Patent Grant
7027533
The invention relates to turbo-reception method and a turbo-receiver as may be used in a mobile communication, for example, and which apply an iterative equalization utilizing a turbo-coding technique to waveform distortions which result from interferences.
A task in the mobile station communication business is how to construct a system capable of acquiring a multitude of users on a limited frequency domain with a high quality. A multi-input multi-output (MIMO) system is known in the art as means for solving such a task. The architecture of this system is shown in
Up to the present time, a study of a specific implementation of an MIMO receiver in an MIMO system is not yet satisfactorily warranted. If one attempts to construct an MIMO receiver in an MIMO system on the basis of MLSE (maximum likelihood estimation) criteria, denoting the number of transmitters by N and the number of multi-paths through which a wave transmitted from each transmitter reaches the MIMO receiver by Q, the quantity of calculation required for the MIMO receiver will be on the order of 2(Q−1)N, and will increase even more voluminously with an increase in the number of transmitters N and the number of multi-paths Q. When information from a single user is transmitted as parallel signals, which are then received, a separation of individual parallel signals from each other requires a quantity of calculation, which increases exponentially with number of multi-paths. Accordingly, the present invention proposes herein an improved calculation efficiency turbo-reception method for a plurality of channel signals. To start with, an existing turbo-receiver for a single user (single transmitter) or a single channel transmitted signal, which illustrates the need for the present invention, will be described.
Turbo-receiver for Single User
An exemplary arrangement for a transmitter and a receiver is illustrated in
For the single user, this corresponds to N=1 in
rm(k)=Σq=0Q−1hm(q)·b(k−q)+vm(k) (1)
where m represents an antenna index, h a channel value (a transmission path impulse response: a transmission path characteristic), b(k−q) a transmitted symbol from a user (transmitter 1), and vm(k) an internal thermal noise of the receiver 20. All outputs from the antennas #1 to #M are denoted by a matrix as indicated by an equation (2) to define an equation (3).
r(k)=[r1(k)r2(k) . . . rM(k)]T (2)
=Σq=0Q−1H(q)·b(k−q)+v(k) (3)
where
v(k)=[v1(k)v2(k) . . . vM(k)]T (4)
H(q)=[h1(q) . . . hM(q)]T (5)
It is to be noted that [ ]T represents an inverted matrix. In cosideration of the number of channels Q of the mutipath, the following matrixes and matrix are defined:
y(k)≡[rT(k+Q−1)rT(k+Q−2) . . . rT(k)]T (6)
≡H·b(k)+n(k) (7)
where
b(k−q)=[b(k+Q−1)b(k+Q−2) . . . b(k−Q+1)]T (9)
n(k)=[vT(k+Q−1)vT(k+Q−2) . . . vT(k)]T (10)
r(k) as defined above is input to the SISO equalizer 21, which is a linear equalizer, deriving a log-likelihood ratio Λ1(LLR) of a probability that each encoded bit {b(i)} is equal to +1 to a probability that it is −1 as an equalization output.
≡λ1[b(k)]+λ2p[b(k)] (12)
where λ1[b(k)] represents an extrinsic information fed to a succeeding decoder 24 and λ2P[b(k)] a priori information applied to the equalizer 21. The log-likelihood ratio Λ1[b(k)] is fed to a subtractor 22 where the a priori information λ2[b(k)] is subtracted therefrom. The result is then fed through a deinterleaver 23 to an SISO channel decoder 24, which calculates a log-likelihood ratio Λ2 as follows:
B: frame length
≡λ2[b(i)]+λ1p[b(i)] (14)
where λ2[b(i)] represents an extrinsic information which is applied as λ2P[b(k)] to the equalizer 21 during the iteration, while λ1[b(k)] is applied as a priori information λ1P[b(i)] to the decoder 24. In a subtractor 25, λ1[b(i)] is subtracted from Λ2[b(i)], and the result is fed through an interleaver 26 to the equalizer 21 and the subtractor 22. In this manner, the equalization and the decoding are iterated to achieve an improvement of an error rate.
To describe the prestage equalizer 21 in detail, the calculation of a linear filter response applied to a received matrix y(k) will be described. Using the a priori information λ2P[b(k)] for the equalizer 21, a soft decision symbol estimate
b′(k)=tan h[λ2P[b(k)]/2] (15)
is calculated. Using the estimate and a channel matrix H, an interference component or a replica H·b′(k) of the interference component is reproduced and subtracted from the received signal. Thus,
y′(k)≡y(k)−H·b′(k) (16)
=H·(b(k)−b′(k))+n(k) (17)
where,
b′(k)=[b′(k+Q−1) . . . 0 . . . b′(k−Q+1)]T (18)
Because the replica H·b′(k) of the interference component cannot be always a correct replica, the interference component cannot be completely eliminated by the equation (16). So a linear filter coefficient w(k) which eliminates any residue of the interference component is determined according to the MMSE (minimum mean square error) technique indicated below.
w(k)=arg min ∥wH(k)y′(k)−b(k)∥2 (19)
where H represents a conjugate transposition and ∥ ∥ a norm. w(k) which mimimizes the equation (19) is determined.
Deriving w(k) in this manner is described in Daryl Reynolds and Xiandong Wang, “Low Complexity Turbo-Equalization for Diversity Channels” (http:/ee.tamu.edu/Reynolds/). A major achievement of this technique lies in a significant reduction in the quantity of calculation. The quantity of calculation according to a conventional MLSE turbo has been proportional to the order of 2Q−1 while a suppression to the order of Q3 is enabled by this technique. It will be seen that wH(k)·y′(k) represents an output from the equalizer 21, and is used to calculate λ1[b(k)], which is then fed through the deinterleaver 23 to the decoder 24 to be used in the decoding calculation.
For purpose of equalization in the equalizer 21, it is necessary to estimate the channel value (transmission path impulse response) h appearing in the equation (1). This estimation is hereafter referred to as a channel estimation. The channel estimation takes place by using a received signal of a known training series such as a unique word which is transmitted as a leader of one frame and a stored training series. A poor accuracy of the channel estimation prevents an equalization in the equalizer 21 from occurring in a proper manner. The accuracy of the channel estimation can be enhanced by increasing the proportion which the training series occupies in one frame, but this degrades the transmission efficiency of the intended data. Accordingly, it is desirable that the accuracy of the channel estimation could be improved while reducint the proportion of the training series in one frame.
This is not limited to a receiver for multiple channel transmitted signals inclusive of MIMO, but the same is true in the channel estimation of a receiver such as RAKE receiver or a receiver using an adaptive array antenna where the certainty of a decoded result is improved by an iterative decoding process.
The described turbo-receiver has following restrictions:
It is an object of the invention to provide compensations for these two restrictions by providing a turbo-reception method and a receiver therefor which allow the receiver mentioned above to be extended to a receiver for a plurality of transmitted series signals such as for multiple users or parallel transmissions from a single user.
It is another object of the invention to provide a reception method and a receiver therefor in which a channel value of a received signal is estimated from the received signal and a known signal serving as a reference signal, the received signal is processed using the estimated channel value, and the processed signal is decoded so that the processing using the estimated channel value and the decoding are iterated upon the same received signal and which allow the channel estimation to be achieved with good accuracy using a relatively short known signal.
According to a first aspect of the present invention, there is provided a turbo-reception method of receiving N series (where N is an integer equal to or greater than 2) transmitted signals. The method comprises calculating a channel value hmn(q) (n=1, . . . , N) from M received signals rm (m=1, . . . , M) and N series known signals, determining a soft decision transmitted symbol b′n(k) on the basis of N series a priori information λ2[bn(k)] which are obtained by the decoding, and using the channel value hmn(q) and the soft decision transmitted symbol b′n(k) to calculate an interference component H·B′(k) formed by an intersymbol interference produced by an n-th transmitted signal itself and transmitted signals other than the n-th transmitted signal as follows:
B′(k)=[b′T(k+Q−1) . . . b′T(k) . . . b′T(k−Q+1)]Tb′(k+q)=[b′1(k+q)b′2(k+q) . . . b′N(k+q)]T
q=Q−1 . . . −Q+1 for q≠0b′(k)=[b′1(k) . . . 0 . . . b′N(k)]Tq=0
where b′(k) has a zero element at n-th position, Q represents the number of multipaths of each transmitted signal wave, q=0, . . . , Q−1 and [ ]T represents a transposed matrix, subtracting the intersymbol interference H·B′(k) from the received matrix y(k) to obtain a difference matrix y′(k) where
y(k)=[rT(k+Q−1)rT(k+Q−2) . . . rT(k)]T
r(k)=[r1(k)r2(k) . . . rM(k)]T
determining an adaptive filter coefficient wn(k) applied to the received signal for the n-th transmitted signal in order to eliminate residual interference component in the difference matrix y′(k) using the channel matrix H or reference signal, filtering the difference matrix y′(k) according to the adaptive filter coefficient wn(k) to obtain a log-likelihood ratio for the n-th series as the received signal for the n-th series transmitted signal from which the interference has been eliminated, and decoding by using the the log-likelihood ratios for N series.
According to a second aspect of the present invention, in the arrangement according to the first aspect fo the invention, when q=0,
b′(k)=[b′1(k) . . . −f(b′n(k)) . . . b′N(k)]T
where an element f(b′n(k)) is located at n-th position, and f( ) represents a function which satisfies f(0)=0 and having as a variable b′n(k) which satisfies d{f(b′n(k))}/d{b′n(k)}≧0.
According to a third aspect of the present invention, the equalization takes place in a plurality of stages, and the number of series in the equalization output is sequentially reduced in the later stages.
According to a fourth aspect of the present invention, in a turbo-reception method in which a channel value of a received signal is estimated from the received signal and a known signal serving as a reference signal, the received signal is processed using the estimated channel value, performing a decoding processing upon the processed signal and the processing which uses the estimated channel value and the decoding processing are iterated upon the same received signal, the certainty that the decoded hard decision information signal has is determined on the basis of the value of an associated soft decision information signal, and a hard decision information signal having a certainty which is equal to or greater than a given value is also used as a reference signal in the channel estimation of the next iteration.
First Aspect of the Invention (1)
In each of N transmitters S1 . . . SN, information series c1(i) to cN(i) are encoded in encoders 11-1, . . . , 11-N, and the encoded outputs are fed through interleavers 12-1, . . . , 12-N to modulators 13-1, . . . , 13-N as modulation signals, thus modulating a carrier signal in accordance with these modulation signals to transmit signals b1(k) to bN(k). In this manner, transmitted signals b1(k) . . . bN(k) from the transmitters S1, . . . , SN form N series transmitted signals.
A received signal r(k) which is received by a multiple output receiver through transmission paths (channels) is input to a multiple output equalizer 31. A signal received by the receiver is converted into a baseband signal, which is then sampled at one-half the symbol period, for example, to be converted into a digital signal, which is then input to the equalizer 31. It is assumed that there are one or more digital signals, the number of which is represented by an integer M. For example, received signals from M antennas are formed into received signals in the form of M digital signals.
The equalizer 31 delivers N log-likelihood ratios Λ1 [b1(k)], . . . Λ1 [bN(k)]. In subtractors 22-1, . . . , 22-N, a priori information λ1 [b1(k)], . . . λ1 [bN(k)] are subtracted from Λ1 [b1(k)], . . . Λ1 [bN(k)], and results are fed through deinterleavers 23-1, . . . , 23-N to be input to soft input soft output (SISO) decoders (channel decoders) 24-1, . . . , 24-N to be decoded, whereby the decoders 24-1, . . . , 24-N deliver decoded information series c′1(i) . . . c′N(i) together with Λ2 [b1(i)], . . . ,Λ2 [bN(i)]. In subtractors 25-1 . . . , 25-N, λ1 [b1(i)], . . . λ1 [bN(i)] are subtracted from Λ2 [b1(i)], . . . ,Λ2 [bN(i)], respectively, and results are fed through interleavers 26-13 . . . , 26-N to be fed as λ2 [b1(k)], . . . λ2 [bN(k)] to the multiple output equalizer 31 and the subtractors 22-1, . . . , 22-N, respectively.
A received signal rm(k) (m=1, . . . ,M) from multiple users (a plurality of transmitters) is a sum of received signals from the plurality of users when it is input to the equalizer 31 as indicated below.
rm(k)=Σq=0Q−1Σn=1Nhmn(q)·bn(k−q)+vm(k) (20)
where q=0, . . . , Q−1, and Q represents the number of multipaths for each transmitted wave. Defining a matrix y(k) by a similar procedure as used for the single user, we have
y(k)≡[rT(k+Q−1)rT(k+Q−2) . . . rT(k)]T (21)
=H·B(k)+n(k) (22)
where
r(k)=[r1(k) . . . rM(k)]T
B(k)=[bT(k+Q−1) . . . bT(k) . . . bT(k−Q+1)]T (25)
b(k+q)=[b1(k+q)b2(k+q) . . . bN(k+q)]Tq=Q−1,Q−2, . . . ,−Q+1 (26)
In an interference elimination step, it is assumed that it is desirable to obtain a signal from an n-th user (transmitter). In this example, a soft decision symbol estimate for signals from all users (transmitters) and a channel matrix (transmission path impulse response matrix) H are used to produce a synthesis of interferences by user signals other than from n-th user and interferences created by the n-th user signal itself, or an interference replica H·B′(k) is reproduced. Then, the interference replica is subtracted from y(k) to produce a difference matrix y′(k).
y′(k)≡y(k)−H·B′(k) (27)
=H·(B(k)−B′(k))+n(k) (28)
where
B′(k)=[b′T(k+Q−1) . . . b′T(k) . . . b′T(k−Q+1)]T (29)
b′(k+q)=[b′1(k+q)b′2(k+q) . . . b′N(k+q)]T:q=Q−1, . . . ,−Q+1, q≠0 (30)
b′(k)=[b′1(k) . . . 0 . . . b′N(k)]T:q=0 (31)
b′(k) has a zero element at n-th position. It is to be understood that b′n(k) represents a soft decision transmitted symbol estimate which is obtained by calculation of b′n(k)=tan h [λ2 [bn(k)]/2]. The matrix B′(k) represents a replica matrix of the interference symbol.
A filter coefficient wn(k) for the n-th user, which is used to eliminate the residue of the interference component, namely, a residual interference based on the imperfectness of the interference component replica H·B′(k) and an interference component created by the n-th signal itself, is determined according to MMSE (minimum mean square error) criteria as one which minimizes the following equation (32):
wn(k)=arg min∥wnH(k)·y′(k)−bn(k)∥2 (32)
Subsequent operation remains the same as for the single user. Specifically, wn(k) which is obtained in this manner is used to calculate wnH(k)·y′(k), and a result of calculation is fed through deinterleaver 23-n to be input as λ1 [bn(i)] to the decoder 24-n where a decoding calculation is made.
The described method of applying a filter (linear equalization) processing upon the received signal rm is repeated for all of users 1 to N. As a consequence, the number of outputs from the equalizer 31 will be equal to N, and all these outputs are decoded by respective decoders 24-1, . . . , 24-N. What has been mentioned above is an extension of a turbo-receiver for single user to a receiver for multiple users (MIMO).
From the foregoing description, it will be seen that an exemplary functional arrangement of the multiple output equalizer 31 will be as shown in
In addition, soft decision transmitted symbol estimates b′1(k) to b′N(k) are supplied to an interference replica matrix generator 314-1 where an interference replica matrix B′1(k) is generated according to the equations (29) to (31), then the matrix B′1(k) is subject to a filter processing according to the channel matrix H in a filter processor 315-1, and a resulting interference replica component H·B′1(k) is subtracted from the received matrix y1(k) in a difference calculator 316-1 to produce a difference matrix y′1(k).
At last the channel matrix H or a reference signal which will be described later is input to a filter coefficient estimator 317-1 to determine the filter coefficient w1(k) which is used to eliminate the residue of the interference component. In the example shown, the channel matrix H and a covariance σ2 of a noise component and soft decision transmitted symbols b′1(k) to b′N(k) from the soft decision symbol generator 313-1 are input to the filter coefficient estimator 317-1 to determine the filter coefficient w1(k) which minimizes the equation (32) according to the minimum mean square error criteria. A specific example of determining the filter coefficient w1(k) will be described later. The difference matrix y′1(k) is processed with the filter coefficient w1(k) in an adaptive filter processor 318-1, and Λ1 [b1(k)] is delivered as an equalized output for the received signal which corresponds to the transmitted signal from user 1.
A processing procedure for the multiple input multiple output turbo-reception method according to the described embodiment of the present invention is shown in
At step S4, the received signal y (k) is generated from the received signal r(k). At step S5, the interference replica matrix B′n (k) is generated according to the equations (29) to (31) using the respective soft decision transmitted symbol estimates b′n (k). At step S6, the interference component replica H·B′n (k) for the received signal from the n-th transmitter is calculated. At step S7, the interference component replica H·B′n(k) is subtracted from the received matrix y (k) to provide the difference matrix y′n (k). At step S8, using the channel matrix H, the soft decision transmitted symbols b′1(k) to b′N(k) and the covariance σ2 of the noise component, the filter coefficient wn (k) which is used to eliminate the residue of interference remaining in the received signal from the n-th transmitter is determined according to the minimum mean square error criteria so as to minimize the equation (32).
At step 9, a filter processing according to the filter coefficient wn (k) is applied to the difference matrix y′n (k) to obtain the log-likelihood ratio Λ1 [bn(k)]. At step S10, the a priori information λ2 [bn(k)] is subtracted from Λ1 [bn(k)] and the result is deinterleaved and decoded to deliver the log-likelihood ratio Λ2 [bn(k)]. The steps S4 to S10 are performed either simultaneously or sequentially for n=1 to N. Subsequently, at step S11, an examination is made to see whether or not the number of decoding operations, namely, the number of turbo-reception processings has reached a given number. If the given number is not reached, the operation goes to step S12 where the extrinsic information λ1 [bn(k)] is subtracted from the log-likelihood ratio Λ2 [bn(k)], and its result is interleaved to determine the a priori information λ2 [bn(k)], thus returning to step S3. If it is found at step S11 that the number of decoding operations has reached the given number, a resulting decoding output is delivered at step S13.
The channel estimator 28 will now be described. Each received signal rm(k) can be represented as follows:
rm(k)=Σq=0Q−1Σn=1Nhmn(q)·bn(k−q)+vm(k) (33)
The channel estimator 28 determines the channel value (transmission path impulse response) hmn(q) appearing in the equation (33) and the mean power (≡σ2) of the noise vm(k). Normally, a unique word (training signal) which is known to the receiver is inserted at the beginning of each frame to be transmitted on the transmitting side, as shown in
The use of the training series in this manner is conventional, but in order to enhance the net transmission rate, it is necessary to reduce the proportion that the unique word occupies in one frame, but this increases the error of the channel estimation. If there is such an error, it results in degrading the iterative equalization response mentioned above. According to the present invention, an iterative estimation of the channel value in the following manner is proposed.
The concept according to the present invention is illustrated in
Initially, using the log-likelihood ration Λ2 [bn(i)] from the decoder 24-n, a soft decision symbol value b′n(i) is determined as follows:
b′n(i)=tan h[Λ2[bn(i)]/2]
This operation is made in order to normalize the logic-likelihood value to 1, thus preventing its absolute magnitude from exceeding 1. Next, a threshold between 0 and 1 is provided, and when the absolute magnitude of a soft decision value b′n(i) is greater than the threshold value, a corresponding hard decision value {circumflex over (b)}n(i) is preserved to be used in the iterative channel estimation. For example, if the threshold value is chosen to be 0.9, those of hard decision values {circumflex over (b)}n(i) which correspond to soft decision values b′n(i) having absolute magnitudes equal to or greater than 0.9 are selected. It is believed that the certainty of the selected hard decision value {circumflex over (b)}n(i) is high in view of the fact that the threshold value is as high as 0.9, and accordingly, it is believed that the accuracy of the iterative channel estimation which is made using such hard decision values can be improved. However, it is also considered that because the number of selected symbols is reduced, the accuracy of the iterative channel estimation may be influenced and becomes degraded. Accordingly, it is necessary that an optimum threshold value be choosed between 0 and 1. To add, if the threshold value is to be 1, if follows that there is no hard decision value {circumflex over (b)}n(i) which is selected, stating to the effect that no iterative channel estimation takes place. Accordingly, a threshold value on the order of 0.2 to 0.8 is chosen, as will be further described later.
Accordingly, those of transmitted symbol estimates (hard decision values) {circumflex over (b)}1(i), . . . , {circumflex over (b)}N(i) for the information symbol series during the first transmission which are determined to be likely to be certain according to the threshold value are fed from the outputs of the interleavers 27-1, . . . , 27-N to a previous symbol memory 32 to be stored therein as a previous transmitted symbol estimate. During the second iteration of the equalization and decoding processing for the received signal r(k) (it being noted that the received signal r(k) is stored in a memory), the unique word is initially used to make a channel estimation, and those of estimated transmitted symbol hard decision estimates {circumflex over (b)}1(i), . . . , {circumflex over (b)}N(i) which have been determined to be likely to be certain are read from the previous symbol memory 32 to be fed to the channel estimator 28 to make a channel estimation, namely, a channel estimation for the entire frame. A resulting estimate hmn(q) and σ2 are used to perform an equalization and decoding (the estimation of transmitted symbol) with respect to the received signal r(k). At this time, those symbol values among the estimated transmitted symbols which had been determined to be likely to certain according to the threshold are iused to update the content of the previous symbol memory 32. Subsequently, an estimation using the unique word and an estimation using those of the previously estimated transmitted signals which are determined to be likely to be certain are used to make a channel estimation of the entire frame during a subsequent iteration of the equalization and decoding. The estimated channel is used to perform the equalization and decoding (the estimation of transmitted symbol) and to update the previous symbol memory 32. Alternatively, those of the transmitted symbol hard decision values {circumflex over (b)}1(i), . . . , {circumflex over (b)}N(i) from the decoders which are determined to be likely to be certain according to the threshold value may be directly stored in the previous symbol memory 32 to update it, and when the symbol values stored in the previous symbol memory 32 are to be utilized, they will be fed through the interleavers 27-1, . . . , 27-8 to be input to the channel estimator 28.
By the iterations which proceed in this manner, an error of the channel estimation can be reduced, the accuracy of the symbol estimation can be improved and the problem of a degraded response in the turbo-equalization due to an error of an channel estimation can be improved.
When a channel estimation is made with respect to information symbol series using the symbol hard decision values which are likely to be certain in the manner mentioned above, a function as indicated in
A procedure of the channel estimation which also utilizes a symbol hard decision value or values which are likely to be certain is shown in
At step S4, a transmitted symbol hard decision is rendered with respect to the log-likelihood ratio Λ2 [bn(i)] to determine a hard decision value {circumflex over (b)}n(i). At step S5, b′n(i)=tan h [Λ2 [bn(i)]/2] is calculated from the log-likelihood ratio Λ2 [bn(i)] , thus estimating a transmitted symbol soft decision value b′n(i). At step S6, by examining whether the symbol soft decision value b′n(i) is equal to or greater than the threshold value Th or not, those of the symbol hard decision values {circumflex over (b)}n(i) which are likely to be certain are determined. At step S7, the symbol hard decision value or values which are likely to be certain are used to update the content of the previous symbol memory 32. At step S8, an examination is made to see whether or not the number of decoding operations has reached a given value, and if not, the operation returns to step S1, or more exactly, going through the step S12 shown in
If it is found at step S2 that the decoding processing is not for the first time, at step S9, a previous stored symbol, namely, a hard decision symbol which is likely to be certain is read from the previous symbol memory 32, and it is used together with information symbol series of the received signal r(k) to make a channel estimation, thus transferring to step S3.
In the above description, even during a second and a subsequent iteration, the channel estimation is made from the beginning using the unique word as a reference signal, but it is also possible that only the hard decision symbol which is likely to be certain may be used as the reference signal during a second and a subsequent iteration. In this instance, as indicated in broken lines in
If it is found at step S1′ that the processing is not for the first time, before the channel estimation is made, a previously stored channel estimate and various processing parameters are set up at S4′, whereupon the operation transfers to step S9.
It is to be noted that a solution of the equation (32) is given as follows:
wn(k)=(HG(k)HH+σ2I)−1·h (34)
where I represents a unit matrix, σ2 an internal noise power of a receiver (covariance of noise component), σ2 I a covariance matrix of noise component and G(k) corresponds a squared error of the channel estimation.
G(k)≡E[(B(k)−B′(k))·(B(k)−B′(k))H]=diag[D(k+Q−1), . . . ,D(k), . . . ,D(k−Q+1)] (35)
where E [ ] represents a mean, diag a diagonal matrix (having elements which are not along the diagonal being zero's).
D(k+q)=diag[1−b′21(k+q), . . . ,1−b′2n(k+b), . . . ,1−b′2N(k+q)] (36)
q=Q−1, Q−2, . . . , −Q+1, q≠0
and when q=0,
D(k)=diag[1−b′21(k), . . . ,1, . . . ,1−b′2N(k)] (37)
‘1’ appearing in the matrix D(k) represents an n-th element (it is assumed that an n-th user's transmitted signal is assumed to be a desired signal).
Thus, h comprises all the elements in the (Q−1)·N+n-th column of H appearing in the equation (23). Input to the filter coefficient estimator 317-1 of the multiple output equalizer 31 as shown in
It will be seen that the equation (34) requires an inverse matrix operation, but the required calculation can be reduced by using the matrix inversion lemma for the inverse matrix. Specifically, by approximating each b′2 appearing in the equations (36) and (37) by 1, it follows that
D(k+q)=diag[0, . . . ,0]=0 (q≠0) (39)
D(k)=diag[0, . . . ,1, . . . ,0] (40)
Thus, D(k) have elements having a value of 1 for those elements which are located at n-row and n-column while all other elements are equal to 0. When the error matrix G(k) of the equation (35) which is determined by the equations (39) and (40) is substituted into the equation (34), we have
wn(k)=(h·hH+σ2I)−1·h (41)
where h is as defined by the equation (38).
With this approximation, wn(k) does not depend on k, and accordingly, an inverse matrix calculation at every discrete time k can be dispensed with, thus reducing the quantity of calculation.
The matrix inversion lemma for the inverse matrix is applied to the equation (41). The lemma states that assuming A and B are (M, M) square matrices, C a (M, N) matrix and D a (N, N) square matrix, when A is given by A−1=B−1+CD−1CH, the inverse matrix of A is given as follows:
A−1=B−BC(D+CHBBC)−1CHB (42)
Applying the lemma to the inverse matrix operation appearing in the equation (41), we have
h(k)·h(k)H+σ2I=B−1+CD−1CH
h(k)·h(k)H=CD−1CH,σ2I=B−1,h(k)=C
I=D−1,h(k)H=CH
Using these equations to calculate the equation (42), the inverse matrix operation appearing in the equation (41) can be calculated. While the equation (42) contains an inverse matrix operation (D+CHBBC)−1, this inverse matrix becomes scalar and can be simply calculated.
Thus, in this instance, it is reduced to the following form:
wn(k)=1/(σ2+hH·h)h (41-1)
1/( ) on the right side of this equation is scalar or assumes a constant value, which may be chosen to be 1. Thus, we can put wn(k)=h, indicating that w (k) can be determined by only h. As indicated in broken lines in
Without being limited to the use of the matrix inversion lemma for the inverse matrix for the approximation by the equations (39) and (40), the approximation also allows the quantity of calculation for the equation (34) to be reduced. In particular, when this approximation is used, and the matrix inversion lemma for the inverse matrix is used, the quantity of the calculation can be further reduced. In addition, if the covariance matrix of the noise component is represented by σ2 I, an approximation: wn(k)=h may be used as indicated by the equation (41-1), whereupon it is independent from the covariance matrix, allowing a further simplification of the calculation.
Second Aspect of the Invention (Reflecting an Error Correction)
In the equalization processing where H·B′(k) is subtracted from the received matrix y(k) represented by the equation (27), an error correction decoding result is reflected in a transmitted signal soft decision value for a signal other than the signal bn(k) being detected, but an error correction decoding result which relates to the signal bn(k) being detected is not. For this reason, it is preferred to employ the following processing.
b′(k) appearing in the equation (29) or the equation (31) is changed as follows;
b′(k)=[b′1(k) b′2(k) . . . b′n−1(k)−f(b′n(k)) b′n+1(k) . . . b′N(k)] (43)
where f(b′n(k)) is an arbitrary function having b′n(k) as an input.
When such change is made, it becomes possible to reflect an error correction decoding result with respect to the signal bn(k) being detected. Thus, rather than using b′n(k)=0, by adding a suitable value depending on b′n(k), it is possible to emphasize a signal being detected which is buried in a noise or an interfering signal, thus allowing bn(k) to be properly detected.
Because the sign of b′n(k) relates to a result of a hard decision rendered upon a symbol which corresponds to b′n(k), and in view of the fact that the greater the absolute magnitude of b′n(k), the higher the reliability of the hard decision symbol which corresponds to b′n(k), it is necessary that f(b′n(k)) satisfies the following requirements:
The function f has a value of 0 for b′n(k)=0 or when the reliability of the hard decision symbol is equal to 0. Or,
f(0)=0 (44)
In addition, the greater the value of b′n(k), the greater the value of the function f. Or,
d{f(b′n(k))}/d{b′n(k)}≧0 (45)
Examples of such f(b′n(k)) include the following:
f(b′n(k))=α×b′n(k) (46)
f(b′n(k))=α×b′n(k)2 (47)
For example, when the equation (46) is used and α is chosen to be a constant, the equation (43) can be implemented in a simple manner. Here, α must satisfy the requirement: 0<α<0.6. If α is greater than 0.6, BER (error rate) will be degraded, preventing a correct decoding result from being obtained. It is also contemplated to make α to be variable in accordance with the reliability of a decoding result. For example, α may be chosen for each iteration of the decoding processing. In this instance, the reliability of the decoding result will be normally improved with the number of iterations of the decoding processings and accordingly, an increased value may be chosen for α depending on the number of iterations of the decoding processing. Alternatively, the reliability of an entire decoded frame may be determined upon each iteration of the decoding processing, and the value of α may be chosen in accordance with the reliability thus determined. To determine the reliability of the decoded frame, a decoding result may be compared against a decoding result which is obtained during an immediately preceding iteration, and a number of hard decision symbols which changed from the previous decoding operation may be counted, for example. Thus, where there is an increased number of changed decision symbols, the reliability may be determined to low while when the number of changed hard decision symbols is small, the reliability may be determined to be high.
As b′n(k) is changed in this manner, the equation (35) which is used when determining the filter coefficient wn(k) for MMSE (minimum mean square error) filter is desirably changed as follows:
G(k)=E[(B(k)−B′(k))·(B(k)−B′(k))H]=diag[D(k+Q−1), . . . , D(k), . . . , D(k−Q+1)]
Using the equations (29) and (31), it follows that assuming
B′(k)=[b′(k+Q−1)b′(k+Q−2) . . . b′(k) . . . b′(k−Q+1)]T
b′(k)=[b′n(k)b′2(k) . . . −f(b′n(k)) . . . b′N(k)]T
b′(k+q)=[b′1(k+q)b′2(k+q) . . . −f(b′n(k+q)) . . . b′N(k+q)]T:q≠0, q=Q−1, . . . , −Q+1
D(k) has elements located at n-row and n-column, which are represented as follows:
E[(bn(k)+f(b′n(k)))·(bn(k)+f(b′n(k)))*]
where ( ) represents a complex conjugate. For BPSK modulation, this expression turns into the following expression:
E[bn(k)2+2bn(k)f(b′n(k))+f(b′n(k))2]=E[bn2(k)]+2E[bn(k)f(b′n(k))+E[f(b′n(k)2)
The first term has a mean value of 1. When bn(k) is approximated by b′(k), the equation (37) turns into the following form:
D(k)=diag[1−b′21(k) 1−b′22(k) . . . 1−b′2n−1(k) 1+2E[f(b′n(k)b′n(k))+E[f(b′n(k)2) 1−b′2n+1(k) . . . 1−b′21(k)] (48)
For example, when the equation (46) is chosen for f(b′n(k)), D(k) turns into the following form:
D(k)=diag[1−b′21(k) 1−b′22(k) . . . 1−b′2n−1(k) 1+(2α+α2)b′2n(k) 1−b′2n+1(k) . . . 1−b′21(k)] (49)
An exemplary functional arrangement which estimates an adaptive filter coefficient wn(k) when reflecting an error correction decoding result into a signal being detected is shown in
In the flow chart of
When it is desired to reflect an error correction decoding result in a signal being detected as mentioned previously, a soft decision transmitted symbol b′n(k) of a signal which is to be detected may be calculated at step S8-1 before entering the step S4, and this may be used at step S4 where the equation (31) is replaced by the equation (43), or in other words, the equations (29), (30) and (43) may be used to generate an interference replica matrix B′ (k), and at step S8-2, the equation (37) may be replaced by the equation (48). In the event f(b′n(k)) is chosen to be equal to α b′n(k) or α b′n(k)2 and when α is chosen to be variable, α may be determined in accordance with the number of processing operations or the reliability of the entire decoded frame at step S8-1-1, and 1+(2α+α2)b′n(k)2 may be calculated and used as f (b′n(k)) at step S8-1-2.
The technique of reflecting an error correcting result into a signal being detected is also applicable to a single user turbo-receiver which has been described initially in connection with the prior art. In the technique of reflecting an error correcting result into a signal being detected, the approximation represented by the equations (39) and (40) can be applied, and in this instance, only a matrix h shown by the equation (38) which is supplied from the channel estimator 28 may be input to the filter coefficient generator 333-1, as indicated in broken lines in
In the above description, the adaptive filter coefficient wn(k) is determined according to the equation (34) or by using the channel matrix H, but the use for the channel matrix H can be dispensed with. Specifically, during the initial decoding processing (turbo-reception processing), the error matrix G appearing in the equation (34) becomes a unit matrix. Accordingly, the difference matrix y′(k) and the training signal either alone or in combination with a hard decision transmitted symbol {circumflex over (b)}n(k), preferably {circumflex over (b)}n(k) having a high reliability in the sense mentioned above are input to the filter coefficient generator 333-1 to calculate the adaptive filter coefficient wn(k) in a sequential manner by application of RLS (recursive least square) technique. Because the error matrix G depends on a discrete time k, during a second and a subsequent iteration of the decoding operation, it becomes necessary to update the adaptive filter coefficient wn(k) from symbol to symbol, and as mentioned previously, it is preferred to determine the adaptive filter coefficient wn(k) by using the channel matrix H.
Fourth Aspect of the Invention (Channel Estimation)
Using not only known information such as a unique word in the iterative channel estimation, but also using a hard decision value of information symbol, in particular one which is likely to be certain as a reference signal is applicable not only in the described multiple input multiple output turbo-reception method, but also generally to a turbo-reception method in which a channel (transmission path) of a received signal is estimated from the received signal and the known signal, the estimated channel value is used to process the received signal and to decode it, and the decoded signal is used in iterating the processing according to the estimated channel value and the decoding processing upon the same received signal.
The turbo-equalizer 41 may comprise the receiver shown in
w(k)=E[y′(k)y′H(k)]·E[b(k)·y′(k)]=[HΛ(k)H+σ2I]·h (50)
where H is as defined by the equation (8), and
h≡[H(Q−1), . . . ,H(0)]T
where H( ) is as defined by the equation (5), σ2=E[∥v∥2] (variance of noises), and
Λ(k)=diag[1−b′2(k+Q−1), . . . ,1, . . . ,1−b′2(k−Q+1)]
In this manner, also in the receiver shown in
The turbo-equalizer 41 shown in
The examples shown in
Again, as mentioned previously in connection with steps S1′ to S4′ with reference to
In the example shown in
Noise Other Than White Gaussian Noise
In the embodiment of the turbo-reception method (according to the first aspect of the invention), the embodiment according to the second aspect of the invention which takes an error correction into consideration and the embodiment of the turbo-reception method characterized in its channel estimation method (according to the fourth aspect of the invention), the processing took place on an assumption that the noise is white Gaussian noise. Specifically, vm(k) appearing on the right side of the equation (29) indicating a received signal rm(k) from each antenna is assumed to be white Gaussian noise. What is meant by white Gaussian noise is a signal which follows the Gaussian distribution and have statistical features expressed as follows:
where E[ ] represents an expected value and σ2 a variance. White Gaussian noise may be exemplified by thermal noise which is generated in an antenna element. What is influenced by the assumption of white Gaussian noise is σ2 I portion appearing in the equation (34) which determines the filter coefficient wn(k) or the equation (50) which determines the filter coefficient wn(k). For example, wn(k) appearing in the equation (34) is calculated through the process indicated below.
wn(k)=(HG(k)HH+E[n(k)·nH(k)])−1h=(HG(k)HH+σ2I)−1h
where vm(k) is calculated as E[n(k)·nH(k)]=σ2I by the assumption of the white Gaussian noise having a variance σ2. The channel matrix H which is estimated by the iterative channel estimator 28 (
When the noise vm(k) is not white Gaussian noise, E[n(k)·nH(k)]=σ2I does not apply. Accordingly, in order to calculate the filter coefficient wn(k), it is necessary to estimate an expected value (covariance) matrix E[n(k)·nH(k)] for the noise component by a separated method. Such method will now be described. A covariance matrix for the noise component will be abbreviated as U≡E[n(k)·nH(k)]. y(k)=H·B(k)+n(k) in the equation (22) is modified into n(k)=y(k)−H·B(k) and is substituted into the covariance matrix U, as indicated below.
U=E[n(k)·nH(k)]=E[(y(k)−H·B(k))·(y(k)−H·B(k))H]
If we can assume that a matrix y(k) is available from a received signal, an estimate Ĥ of a channel matrix H from the channel estimate and B(k) is available from a reference signal, it is possible to estimate the matrix U according to the time average method as follows:
Û=Σk=0Tr(y(k)−Ĥ·B(k))·(y(k)−Ĥ·B(k))H (51)
where Tr represents the number of reference symbols.
During an iterative channel estimation which takes place in the iterative channel estimator 28 or 42, the covariance matrix Û is estimated using the channel matrix H together with the equation (51). A procedure therefor is illustrated in
wn(k)=(ĤG(k)ĤH+Û)−1h (52)
and the filter coefficient wn(k) is used to apply a first equalization upon the received signal, thus estimating transmitted information symbol.
During a second iteration, the unique word as well as one of information signals (*) estimated during the initial equalization which is determined to be likely to be certain according to the threshold value are both used as reference signals to estimate H again with the same procedure as used during the initial processing, thus estimating U again. As this operation is repeated, the channel matrix estimate Ĥ becomes more accurate with the iteration, and the estimate of U becomes more accurate, thus improving the accuracy of the filter coefficient wn(k) to improve the response of the equalizer.
In this manner, a turbo-reception when a noise other than white Gaussian noise is contained in a received signal is made possible.
A functional arrangement in which a linear equalization is performed by estimating a covariance matrix U of a noise contained in a received signal is shown in
A unique word from a unique word memory 29 or a previous symbol hard decision from a previous symbol memory 32 which is likely to be certain is input to a reference matrix generator 319, which then generates a reference matrix B(k) according to the equations (25) and (26). The reference matrix B(k), an estimation channel matrix Ĥ from a channel estimator 28, and a received matrix y (k) from a received matrix generator 311 are supplied to a covariance matrix estimator 321, which then calculates the equation (51) to obtain an estimated matrix Û for a covariance matrix U.
Soft decision transmitted symbols b1′(k), . . . ,bn′(k) from a soft decision symbol generator 313-1 are input to an error matrix generator 322-1, where an error matrix G1(k) corresponding to the square error of the channel estimation is generated according to the equations (35), (36) and (37). The error matrix G1(k), the estimated covariance matrix Û and the estimatied channel matrix Ĥ are supplied to a filter estimator 323-1, where the equation (52) is calculated to estimate a filter coefficient w1(k). The filter coefficient w1(k) and the difference matrix y′(k) from a difference calculator 316-1 are fed to an adaptive filter 318-1 where a filter processing w1(k)Hy′(k) is applied to y′(k), and its result is delivered as a log-likelihood ratio Λ1 [b1(k)].
When reflecting an error correction recording result into a signal being detected, a function calculator 331-1 as shown in
The procedure shown in
At step S4, the estimated channel matrix Ĥ, the estimated covariance matrix Û and an error matrix G(k) which comprises symbol soft decision values are used to calculate the equation (52) to estimate a filter coefficient wn(k).
At step S5, the estimated channel matrix Ĥ and the filter coefficient wn(k) are used to equalize the received signal or to calculate the equation (27) to determine wnH (k)·y′(k) to obtain a log-likelihood ratio Λ1 [bn(k)], subsequently performing a decoding process to estimate a hard decision value and a soft decision value of a transmitted symbol.
Purpose of step S6 is to determine a symbol hard decision value which corresponds to a symbol soft decision value which exceeds a threshold value and which is likely to be certain (or having a high reliability). This symbol hard decision value is used to update a symbol hard decision value which is stored in a previous symbol memory 32. Subsequently, an examination is made at step S8 to see if the number of the decoding processings has reached a given value, and if not, the operation returns to step S1. However, if a given number is reached, the processing upon this received frame is completed.
If it is found at step S2 that the iterative processing is not for the first time, namely, for a second or a subsequent iteration, a symbol hard decision value is read from the previous symbol memory 32 at step S9, and is used together with information symbol in the received signal to estimate the channel matrix H, subsequently transferring to step S3.
Again, by changing the steps S1 and S2 in the similar manner as steps S1′ to S4′ shown in broken lines in
(1) A reception method for a multiple series transmitted signal containing an unknown interfering signal is cited. As shown in
rm(k)=Σq=0Q−1Σn=1Nhmn(q)·bn(k−q)+i(k)+vm(k) (20)′
In this model, putting i(k)+vm(k)≡v′m(k), we have
rm(k)=Σq=0Q−1Σn=1Nhmn(q)·bn(k−q)+v′m(k) (20)″
Treating v′m(k) as a noise signal other than white Gaussian noise, H and U are estimated in a manner mentioned previously, and wn(k) is estimated, and a turbo-reception can be made by iterating an equalization of a received signal and an estimation of transmitted symbols.
(2) In a communication system which employs a transmission/reception separation filter, when an oversampling of a received signal is made at a higher rate than a symbol period, there occurs a correlation between noise components which are contained in received signals which are sampled at individual times, and this prevents the noises in the received signals from being treated as white Gaussian noise. In other words, the equation (20) does not apply. Accordingly, an assumption represented as
E[n(k)·nH(k)]=σ2I
does not hold. A processing upon a received signal which is separated by the transmission/reception separation filter may utilize equation (51) to determine a covariance matrix U, thereby allowing the received signal to be properly processed.
(3) In the described turbo-reception method, the arrangement is such that every multipath component from each transmitter (user) on Q paths are synthesized. However, in the event there exists a prolonged delay wave on channels (for example, assume that paths include one symbol delay, two symbol delay and three symbol delay path and there exist separately a thirty symbol delay path: in this instance, the thirty symbol delay path component is treat as a prolonged delay wave), it is possible to prevent the prolonged delay wave from being synthesized, but to treat it as an unknown interference which can be eliminated by an adaptive filter. When the prolonged delay wave component is treated as the interfering signal i(k) in the example according to the first aspect of the invention (1), it may be eliminated.
In the processing of a received signal containing a noise other than white Gaussian noise, the estimation of the covariance matrix U is applicable to a single user turbo-reception method by allowing it to serve in place of σ2 I in the equation (50). In a similar manner, it may be used in a RAKE synthesis processing reception illustrated in
Third Aspect of the Invention (Multistage Equalization)
In the forgoing description, received signals r1, . . . ,rM are equalized in a multiple output equalizer 31 to determine log-likelihood ratios Λ1[b(k)], . . . , ΛN[b(k)], but in a modification (21313) of the first aspect of the present invention, there are provided a plurality of equalizer stages in cascade connection in a manner such that the number of outputs is reduced toward a later stage equalizer. By way of example,
Even when an equalization takes place in a cascade manner and a linear filter is used in a prestage processing, it is possible to prevent the quantity of calculation from increasing prohibitively.
An arrangement of a multiple output turbo-receiver according to an embodiment which is based on this fundamental concept of the first aspect of the invention (2) of the turbo-reception method and an exemplary arrangement of MIMO system which incorporates the present invention is shown in
Transmitted signals from each transmitter is received through transmission paths (channels) by a turbo-receiver 30. The received signal r(k) is input to a multi-user equalizer 71, from which signals from N transmitters are delivered in the form of signals u1(k), . . . , uN(k), each of which is provided in the form it is free from interferences by signals from other transmitters, and channel values α1(k), . . . , αN(k) to be input to single user equalizers 21-1, . . . ,21-N. These SISO equalizers 21-1, . . . ,21-N deliver log-likelihood ratios Λ1 [b1(k)], . . . , Λ1 [bN(k)]. Subsequent processing remains similar to
The operation will now be described more specifically.
Equations (23) to (26) are defined in a similar manner as described above in connection with
The purpose of the poststage equalizers 21-1, . . . ,21-N shown in
Initially, using the a priori information λ2p [bn(k)] (where n=1, . . . ,N) of the equalizer 71 which is fed back from the decoders 24-1, . . . , 24-N, a soft decision transmitted symbol estimate b′(k) is determined according to the equation (15).
This soft decision transmitted symbol b′n(k) and a channel matrix H are used to generate a replica H·B′(k) of an interfering signal, which is then subtracted from the received matrix y(k).
y′n(k)≡y(k)−H·B′(k) (27)′
=H·(B(k)−B′(k))+n(k) (28)′
where
B′(k)=[b′T(k+Q−1) . . . b′T(k) . . . b′T(k−Q+1)]T (29)′
b′(k+q)=[b′1(k+q)b′2(k+q) . . . b′n(k+q) . . . b′N(k+q)]T:q=Q−1, . . . ,1 (53)
b′(k+q)=[b′1(k+q)b′2(k+q) . . . 0 . . . b′N(k+q)]T:q=0, . . . ,−Q+1 (54)
it being noted that b′(k+q) has a zero element at n-th position.
The operation of subtracting the interference in this manner will be referred to hereafter as a soft interference cancel. Assuming that a replica of the interfering signal is generated in an ideal manner, it will be seen that y′n(k) resulting from the subtraction can have only the symbol bn(k) of the n-th user and an intersymbol interference component caused by the symbol [bn(k−1), . . . , bn(k−Q+1)] of the n-th user itself which results from putting the n-th element of b′(k+q) equal to 0 for q=1, . . . , −Q+1 in the equation (54).
In effect, a contribution from the signal of the n-th user (transmitter) to the received matrix r(k) is only that resulting that from the symbol [bn(k), bn(k−1), . . . , bn(k−Q+1)]. However, it will be understood from the definition of the received matrix y(k) given by the equation (21) that a contribution from the signal of the n-th user (transmitter) within the received matrix y(k) which results as synthesis of the multipaths will contain, when based on the k-th symbol bn(k), intersymbol interference components caused by future symbols [bn(k+Q−1), bn(k+Q−2), . . . , bn(k+1)]. Thus, the interference replica includes interference components from the future symbols. In this respect, the difference matrix y′(k) defined by the equation (27)′ is distinct from the difference matrix y′(k) defined by the equation (27).
Accordingly, a next step in the prestage processing in the equalizer 71 is to eliminate the residue interference which remains after the soft interference cancel, namely, a residual interference component which results from an imperfect synthesis of the interference replica H·B′(k) and interference components between future symbols from y′n (k) using MMSE (minimum mean square error) criteria linear filter. In other words, this elimination takes place by an arrangement such that a filtering of y′n (k) using the filter characteristic wn(k) as indicated by the equation (55) is equal to a sum of the symbols [bn(k), bn(k−1), . . . , bn(K−Q+1)] each multiplied by channel values α1n(k), α2n(k), . . . , αQn(k).
wnH(k)·y′n(k)≈Σq=0Q−1αq(k)·bn(k−q)=αnH(k)·bn(k) (55)
Accordingly, what is required is to calculate the equation (55) by determining the filter characteristic wn(k) and the post-equalization channel value (channel information) αn(k). The derivation of wn(k) and αn(k) will be described. It is to be noted that while the filter characteristic wn(k) is distinct from the filter coefficient wn(k) given by the equations (32) and (34), similar denotations will be used for purpose of convenience.
Desired solutions are defined as solutions of the following optimization problem:
(wn(k),αn(k))=arg min∥wnH(k)·y′n(k)−αnH(k)·bn(k)∥2 (56)
provided α1n(k)=1.
In other words, wn(k) and αn(k) which minimizes the right side of the equation (56) are determined. The constraint requirement α1n(k)=1 is added in order to avoid solutions which result in αn(k)=0 and wn(k)=0. While solutions can be obtained under the constraint requirement,
∥αn(k)∥2=1
a solution for α1n(k)=1 will be described below herein. For brevity, the problem will be redefined. Namely, the right side of the equation (56) is defined as mn(k) which is minimized in terms of w and α.
mn(k)=arg min∥mnH(k)·zn(k)∥2 (57)
provided mnH(k)·e MQ+1=−1 (which is equivalent to α1n(k)=1) and where
mn(k)≡[wnT(k),−αn(k)T]T (58)
zn(k)≡[ynT(k), b(k)nT]T (59)
eMQ+1=[0 . . . 1 . . . 0]T (60)
it being understood that e MQ+1 has “1” element at (MQ+1-th position).
A solution of the optimization problem is given as follows according to Lagrange's method of indeterminate coefficients described in literature [2], S. Haykin, Adaptive Filter Theory, Prentice Hall, pp. 220–227;
mn(k)=−RZZ−1·eMQ+1/(eMQ+1H·RZZ−1·eMQ+1) (61)
where
RZZ=E[zn(k)·znH(k)] (62)
E[A] representing an expected value (a mean value) of A.
Λn(k)=diag[Dn(k+Q−1), . . . ,Dn(k), . . . ,Dn(k−Q+1)] (64)
where I represents a unit matrix, and σ2 noise power (a covariance of white Gaussian noise).
D
n(k+q)=diag[1−b′21(k+q), . . . ,1−b′2n(k+q), . . . ,1−b′2Nk+q]]:q=Q+1, . . . ,1 (66)
Dn(k+q)=diag [1−b′21(k+q), . . . ,1, . . . ,1−b′2N(k+q)]:q=0, . . . ,−Q+1 (67)
where diag represents a diagonal matrix (all elements other than those located along the diagonal of the matrix being zeros). Thus, if the channel matrix H and σ2 are known, mn (k) can be determined according to the equation (61). Accordingly, wn(k) and αn(k) can then be determined according to the equation (58).
Using the filter characteristic wn(k) which is calculated in this manner, y′n (k) is filtered according to the following equation;
un(k)=wnH(k)·y′n(k) (68)
where H represents a conjugate transposed matrix.
These filtered n processed results are fed to corresponding equalizers 21-n which follow. In this manner, a received signal un(k) which corresponds to the left side of the equation (1) from the n-th user is obtained, αmn(k) which corresponds to the channel value hmn(q) on the right side of the equation (1) is obtained, and the equation (55) which corresponds to the equation (1) is determined. Accordingly, αn(k) is applied as an equalizer parameter (channel value) to a succeeding equalizer 21-n. This completes the prestage processing by the equalizer 71.
A processing which takes place in the succeeding equalizer 21-n and thereafter will now be described. As mentioned previously, because the equation (55) corresponds to the equation (1), the operation which takes place in the equalizer 21-n for every user may proceed in the similar manner as that of the equalizer 21 shown in
≡λ1[bn(k)]+λ2p[bn(k)] (70)
where λ1 [bn(k)] represents an extrinsic information fed to a succeeding decoder 24-n, and λ2P [bn(k)] a priori information applied to the equalizer 31. Decoder 24-n calculates the log-likelihood ratio Λ2 according to the following equation:
where λ2 [bn(i)] represents an extrinsic information applied to the equalizer 71 and the equalizer 21 during the iteration and the λ1P [bn(k)] a priori information applied to the decoder 24-n. The arrangement shown in
A functional arrangement of the multi-user equalizer 71 will be briefly described with reference to
On the other hand, the received signal r(k) from the receiver 70, and a known series signal such as a unique word series used for channel estimation which corresponds to each transmitter and which is fed from a unique word memory 29 are input to a channel estimator 28 in order to estimate a channel matrix H.
A priori information λ1P [bn(i)], . . . , λ1P [bN(i)] are subtracted from the log-likelihood ratios Λ2 [b1(i)], . . . ,Λ2 [bN(i)] delivered from the respective decoders 24-1, . . . , 24-N to derive extrinsic information λ2 [b1(k)], . . . , λ2 [bN(k)], which is then input to soft decision symbol estimators 313-1, . . . , 313-N where soft decision transmitted symbols b′1(k), . . . , b′N(k) are calculated according to the equation (15) and are then input to an interference matrix generator 72. In the interference matrix generator 72, a matrix B′(k) of symbol estimates which can be interference signals from other transmitters are generated for each n according to the equations (29)′, (53) and (54). A product of these N matrixes B′(k) and the channel matrix H is generated by other interfering signal estimators 73-1, . . . , 73-N, respectively, thus determining the replica of interfering components H·B(k).
These N interfering component replicas H·B(k) are subtracted from the received matrix y(k) in subtractors 74-1, . . . , 74-N, respectively, thus providing difference matrixes y′1(k), . . . , y′N(k).
The soft decision transmitted symbols b′1(k), . . . ,b′N(k) are input to an error matrix generator 75 where error matrices Λ1(k), . . . , ΛN(k) are generated according to the equations (64), (66) and (67). These error matrices, the channel matrix H and the noise power σ2 are input to a filter characteristic estimator 76 where the filter characteristic wn(k) and the post-equalization channel information αn are estimated according to the equations (58), (60), (61), (63) and (65). These filter characteristics w1, . . . ,wN and difference matrixes y′1(k), . . . , y′N(k) are multiplied together in filter processors 77-1, . . . , 77-N, respectively, or the difference matrixes are filtered, thus determining a component u1(k), . . . , uN(k) of the received signal for the symbol [bn(k), bn(k−1), . . . , bn(K−Q+1)] from each user and for each path, from which interferences from other user signals are eliminated. These components are fed, together with the post-equalization channel information α1(k), . . . , αN(k) which are determined in the filter characteristic estimator 76, to the single user equalizers 21-1, . . . , 21-N shown in
A processing procedure for the turbo-reception method according to the first aspect of the invention (2) is shown in
In the forgoing description, the extent of equalization in the poststage equalizer 21-n is defined as a zone for intersymbol interference by the symbol [bn(k), bn(k−1), . . . , bn(K−Q+1)] (where n=1, . . . , N), but such extent of equalization is adjustable. For example, when Q has a very high value, a computational load on the poststage equalizer 21-n will be much greater. In this instance, the extent of equalization by the poststage equalizer 21-n is chosen to be Q′<Q while the prestage equalizer 71 may be rearranged so as to eleminate intersymbol interferences between the signal of the same user outside the zone [bn(k), bn(k−1), . . . , bn(K−Q′+1)] (where Q′<Q and n=1, . . . , N). Such modification will be described later. When the equalization is divided into the prestage and poststage, a previous symbol memory 32 may be provided, as indicated in broken lines in
In the example shown in
By way of example,
Similarly, the equalized signal series er2(k) and the channel information eα2(k) are input to the equalizer 82-2 in the second stage to provide an equalized signal series er6(k) and an associated post-equalization channel information eα6(k), and an equalized signal series er7(k) and its associated post-equalization channel information eα7(k). When N=5, equalizers 83-1 to 83-5 in a third stage represent single user equalizers shown in
What has been described above can be generalized by stating that equalizers in a first stage deliver a plurality of equalized signal series and a set of post-equalization channel information, and one or more equalizers may be provided in each of one or a plurality of stages which are in cascading connection for each equalized signal series and its associated set of post-equalization channel information so that an equalized output or a log-likelihood ratio Λ1 [bn(k)] may be delivered finally for each of the 1st to N-th transmitted series.
When the equalization takes place in multiple stages which are in cascade connection, it is preferred that the number of paths Q for which interferences are to be eliminated be reduced toward a later stage so that the quantity of calculation can be reduced. In this instance, an interferring component from a path which disappears in a later stage be eliminated in an immediately preceding equalizer stage.
An equalization processing which occurs in the arrangement of
In a similar manner as described above in connection with the embodiment shown in
b′(k+q)=[b′1(k+q)b′2(k+q) . . . b′n(k+q) . . . b′N(k+q)]T:q=Q−1, . . . 1 (53)
b′(k+q)=[0 . . . 0b′U+1(k+q) . . . b′N(k+q)]T:q=0, . . . ,−Q′+1 (54)′
b′(k+q)=[b′1(k+q)b′2(k+q) . . . b′n(k+q) . . . b′N(k+q)]T:q=Q′, . . . ,−Q+1 (73)
The equation (54)′ is intended to provide symbols for a first to U-th transmitted series themselves, and to provide an equalization except for intersymbol interference caused upon each series by itself and relative to each other due to multipaths Q′ while the equation (73) is intended to eliminate the intersymbol interferences upon the 1st to U-th transmitted series themselves and relative to each other due to (Q′+1)-th to Q-th path in as much as the number of multipaths is reduced to Q′ in the poststage equalization.
The interferences matrix B′(k) which is obtained in this manner is used to generate an interference signal replica H·B′(k) which is then subtracted from a received matrix y(k) as follows:
y′g(k)≡y(k)−H·B′(k) (27)″
≡H·(B(k)−B′(k))+n(k) (28)″
This operation of subtracting the interference is referred to hereafter as a soft interference cancel. Assuming that a replica H·B′(k) of an interfering signal is generated in an ideal manner, it will be seen that y′g(k) can only have signal components for symbols [bn(k), bn(k−1), . . . , bn(k−Q′+1)] (where n=1 to U) for 1st to U-th transmitted symbols.
A residue of interferences which remain after the soft interference cancel is eliminated with a linear filter of a MMSE criteria in a similar manner as mentioned previously. In this instance, the equation (55) is replaced by an equation (55)′ indicated below.
wgH(k)·y′g(k)≈Σn=1UΣq=0Q′−1αnq(k)·bn(k−q)=αgH(k)·bg(k) (55)′
where
αg(k)=[α1,0(k), . . . ,α1,Q′−1(k), . . . ,αU,0(k), . . . ,αU,Q′−1(k)]T (55-1)
bg(k)=[b1(k), . . . ,b1(k−Q′+1), . . . ,bU(k), . . . ,bU(k−Q′+1)]T (55-2)
The derivation of wg(k) and αg(k) takes place in a similar manner as described previously to determine wg(k) and αg(k) which minimizes the right side of the following equation, which stands for the equation (56):
(wg(k),αg(k))=arg min∥wgH(k)·y′g(k)−αgH(k)·bg(k)∥2 (56)′
provided α1,0(k)=1.
The constraint requirement is added in order to avoid solutions which may result in αg(k)=0 and wg(k)=0. While a constraint requirement that ∥αg(k) ∥2=1 may also be used to provide a solution, in the description to follow, the problem is rewritten as follows for α1,0(k)=1:
mg(k)=arg min∥mgH(k)·zg(k)∥2 (57)′
provided mgH(k)·eMQ′+1=−1
where
mg(k)≡[wgT(k),−αgT(k)]T (58)′
zg(k)≡[ygT(k),b(k)gT]T (59)′
eMQ′+1=[0 . . . 1 . . . 0]T (60)′
it being understood that eMQ′+1 has “1” element at (MQ′+1)-th position.
A solution of the optimization problem is given as follows according to Lagrange's method of indeterminate coefficients disclosed in literature [2];
mg(k)=−Rzz−1·eMQ′+1/(eMQ′+1H·Rzz−1·eMQ′+1) (61)′
where
Λn(k)=diag[Dn(k+Q−1), . . . ,Dn(k), . . . ,Dn(k−Q+1)] (64)′
D
n(k+q)=diag[1−b′21(k+q), . . . ,1−b′2n(k+q), . . . ,1−b′2N(k+q)]:q=Q+1, . . . ,1 (66)
Dn(k+q)=diag[1, . . . ,1,1−b′2U+1(k+q), . . . ,1−b′2N(k+q)]:q=0, . . . ,−Q′+1 (67)′
Dn(k+q)=diag[1−b′21(k+q), . . . ,1−b′2n(k+q), . . . ,1−b′2N(k+q)]:q=Q′, . . . −Q+1 (74)
Thus when channel parameters are known, mg (k) can be determined according to the equation (61)′. In addition, wg (k) and αg(k) (=eα1(k)) can be determined according to the equation (58)′. Such calculations can be made in the filter characteristic estimator (76) shown in
er1(k)=wgH(k)·y′g(k)
This equalized output er1(k) and the post-equalization channel information eα1(k)=αg(k) are fed to the poststage equalizer 82-1.
When there are five transmitted series (users), for example, which are divided into a group of three transmitted series (users) and a group of two transmitted series (users), in the manner mentioned above, the above algorithm is carried out with U=3 and 2, and the two equalized outputs er1(k), eα1(k) and er2(k), eα2(k) are input to equalizers which are designed to deal with the three transmitted series and the two transmitted series, respectively, thus obtaining an equalized output for each transmitted series.
Reflecting an error correction decoding result for a signal being detected into a soft decision transmitted symbol in the manner mentioned above is also applicable to a single user turbo-equalizer receiver shown in
In
First Aspect of the Invention (2) (Parallel Transmission)
There is a proposal that information series c(i) from a single user be transmitted in a plurality of parallel series in order to achieve a high rate transmission with a high frequency utilization efficiency. An embodiment of a turbo-receiver incorporating the present invention which may be used for such transmitted signal will now be described.
Referring to
These N series signals are propagated through channels (transmission paths) to be received by the turbo-receiver according to the present invention. The receiver has one or more receiving antenna, and the received signal is input to a multiple output equalizer 31 as a baseband digital received signal rm(k) (where m=1, 2, . . . , M) including one or more (M) signals. The received signal rm(k) is generated in a manner as shown in
The multiple output equalizer 31 is constructed in the same manner as shown in
Accordingly, N series of received signals are subject to a linear equalization in the multiple output equalizer 31 in the similar manner as mentioned previously, delivering N log-likelihood ratio series Λ1 [b1(k)], . . . Λ1 [bN(k)], which are then input to a parallel-series converter 16 to be converted into a single log-likelihood ratio series Λ1[b(j)] to be supplied to a subtractor 22. With this arrangement, the input signal format to the multiple output equalizer 31 is similar to that described in connection with
The turbo-reception method and the turbo-receiver according to the present invention are also applicable to the reception of convoluted code/turbo-code+interleaver+multi-value modulation such as QPSK, 8PSK, 16QAM, 64QAM etc., TCM (trellis coded modulation)/turbo TCM.
Generation of M Received Signals
M received signals r1(k), . . . , rM(k) are derived from M antennas #1, . . . , #M, but may be derived from a single antenna. Alternatively, M (which is greater than L) received signals may be obtained from L (which is an integer equal to or greater than 2) antennas. While not specifically shown in
As shown in
Effects of the Invention
As discussed above, according to the first aspect of the invention (1), there is realized a multiple output (MIMO) reception method. To illustrate a quantitative effect, an error rate response is graphically shown in
No approximation by the matrix inversion lemma for the inverse matrix is used in the calculation of the filter coefficient w.
With the channel estimation method mentioned above, by determining whether a hard decision value is or is not likely to be certain on the basis of a decoded soft decision value, and by using symbol information having a hard decision value which is likely to be certain in the channel estimation during the next iteration, the channel estimation can be performed more correctly, allowing a decoding quality to be improved.
In order to confirm the effect of an embodiment in which a covariance matrix Û (for noise other than Gaussian noise) is estimated, a simulation is made with parameters indicated below.
Three users (transmitters) are chosen to be of an equal power.
In order to confirm the effect of the embodiment (according to the second aspect of the invention) in which an error correction decoding result is reflected into a symbol soft decision value b′n(k) of a received signal from an intended user (transmitter), a simulation is made with parameters as indicated below
When BPSK modulation is used for a number of users (transmitters) which is equal to N, a number of multipaths from each transmitter which is equal to Q and a number of receiver antennas which is equal to M, the quantity of calculation which is required in an equalizer when a conventional single user turbo-receiver is directly extended to a multiple output (MIMO) is on the order of 2N(Q−1), as mentioned previously, but with the turbo-reception method according to the third aspect of the invention, the quantity of calculation can be reduced to the oreder of N(MQ)3. By way of example, assuming that N=8, Q=20 and M=8, 2N(Q−1)≈5·1045 while N(MQ)3≈37·107, thus demonstrating that the quantity of calculation can drastically be reduced according to the turbo-reception method according to the second aspect of the present invention.
A simulation has been conducted under conditions given below in order to confirm that a good bit error rate characteristic can be obtained according to the turbo-reception method according to the third aspect of the invention. It is assumed that the channel matrix H is known.
It is assumed that the channel estimation takes place in an ideal manner.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2001-043213 | Feb 2001 | JP | national |
| 2001-111095 | Apr 2001 | JP | national |
| 2001-258161 | Aug 2001 | JP | national |
| 2002-010839 | Jan 2002 | JP | national |
| Number | Name | Date | Kind |
|---|---|---|---|
| 6307901 | Yu et al. | Oct 2001 | B1 |
| 6813219 | Blackmon | Nov 2004 | B1 |
| 6819630 | Blackmon et al. | Nov 2004 | B1 |
| 20020167998 | Penther | Nov 2002 | A1 |
| 20050018794 | Tang et al. | Jan 2005 | A1 |
| Number | Date | Country |
|---|---|---|
| WO 03092170 | Nov 2003 | WO |
| Number | Date | Country | |
|---|---|---|---|
| 20020161560 A1 | Oct 2002 | US |
