method and apparatus that permit reduction of the computational complexity for deriving the tap coefficient of the linear equalizer for iterative equalization and hence allow shortening the time for computation.
According to a first aspect of the present invention, a received signal sample value and a known signal are used to estimate the impulse response of the channel, and a received signal sample value sequence is used to adaptively calculate the tap coefficient of a linear filter. The tap coefficient is used to perform linear filtering of the received signal sample value sequence, and the result of linear filtering and the estimated value of the impulse response are used to derive a soft decision value.
With this construction, in the case of using the linear equalizer for iterative equalization, the received signal sample value sequence is input thereto to adaptively derive the tap coefficient of the linear filter—this permits reduction of computational complexity as compared with the prior art method involving the inverse matrix calculation.
According to a second aspect of the present invention, in second and subsequent processing by an adaptive iterative equalizer for the iteration of equalization and decoding, an estimated value vector of the code bit based on the likelihood of a soft decision value from a decoder is subjected to linear filtering with an estimated impulse response value Hm(n) to generate a replica of the received signal. The replica is subtracted from the received signal to create a difference signal Rc(n) having removed therefrom the intersymbol interference component, then the tap coefficient of the linear filter is calculated, for example, using the Matrix Inversion Lemma, from the estimated impulse response value vector HL(n) approximated with the intersymbol interference component regarded as zero, then the difference, then the difference signal Rc(n) is subjected to linear filtering using the tap coefficient, and the result of linear filtering and the estimated impulse response value vector are used to derive the soft decision value.
With this construction, the tap coefficient of the linear filter in second and subsequent iterative equalization by the linear equalizer can be calculated, for example, using the Matrix Inversion Lemma, by which it is possible to achieve adaptive equalization with less computational complexity than in the case of the conventional that involves the inverse matrix calculation of Eq. (20).
According to a third aspect of the present invention, a received signal sample value sequence and a known signal are used to estimate the impulse response of the channel, then a threshold value is set accordingly, and components of values smaller than the threshold value are removed from the estimated impulse response value vector, that is, the dimension of the estimated impulse response value vector is reduced. Further, components corresponding to those of the values smaller than the threshold value and hence removed from the estimated impulse response value vector are removed from the tap coefficient of a linear filter calculated from the received signal sample value sequence and the received signal vector to thereby reduce their dimension as well. The soft decision value is derived using the estimated impulse response value vector, the tap coefficient of the linear filter and the received signal vector of the thus reduced dimensions.
The above scheme permits reduction of the computational complexity for deriving the soft decision value when the linear equalizer is used for iterative equalization.
According to a fourth aspect of the present invention, the likelihood of the soft decision value from a decoder is calculated in second and subsequent processing by an adaptive equalizer for iteration of equalization and decoding, then the tap coefficient of the linear filter is calculated, for instance, using the Matrix Inversion Lemma from the estimated impulse response value vector reduced in dimension in the first round of iteration and stored in a memory, then the tap coefficient is used to perform linear filtering of a difference signal having subtracted therefrom an intersymbol interference component, and the result of linear filtering and the estimated impulse response value vector are used to derive the soft decision value.
This scheme allows reduction of the computational complexity for deriving the soft decision value in the second and subsequent iterative equalization by the linear equalizer as well.
In the method set forth in the afore-mentioned literature that employs a linear equalizer for iterative equalization, the likelihood b′(k) of the code bit is calculated by Eq. (12) using the a priori LLR value λ2[b(k)] of the code bit string. In the first equalization processing, since the a priori LLR value λ2[b(k)] in Eq. (12) is zero in the absence of the a priori information, the likelihood b′(k) is all zeros as shown below.
b′(k)=[00 . . . 0 . . . ]T
Therefore, the difference vector Rc(n) by Eq. (12) becomes as follows:
Rc(n)=R(n)−Hm(n)B′(n)=R(n) (27)
and Λ(n) becomes a (2J−1)×(2J−1) whose diagonal components are all ones as shown below.
Λ(n)=Cov{B(n)−B′(n)}=diag{1,1, . . . , 1,1} (28)
Accordingly, the optimum tap coefficient G(n) of the linear filter by Eq. (20) can be derived by the following calculation.
G(n)=[Hm(n)Hm(n)H+σ2I]−1Hm(n)ej (29)
From Eq. (29) the tap coefficient G(n) is dependent on the value Hm(n) corresponding to the impulse response of the channel. In the case where temporal variations of the channel due to high transmission rate or the like, that is, where the duration of a received burst path is so short that the channel characteristic of the received signal does not change in that time interval, the tap coefficient G(n) is substantially constant. Accordingly, by precalculating the tap coefficient G(n) prior to the processing of the information symbol period and using the precalculated value for processing of each information symbol, the computational complexity can be reduced as compared with that in the conventional system that derives the tap coefficient G(n) for each information symbol. Moreover, since the above-mentioned temporal variations need not be taken into account as well in the calculation of the tap coefficient by Eq.(20), an adaptive algorithm can be used—this avoids the necessity for conducting the inverse matrix calculation to derive the tap coefficient G(n), permitting reduction of computational complexity.
In view of the above, in the first embodiment of the present invention, the tap coefficient calculation is conducted by an adaptive algorithm to obtain G(n) in a known signal period or training signal period prior to the processing of the information symbol period, and the value thus obtained is used to perform the processing in the information symbol period. This eliminates the needs for the inverse matrix calculation and the derivation of G(n) at each point in time of the information symbol, enabling the computational complexity to be made lower than in the conventional scheme.
The adaptive equalizer of the first embodiment comprises an impulse response estimating part 100, a linear filter part 110, a soft decision value calculating part 120, a switch 101, a likelihood calculating part 130, and a switch 160. The impulse response estimating part 100 is made up of a transversal filter 103, a subtractor 105, and an adaptive estimating part 106. The linear filter part 110 is composed of a transversal filter 111, a tap coefficient calculating part 112, and a subtractor 113.
A description will be given, with reference
In the linear filter part 110, the received signal sample value sequence R(n) is input to the transversal filter 111 as a linear filter, by which it is subjected to linear filtering with the tap coefficient G(n) calculated in the tap coefficient calculating part 112, then the filtered output Z(n)=GH(n)HR(n) is subtracted by the subtractor 113 from the training signal sequence b(n), and the difference is input to the tap coefficient calculating part 112 to update the tap coefficient G(n) of the linear filter. This updating calculation utilizes an adaptive algorithm. That is, in the first iteration of equalization, since R(n)=Rc(n) from Eq. (27), the tap coefficient G(n) is so determined by the adaptive algorithm as to minimize ∥b(n)−G(n)HR(n)∥ from Eq. 16. On this account, the tap coefficient G(n) can be calculated with less complexity than in the case of conducting the inverse matrix calculation by Eq. (20). The updating of the tap coefficient G(n) stops with the termination of the training signal sequence b(n), and the tap coefficient at this time is held unchanged.
The received signal after termination of the training signal sequence b(n), that is, the information-symbol received signal sample sequence R(n), is subjected to linear filtering by the transversal filter 111 with the most recently updated tap coefficient G(n). The filtering output Z(n) and the ultimately estimated channel impulse response value Hm(n) are used to calculate, as the first equalization output, the soft decision value λ1[b(n)] in the soft decision value calculating part 120. In the first iteration of equalization, since the a priori information λ2[b(n)]=0, Λ1=[b(n)]=λ1[b(n)]. The soft decision value λ1[b(n)] is fed to the de-interleaver 22 (see
Next, a description will be given first of the principle of equalization in the second and subsequent rounds of iterative equalization and then of concrete equalization processing with reference to
B′(n)≈[,±1, ±1, . . . , ±1,0,±1, . . . , ±1,±1]T (30)
The use of thus approximated b′(n) permits approximation of Eq. (19) to the following equation.
Λ(n)=Cov{B(n)−B′(n)}=diag{0,0, . . . 0,1,0, . . . , 0,0} (31)
Substituting Eq. (31) into Eq. (20), the tap coefficient G(n) of the linear filter can be obtained by conducting the following calculation.
G(n)=[HL(n)HLH(n)+σ2I]−1HL (32)
where HL(n) is the vector of one column of M by J rows expressed by
HL(n)=[h(n;J−1) . . . h(n; 0)]T=[h0(n;J−1) . . . hM−1(n;J−1) h0(n;J−2) . . . hM−1(n;J−2) . . . h0(n; 0) . . . hM−1(n; 0)]T.
In this instance, the use of the Matrix Inversion Lemma in the calculation of the tap coefficient G(n) of the linear filter by Eq. (32) allows reduction of the computational complexity therefor. With such approximation of the estimated intersymbol interference code vector B(n) as expressed by Eq. (30), HL(n) becomes the vector of one column of M by J rows as mentioned above—this avoids the need for conducting the inverse matrix calculation, permitting substantial reduction of the computational complexity as compared with that needed by the conventional scheme. Thus, according to the present invention, in the second and subsequent rounds of iterative equalization the computational complexity in the tap coefficient calculating part for deriving the tap coefficient G(n) of the linear filter can be reduced through utilization of the approximation by Eq. (31) and the Matrix Inversion Lemma.
The tap coefficient G(n) of the linear filter is calculated by Eq. (32) using, as the input therefor, only the estimated channel impulse response value HL(n) stored in the storage part 106B unlike in the scheme for deriving the tap coefficient of the linear filter in the first iteration of iteration.
This calculation utilizes the afore-mentioned Matrix Inversion Lemma. That is, when this Lemma is expressed by A=B−1+CD−1CH, where A and B represent (M by M) positive definite matrixes, C an (M by N) matrix, D an (N by N) positive definite matrix, an inverse matrix of A is given by
A−1=B−BC(D+CHBBC)−1CHB (33)
Applying this Lemma to the calculation of the inverse matrix in Eq. (32),
HL(n)HLH(n)+σ2I=B−1+CD−1CH,
HL(n)HLH(n)=CD−1CH,
σ2I=B−1,
h(n)=C,
D−1=I,
HLH(n)=CH
By using them to calculate Eq. (33), the inverse matrix calculation in Eq. (32) is solved. Incidentally, Eq. (33) also contains an inverse matrix calculation (D+CHBBC)−1, but this inverse matrix is also scalar, and hence it can similarly be calculated.
The thus calculated tap coefficient value G(n) is used to perform linear filtering of the difference value Rc(n) by the transversal filter 111, and the filtering result Z(n) and the estimated channel impulse response value HL(n) stored in the storage part 106B are used to calculate Eq. (25) in the soft decision value calculating part 120 to derive the soft decision value Λ1[b(n)]. The equivalent amplitude μ(n) in Eq. (25) is given by the following equation by substituting Eq. (31) for Λ(n) in Eq. (23).
Incidentally, in the first iteration of equalization the tap coefficient calculating part 112 of the linear filter part 110 may also use the Matrix Inversion Lemma to calculate the tap coefficient G(n).
As described above, this embodiment permits reduction of the computational complexity for deriving the tap coefficient of the linear equalizer that is used for iterative equalization.
In
In
While the examples of
As described previously, the one mode of the first embodiment utilizes the fact that the impulse response of the channel does not so vary over a short range of time, and hence it is characterized in that the training signal at the beginning of the received burst path (frame) or the known signal is used to obtain the estimated impulse response value Hm(n), which is used to the subsequent processing.
Further, according to the other mode of this embodiment, in the second iterations of iteration, only a J-th element of a diagonal matrix is set to 1 which is a covariance matrix of the difference between the code bit vector B(n) and the estimated intersymbol interference code vector B′(n) as expressed by Eq. (31), and the other diagonal elements are approximated to zeros, by which the calculation for the tap coefficient G(n) becomes a vector calculation as indicated by Eq. (32)—this avoids the necessity of conducting the inverse matrix calculation and hence allows reduction of computational complexity. In the first processing the known signal (training signal) need not always be used, but instead the output from a discriminating part 150, which discriminates the output from the transversal filter 103 between two value in binary, may be used in place of the signal from the output of the switch 101 as indicated by the broken lines in
In the first embodiment described above with reference to
That is, in the first embodiment, path components within the range of the maximum number J of delayed symbols, even if very small, in extreme cases, zero in received power, are also subjected to equalization, and consequently, much time is needed for calculation. As a solution to this problem, this embodiment is adapted to omit particular ones of the dimensions corresponding to multipath components of negligibly small received power to reduce the sizes of vectors and matrixes to be handled, thereby reducing the computational complexity and hence shortening the calculating time.
Calculating the likelihood b′(n) of the soft decision value λ2[b(n)] for the code bit string b(n) that is the decoder output for the result Λ1[b(n)] of the first iteration of equalization, by Eq. (12) as in the second iterations of equalization in the first embodiment, the calculated value is virtually +1 or −1. Through utilization of this fact for the approximation of the estimated intersymbol interference code vector B′(n) as expressed by Eq. (30), the tap coefficient G(n) of the linear filter 111 can be calculated using the Matrix Inversion Lemma as follows:
where HL(n) is a column vector of a M by J length as shown below.
By the approximation of Λ(n) in Eq. (23) as indicated by Eq. (32), the equivalent amplitude μ(n) of the output signal is also calculated as expressed by (34).
On the other hand, Z(n) is given by
Z(n)=G(n)HRc(n) (37)
as is the case with Eq. (15). By using in Eq. (25) the linear filter output Z(n) obtained by Eq. (37), the extrinsic information value Λ1[b(n)] derived by the linear equalizer can be used as the results of second and subsequent equalizations.
Now, assume that path components j=1 to j=J−2 within the range of the maximum number J of delayed symbols to be considered in the equalizer have not arrived but that path components j=0 and j=J−1 have arrived. If the impulse response of the channel can accurately be estimated, other path components than effective ones are such that h(n;1),h(n;2), . . . , h(n;J−2)=≡0. Accordingly, it follows from Eq. (35) that
Since the tap coefficient G(n) of the linear filter can be calculated from HL(n) as shown by Eq. (35), it follows that
G(n)=[g0(n;J−1) . . . gM−1(n;J−1)0 . . . 0 g0(n;0) . . . gM−1(n;0)]T (39)
The derivation of the soft decision value Λ1[b(n)] by the linear equalizer by Eq. (25) requires the calculation of the equivalent amplitude μ(n) of the output signal by Eq. (36) and the linear filter output Z(n) by Eq. (37). The equivalent amplitude μ(n) and the linear filter output Z(n) are calculated as shown below.
Here, in the case where zero-elements of HL(n)H and G(n) are omitted, that is, where the dimensions of HL(n)H and G(n) are lowered as shown below, too, the value of μ(n) naturally remains unchanged.
HL′(n)H=[h0(n;J−1) . . . hM−1(n;J−1)h0(n;0) . . . hM−1(n;0)] (41)
G′(n)=[g0(n;J−1) . . . gM−1(n;J−1)g0(n;0) . . . gM−1(n;0)]T (42)
And, Z(n) becomes as follows:
In Eq. (44), since G(n)H has 0-elements, the values of Rc(n) corresponding to the 0-elements are unnecessary in the derivation of Z(n) as shown below.
Rc′(n)=[r0(n+J−1) . . . rM−1(n+J−1)r0(n) . . . rM−1(n)] (45)
Since the dimension of Rc(n) can be lowered as described above, the dimension of the received signal vector R(n) can also be lowered by Eq. (14). Further, since the dimension of the intersymbol interference component replica Hm(n)B′(n) can also be reduced, the dimension of the channel matrix Hm(n) can be reduced as well.
From the above, it can be seen that calculations for the path components having arrived can be dispensed with in the calculation for deriving the extrinsic information by the linear equalizer. That is, in the estimated impulse response value of the channel, the tap coefficient G(n) of the linear filter, the received signal vector R(n) and Rc(n) obtained by subtracting the intersymbol interference component from the received signal vector, those elements of vectors and matrixes corresponding to path components having not arrived can be removed. Accordingly, it is possible to decrease the number of dimensions of vector components and the number of elements of matrixes necessary for the calculation involved in the derivation of the soft decision value of the linear equalizer.
However, the estimated impulse response value does not become zero due to an error in the estimation of the impulse response of the channel. Hence, a certain threshold value hth, is set for comparison and discrimination of the estimated impulse response value as described below. For example, if h(n;1),h(n;2), . . . h(n;J−2)≦hth, then it is regarded as h(n;1),h(n;2), . . . h(n;J−2)≡hth. Letting L represent the number of effective received path components larger than the threshold value hth, the dimension of the estimated impulse response vector HL(n), which indicates all estimated impulse response values within the range of the maximum number J of delayed symbols, can be lowered from an M*J-th dimensional vector to an M*L-th dimensional vector H′L(n) as expressed below.
HL(n)=[h0(n;J−1) . . . hM−1(n;J−1)0 . . . 0 h0(n;0) . . . hM−1(n;0)]T (47)
HL′(n)=[h0(n;J−1) . . . hM−1(n;J−1)h0(n;0) . . . hM−1(n;01)]T (48)
Further, the number of row elements of the channel matrix Hm(n) can be lowered from 2J−1 to 2L−1.
If
h(n;1),h(n;2), . . . h(n;J−2)≦hth,
then
g0(n;1) . . . gM−1(n;1),g0(n;2) . . . gM−1(n;2), . . . , g0(n;J−2) . . . gM−1(n;J−2)0
is set; the tap coefficient vector G(n) of the linear filter in the second iterations of iteration is given by the following equation.
G′(n)=[g0(n;J−1) . . . gM−1(n;J−1)g0(n;0) . . . gM−1(n;0)]T (51)
This is apparent from Eq. (35) in the calculation of HL′(n)HHL′(n). Moreover, the tap coefficient vector G(n) can also be lowered from the M*J-th dimensional vector to the M*L-th dimensional vector G′(n).
Similarly, the received signal vector R(n) and the difference vector Rc(n) can also be lowered from the M*J-th to the M*L-th dimension.
The equivalent amplitude μ(n) of the output signal can be calculated by Eq. (43) from HL′(n) and G′(n), and the linear filter output Z′(n) can be calculated by Eq. (46) from G′(n)H and Rc′(n). Accordingly, they can each be derived by calculations of vectors of low dimensionality.
Furthermore, it is possible to lower the dimension of the number of column elements at positions of path components regarded as zeros in the channel matrix Hm′(n) of Eq. (50) generated from the estimated impulse response value as expressed by the following equation, and the dimension of the channel matrix for deriving the soft decision value by Eq. (25) can also be reduced. In an example in which only paths of j=0 and j=J are set as effective paths, the number of column elements can be decreased from (2J−1) to (2L−1).
In the first place, the switch 101 is connected to the terminal 102, and the switches 160 and 170 are both connected to the terminal 104. In the first iteration of equalization the processes for obtaining the estimated impulse response value Hm(n) and the tap coefficient G(n) are the same as in the first embodiment. Further, in
Moreover, the switch 160 is switched to the identifying part 140, in which only an information symbol received signal R′(n) corresponding to the effective path in the signals received after the training signal, that is, in the information symbol received signals R(n), is selected, and the thus selected signal is subjected to linear filtering by the transversal filter 111 using its tap coefficient G′(n) stored in the storage part 112B most recently. The linear filtering output Z′(n) and the most recently estimated impulse response value H′L(n) are used to calculate the soft decision value Λ1[b(n)] in the soft decision value calculating part 120.
In the second and subsequent rounds of equalization, the switch 101 is connected to the likelihood calculating part 130, the switch 160 to the identifying part 140 and the switch 170 to the output of the subtractor 105 as depicted in
As described above, the second embodiment permits reduction of the computational complexity for deriving the soft decision value of the linear equalizer.
The modulation system used is BPSK; the information transmission rate is 10 Mbps; the maximum Doppler frequency indicating the fading variation is 1000 Hz; and the frame configuration is one that a training signal of a known pattern of 63 symbols is added as an information signal to 256 symbols. A channel, in which only path components j=0 and j=4 as indicated by the solid lines in
In
As is evident from
As described above, the first embodiment of the present invention enables the linear equalizer for iterative equalization enables to reduce the computational complexity for calculating the tap coefficient of the linear filter and hence shorten the time for the calculation.
According to the second embodiment of the invention, in a channel environment in which path components of relatively large power have arrived apart in time from other path components, it is possible to adaptively reduce the computational complexity for calculating the extrinsic information by the linear equalizer that performs iterative equalization.
Number | Date | Country | Kind |
---|---|---|---|
2000-385699 | Dec 2000 | JP | national |
Number | Name | Date | Kind |
---|---|---|---|
5673294 | Namekata | Sep 1997 | A |
5920599 | Igarashi | Jul 1999 | A |
6269124 | Nagayasu et al. | Jul 2001 | B1 |
6570918 | Rademacher | May 2003 | B1 |
Number | Date | Country | |
---|---|---|---|
20020110188 A1 | Aug 2002 | US |