TECHNOLOGICAL FIELD

The subject of this invention is an orthogonal frequency division multiplexing receiver with iterative channel estimation and a corresponding method. It finds application in radio communications and more particularly in Orthogonal Frequency Division Multiplexing or OFDM technology. It may be applied to—among other systems—the European portable radio system HIPERLAN II.

STATE OF THE PRIOR ART

OFDM technology [

1

] is a multi-carrier technology which permits division of users within a time-frequency plane in a simple way. In addition it permits the transmission of signals at a high rate without having to use an equalizer. This method has been widely used in the context of Digital Video Broadcasting or DVB-T, [

2

] and Digital Audio Broadcasting or DAB [

3

]. In a portable radio context, OFDM is present in the HIPERLAN II Standard.

OFDM technology is both a multiple access technology and a modulation technology. The basic principle of OFDM technology is to produce a certain number of narrow band signals all orthogonal to one another. By taking using precautions, these properties of orthogonality are used to recover the transmitted data. The creation of such a system calls upon the use of an inverse Fourier transform on emission and a Fourier transform on reception.

FIG. 1

appended illustrates a traditional OFDM transmission chain with a single sensor. This chain, comprises a serial to parallel conversion circuit

10

receiving symbols A, an inverse Fourier transform circuit

12

, transmission means

14

, reception means

20

, a Fourier transform circuit

22

, a parallel to serial converter

24

and finally a decision means

26

which reconstructs the estimated symbols Â.

The traditional OFDM transmitter processes the flow of data by block. It manages this flow by sequences of N

t

symbols and carries out the inverse Fourier transform on them. This means that the inverse Fourier transform produces N

f

sub-carriers, each carrying one of the symbols of the starting sequence. This block, called an OFDM symbol, contains the data symbols and may also contain pilot symbols which can be used for purposes of synchronization or of channel estimation. In contrast to the case of Code Division Multiple Access or CDMA signals or Time Division Multiple Access or TDMA signals, where one pilot symbol right away occupies the whole of the transmission band, OFDM technology requires the true distribution of the pilot symbols over the whole of the time-frequency plane.

The mobile radio channel taken when there is communication between a transmitter and a receiver is generally of the multi-path type with rapid Rayleigh fading. This phenomenon is due to the conjunction of the movement of the mobile and the propagation of the radio wave along several paths.

The receiver processes the signal received through an OFDM block of symbols (a time-frequency block). The signal is received on a network of L sensors, creating L branches of diversity. The channel estimation is carried out on each of these branches and the results are combined by Maximum Ratio Combining (MRC) to finally estimate the transmitted data.

A receiver with L branches of diversity is shown in FIG.

2

. It comprises L sensors

30

1

,

30

2

, . . . ,

30

L

, L Fourier transform circuits

32

1

,

32

2

, . . . ,

32

L

, L parallel to serial converters

34

1

,

34

2

, . . . ,

34

L

, L channel estimation circuits

36

1

,

36

2

, . . . ,

36

L

, and an adder

38

supplying the estimated symbols Â.

From the point of view of the receiver, after demodulation, the channel allocating a time-frequency block can be shown in the form of a time-frequency matrix, or a surface in time-frequency-amplitude space. However the problem is processed in bi-dimensional space, in contrast to TDMA [

4

] where the problem is uni-dimensional.

The channel estimation is based on the use of pilot symbols. They enable a channel estimation to be provided directly to the locations of the pilots with a view to interpolation in order to estimate the channel allocating the rest of the symbols.

These techniques have disadvantages. In effect, the channel seen by the receiver can vary in a significant manner from one time-frequency block to another. This variation is mainly due to changes in propagation conditions between the transmitter and the receiver. From a physical point of view, the variable character of the channel can be characterized by the product B

d

×T

m

where B

d

represents the width of the Doppler band and T

m

the spread of the delays. The greater the product B

d

×T

m

, the more the channel varies rapidly within the time and frequency domains.

The reception method of the prior art does not seek to optimize the channel estimation. They are content to carry out an estimation of the channel at the positions of the pilot symbols and then to extend this estimation to the data by interpolation. The interpolations are generally carried out in a linear manner. Three of the methods most commonly used may be described:

The first considers the three pilot symbols closest to the symbol at which one wishes to estimate the channel. The plane passing through the-three pilot symbols is calculated and from this the channel is deduced at the point being considered. Even by respecting the Nyquist criterion with respect to the pilot symbols, that is to say, using sufficient pilot symbols and distributing them in a manner that correctly samples the time-frequency plane, this method is sensitive to strong channel variations and does not allow one to carry, out a reliable estimation of the channel, especially in the case where the product B

d

×T

m

is high.

The second method is a simple form of the Minimum Mean Square Error (MMSE) technique: it consists of looking for the constant plane that averages the values of the channel at the pilot 'symbols and of deducing from it the values of the channel allocating the transmitted data. This channel modeling is well suited to channels varying very slightly over the received block, that is to say for low B

d

×T

m

products. However, as soon as the channel becomes more selective, the planar modeling shows its limits and performance is reduced.

The third method is another form of MMSE with a non-constant plane being looked for. This method is therefore better suited to cases where the channel varies slowly, but is less suitable than the second method in the case of channels that are almost constant.

These three methods are suited to highly specific propagation cases, but are in no way suitable for channels of the multi-path type that are selective in time and in frequency.

The precise purpose of this invention is to remedy this disadvantage.

DESCRIPTION OF THE INVENTION

The main aim of this invention is to improve the performance of existing OFDM systems and those to come. This improvement, obtained by optimization of the channel estimation, permits the capacity of the system to be substantially increased. This improvement is brought about by optimization of the operation of the OFDM receiver in the case of slow fading and also in the more complex case of very rapid fading.

It is then possible to prevent the reduction in performance brought about by rapid channel variation over the time-frequency block being considered on reception.

At constant reception quality, the invention enables one to reduce the relative number of and/or the power of the pilot symbols. This aim is achieved by taking into consideration, in an optimum manner, an arbitrary number of pilot symbols from consecutive time-frequency blocks, in the channel estimation. The aim is also achieved by the optimum character, in the channel estimation, of the consideration (of one part or of the totality) of the data symbols of these blocks, which are of course more numerous than the pilot symbols.

The invention may also be used whatever the way in which the pilot symbols are inserted into the stream of transmitted information.

The receiver of the invention carries out a block by block processing every time a given number of OFDM symbols is available. On each branch of diversity, first of all, the multi-path channel is roughly estimated using the pilot symbols associated with the received block and possibly with other blocks. The purpose of this estimation is initialization of the iterative channel estimation algorithm. Next, all of the symbols (data and pilot) are processed to obtain the channel estimation which permits generation of flexible outputs of the transmitted data symbols. The flexible outputs obtained at the end of an iteration can be used once again, in conjunction with the pilot symbols, to provide a extra improvement in the channel estimation, and therefore to further improve the flexible estimations of the data symbols.

In addition, the proposed technique enables one to take into account the coded structure of the data symbols and may be optimized in this sense, which leads to the production of flexible outputs of better quality.

The estimation of the multi-path channel rests, on the one hand on the use of the iterative algorithm called Expectation Maximization or E.M. [

5

], [

6

], [

7

] to find the most probable channel implementation conditional on the received block to be processed and on the coding of the channel possibly being used. It also rests on the decomposition of the bi-dimensional multi-path channel onto each branch of diversity in accordance with the Karhunen-Loève expansion theorem [

8

]. This decomposition permits flexible characterization of the temporal variations of the paths due to the Doppler effect and frequency variations due to temporal spreading and is easily integrated into the E.M. algorithm itself.

More precisely, a subject of this invention is a receiver for radio communications with Orthogonal Frequency Division Multiplexing (OFDM) comprising:

i) a plurality of L branches of diversity processing blocks of digital symbols, each block comprising data symbols and pilot symbols distributed within a bi-dimensional time-frequency block at N

t

intervals of time and N

f

intervals of frequency, each branch of diversity comprising a radio sensor, means supplying an output signal with N components constituting the components of a vector R

l

, where l designates the row of the branch of diversity (l ranging from 0 to L−1),

ii) a channel estimator processing the L signals supplied by the L branches of diversity and supplying flexible estimations of the data symbols,

iii) a decision making device receiving the flexible estimations of the data symbols and supplying an estimation of the data symbols,

this receiver being characterized in that

(a) the channel estimator processes a vector C

l

with N components characterizing the channel in a bi-dimensional time-frequency block, these means of estimation being capable of defining a base of N vectors B

k

which are the N eigenvectors standardized from the time-frequency covariance matrix of the channel, these means breaking down each vector C

l

in this base, the N coefficients from this decomposition being designated G

k

l

with k ranging from 0 to N−1, the coefficients defining, for each branch of diversity l, a vector G

l

, which is a representation of the channel seen at the output from said branch of diversity.

(b) the channel estimator processes a finite number (D) of iterations in accordance with an estimation-maximization (EM) algorithm based on the criterion of maximum probability a posteriori (MAP), the means of estimation initially being implemented by taking into consideration the pilot symbols contained in the bi-dimensional time-frequency block being considered and possibly the pilot symbols contained in the neighboring time-frequency blocks, which leads to a 0 order estimation, the channel estimator then taking into consideration the data symbols for the other iterations and so on, the channel estimator finally supplying after a final iteration D, the optimum coefficients G

k

l(D)

(k from 0 to (N−1) and l from 0 to L−1), defining each branch of diversity l, the vector G

l

representing the channel.

In one particular embodiment N

t

=N

f

and the time-frequency blocks are square.

Another subject of this invention is a reception method for which the operations correspond to the functions fulfilled by the various means of the receiver which has just been described.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1

, already described, shows a traditional OFDM transmission chain with a single sensor

FIG. 2

, already described, shows a traditional OFDM receiver with several sensors and L branches of diversity;

FIG. 3

illustrates a receiver conforming to the invention;

FIG. 4

illustrates the process of iterative estimation according to the invention;

FIG. 5

illustrates a particular embodiment of the receiver of the invention;

FIG. 6

shows an example of distribution of the pilot symbols and the data symbols in a time-frequency block;

FIG. 7

is a representation of the eigenvectors of the correlation matrix of the channel with a traditional Doppler spectrum and an exponential multi-path intensity profile for B

d

T

m

=10

−5

;

FIG. 8

is a representation of the same eigenvectors but for B

d

T

m

=10

−3

;

FIG. 9

gives variations in the binary error rate (BER) in relation to the ratio E

s

/I

o

for a receiver conforming to the invention and for various traditional receivers in the case of a product B

d

T

m

equal to 10

−5

with 16 pilot symbols distributed as indicated in

FIG. 5

;

FIG. 10

gives these same variations but for a product B

d

T

m

equal to 10

−3

.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

A receiver conforming to the invention is represented diagrammatically in FIG.

3

. This receiver comprises means already shown in FIG.

2

and which bear the same reference numbers. However the receiver comprises means to implement an iterative estimation algorithm which is diagrammatically shown by the block (E) which supplies the decision device

42

.

The elementary entity of the OFDM signal corresponds to the inverse Fourier transform of a sequence of symbols. The receiver of the invention processes the received signal block by block. The size of the processed block does not necessarily depend on the number of carriers of the OFDM system and may take into consideration all or a part of one or more OFDM symbols. The shape and the size of the block processed on reception is free, so that it may be best matched to the system.

The channel estimation is carried out block by block. A block is made up of N symbols a

mn

of energy E

mn

of bi-dimensional location (mF, nT) where F and T are the relative frequency and time spacings between two adjacent symbols. These symbols take their values in an alphabet &OHgr; of the arbitrary phase shift keying (PSK) type. Each block is made up of N

D

indexed data symbols in the assembly S

D

and N

P

indexed pilot symbols in the assembly S

P

.

As a general rule, the traditional receivers use pilot symbols of greater power than the data symbols. This difference in power permits one to estimate the channel in the best way, but risks the introduction of interference between carriers and hence a reduction in the capacity of the OFDM system. The technique of channel estimation according to the invention enables one to carry out an optimum channel estimation whatever the value of the power of the pilot symbols. In what follows, E

P

designates the energy of the pilot symbols and E

D

the energy of the data symbols.

The multi-path channel taken by the OFDM signal is made up of several paths which have or may have time and frequency variations due to the Doppler effect. Each path is characterized by a given mean power and a given Doppler Power Spectrum (DPS) which depend on the environment and the speed of the mobile. Furthermore, the fading to which each path is subjected can be either the Rayleigh type or the Rice type.

J

0

(.) denotes the first species, zero order Bessel function. By way of examples, the time-frequency auto-correlation function of the channel with a traditional Doppler power spectrum and with the exponential multi-path intensity profile of mean power &phgr;(0,0) seen on a branch of diversity, is given by

φ

⁢

⁢

(

Δ

⁢

⁢

f

,

Δ

⁢

⁢

t

)

=

φ

⁢

⁢

(

0

,

0

)

⁢

⁢

J

0

⁢

⁢

(

π

⁢

⁢

B

d

⁢

⁢

Δ

⁢

⁢

t

)

1

+

j2

⁢

⁢

π

⁢

⁢

T

m

⁢

⁢

Δ

⁢

⁢

f

The multi-sensor OFDM receiver of the invention is made up of L sensors

30

1

,

30

2

, . . . ,

30

L

spatially decorrelated, giving rise to L branches of diversity. On each of these branches, the received signal is, in the first place demodulated by the Fourier transform in the circuits

32

1

,

32

2

, . . . ,

32

L

. It is assumed that the signal at the output from the l

th

branch of diversity associated with the symbols a

mn

is written as

R

mn

l

=c

mn

l

a

mn

l

+N

mn

l

where c

mn

l

is the gain factor of the discrete channel from the l

th

branch of diversity seen by the symbol a

mn

and N

mn

l

is an additive complex white Gaussian noise of variance N

0

. The gain factors are independent from one branch of diversity to another, but are correlated in time and in frequency between themselves on one and the same branch.

The purpose of the invention is to estimate the gain factors c

mn

l

of the channel.

Let (.)

T

be the transposition operator. For reasons of notation, the indexation function &dgr;(k)=(m(k),n(k) is inserted between the mono-dimensional assembly {k}

k=0

N−1

and the bi-dimensional indexation assembly S

D

∪S

P

. Furthermore, for every block transmitted, the vector signal is inserted at the output from the filter matched to the l

th

branch of diversity

R

l

=(R

l

&dgr;(°0)

, . . . ,R

&dgr;(N−1)

l

)

T

In order to remove the dependence of the amplitude of each PSK symbol a

mn

on its index (m, n), the normalized vector of the transmitted block is inserted:

A=(A

67 (0)

, . . . , A

&dgr;(N−1)

)

T

with A

&dgr;(k)

=a

&dgr;(k)

/|a

&dgr;(k)

|. On these bases, it is possible to rewrite the components of the received vector on the l

th

branch of diversity:

R

&dgr;(k)

l

=C

&dgr;(k)

l

A

&dgr;(k)

+N

&dgr;(k)

l

where C

&dgr;(k)

l

is the &dgr;(k)

th

component of the equivalent multiplicative discrete channel vector on the l

th

branch:

C

l

=(|a

&dgr;(0)

|c

&dgr;(0)

l

, . . . , |a

&dgr;N−1

|c

&dgr;(N−1)

l

)

T

One is seeking to estimate the vector C

l

for each block and on each branch.

For the channel estimation, in accordance with the Maximum a Posteriori criterion, a suitable representation of the discrete multi-path channel is used for each branch of diversity. This representation is based on the Karhunen-Loève theorem of orthogonal decomposition. The vector representing the equivalent discrete multi-path channel on the l

th

branch of diversity C

l

is expressed in the following way:

C

1

=

∑

k

=

0

N

-

1

⁢

⁢

G

k

1

⁢

⁢

B

k

where {B

k

}

k=0

N−1

are the N normalized eigenvectors from the time-frequency auto-correlation matrix of the discrete channel and F=E└C

l

C

l-T

┘ and {G

k

l

}

k=0

N−1

are random complex Gaussian variables which are independent and centered and of variances equal to the eigenvalues {&Ggr;

k

}

k=0

l

of the hermitian matrix F. The (p,q)

th

entry of the matrix F is given by

E

pq

={square root over (E

&dgr;(p)

E

&dgr;(q)

)}&phgr;([

m

(

p

)−

m

(

q

)]

F,[n

(

p

)−

n

(

q

)]

T

)

The vectors {G

l

}

l=0

L−1

, with G

l

=(G

0

l

, . . . G

0N−1

l

)

T

are suitable representation of the discrete multiplicative channel seen at the output from the L branches of diversity.

The estimation of the channel therefore comes down to estimating {G

k

l

}

k=0,l=0

N−1,L−1

. This estimation is made iteratively by the following formula by designating G

P

l(d)

the estimation of G

P

l

at the d

th

iteration of the algorithm:

G

P

l

⁢

⁢

(

d

+

1

)

=

w

p

⁢

⁢

∑

k

=

0

N

-

1

⁢

⁢

(

R

δ

⁢

⁢

(

k

)

l

⁢

⁢

(

∑

A

∈

Ω

⁢

⁢

AP

⁢

⁢

(

A

δ

⁢

⁢

(

k

)

=

A

|

{

R

1

}

l

=

0

L

-

1

,

{

G

1

⁢

⁢

(

d

)

}

l

=

0

L

-

1

)

)

*

⁢

⁢

B

p

⁢

⁢

δ

⁢

⁢

(

k

)

*

where B

p&dgr;(k)

is the k

th

component of B

p

and

w

p

=

1

1

+

N

0

/

Γ

p

The encoding is not taken into consideration in this formula. With regard to this, if a part of the transmitted vector A is encoded by any code (convolute, en bloc etc.) and then on each iteration of the EM algorithm, the conditional discrete probabilities P(A

&dgr;(k)

=A|{R

l

}

l=0

L−1

,{G

l(d)

}

l=0

L−1

can be calculated exactly by using the trellis of this code and the Bahl algorithm [

9

]. The initialization of the algorithm is carried out by the projection of the received pilot symbols onto the N eigenvectors {B

k

}

k=0

N−1

of the correlation matrix F.

Therefore the equation

G

p

l

⁢

⁢

(

0

)

=

w

p

⁢

⁢

∑

δ

⁢

⁢

(

k

)

∈

S

p

⁢

⁢

R

δ

⁢

⁢

(

k

)

1

⁢

⁢

D

δ

⁢

⁢

(

k

)

*

⁢

⁢

B

p

⁢

⁢

δ

⁢

⁢

(

k

)

*

is used as the p

th

component of the initial estimation G

l(0)

.

The vectors {B

k

}

k=0

N−1

are known elements at the receiver. They correspond to a chosen channel model. This family of vectors is obtained by calculating the theoretical correlation matrix F of, the corresponding model and by deriving from this these eigenvectors {B

k

}

k=0

N−1

and its associated eigenvalues {&Ggr;

k

}

k=0

N−1

.

The recombination of the L branches that enable one to benefit from the spatial diversity of the receiver is carried out during the iterative processing of the probabilities P(A

&dgr;(k)

=A|{R

l

}

l=0

L−1

,{G

l(d)

}

l=0

L−1

). After a chosen number D of iterations of the algorithm, the probabilities P(A

&dgr;(k)

=A|{R

l

l=0

L−1

,{G

l(d)

}

l=0

L−1

) enable one to obtain a flexible estimation of the data symbols. The decision is made by processing these flexible outputs either directly by a decision device if the data are not encoded or through a decoder if the data are encoded.

The improved channel estimation algorithm according to the invention is illustrated in FIG.

4

. The algorithm E.M. is symbolized by the block

50

, the selection of the suitable base by the block

52

which receives the product B

d

T

m

and the calculation of the weightings by the block

54

which receives B

d

T

m

and N

0

. The algorithm: E.M. of the block

50

is iterative and comprises an initialization represented diagrammatically by the block ℑ

0

and D iterations ℑ

d

. The demodulation is represented by the block

58

which supplies the probabilities P(A∈&OHgr;|{R

l

}

l=0

L−1

,{G

l(d)

}

l=

L−1

).

A receiver conforming to the general description of the invention is shown diagrammatically in FIG.

5

. This receiver comprises means already shown in FIG.

2

and which bear the same reference numbers. However the receiver comprises means to implement an iterative estimation algorithm which is shown on the diagram by the looping of the output from the adder

38

onto the estimation means,

36

l

, . . . ,

36

L

. By this looping, a signal designated &Lgr;

&dgr;(k)

(d)

where d represents the row of the iteration, is applied to these means. The receiver shown additionally comprises a symbol switch

40

which closes on the final iteration D in order to power the decision device

42

.

It is assumed, in this particular embodiment that the received OFDM signal is made up of symbols which take their values in an alphabet &OHgr; of the phase shift keying type with 2 or 4 states. The other characteristics of the received signal such as the shape of the blocks, their size, the distribution and the power of the pilot symbols, as well as the characteristics of the channel are the same as in the general case previously described.

The assumption made in this particular case enables one to obtain an analytic expression of the estimation G

p

l(d+1)

. In the case where the symbols come from a constellation of the PSK-2 type, the G

p

l(d+1)

expression is as follows:

G

p

l

⁢

⁢

(

d

+

1

)

=

w

p

⁢

⁢

(

∑

δ

⁢

⁢

(

k

)

∈

S

D

⁢

⁢

R

δ

⁢

⁢

(

k

)

1

⁢

⁢

tanh

⁡

[

2

⁢

⁢

Re

⁢

{

Λ

δ

⁢

⁢

(

k

)

1

}

]

⁢

⁢

B

p

⁢

⁢

δ

⁢

⁢

(

k

)

*

+

∑

δ

⁢

⁢

(

k

)

∈

S

D

⁢

⁢

R

δ

⁢

⁢

(

k

)

1

⁢

⁢

D

δ

⁢

⁢

(

k

)

*

⁢

⁢

B

p

⁢

⁢

δ

⁢

⁢

(

k

)

*

)

In the case where the symbols come from a constellation of the PSK-4 type, the G

p

l(d+1)

expression is as follows:

G

p

l

⁢

⁢

(

d

+

1

)

=

w

p

⁢

⁢

∑

δ

⁢

⁢

(

k

)

∈

S

D

⁢

⁢

(

R

δ

⁢

⁢

(

k

)

1

⁡

[

1

2

⁢

⁢

tanh

⁡

[

2

⁢

⁢

Re

⁢

{

Λ

δ

⁢

⁢

(

k

)

1

}

]

+

j

2

⁢

⁢

tanh

⁡

[

2

⁢

⁢

Im

⁢

⁢

{

Λ

δ

⁢

⁢

(

k

)

1

}

]

]

*

⁢

B

p

⁢

⁢

δ

⁢

⁢

(

k

)

*

+

∑

δ

⁢

⁢

(

k

)

∈

S

D

⁢

⁢

R

δ

⁢

⁢

(

k

)

1

⁢

⁢

D

δ

⁢

⁢