WO2009069088A2

WO2009069088A2 - Ici cancellation apparatus and method for ofdm systems

Info

Publication number: WO2009069088A2
Application number: PCT/IB2008/054972
Authority: WO
Inventors: Xiaobo Zhang; Gang Wu; Ni Ma
Original assignee: Nxp B.V.
Priority date: 2007-11-30
Filing date: 2008-11-26
Publication date: 2009-06-04
Also published as: WO2009069088A3

Abstract

An inter-channel interference (ICI) cancellation method and apparatus for OFDM based systems. The method includes configuring one or more redundant sub-carriers to reduce or cancel intra-band and inter-band ICI experienced by the target sub-carriers. The number and positions of the redundant sub-carriers are highly flexible.

Description

ICI CANCELLATION APPARATUS AND METHOD FOR OFDM SYSTEMS

Orthogonal frequency division multiplexing (OFDM) is a multi-carrier modulation method with which the transmission data is modulated over multiple sub-carriers and then transmitted simultaneously. This method is widely applied in wireless communication systems due to its good characteristics of resisting frequency-selective fading and narrowband interference. However, OFDM system is very sensitive to frequency offsets, such as the carrier frequency offset caused by the frequency offset between the transmitter and the receiver. The carrier frequency offset can lead to a series of problems, for example, sub- carrier phase rotation, amplitude fading and inter-carrier interference (ICI), which limit the application and performance of OFDM technology. Therefore, techniques for canceling the ICI is a very important consideration for the implementation of OFDM systems.

A transmission method and apparatus for canceling inter-carrier interference in OFDM systems is disclosed in a patent application No. EP 1496659A1 published by the European Patent Office on January 12, 2005, entitled "Transmitting and receiving apparatus and method in an orthogonal frequency division multiplexing system using an insufficient cyclic prefix." The OFDM system has N sub-carriers, wherein K sub-carriers are designated as redundant sub-carriers. A transmission apparatus, provided by the patent application, comprises a P filter, for receiving (N-K) data symbols and generating K virtual data symbols, and an inverse fast Fourier transformer (IFFT) having N input taps corresponding to the N sub-carriers. The IFFT receives the (N-K) data symbols and the K virtual data symbols corresponding to the redundant sub-carriers, and performs inverse fast Fourier transformation on the (N-K) data symbols and the K virtual data symbols to output a data frame. The K virtual data symbols are set to a certain value so that the value of the time domain signals that generate ICI is zero in the data frame, resulting in cancellation of the interferences generated among multiple sub-carriers.

In a practical communication system, a plurality of sub-carriers corresponding to an OFDM symbol can generally carry data with different characteristics, specifically, carry data on the common channels and data on the traffic channels simultaneously. Data with different characteristics will generate different ICI. For example, data on the broadcast channels and the synchronization channels generally will bring larger interference to data transmitted in parallel on the traffic channel due to its higher transmitting power, and sometimes will even become a bottle-neck problem for the transmission design. Therefore, it is desirable to provide an effective transmission method and an apparatus to cancel ICI experienced by a set of sub-carriers caused by data transmission on another set of sub-carriers. It is also desirable to provide a method and an apparatus to prevent or reduce the ICI among the sub-carriers of the same set without significant impact on transmission bandwidth efficiency. It is still desirable to provide a method and an apparatus to allow flexible allocation of sub-carriers among different users of an OFDM based system.

According to one embodiment of the present invention, an ICI cancellation method for OFDM system is provided. The method includes: configuring one or more target sub- carriers for transmitting a first data; configuring one or more user sub-carriers for transmitting a second data; configuring one or more redundant sub-carriers for transmitting a third data; determining the third data such that a first ICI sum experienced by the target sub- carriers resulting from the redundant sub-carriers cancels a second ICI sum and a third ICI sum experienced by the target sub-carriers resulting from the user sub-carriers and the target sub-carriers, respectively; and transmitting the first data, the second data, and third data on the target sub-carriers, the user sub-carriers, and the redundant sub-carriers, respectively. The frequencies of the target sub-carriers and user sub-carriers can be flexibly assigned. The frequencies of the one or more redundant sub-carriers can be flexibly assigned. The third data transmitted on the redundant sub-carriers can be determined based on weighted sum of the first data and the second data transmitted on the target sub-carriers and the user sub- carriers, respectively.

In another embodiment according to the present invention, an apparatus for canceling ICI in OFDM based systems is provided. The apparatus includes: a configuration unit for configuring one or more target sub-carriers for transmitting a first data, one or more user sub- carriers for transmitting a second data, and one or more redundant sub-carriers for transmitting a third data; a determination unit for determining the third data such that a first ICI sum experienced by the target sub-carriers resulting from the redundant sub-carriers cancels a second ICI sum and a third ICI sum resulting from the user sub-carriers and target sub-carriers, respectively; and a transmission unit for transmitting the first data, the second data, and the third data on the target sub-carriers, the user sub-carriers, and the redundant sub- carriers, respectively.

The frequencies of the target sub-carriers and user sub-carriers can be flexibly assigned. The frequencies of the one or more redundant sub-carriers can be flexibly assigned. The third data transmitted on the redundant sub-carriers can be determined based on weighted sum of the first data and the second data transmitted on the target sub-carriers and the user sub-carriers, respectively.

These and/or other embodiments and features of the invention will become apparent and more readily appreciated from the following description of certain exemplary embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is a diagram showing how the real and imaginary components of the sub-carrier interference weighting coefficients vary with the carrier frequency offset in a conventional

OFDM system.

FIG. 2 is a block diagram showing the generation of an exemplary Single Carrier Frequency Division Multiple Access (SC-FDMA) signal.

FIG. 3 is a diagram showing an exemplary frequency allocation of the downlink broadcasting channel and synchronization channel in the Third Generation Partnership Project (3 GPP)

Long Term Evaluation (LTE).

FIG. 4 is a graph illustrating an exemplary Time Division Duplex FS2 frame structure. FIG. 5 A, 5B are graphs illustrating localized and distributed sub-carriers allocations schemes, respectively.

FIG. 6 is a graph illustrating an exemplary sub-carriers allocation scheme of a SC-FDMA system.

FIG. 7 is a flowchart illustrating a method for canceling ICI according to an embodiment of the present invention.

FIG. 8 is a block diagram of an apparatus for canceling ICI according to an embodiment of the present invention.

Detailed descriptions will be made below in reference to certain exemplary embodiments according to the present invention to provide a method and an apparatus for ICI cancellation, in conjunction with the accompanying drawings. The drawings and descriptions are to be regarded as illustrative in nature and not restrictive.

Embodiments of the present invention provide a method and an apparatus for reducing inter- band and intra-band ICI for both "localized" and "distributed" resource allocation scenarios in OFDM based systems by determining and transmitting specific data values on one or more redundant sub-carriers. Furthermore, the number and position of the one or more redundant sub-carriers are flexible so as to support flexible sub-carrier allocation.

As an inherent interference problem of OFDM based systems, ICI is caused by incomplete orthogonality of the sub-carriers, which can result from carrier frequency offset between a transmitter and a receiver, and Doppler effect due to movement of the transmitter and/or the receiver. See, Jean Armstrong, Analysis of New and Existing Methods of Reducing Inter-carrier Interference Due to Carrier Frequency Offset in OFDM, IEEE Trans. Commun., 1999, 47, 3:365-369. Taking a sixteen sub-carriers OFDM system as an example, the data on a sub-carrier is interfered by the data on the other fifteen sub-carriers as shown by Equation 1 :

d\ = C₀Cl₁ + ∑c,_,d, (θ < / < 15) Equation 1

Where d, is the data sent on the / ■th sub-carrier, d_t is the corresponding data received at the receiver, c_t__τ is the weighting coefficient for the interference on the i^th sub-carrier resulting from the data on the I^th sub-carrier, Co is the transmission coefficient for the useful signal d_t, and 0 < / < 15 , -15 </ - / < 15 .

FIG. 1 is a diagram showing how the real and imaginary components of the sub-carrier interference weighting coefficients vary with the carrier frequency offset in a conventional OFDM system. The horizontal axis denotes the carrier frequency offset between the interfering source sub-carrier and the target sub-carrier, which is multiple times of the sub- carrier frequency band, and the vertical axis denotes the real and imaginary components of the sub-carrier interference coefficient, whose value vary with respect to the carrier frequency offset. It can be seen from FIG. 1 that the amplitudes of the real (i.e., triangle) and imaginary (i.e., plus sign) components of the interference coefficients between adjacent sub-carriers change slightly, and the amplitudes for the interference coefficients decrease gradually while the carrier frequency offset between the interfering source sub-carrier and the target sub- carrier increases. Based on this observation, ICI self-cancellation scheme, by transmitting each data symbol in two or multiple adjacent sub-carriers, has been proposed. See, Y. Zhao and S. -G. FTaggman, "Sensitivity to Doppler Shift and Carrier Frequency Errors in OFDM Systems — The Consequences and Solutions," in IEEE 46th Vehicular Technology Conf, Atlanta, GA, Apr. 1996, pp. 1564-1568. However, this self-cancellation scheme eliminates the ICI at the expense of reduced transmission efficiency, which is unacceptable in many practical implementations. As defined in the Third Generation Partnership Project (3 GPP) Long Term Evaluation

(LTE), Uplink (UL) Single Carrier Frequency Division Multiple Access (SC-FDMA) with cyclic prefix can be regarded as a kind of broad sense OFDM implementation, and hence, it also faces the ICI problem as conventional OFDM based systems. Frequency-domain generation of a SC-FDMA signal, sometimes known as DFT-spread OFDM, is illustrated in FIG. 2. See, 3GPP TR 25.814 vl.22, "Physical Layer Aspects of Evolved UTRA." The main purpose of employing SC-FDMA is to reduce the PAPR (Peak-to-Average Power Ratio) in UL because of its inherent single carrier structure.

Basic Downlink (DL)/Uplink (UL) Frequency Allocation in LTE

The basic LTE scheme supports a varied transmission bandwidth from 1.25 MHz to 20 MHz in both UL and DL.

DL Frequency Allocation The center frequency of the center sub-carrier over the overall transmission bandwidth in each cell/sector is designed to satisfy the Evolved Universal Terrestrial Radio Access (E-UTRA) raster condition regardless of the overall transmission bandwidth in the cell/sector. Therefore, the Broadcasting Channel (BCH) and Synchronization Channel (SCH) are transmitted in the central part (100) of the transmission bandwidth of the cell as shown in FIG. 3.

UL Frequency Allocation

In order to support the random-access procedure, the Physical Random Access Channel (PRACH) on UL Pilot Channels (UpPCH) are used for Ll random access procedure regarding LTE Time Division Duplex (TDD) Frame Structure 2 operation as shown in FIG. 4. The RACH and user data are mixed in the UpPCH. Due to the frequency asynchronization of RACH and PRACH channels, other scheduled data channels will also experience ICI. Localized Allocation and Distributed Resource Allocation

If the sub-carriers allocated to one user are continuous in the frequency domain, the allocation is named as "localized" as shown in FIG. 5A. Otherwise, if the sub-carriers allocated to one user are not continuous, the allocation is named as "distributed" as shown in FIG. 5B. In both FIGs. 5A and 5B, the sub-carriers allocated to a first user is shown as non- shaded blocks, and the sub-carriers allocated to a second user is shown as shaded blocks. During signal transmission on the PRACH/PSH/SSH, when a user equipment (UE) has not acquired frequency synchronization with an Evolved Universal Terrestrial Radio Access Network Base Station (eNB), two types of ICI can occur: intra-band ICI and inter-band ICI. When intra-band ICI occurs, frequency asynchronization between the UE and the eNB causes a receiver to experience ICI caused by the signals of other sub-carriers of the same UE. When inter-band ICI occurs, frequency asynchronization between the UE and the eNB causes the receiver to experience ICI caused by the signals of the sub-carriers of different UEs.

In addition, even after synchronizing the UE and the eNB, ICI can still occur due to the UE' s mobility (i.e., Doppler frequency offset).

Embodiments of the present invention will now be described to provide a method and an apparatus to reduce or cancel intra-band ICI and inter-band ICI experienced by the UE. In an exemplary SC-FDMA system (i.e., OFDM based system), received data at the base station on a sub-carrier is subject to the interference caused by the data transmitted on other sub-carriers, as described by Equation 1.

Referring to Equation 1, C_1^ is the ICI complex coefficient representing the ICI power level of the / ^th sub-carrier over the i ^th sub-carrier, and 1 - N ≤ / -/ ≤ N- 1 :

where, N is the total number of sub-carriers, Δf is the frequency offset between the UE (using sub-carrier i ) and the base station, and T is the time duration of one OFDM symbol. Therefore, Equations 3, 4 and 5 can be derived from Equation 2 as:

C_[

= F(AfT, N) Λ/ ^y _{r /} _ ._Λ Equation 3

1 + tg^-^-ctgr*

N U where F (AfT, N) is a function of AfT and N :

Equation 4

When Δ/Γ is substantially small, since tg ^ ^π ctgπ\ -^- « 1 , Equation 3 can be reduced as:

N _\ N J c,_, « /(Δ/T, N/ rfg J ^l - j J Equation 5

Therefore, the ICI coefficient in Equation 2 can be approximately represented as (almost no error within quite a large scale of Doppler frequency offset, e.g., offset can be about 0.2): c Equation 6

As such, the ICI coefficient as shown in Equation 6 does not change along with the change of frequency offset.

Equation 6 shows that an unitary ICI coefficient can be determined by only using the frequency gap between the interference source sub-carriers and the target sub-carrier. That is, the unitary ICI can be determined irrespective of the actual frequency position of the interference source sub-carriers and the target sub-carriers.

Therefore, it should be appreciated by one of ordinary skill in art that one or more redundant sub-carriers can be allocated to one UE to compensate the inter-band ICI (i.e., ICI from the sub-carriers of other UEs) and/or the intra-band ICI (i.e., ICI from the sub-carriers of the same UE). The value of data to be transmitted on the redundant sub-carriers can be determined from the transmitted signals on the interference source sub-carriers.

Theoretically, one redundant sub-carrier can reduce the ICI on a target sub-carrier to substantially zero and at the same time substantially reduce the ICI on an adjacent target sub- carrier to a small value. In addition, when the number of selected target sub-carriers exceeds the number of redundant sub-carriers, the redundant sub-carriers can be configured to certain specific values to minimize the ICI sum of the target sub-carriers.

Referring to FIG. 6, in an exemplary SC-FDMA system, a user equipment UEl and multiple other UEs share all the available sub-carriers, and redundant sub-carriers are allocated to UEl for ICI compensation. The horizontal axis denotes time, each grid corresponding to an OFDM symbol interval. The vertical axis denotes frequency, each grid corresponding to a unit of sub-carrier. An OFDM symbol includes multiple sub-carriers. The non-shaded blocks represent data sub-carriers allocated to the UEl, the diagonal-hatched blocks represent the sub-carriers allocated to other UEs, and the solidly-shaded blocks represent the redundant sub-carriers allocated to UEl. Each row of blocks in FIG. 6 represents a sub-carrier for data transmission. However, one of ordinary skill in the art should appreciate that sub-carriers allocation is not limited to the exemplary embodiment shown in FIG. 6. Other allocation schemes are possible. The data sub-carriers allocated to UEl can be localized or distributed, and the position of the redundant sub-carriers are flexible. In another exemplary embodiment, it can be assumed that: the available sub-carrier number is M with the indices 1,2, • • • , M ; UEl occupies U data sub-carriers with the indices U₁, U₂ - - -,U_1J , where the corresponding user data in the U data sub-carriers are d_l, d₂ - - -, d_u ; R redundant sub-carriers are provided and indexed by r_x, r₂ - - -, r_R ; and T target sub-carriers are allocated with indices t_λ,t₂ - - -,t_τ . According to the exemplary embodiment of the present invention, a method is provided to compute the corresponding user data S₁ , S₂ ^{■ ■ ■} , s_R to be transmitted in the corresponding redundant sub-carriers r_x, r₂ ^{■ ■} -, r_R to reduce or cancel the ICI experienced by the T target sub-carriers.

FIG. 7 is a flowchart illustrating an exemplary method for reducing or canceling the ICI experienced by the T target sub-carriers.

In step (SlO), one or more target sub-carriers are configured to transmit a first data and allocated to a first UE. In step (S20), one or more user sub-carriers are configured to transmit a second data and allocated to other UEs. In step (S30), one or more redundant sub-carriers are configured to transmit a third data and allocated such that a first ICI sum experienced by the target sub-carriers resulting from the redundant sub-carriers cancels a second ICI sum resulting from the user sub-carriers and a third ICI sum resulting from the target sub-carriers. In step (S40), the third date transmitted on the one or more redundant sub-carriers are determined. In step (S50), the first data, second data, and third data are transmitted on the target sub-carriers, the user sub-carriers, and the redundant sub-carriers. The detail of determining the third data transmitted on the redundant sub-carriers will now be further discussed. First, a unitary ICI sum of all T target sub-carriers t_x,t₂ - - -,t_τ are represented by Equation 7: ^p~ Equation 7

Ψhere f{t

Then assume s_r = x_r + y_r , so P_ιcι is a function of x_r ² , y_r ² , x_ry_r (r = r_x , ^{■ ■ ■} r_R ) . In order to approach the minimum value of P_ιcι , its differential coefficients to x_r,y_r(r = r₁,- - -r_R ) should dP dP be zero (i.e., — — = 0, — — = 0), which can be simplified as: dx_r dy_r

∑∑f{r - t)- s_r +∑F(t) = 0 Equation 8

Z=Z₁ r=r_λ t=t_λ

Where F(t) = ∑f{u -t).d_u

When T ≤ R , the redundant sub-carriers can reduce the ICI experienced by the target sub- carriers to substantially zero by transmitting the third data determined by the following equation:

∑f\r - t)- s_r +F(t) = O,t = t_l - - -t_T Equation 9

When T > R , the T target sub-carriers are divided into R groups according to following two principles: 1) Sub-carriers of one group should be as close as possible; and 2) sub-carriers with more serious ICI should be put into a group with less number of sub-carriers. The redundant sub-carriers can reduce the ICI sum of each group of sub-carriers to substantially zero by transmitting the third data determined by the following equation (assuming g_Λ, g_l2r ", g,_G is the indices of G sub-carriers of the / ^th group, i = l,2,- - -, R ):

∑∑/('-'h_r +∑n0 = 0,i = l,2,-,« Equation 10 t=Sύ ^r=^r\ <=g,\

FIG. 8 illustrates another exemplary embodiment according to the present invention. FIG. 8 shows an apparatus (200) for reducing inter-band and intra band ICI experienced by target sub-carriers allocated to a first UE. The apparatus includes a configuration unit (10) for configuring one or more target sub-carriers to transmit a first data, one or more user sub-carriers to transmit a second data, and one or more redundant sub-carriers to transmit a third data; a determination unit (20) for determining the third data transmitted on the redundant sub-carriers such that a first ICI sum experienced by the target sub-carriers resulting from the redundant sub- carriers cancels a second ICI sum resulting from the user sub-carriers and a third ICI sum resulting from the target sub-carriers; and a transmission unit (30) for transmitting the first data, the second data and the third data on the target sub-carriers, the user sub-carriers, and the redundant sub-carriers, respectively. It should be appreciated by a person skilled in the art that the sub-carriers allocation of the user sub-carriers, the target sub-carriers, and the redundant sub-carriers are flexible and not fixed to any particular order.

Although certain exemplary embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the present invention as disclosed in the accompanying claims and their equivalents.

Claims

What is Claimed is:

1. An inter-channel interference (ICI) cancellation method for OFDM based systems, the method comprising: configuring one or more target sub-carriers (SlO) for transmitting first data; configuring one or more user sub-carriers (S20) for transmitting second data; configuring one or more redundant sub-carriers (S30) for transmitting third data; determining the third data (S40) such that a first ICI sum experienced by the target sub-carriers resulting from the redundant sub-carriers cancels a second ICI sum and a third ICI sum experienced by the target sub-carriers resulting from the user sub-carriers and the target sub-carriers, respectively; and transmitting the first data (S50), the second data, and the third data on the target sub- carriers, the user sub-carriers, and the redundant sub-carriers, respectively.

2. The method of claim 1, wherein frequencies of the one or more target sub- carriers and the one or more user sub-carriers are flexibly assigned.

3. The method of claim 1, wherein frequencies of the one or more redundant sub- carriers are flexibly assigned.

4. The method of claim 1, wherein the third data transmitted on the redundant sub-carriers are determined based on weighted sum of the first data transmitted on the target sub-carriers and the second data transmitted on the user sub-carriers.

5. The method of claim 1, wherein the third data transmitted on the one or more redundant sub-carriers are determined by:

∑∑f(r -t)s_{r +}∑F(t) = 0

I=I₁ r=r_λ I=I₁

F(ή= ∑f(u -ή.d_u

where s_r is the third data transmitted on the redundant sub-carriers, d_u is the second data transmitted on the user sub-carriers, ti and tr are the sequence numbers for the first and the T* target sub-carriers, rj and V_R are the sequence numbers for the first and the R redundant sub-carriers, ui and Uu are the sequence number of the first and U^th user sub- carriers, and N is the total number of sub-carriers.

6. The method of claim 1, wherein the number of the target sub-carriers is less than or equal to the number of the redundant sub-carriers, the third data transmitted on the one or more redundant sub-carriers are determined by:

∑f{r -t)-s_r +F(t) = O,t = t₁ -t_τ

F(ή= ∑f(u -ή.d_u

where s_r is the third data transmitted on the redundant sub-carriers, d_u is the second data transmitted on the user sub-carriers, ti and tj are the sequence numbers for the first and the T^th target sub-carriers, r_} and r_R are the sequence numbers for the first and the R^Λ redundant sub-carriers, ui and uu are the sequence number of the first and U* user sub- carriers, and N is the total number of sub-carriers.

7. The method of claim 1, wherein the number of the target sub-carriers is more than the number of the redundant sub-carriers, the target sub-carriers being allocated into R sub-target groups comprising a first sub-target group and a second sub-target group, R being equal to the number of redundant sub-carriers, target sub-carriers having proximate carrier frequencies being allocated to a same sub-target group among the sub-target groups, the first sub-target group being smaller than the second sub-target group when target sub-carriers allocated to the first sub-target group experience higher ICI than target sub-carriers allocated to the second sub-target group, and the third data transmitted on the one or more redundant sub-carriers being determined by:

∑∑f(r -t)-s_r +∑F(t) = 0,i = l,2,.~,R t=g,ι ^r=r\ ^t=Sι\

/(O = <**(%)- J

F(ή= ∑f(u -ή.d_u

where g_Λ , g_l2 , ^{■ ■ ■} , g_lG are indices of G sub-carriers of the / • th group, s_r is the third value transmitted on the redundant sub-carriers, t/_ais the second data transmitted on the user sub-carriers, r_} and r_R are the sequence numbers for the first and the R^Λ redundant sub- carriers, Ui and UJ_J are the sequence number of the first and U* user sub-carriers, and N is the total number of sub-carriers.

8. An apparatus (200) for canceling inter-channel interference (ICI) in OFDM based systems, the apparatus comprising: a configuration unit (10) for configuring one or more target sub-carriers for transmitting first data, one or more user sub-carriers for transmitting second data, and one or more redundant sub-carriers for transmitting third data; a determination unit (20) for determining the third data such that a first ICI sum experienced by the target sub-carriers resulting from the redundant sub-carriers cancels a second ICI sum and a third ICI sum resulting from the user sub-carriers and the target sub- carriers, respectively; and a transmission unit (30) for transmitting the first data, the second data, and the third data on the target sub-carriers, the user sub-carriers, and the redundant sub-carriers, respectively.

9. The apparatus of claim 8, wherein frequencies of the one or more target sub- carriers and the one or more user sub-carriers are flexibly assigned.

10. The apparatus of claim 8, wherein frequencies of the one or more redundant sub-carriers are flexibly assigned.

11. The apparatus of claim 8, wherein the third data transmitted on the redundant sub-carriers are determined based on weighted sum of the first data transmitted on the target sub-carriers and the second data transmitted on the user sub-carriers.

12. The apparatus of claim 8, wherein the third data transmitted on the one or more redundant sub-carriers are determined by:

t=t_λ r=r_λ t=t_λ

F(t) = ∑f(u -t).d_u

where s_r is the third data transmitted on the redundant sub-carriers, d_u is the second data transmitted on the user sub-carriers, tj and tj are the sequence numbers for the first and the T* target sub-carriers, ri and Γ_R are the sequence numbers for the first and the R redundant sub-carriers, ui and Uu are the sequence number of the first and U^th user sub- carriers, and N is the total number of sub-carriers.

13. The apparatus of claim 8, wherein the number of the target sub-carriers is less than or equal to the number of the redundant sub-carriers, the third data transmitted on the one or more redundant sub-carriers being determined by: f_tf(r -t)-s_r +F(t) = O,t = t₁ -t_T

F(ή= ∑f(u -ή.d_u

14. The apparatus of claim 8, wherein the number of the target sub-carriers is more than the number of the redundant sub-carriers, the target sub-carriers being allocated into R sub-target groups comprising a first sub-target group and a second sub-target group, R being equal to the number of redundant sub-carriers, target sub-carriers having proximate carrier frequencies being allocated to a same sub-target group among the sub-target groups, the first sub-target group being smaller than the second sub-target group when target sub- carriers allocated to the first sub-target group experience higher ICI than target sub-carriers allocated to the second sub-target group, and the third data transmitted on the one or ^■ more redundant sub-carriers being determined by:

∑∑f(r-t)-_Sr +∑F⁽t) = 0,i = l,2,-,R t=g,ι ^r=r\ ^t=Sι\

/(O = <**(%)- J

F(ή= ∑f(u -ή.d_u

where g_Λ , g_l2 , ^{■ ■ ■} , g_lG are indices of G sub-carriers of the / ^th group, s_r is the third data transmitted on the redundant sub-carriers, d_u is the second data transmitted on the corresponding user sub-carrier, r_} and r_R are the sequence numbers for the first and the R^th redundant sub-carriers, ui and UJ_J are the sequence number of the first and U* user sub- carriers, and N is the total number of sub-carriers.