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Title:
RECEIVER DEVICE AND METHOD THEREOF
Document Type and Number:
WIPO Patent Application WO/2017/125124
Kind Code:
A1
Abstract:
The invention relates to a receiver device for a communication system (500), the receiver device (100) comprising a receiver (102) configured to receive a data signal r comprising data precoded with an orthogonal projection precoder matrix G; compute Signal-to-Noise and Interference Ratio, SNIR, for transmitted data symbols of the data signal r based on the precoder matrix G; filter the data signal r using the precoder matrix G so as to obtain a filtered data signal; compute the likelihoods for the transmitted data symbols based on the computed SNIR and the filtered data signal r. Furthermore, the invention also relates to a corresponding method, a wired or a wireless communication system, a computer program, and a computer program product.

Inventors:
PITAVAL RENAUD-ALEXANDRE (SE)
POPOVIC BRANISLAV (SE)
Application Number:
PCT/EP2016/050910
Publication Date:
July 27, 2017
Filing Date:
January 18, 2016
Export Citation:
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Assignee:
HUAWEI TECH CO LTD (CN)
PITAVAL RENAUD-ALEXANDRE (SE)
POPOVIC BRANISLAV (SE)
International Classes:
H04L27/26; H04L25/03
Domestic Patent References:
WO2012100279A12012-08-02
Foreign References:
US20080188190A12008-08-07
Other References:
KALYANI S ET AL: "Interference Mitigation in Turbo-Coded OFDM Systems Using Robust LLRs", IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS, 2008 : ICC '08 ; 19 - 23 MAY 2008, BEIJING, CHINA, IEEE, PISCATAWAY, NJ, USA, 19 May 2008 (2008-05-19), pages 646 - 651, XP031265448, ISBN: 978-1-4244-2075-9
Attorney, Agent or Firm:
KREUZ, Georg (DE)
Download PDF:
Claims:
CLAIMS

1 . Receiver device for a communication system (500), the receiver device (100) comprising a receiver (102) configured to:

receive a data signal r comprising data precoded with an orthogonal projection precoder matrix G;

compute Signal-to-Noise and Interference Ratio, SNIR, for transmitted data symbols of the data signal r based on the precoder matrix G,

filter the data signal r using the precoder matrix G so as to obtain a filtered data signal; compute the likelihoods for the transmitted data symbols based on the computed SNIR and the filtered data signal r.

2. Receiver device (100) according to claim 1 , wherein the receiver (102) is configured to: a) filter the data signal r using the precoder matrix G and soft-symbol estimates for the transmitted data symbols computed in a previous iteration so as to obtain the filtered data signal; b) compute the likelihoods for the transmitted data symbols based on the computed SNIR; c) compute soft-symbol estimates for the transmitted data symbols based on the computed likelihoods;

repeat a) to c) for a number of iterations.

3. Receiver device (100) according to claim 2, wherein the receiver (102), in the first iteration, is configured to filter the data signal r based on predetermined soft-symbol estimates for the transmitted data symbols. 4. Receiver device (100) according to any of the preceding claims, wherein the receiver (102) is configured to compute the SNIR based on the diagonal elements of the precoder matrix G.

5. Receiver device (100) according to claim 4, wherein the receiver (102) is configured to compute the SNIR for the transmitted data symbol a with transmission index i according to the formula:

SINR; = - ¾——

(l-0u) + N0 where g i are the values of the diagonal elements of the precoder matrix G, and N0 is the noise power of the Additive White Gaussian Noise, AWGN.

6. Receiver device (100) according to claim 5, wherein the receiver (102) is configured to compute the likelihood Pr for the transmitted data symbol a with transmission index i according to the formula:

D f - j) \ j \ SINRt -SINRjxI -al2

Pr ri |"i = a) = e ' ' where is the i-th component of the filtered data signal, and dt is the i-th transmitted data symbol.

7. Receiver device (100) according to any of claims 1 -6, wherein the receiver (102) is configured to filter the data signal r using the precoder matrix G and the soft-symbol estimates for all transmitted data symbols.

8. Receiver device (100) according to any of claims 1 -6, wherein the receiver (102) is configured to filter the data signal r using the precoder matrix G and only the soft-symbol estimates for the interfering transmitted data symbols.

9. Receiver device (100) according to any of claims 1 -8, wherein the communication system (500) is an Orthogonal Frequency Division Multiplexing, OFDM, system. 10. Receiver device (100) according to any of claims 1 -8, wherein the communication system (500) is single carrier frequency division multiple access, SC-FDMA, system.

1 1 . Receiver device (100) according to any of the preceding claims, wherein the receiver (102) is configured to decode the filtered data signal r based on the computed likelihoods for the transmitted data symbols.

12. Communication system (500) comprising at least one receiver device (100) according to any of the preceding claims. 13. Method for a communication system (500), the method (200) comprising:

receiving (202) a data signal r comprising data precoded with an orthogonal projection precoder matrix G, computing (204) Signal-to-Noise and Interference Ratio, SN IR, for transmitted data symbols of the data signal r based on the precoder matrix G,

filtering (206) the data signal r using the precoder matrix G so as to obtain a filtered data signal;

computing (208) the likelihoods for the transmitted data symbols based on the computed

SN IR and the filtered data signal r.

14. Computer program with a program code for performing a method according to claim 13 when the computer program runs on a computer.

Description:
RECEIVER DEVICE AND METHOD THEREOF

TECHNICAL FIELD

The invention relates to a receiver device for wired or wireless communication systems. Furthermore, the invention also relates to a corresponding method, a wired or wireless communication system, a computer program, and a computer program product.

BACKGROUND

Orthogonal frequency division multiplexing (OFDM) is the air-interface of many communications systems, e.g. Long Term Evolution (LTE). A main disadvantage of OFDM is the high out-of-band (OOB) emission. Out-of-band emission reduces the overall systems performance as it either causes interference in the neighbouring frequency bands, or obliges the inclusion of large guard bands to limit interference. To solve this issue, spectral precoding is a solution that reduces OOB by precoding the data symbols before feeding the OFDM modulator at transmission. A projection precoder is a spectral precoding method that projects the data symbol vector in order to confine the transmission in a specific data subspace g. This subspace is a-priori determined to guarantee a certain level of OOB emission. One method to restrict the transmission to a given subspace g is to use an orthogonal projection. Namely, the vector of " data symbols is spectrally-precoded before feeding the OFDM modulator as:

d = Gd (1 ) where G is a K x K orthogonal projection of rank(G)= K - M where M > 0 is a design parameter. An orthogonal projection matrix is by definition a matrix that is idempotent, i.e. G 2 = G, and Hermitian, i.e. it is equal to its own conjugate-transpose: G = G H . Namely, the image of a projection projects on itself and the range and the null space of the projection is orthogonal. The precoder G projects d ε C K onto the subspace g c C K of dimension (K - M) < K, so that d always belongs to g. A projection is a non-invertible operation, i.e. a vector d ε g is the image of an infinite number of vectors d ε C K that could have projected onto d. However, the transmitted data in d are typically selected from a discrete constellation, i.e. d £ C K where C is for example a QAM constellation, and thus there is in fact only a finite number of possible d that can be the invert image of d. Even if the projection from to g. would be a one-to-one mapping, inverting G by exhaustive search would be too prohibitive as " is typically large. One can nevertheless exploit the discreetness of the constellation in a lower complexity per-index symbol estimation using a non-linear iterative receiver.

SUMMARY

An objective of embodiments of the invention is to provide a solution which mitigates or solves the drawbacks and problems of conventional solutions. The above objective and further objectives are achieved by the subject matter of the independent claims. Further advantageous implementation forms of the invention are defined by the dependent claims.

According to a first aspect of the invention, the above mentioned and other objectives are achieved with a receiver device for a communication system, the receiver device comprising a receiver configured to:

receive a data signal r comprising data precoded with an orthogonal projection precoder matrix G;

compute Signal-to-Noise and Interference Ratio, SN IR, for transmitted data symbols of the data signal r based on the precoder matrix G,

filter the data signal r using the precoder matrix G so as to obtain a filtered data signal; compute the likelihoods for the transmitted data symbols based on the computed SN IR and the filtered data signal r. A number of advantages are provided by a receiver device according to the first aspect. By using information about the projector precoder for computing SN IR and use the computed SNIR for computing the likelihoods e.g. improved symbol estimation and decoding is achieved compared to conventional solutions. In a first possible implementation form of a receiver device according to the first aspect, the receiver is configured to:

a) ilter the data signal r using the precoder matrix G and soft-symbol estimates for the transmitted data symbols computed in a previous iteration so as to obtain the filtered data signal, b) compute the likelihoods for the transmitted data symbols based on the computed SNIR, c) compute soft-symbol estimates for the transmitted data symbols based on the computed likelihoods,

repeat a) to c) for a number of iterations. An advantage with this possible implementation form is that by iterating the steps a) to c) a number of iterations the computed likelihoods are even more improved. This also have the direct consequence to provide even more improved symbol estimations e.g. for decoding.

In a second possible implementation form of a receiver device according to the first implementation form of the first aspect, the receiver, in the first iteration, is configured to filter the data signal r based on predetermined soft-symbol estimates for the transmitted data symbols.

An advantage with this possible implementation form is that the computed likelihoods at the first iteration are improved, which will improve the likelihood at every iteration if the predetermined soft-symbol estimates are chosen wisely.

In a third possible implementation form of a receiver device according to any preceding implementation forms of the first aspect or to the first aspect as such, the receiver is configured to compute the SNIR based on the diagonal elements of the precoder matrix G.

An advantage with this possible implementation form is that the computational complexity and memory storage needed can be reduced while the performance is the upheld.

In a fourth possible implementation form of a receiver device according to the third implementation form of the first aspect, the receiver is configured to compute the SNIR for the transmitted data symbol a with transmission index i according to the formula:

SI R; = - ¾——

(l-flf M ) + N 0 where g i are the values of the diagonal elements of the precoder matrix G, and N 0 is the noise power of the Additive White Gaussian Noise, AWGN.

An advantage with this possible implementation form is that the formula gives an explicit expression for the SNIR computation. In a fifth possible implementation form of a receiver device according to the fourth implementation form of the first aspect, the receiver is configured to compute the likelihood Pr for the transmitted data symbol a with transmission index i according to the formula: where is the i-th component of the filtered data signal, and is the i-th transmitted data symbol. An advantage with this possible implementation form is that the formula gives an explicit expression for the likelihood computation.

In a sixth possible implementation form of a receiver device according to any of the first to fifth implementation forms of the first aspect or to the first aspect as such, the receiver is configured to filter the data signal r using the precoder matrix G and the soft-symbol estimates for all transmitted data symbols.

An advantage with this possible implementation form is that no selection has to be made among the soft-symbol estimates.

In a seventh possible implementation form of a receiver device according to any of the first to fifth implementation forms of the first aspect or to the first aspect as such, the receiver is configured to filter the data signal r using the precoder matrix G and only the soft-symbol estimates for the interfering transmitted data symbols.

An advantage with this possible implementation form is that the signal reconstruction is improved.

In an eight possible implementation form of a receiver device according to any of the first to seventh implementation forms of the first aspect or to the first aspect as such, the communication system is an Orthogonal Frequency Division Multiplexing, OFDM, system.

An advantage with this possible implementation form is that the receiver device according to the first aspect is well suited for OFDM system. In a ninth possible implementation form of a receiver device according to any of the first to seventh implementation forms of the first aspect or to the first aspect as such, the communication system is single carrier frequency division multiple access, SC-FDMA, system. An advantage with this possible implementation form is that the receiver device according to the first aspect is well suited for SC-FDMA system.

In a tenth possible implementation form of a receiver device according to any of the preceding implementation forms of the first aspect or to the first aspect as such, the receiver is configured to decode the filtered data signal r based on the computed likelihoods for the transmitted data symbols.

An advantage with this possible implementation form is that the error rate is reduced compared to conventional solutions. The improved performance in the respect of error rate is especially the case for high MCSs.

According to a second aspect of the invention, the above mentioned and other objectives are achieved with a communication system, being wired or wireless, comprising a receiver device according to the first aspect.

According to a third aspect of the invention, the above mentioned and other objectives are achieved with a method comprising:

receiving a data signal r comprising data precoded with an orthogonal projection precoder matrix G;

computing Signal-to-Noise and Interference Ratio, SNIR, for transmitted data symbols of the data signal r based on the precoder matrix G,

filtering the data signal r using the precoder matrix G so as to obtain a filtered data signal; computing the likelihoods for the transmitted data symbols based on the computed SNIR and the filtered data signal r.

In a first possible implementation form of a method according to the third aspect, the method comprises:

a) filtering the data signal r using the precoder matrix G and soft-symbol estimates for the transmitted data symbols computed in a previous iteration so as to obtain the filtered data signal; b) computing the likelihoods for the transmitted data symbols based on the computed SNIR; c) computing soft-symbol estimates for the transmitted data symbols based on the computed likelihoods,

repeating a) to c) for a number of iterations.

In a second possible implementation form of a method according to the first implementation form of the third aspect, the method, in the first iteration, comprises filtering the data signal r based on predetermined soft-symbol estimates for the transmitted data symbols.

In a third possible implementation form of a method according to any preceding implementation forms of the third aspect or to the third aspect as such, the method comprises computing the SNIR based on the diagonal elements of the precoder matrix G.

In a fourth possible implementation form of a method according to the third implementation form of the third aspect, the method comprises computing the SNIR for the transmitted data symbol with transmission index i according to the formula:

SINR; =

(l-0u) + N 0 where g i are the values of the diagonal elements of the precoder matrix G, and N 0 is the noise power of the Additive White Gaussian Noise, AWGN.

In a fifth possible implementation form of a method according to the fourth implementation form of the third aspect, the method comprises computing the likelihood Pr for the transmitted data symbol a with transmission index i according to the formula: where r^' is the i-th component of the filtered data signal, and is the i-th transmitted data symbol.

In a sixth possible implementation form of a method according to any of the first to fifth implementation forms of the third aspect or to the third aspect as such, the method comprises filtering the data signal r using the precoder matrix G and the soft-symbol estimates for all transmitted data symbols.

In a seventh possible implementation form of a method according to any of the first to fifth implementation forms of the third aspect or to the third aspect as such, the method comprises filtering the data signal r using the precoder matrix G and only the soft-symbol estimates for the interfering transmitted data symbols.

In an eight possible implementation form of a method according to any of the first to seventh implementation forms of the third aspect or to the third aspect as such, the communication system is an Orthogonal Frequency Division Multiplexing, OFDM, system.

In a ninth possible implementation form of a method according to any of the first to seventh implementation forms of the third aspect or to the third aspect as such, the communication system is single carrier frequency division multiple access, SC-FDMA, system.

In a tenth possible implementation form of a method according to any of the preceding implementation forms of the third aspect or to the third aspect as such, the method comprises decoding the filtered data signal r based on the computed likelihoods for the transmitted data symbols.

The advantages of the method according to the third aspect are the same as the corresponding receiver device according to the first aspect. Embodiments of the invention also relates to a computer program, characterized in code means, which when run by processing means causes said processing means to execute any method according to the invention. Further, the invention also relates to a computer program product comprising a computer readable medium and said mentioned computer program, wherein said computer program is included in the computer readable medium, and comprises of one or more from the group: ROM (Read-Only Memory), PROM (Programmable ROM), EPROM (Erasable PROM), Flash memory, EEPROM (Electrically EPROM) and hard disk drive.

Further applications and advantages of the invention will be apparent from the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

The appended drawings are intended to clarify and explain different embodiments of the invention, in which:

• Fig. 1 shows a receiver device according to an embodiment of the invention;

· Fig. 2 shows a corresponding method according to an embodiment of the invention;

• Fig. 3 shows a receiver device according to a further embodiment of the invention;

• Fig. 4 shows a wireless communication system according to an embodiment of the invention; and

• Fig. 5 shows comparative performance results.

DETAILED DESCRIPTION

Embodiments of the invention relates to using spectral precoder knowledge in a soft-symbol estimation receiver. Embodiments of the invention are applicable for any transmission where data of any kind are precoded by an orthogonal projection precoder, such as a spectral precoder. Once the projection precoded data have been received, the received data symbols are processed by the present receiver. It has been realized by the inventors that projection precoding at the transmitter device creates different static interference levels among the symbol indexes. The receiver can thus improve its symbol estimation based on the knowledge of the projection precoder that was used at the transmitter device.

A drawback of conventional solutions contrary to the present solution is that the same symbol estimation is done for every indexes even if they include different interference level from the spectral precoder. As a result, the performance of conventional solutions, especially for high modulation and coding schemes (MCSs), corresponding to the high signal to noise ratio (SNR) regime, is interference-limited and shows more severe degradation.

Fig. 1 shows an embodiment of a receiver device 1 00 according to the invention. The receiver device 1 00 may be part of a wireless communication device and/or a wired communication device, such as a base station (BS), a user equipment (UE), or a computer having modem for wired communication.

The receiver device 100 comprises a receiver 1 02 which in this particular case is optionally coupled to receiving means 104 (such as an antenna for wireless communication or a modem for wired communication) configured to receive a wireless and/or a wired communication signal S from a transmitter device 300 (see Fig. 5). The communication signal S comprises data precoded by an orthogonal projector precoder G. The communication signal S is processed, such as demodulated, so as to provide a demodulated data signal r comprising the precoded data. The present receiver 1 02 according to the embodiment in Fig. 1 is configured to receive the data signal r comprising data precoded. The receiver 1 02 is further configured to compute Signal-to- Noise and Interference Ratio (SNIR) for the transmitted data symbols of the data signal r based on the precoder matrix G. The receiver 1 02 is further configured to filter the data signal r using the precoder matrix G so as to obtain a filtered data signal. The receiver 1 02 is further configured to compute the likelihoods for the transmitted data symbols based on the computed SNIR and the filtered data signal r.

Typically, the likelihoods are likelihood probabilities in the form of e.g. log-likelihood ratios (LLRs), but other suitable probabilities known in the art can be used, such as maximum-a-posteriory (MAP) probabilities. The computed likelihoods may e.g. be used for decoding and/or interference cancellation by computing symbol estimation.

Fig. 2 shows a corresponding method 200 which may be implemented in a receiver device 1 00, such as the one shown in Fig. 1 . The method 200 comprises the step of receiving 202 a data signal r comprising data precoded with an orthogonal projection precoder matrix G. The method 200 further comprises the step of computing 204 SNIR for the transmitted data symbols of the data signal r based on the precoder matrix G. The method 200 further comprises the step of filtering 206 the data signal r using the precoder matrix G so as to obtain a filtered data signal. The method 200 further comprises the step of computing 208 the likelihoods for the transmitted data symbols based on the computed SNIR and the filtered data signal r.

One application of the present solution is in decoding of the filtered data signal. This means that the computed likelihoods for the transmitted data symbols are used when decoding the filtered data signal. In this exemplary application likelihood probabilities are used for decoding of Forward- Error-Correcting (FEC) codes, such as. turbo codes and convolutional codes. The computed symbol likelihood probabilities are used to compute bit likelihood probabilities, typically in the form of a likelihood ratio (LLR). In a further embodiment of the invention, the present solution is implemented in an iterative receiver 1 02 which is shown in Fig. 3. The receiver 1 02 in Fig. 3 comprises the major function blocks described below. It should be noted that the function blocks may be hardware standalone devices or means, or software implemented function blocks, e.g. implemented in one or more processors, or combinations thereof.

The receiver 1 02 in the embodiment in Fig. 3 comprises a precoder loader block 108 configured to load the precoder matrix G. The precoder matrix G is the precoder matrix G that was used by the transmitter device 300 to precoding the data transmitted to the receiver device 1 00.

The receiver 1 02 in the embodiment in Fig. 3 comprises a signal reconstruction block 1 06 configured to receive a data signal r and cancel interference in the data signal r based on the precoder G and previous soft symbol estimates for the transmitted data symbols from the soft symbol estimation block 1 14 (see below). The interference cancelation may be performed after matched filtering which is more explained in the following disclosure. The signal reconstruction block 1 06 forwards a filtered data signal ϋ) to the likelihood computation block 1 1 2. The filtered data signal w is also denoted as a reconstructed signal in the present disclosure.

The receiver 1 02 in the embodiment in Fig. 3 comprises a SNIR computation block 1 10 configured to compute the per transmission symbol index i SNIR based on the precoder matrix G. Mentioned SN IR is only computed once and not for each iteration step j. In one embodiment only the diagonal elements of the precoder matrix G are used for computing the SNIRs. In a further embodiment the SNIR is computed based on the precoder matrix G and the noise statistics, such as noise power which is more explained below.

The receiver 1 02 in the embodiment in Fig. 3 comprises a likelihood computation block 1 12 configured to receive the filtered data signal ϋ) and compute the likelihoods for the transmitted data symbols based on the SINR computation computed by the SNIR computation block 1 1 0. The receiver 1 02 in the embodiment in Fig. 3 comprises a soft symbol estimation block 1 14 configured, for each iteration step j, to compute the per soft-symbol estimation for the transmitted data symbols based on the computed likelihoods and feed the computed soft-symbol estimation to the signal reconstruction block 1 06 for the next iteration step. Hence, the receiver 1 02 first reconstructs the data signal by cancelling interference in the data signal r according to soft-symbol estimations provided in the previous iteration step. Then, the receiver 1 02 computes new soft-symbol estimations based on likelihoods computed based on the filtered data signal ϋ) . Knowledge of the projection precoder is used in both of these steps, i.e. in the filtering of the data signal and in the computation of the likelihoods. This process is performed iteratively for an arbitrary number of iterations.

Optionally, at end of the iterations, i.e. in the last iteration step, the likelihoods for the transmitted symbols are sent to a decoder block 1 1 6 for decoding. The output of the decoder block 1 1 6, i.e. the decoded symbols, can be used for further processing and/or applications well understood by the skilled person. It is however noted that the decoding can also performed in the non-iterative embodiments of the present solutions.

In one further embodiment, the receiver 1 02, in the very first iteration step, is configured to filter the data signal r based on predetermined soft-symbol estimates for the transmitted data symbols. The predetermined soft-symbol estimates may be based on an assumption of the soft-symbol estimates. This is due to the fact that no soft-symbol estimates have been computed previously when the very first iteration step is executed. A typical assumption may be the average of the symbol constellation if no a priori knowledge is available which e.g. for quadrature amplitude modulation (QAM) is zero.

The present receiver device 1 00 can be used in wired or wireless communication systems 500. In the following disclosure further embodiments of the invention are described in a wireless OFDM system context with its associated terminology. Embodiments of the invention is however not limited thereto and the present solution may e.g. be applied in single carrier frequency division multiple access (SC-FDMA) systems with good performance, or in any other suitable wired or wireless communication system, or combinations thereof.

Fig. 4 illustrates the example in an OFDM system in which a BS comprising a transmitter device 300 transmits data being projector precoded in a wireless communication signal S. A UE comprising the receiver device 1 00 receives the wireless communication signal S and that the receiver 1 02 process the data signal r as described in this disclosure. The UE may comprise the transmitter device 300 whilst the BS comprises the receiver device 1 00, i.e. the reverse case. Moreover, the UE and BS may also comprise both a receiver device 100 and a transmitter device 300 each for bi-directional communications.

Aforementioned, embodiments of the invention disclose to compute likelihood probabilities based on precoder knowledge of the projection precoder G used at the transmitter device 300, i.e. based on G. In the following sections this is described in more detail.

Define the elements of the projection precoder as G = {gt } K ._ and the columns of G as where g { = [g^, - , g K ,i ] T is the ith column of G. Rewrite the received signal r after OFDM demodulation as: r = Gd + n

The symbol has a contribution in every received component of r. Consider matched filtering r with g { to detect d { :

(3)

= g"gidi + ^ g"9i d k + g" n

k≠i In matrix form, this gives f = G H r, and since G is Hermitian, one has: f = Gr

= Gd + Gn (4) where the last equality comes from the fact that G 2 = G. Writing the noise term as n = Gn + G^n, matched filtering has the effect of removing by projection the term G^n which is the noise contribution in the plane g, L .

The received data signal per-symbol index of Eq. (3) is then equal to: = 9i,idi + ^ 9i,k d k + ^ 9i,k n k

(5) k≠i k=l where g d { is the desired signal,∑k≠i 9i,k d k is the interference, and n k is the k-\ component of the noise vector. One can compute the SINR per-index according to Eq. (5). After averaging over the i.i.d. symbols with unit power, the SINR at index i reads:

(i+J o)∑ k =ils£,kl -\ai,i\

As G is an orthogonal projector, it is Hermitian and the diagonal elements are real and non- negative, i.e. g u ≥ 0. Moreover, by construction a projector is idempotent and it verifies GG H = G 2 = G. Accordingly, the diagonal elements of GG H , i.e. the square norm of the rows of G, are equal to the diagonal element of G, leading to:

[GG"] i = 9i,k 9ί,ί

(7) k=l and the SINR expression of Eq. (6) reduces, according to an embodiment, to the formula:

9i,i

SINR j =

9i,i - 9u + 9u N o

9i,i (8) (l-0u) + No

This SINR expression corresponds to the inter-index interference created only by the precoder and known a-priori from the precoder knowledge. It also only depends on the diagonal elements of the precoder matrix G.

We use this fixed computed per-index SINR to compute the likelihood probabilities for constellation symbols at each iteration j. Using a Gaussian assumption of the interference (which is justified for large K by the central limit theorem), the likelihood probabilities for each constellation symbol a and each index i can be computed, according to an embodiment, by the formula: where is the i-th component of reconstructed signal r w which also is denoted as filtered data signal.

In order to cancel the interference, the receiver 102 is configured to make a soft-symbol estimation based on the likelihood probabilities. A soft-symbol estimation can be obtained, e.g. by averaging the constellation symbols over their likelihood probabilities using the formula:

ge c a Pr (? V fc = a)

(10) ∑ae c Pr (r fc 0) |d fc = a)

This soft-symbol estimation is fed back to for the interference cancelation in the signal reconstruction block 106 as previously described.

Two different embodiments which include the match filtering of Eqs. (3) and (4) as part of the signal reconstruction is described.

In one embodiment, the iterative receiver estimates and cancels the distortion of the transmitted vector d. Since the distortion always belongs to the orthogonal plane of the transmission, g> L , one can reduce the estimation error by projecting the estimated distortion to this subspace using the knowledge of the projection precoder. The signal reconstruction by filtering is performed according to: ω = Gr + (/ - G)d^ _1) (11) In this embodiment, the signal reconstruction r w for estimating d { includes a contribution of dp for all k. This means that soft symbol estimates for all constellation symbols are used in this embodiment.

In another embodiment, the signal reconstruction by filtering is performed by cancelling interfering symbol d k in f { as defined in Eq. (5). In this embodiment the signal reconstruction for estimating di is on for only k≠ i. Define the interference matrix as:

Gint = G— G s

where (1 2)

G s = diag(5( 1 , ... , g KiK ) is a diagonal matrix with useful main diagonal components of G. Then from Eq. (3) we have: f = G s d + G int d + Gn. (13) which corresponds to the splitting between interference and desired signal on a per-subcarrier basis in Eq. (5). Accordingly, given the previous symbol vector estimate d (j _1) , the receiver cancels the interference as: so that the initial state is (1) = f when there is no initial symbol estimation, i.e. d (0) = 0.

For consistency, one finally normalizes the symbol reconstruction by the desired symbol power:

= G^Gr - G^G^ (1 5)

= G s x Gr + (/ - G S - X G) d^ '"1 )

This means that the only the soft-symbol estimates for the interfering constellation symbols are used in this embodiment. The computational complexity of the present iterative solution including decoding is the same as for some conventional solutions. The present iterative receiver 1 02 is a per-index estimation whose complexity grows linearly with the number of constellation symbols. However, embodiments of the invention provide lower error rates compared to conventional solutions.

An example of performance gain is shown in Fig. 5 for the example of K = 600 spectrally precoded subcarriers with M = 10 (the dimension of the null space of the projector matrix G) in an OFDM system. The x-axis shows the signal to noise ratio (SNR) and the y-axis shows the bit error probability. Further, line A shows the result for a plain OFDM; line B shows the result for a conventional solution; and line C shows the result for the present solution. Signal reconstruction for the results show in Fig. 5 was done according to the embodiment using Eq. (1 5). It is observed from Fig. 5 that a SNR gain at 10 ~3 biter error rate (BER) of 0.5dB for 64 quadrature amplitude modulation (QAM) modulation with rate 2/3, and 1 .5dB for 64 QAM with rate 5/6. Furthermore, any methods according to embodiments of the invention may be implemented in a computer program, having code means, which when run by processing means causes the processing means to execute the steps of the method. The computer program is included in a computer readable medium of a computer program product. The computer readable medium may comprises of essentially any memory, such as a ROM (Read-Only Memory), a PROM (Programmable Read-Only Memory), an EPROM (Erasable PROM), a Flash memory, an EEPROM (Electrically Erasable PROM), or a hard disk drive.

Moreover, it is realized by the skilled person that the receiver device 1 00 comprise the necessary communication capabilities in the form of e.g., functions, means, units, elements, etc., for performing the present solution. Examples of other such means, units, elements and functions are: processors, memory, buffers, control logic, encoders, decoders, rate matchers, de-rate matchers, mapping units, multipliers, decision units, selecting units, switches, interleavers, de- interleavers, modulators, demodulators, inputs, outputs, antennas, amplifiers, receiver units, transmitter units, DSPs, MSDs, TCM encoder, TCM decoder, power supply units, power feeders, communication interfaces, communication protocols, etc. which are suitably arranged together for performing the present solution.

Especially, the processors of the present receiver 1 02 may comprise, e.g., one or more instances of a Central Processing Unit (CPU), a processing unit, a processing circuit, a processor, an Application Specific Integrated Circuit (ASIC), a microprocessor, or other processing logic that may interpret and execute instructions. The expression "processor" may thus represent a processing circuitry comprising a plurality of processing circuits, such as, e.g., any, some or all of the ones mentioned above. The processing circuitry may further perform data processing functions for inputting, outputting, and processing of data comprising data buffering and device control functions, such as call processing control, user interface control, or the like.

Finally, it should be understood that the invention is not limited to the embodiments described above, but also relates to and incorporates all embodiments within the scope of the appended independent claims.