WO2007078075A1

WO2007078075A1 - Ofdm transmitter, system and encoding method for removing ici

Info

Publication number: WO2007078075A1
Application number: PCT/KR2006/005621
Authority: WO
Inventors: Cheol Jin Park
Original assignee: Huconex Co., Ltd.
Priority date: 2006-01-03
Filing date: 2006-12-21
Publication date: 2007-07-12
Also published as: KR100757078B1; KR20070072976A

Abstract

The present invention relates to an OFDM transmitter, an OFDM system and an encoding method, and more particularly to an OFDM transmitter, an OFDM system and an encoding method which removes an ICI that reduces a performance of an OFDM in a high speed mobile environment (i.e., an environment with a large Doppler frequency) .

Description

[DESCRIPTION]

[invention Title]

OFDM TRANSMITTER, SYSTEM AND ENCODING METHOD FOR REMOVING ICI

[Technical Field]

The present invention relates to an OFDM transmitter, an OFDM system and an encoding method, and more particularly to an OFDM transmitter, an OFDM system and an encoding method which removes an ICI that reduces a performance of an OFDM in a high speed mobile environment (i.e., an environment with a large Doppler frequency).

[Background Art]

Since an OFDM (orthogonal frequency division multiplexing) method is advantageous in that a data may be transmitted in a high speed through a frequency-selective channel, the OFDM method has been at the center of the attention as an effective modulation technique. In accordance with the OFDM method, the data is transmitted by dividing a frequency-selective broadband channel into a plurality of sub-channels. Since each of the plurality of sub-channels is approximated to a non-selective channel, a compensation of the channel is possible using a simple 1- tap equalizer in a receiver.

However, the channel is changed in a single OFDM symbol interval, an orthogonality between the sub-channels are damaged. Such phenomenon is called an ICI (intercarrier interference) . As a moving speed and carrier frequency increase, a Doppler frequency that represents a change speed of the channel is increased. As the Doppler frequency increases, a performance degradation due to the ICI becomes more serious. While the OFDM method was mainly used in a standard such as a wireless LAN which is used by a fixed user or a pedestrian moving at a low speed in the past, the OFDM method is expanded to a standard considering a user in a vehicle or an express train moving at a high speed. Therefore, the Doppler frequency is increased more, and the performance degradation due to the ICI becomes much more serious .

In order to solve the problem of ICI, an ICI self- cancellation technique was proposed. The ICI self- cancellation technique is disclosed "Polynomial cancellation coding of OFDM to reduce intercarrier interference due to Doppler spread", in Proc. GLOBECOM, 1998, pp. 2771-2776. by J. Armstrong, P. Grant, and G. Porey, and "Intercarrier interference self-cancellation scheme for OFDM mobile communication systems", IEEE Trans. Commun., vol. 49, no. 7, pp. 1185-1191, July. 2001 by Y. Zhao and S. -G. Haggman. The technique utilizes a principle Othat a difference between adjacent frequencies of the ICI propagated from one sub-channel to other sub-channels is small. In order to achieve this, data symbols are modulated such that signs thereof are opposite to one another in two adjacent sub-channels. That is, a symbol d_n is transmitted via a 2n^th sub-channel, a symbol -d_n is transmitted via a (2n+l)^th sub-channel. In the receiver, a difference between the 2n^th sub-channel and the (2n+l)^th sub-channel are obtained for demodulation. As a result, the ICI that propagates from each of the sub-channels is canceled to reduce an ICI power.

However, the conventional technique is disadvantageous in that an effect of the reduction of the ICI power is degraded as the Doppler frequency increases. That is, the difference between the adjacent frequencies of the ICI propagated from one sub-channel to other subchannels increases as the Doppler frequency increase, thereby degrading the effect of the reduction of the ICI power.

[Disclosure] [Technical Problem]

It is an object of the present invention to provide an OFDM transmitter, an OFDM system and an encoding method which removes an ICI more accurately. [Technical Solution]

In accordance with a first aspect of the present invention, there is provided an OFDM transmitter comprising an ICI cancellation encoder, an IFFT and a guard interval adder, wherein the ICI cancellation encoder comprises: a redundant symbol generator for generating a redundant symbol vector obtained by multiplying an input symbol vector to one of Q₀ and Q_E; and a multiplexer for multiplexing the input symbol vector and the redundant symbol vector to generate an encoded symbol vector to be transmitted to the IFFT, where Q₀ = - (S_EPI_CIS_O ^T)

QE = - (S₀PI_CIS_E ^T) ^"1S_oPiciSo^T, an element (m, k) of Pici is expressed

N-\ ^{a s p} _{m t} = ^∑⁽ⁿ-^(N-^{v) / 2}>^e~j2mlm~kVN ' is expressed as

and is expressed as

In accordance with a second aspect of the present invention, there is provided a n OFDM transmitter comprising an ICI cancellation encoder, an IFFT and a guard interval adder, wherein the ICI cancellation encoder receives an input symbol vector X_1N, and outputs an encoded symbol vector X corresponding to S_E ^TX_IN + S₀ ¹QoXiN to the IFFT,

1 0 0 0 0 0 0

0 0 1 0 0 ... o 0 where S_E is expressed as S_t = 0 0 0 0 1 0 0 I S

0 0 0 0 0 1 0

expressed as S₀ - Qo is expressed as Q₀

= - ( S_EP_ICiS₀ ^T ) ^{' 1}S_EP_1CIS_E ¹ , and an element (m, k) of P_ICi i s

1 N-\ expressed as p_mk = —Y {n-(N -l)/2)e^''^2!m( m-k)I N

In accordance with a third aspect of the present invention, there is provided an OFDM transmitter comprising an ICI cancellation encoder, an IFFT and a guard interval adder, wherein the ICI cancellation encoder receives an input symbol vector X_1N, and outputs an encoded symbol vector X corresponding to S₀ ^TXi_N + S_E ^TQ_EX_IN to the IFFT, where

0 0 0 0 0

1 0 0 ^{■ • •} 0 0

S_E is 0 0 1 0 0 , S₀ is expressed

0 0 0 ^{■ ■ •} 1 0

as So Q_E is expressed as Q_E = -

(S₀PiciS_E ) SoPiciSo , and an element (m, k) of Pici is

expressed as .

In accordance with a fourth aspect of the present invention, there is provided an OFDM system comprising an OFDM transmitter in accordance with the second or the third aspect of the present invention, and an OFDM receiver, wherein the OFDM receiver comprises a guard interval remover, a FFT and an ICI cancellation decoder, the ICI cancellation decoder receiving a FFT output vector outputted from the FFT so as to output elements corresponding to an input symbol vector of even elements and odd elements of the FFT output vector.

In accordance with a fifth aspect of the present invention, there is provided an encoding method comprising steps of: (a) preparing an encoding matrix; (b) generating a redundant symbol vector obtained by multiplying the encoding matrix to an input symbol vector; and (c) multiplexing the input symbol vector and the redundant symbol vector to generate an encoded symbol vector, where the encoding matrix is one of Q₀ and Q_E expressed as Q₀ = - (S_EP_ICiS₀ ^T) ^"1S_EP_ICIS_E ¹, Q_E = - (S₀P_ICIS_E ^T) ^"1S_OP_ICIS_O ¹, an element

1 N-]

(m, k) of P₁Ci is expressed as p_{m k} = — ^n - (N ~ \)/2)e^~j2m(n>-^k)/N , S_E

N n=o 1 0 0 0 0 0 0

0 0 1 0 0 ^{■ • •} 0 0 is expressed as S_E = 0 0 0 0 1 0 0 and is

0 0 0 0 0 1 0

expressed as S₀ =

[Advantageous Effects]

As described above, in accordance with the OFDM transmitter, the OFDM system and the encoding method of the present invention, the ICI effectively removed to reduce the BER.

[Description of Drawings]

Fig. 1 is a diagram illustrating an OFDM system in accordance with an embodiment of the present invention.

Fig. 2 is a diagram illustrating an encoding method for removing an ICI in accordance with an embodiment of the present invention.

Figs. 3 and 4 are diagrams illustrating a result of a simulated experiment comparing performances of an OFDM transmitter in accordance with the present invention and a conventional OFDM transmitter.

[Description of the reference numerals^ 100: OFDM transmitter

110: ICI cancellation encoder

111: redundant symbol generator

112: multiplexer

113: look-up table

120: inverse fast fourier transformer

130: guard interval adder

200: OFDM receiver

210: guard interval remover

220: fast fourier transformer

230: ICI cancellation decoder

[Mode for Invention]

The present invention will now be described in detail with reference to the accompanied drawings. The interpretations of the terms and wordings used in Description and Claims should not be limited to common or literal meanings. The embodiments of the present invention are provided to describe the present invention more thoroughly for those skilled in the art.

Referring to Fig. 1, the OFDM system comprises an OFDM transmitter 100 and an OFDM receiver 200. The OFDM transmitter 100 comprises an ICI cancellation encoder 110, an IFFT (inverse fast fourier transformer) 120, the guard interval adder 130. The OFDM receiver 200 comprises a guard interval remover 210, a FFT (fast fourier transformer) 220 and an ICI cancellation decoder 230.

The ICI cancellation encoder 110 outputs an encoded symbol vector X which is obtained by encoding an input symbol vector X_1N. Throughout the description of the present invention, a vector is denoted by a bold character. The input symbol vector XIN may be transmitted from a modulator (not shown) . The ICI cancellation encoder 110 carries out the encoding as expressed in equation 1 or equation 2.

[Equation 1]

[Equation 2]

X = S₀ X IN SE XRE

— SQ XIN + SE QEXIN

Equation 1 represents an example wherein symbols included in the input symbol vector X_IN are mapped to even elements of the encoded symbol vector X, and equation 2 represents an example wherein the symbols included in the input symbol vector X_1N are mapped to odd elements of the encoded symbol vector X. That is, in accordance with equation 1, the symbols included in the input symbol vector Xi_N are mapped to even sub-channels, and symbols included in the redundant symbol vector X_RE are mapped to odd subchannels. In accordance with equation 2, the symbols included in the input symbol vector X_1N are mapped to the odd sub-channels, and symbols included in the redundant symbol vector X_RE are mapped to the even sub-channels. When a magnitude of the IFFT is N in equations 1 and 2, the encoded symbol vector X is a Nx 1 matrix, the input symbol vector XIN and the redundant symbol vector XRE are a (N/2)^χl matrix respectively, S_E and S₀ are a (N/2)*N matrix respectively, and Q₀ and Q_E are a (N/2) * (N/2) matrix respectively. In accordance with equations 1 and 2, Q₀ and Q_E are referred to as an encoding matrix. S_E, S₀, Qo and Q_E are expressed in equations 3 through 6, respectively. [Equation 3]

[Equation 4 ]

[ Equation 5 ]

Qo — - ( SEPICI SO ) SEPICISE

[ Equation 6 ]

QE = - ( SQPICI SE⁷ T¹SOPICISC/

An element (m, k) of P_ICi in equations 5 and 6 is expressed as equation 7.

[Equation 7]

P_m,k=^∑(n-(N-l)/2)e- ]2m(m-k)IN

Preferably, the ICI cancellation encoder 110 comprises a redundant symbol generator 111 and a multiplexer 112 in order to carry out an operation of equation 1 or equation 2. The redundant symbol generator 111 generates the redundant symbol vector X_RE obtained by multiplying the input symbol vector X_IN to Q₀ or Q_E. For this, the ICI cancellation encoder 110 may comprise a lookup table 113 storing the Q₀ or Q_E. An n^th row of the Q₀ or Q_E is merely a shifted (n-l)^th row. It is sufficient that the look-up table 113 stores one row of Q₀ or Q_E, i.e. elements of l^χ(N/2). The multiplexer 112 multiplexes the input symbol vector X_1N and the redundant symbol vector X_RE to generate the encoded symbol vector X. More specifically, the multiplexer 112 maps the symbols included in the input symbol vector X_1N to even symbols of the encoded symbol vector X and the symbols included in the redundant symbol vector X_RE to odd symbols of the encoded symbol vector X, or the multiplexer 112 maps the symbols included in the input symbol vector X_1N to the odd symbols of the encoded symbol vector X and the symbols included in the redundant symbol vector X_RE to the even symbols of the encoded symbol vector X.

The IFFT 120 subjects the encoded symbol vector X outputted from the ICI cancellation encoder 110 to a fast fourier transform.

The guard interval adder 130 carries out a function of adding a guard interval to an output of the IFFT 120. An example of adding the guard interval includes a CP (cyclic prefix) scheme or a ZP (zero padding) scheme. In accordance with the CP scheme, samples at an end portion of an N*l vector which is the output of the IFFT 120 are copied and added to a beginning portion of the N*l vector. In accordance with the ZP scheme, a plurality of zeros are inserted to the end portion of the N*l vector. Preferably, the guard interval adder 130 employs the ZP scheme.

The guard interval remover 210 removes the guard interval added by the guard interval adder 130 from a data received via a channel 300. For instance, in case of the CP scheme, a cyclic prefix added by the guard interval adder 130 is discarded, and a remaining of the N*l vector is outputted to the FFT 220. In case of the ZP scheme, the N*l vector obtained by adding the plurality of zeros added by the guard interval adder 130 to the beginning portion of the NxI vector is outputted to the FFT 220.

The FFT 220 outputs a FFT output vector R obtained by subjecting a data outputted by the guard interval remover 210 to the fast fourier transform. More specifically, the FFT 220 subjects the data outputted by the guard interval remover 210 to the fast fourier transform, and outputs the FFT output vector R obtained by an equalization preferably using a 1-tap equalizer (not shown) .

The ICI cancellation decoder 230 receives the FFT output vector R to generate an output symbol vector RQ_UT corresponding to the input symbol vector X_1N. The generated output symbol vector R_0UT ^m^y be transmitted to a demodulator (not shown) . When the symbols included in the input symbol vector X_1N are mapped to the even elements of the encoded symbol vector X, the ICI cancellation decoder 230 simply outputs even symbols included in the FFT output vector R as the output symbol vector RQ_UT- When the symbols included in the input symbol vector X_1N are mapped to the odd elements of the encoded symbol vector X, the ICI cancellation decoder 230 simply outputs odd symbols included in the FFT output vector R as the output symbol vector ROUT-

A principle of removing the ICI in accordance with the embodiment of the present invention shown in Fig. 1 will be described below. For description's purpose, the channel 300 is assumed to be a finite impulse response filter having an order of L and to be piecewise linear, and an impulse response thereof is assumed to vary according to time. In this case, the impulse response of 1^th path (where 1 is an integer satisfying O≤l≤L) and n^th sample (where n is an integer satisfying O≤n≤N+L, and N is a magnitude of the IFFT) may be simply expressed as equation 8.

[Equation 8] hi[n] = hi,o + hi,! ^x (n-1- (N-I) /2 ) , where hi,₀ and hi,i are predetermined constants.

In this case, the FFT output vector R that passed through the channel 300 may be expressed as equation 9.

[Equation 9]

R = H₀X + HiPiciX, where H₀ and Hi are NxN diagonal matrixes, respectively.

M^th diagonal element H₀ and Hi may be expressed as equations 10 and 11, respectively. [Equation 10]

[Equation 11]

-llidmlN

1=0

When the input symbol vector X_1N and the redundant symbol vector X_RE are transmitted to the even sub-channel and the odd sub-channel in the OFDM transmitter 100 respectively, only the output symbol vector R_OUT transmitted through the even sub-channel is filtered. The output symbol vector R_OOT may be expressed as equation 12 using equations 1 through 11.

[Equation 12]

ROUT ⁼ SgR ⁼ S^HoSg XE

As expressed in equation 12, the output symbol vector R_OUT does not include the ICI component.

Referring to Fig. 2, the encoding method for removing the ICI comprises an encoding matrix preparation step Sl, a redundant symbol generation step S2 and multiplexing step S3. In the encoding matrix preparation step Sl, the encoding matrix Q₀ or Q_E is prepared. In the encoding matrix preparation step Sl, the encoding matrix may be prepared by storing the encoding matrix Q₀ or Q_E in a lookup table, or by carrying out an operation corresponding to equation 5 or equation 6. As described above, when the symbols included in the input symbol vector X_1N are mapped to the even symbols of the encoded symbol vector X, the encoding matrix Q₀ is used. When the symbols included in the input symbol vector X_1N are mapped to the odd symbols of the encoded symbol vector X, the encoding matrix Q_E is used.

In the redundant symbol generation step S2, the encoding matrix Q₀ or Q_E and the input symbol vector X_1N are multiplied to generate the redundant symbol vector X_RE.

In the multiplexing step S3, the encoded symbol vector X is generated by multiplexing the input symbol vector X_1N and the redundant symbol vector X_RE. The multiplexing is carried out by mapping the symbols included in the input symbol vector X_1N to the even symbols of the encoded symbol vector X and mapping the symbols included in the input symbol vector X_RE to the odd symbols of the encoded symbol vector X when the encoding matrix Q₀ is used in the redundant symbol generation step S2. The multiplexing is carried out by mapping the symbols included in the input symbol vector X_ΪN to the odd symbols of the encoded symbol vector X and mapping the symbols included in the input symbol vector X_RE to the even symbols of the encoded symbol vector X when the encoding matrix Q_E is used in the redundant symbol generation step S2.

Figs. 3 and 4 are diagrams illustrating a result of a simulated experiment comparing performances of an OFDM transmitter in accordance with the present invention and a conventional OFDM transmitter, wherein Fig. 3 illustrates the result of the simulated experiment using a Rayleigh fading channel having a power delay profile expressed in equation 13, and Fig. 4 illustrates the result of the simulated experiment using a Rayleigh fading channel having a power delay profile expressed in equation 14.

[Equation 13]

E(| h,[n] |²) oc e^"1/4, 0 < 1 < 10

[Equation 14]

E(|h,[n]|²)=l/10,0<l<10

In Figs. 3 and 4, ^λSys. 1' denotes an OFDM system of the ZP type wherein a BPSK (binary phase-shift keying) modulation is carried out without using any ICI cancellation technique. ^λSys. 2' denotes an OFDM system of the ZP type wherein a QBPSK (quadrature phase-shift keying) modulation is carried out using a conventional ICI self- cancellation technique. ^λSys. 3' denotes an OFDM system of the ZP type wherein the QBPSK (quadrature phase-shift keying) modulation is carried out using the ICI cancellation technique in accordance with the present invention.

In Figs. 3 and 4, (a) is the result of the simulated experiment wherein a normalized Doppler frequency corresponds to 0.01, (b) is the result of the simulated experiment wherein the normalized Doppler frequency corresponds to 0.2, and (c) is the result of the simulated experiment wherein a normalized Doppler frequency corresponds to 0.5. The normalized Doppler frequency is a value obtained by multiplying a Doppler frequency to a symbol period, wherein the ICI is increased as the value increases .

Referring to Figs. 3 and 4, when the normalized Doppler frequency is low, that is, in case of (a) wherein a small amount of the ICI is generated, a performance difference between the ICI cancellation technique in accordance with the present invention (Sys. 3) and conventional techniques (Sys. 2 and Sys. 3) is small. However, when the normalized Doppler frequency is high, that is, in case of (b) and (c) wherein a large amount of the ICI is generated, the ICI cancellation technique in accordance with the present invention (Sys. 3) shows improved performance compared to the conventional techniques (Sys. 2 and Sys. 3). Particularly, since the ICI is a main factor of a noise when E_b/No (signal energy to noise power spectral density ratio) is large, the system in accordance with the present invention (Sys. 3) which effectively removes the ICI provides a much higher performance compared to the conventional techniques (Sys. 2 and Sys. 3) . As shown, when E_b/N₀ is 35dB, a BER (bit error rate) of the system in accordance with the present invention (Sys. 3) is improved 10^"1 times compared to that of the conventional ICI self-cancellation technique (Sys. 2) .

It will be described below that the ICI cancellation technique in accordance with the present invention has an improved effect compared to the conventional ICI self- cancellation technique when N=4.

When N=4, S_E, S₀, Pici and Q₀ may be expressed as equation 15.

[Equation 15]

0 1 0 0

So- 0 0 0 1

0 -0.5-0.5; -0.5 -0.5 + 0.5;

-0.5 + 0.5; 0 -0.5-0.5; -0.5

"/CI ~ -0.5 -0.5 + 0.5; 0 -0.5-0.5;

-0.5-0.5; -0.5 -0.5 + 0.5; 0

-0.25-0.25; -0.25 + 0.25;

Qo = -0.25 + 0.25; -0.25-0.25;

Two elements X_IN[O] and X_IN[I] of the input symbol vector Xi_N are assumed as equation 16. [Equation 16]

X_IN[0] = l+j

In this case, outputs X[O], X[I], X[2] and X[3] of the ICI cancellation decoder 230, outputs X [0] , X [1] , X [2] and X[3] of the IFFT and outputs X[O], X[I], X[2] and X[3] of the guard interval adder are shown in tables 1, 2 and 3, respectively.

[Table 1]

X[4] -X[2]=-l+j

[Table 2]

[Table 3;

The channel is a 2-tap time-varying channel, and input x[n] and output y[n] of the channel are assumed to satisfy equation 17 and table 4.

[Equation 17] y[n] = h_o[n]x[n] + hi[n]x[n-l]

[Table 4]

In this case, inputs x[0], x[l], x[2], x[3] and x[4] of the guard interval remover and inputs x[0], x[l], x[2] and x [3] of the FFT are shown in table 5 and 6, respectively. A result of a comparison between the two elements X_IN[0] and X_1N[I] of the input symbol vector X_1N, and two elements Xouτ[0] and Xouτ.1] of ^an output symbol vector X_0UT that are obtained by passing through the FFT and the ICI cancellation decoder, i.e. that are obtained by being subjected to the FFT, the 1-tap equalization and the ICI cancellation decoding is shown in table 7. [Table 5]

[Table 6]

[Table 7]

As shown in table 7, the embodiment in accordance with the present invention provides more accurate result than the conventional art.

Claims

[CLAIMS]

1. An OFDM transmitter comprising an ICI cancellation encoder, an IFFT and a guard interval adder, wherein the ICI cancellation encoder comprises: a redundant symbol generator for generating a redundant symbol vector obtained by multiplying an input symbol vector to one of Q₀ and Q_E; and a multiplexer for multiplexing the input symbol vector and the redundant symbol vector to generate an encoded symbol vector to be transmitted to the IFFT, where Q₀ -

SQPICISO , an element (m, k) of P_ICi is expressed as

P_m,k=^∑(n-(N-l)/2)e-^j2m (m-k)I N

S_E is expres sed as

S₀ is expres sed as

0 1 0 0 0 0 0

0 0 0 1 0 0 ^{■ ■} • 0

So = 0 0 0 0 0 1 0

0 0 0 0 0 0 ^{• • ■} 1

2. The OFDM transmitter in accordance with claim 1, wherein the redundant symbol generator comprises a look-up table for storing one of the Q₀ and Q_E.

3. The OFDM transmitter in accordance with claim 1, wherein the multiplexer maps symbols included in the input symbol vector to even symbols of the encoded symbol vector, and maps symbols included in the redundant symbol vector to odd symbols of the encoded symbol vector when the redundant symbol generator generates the redundant symbol vector obtained by multiplying the input symbol vector to the Q₀.

4. The OFDM transmitter in accordance with claim 1, wherein the multiplexer maps symbols included in the input symbol vector to odd symbols of the encoded symbol vector, and maps symbols included in the redundant symbol vector to even symbols of the encoded symbol vector when the redundant symbol generator generates the redundant symbol vector obtained by multiplying the input symbol vector to the Q_E .

5. The OFDM transmitter in accordance with claim 1, wherein the guard interval adder adds a guard interval using a ZP method or a CP method.

6. An OFDM transmitter comprising an ICI cancellation encoder, an IFFT and a guard interval adder, wherein the ICI cancellation encoder receives an input symbol vector X_IN, and outputs an encoded symbol vector X corresponding to S_E ^TX_IN + S_O ^TQ_OX_IN to the IFFT, where S_E is expressed as

1 0 0 0 0 0 0

0 0 1 0 0 ^■ • • 0 0 S_£ = 0 0 0 0 1 0 0

0 0 0 0 0 • • • 1 0

S₀ is expressed as

Q₀ is expressed as

Q₀ = - ( S_EP_IciS₀ ^T) ^~1S_EP_IciS_E ^T, and an element (m, k) of P_ICI is expressed as

P_m,k=^∑(n-(N-\)/2)e-^j2™^im-^k)<N .

7. An OFDM transmitter comprising an ICI cancellation encoder, an IFFT and a guard interval adder, wherein the ICI cancellation encoder receives an input symbol vector X_1N , and output s an encoded symbol vector X corresponding to S_O ^TX_IN + S_E ^TQ_EX_IN to the I FFT , where S_E is expressed as

S₀ is expressed as

Q_E i s expres sed as

Q_E = - - 1 « ( S₀P₁CISE¹ ) ^{" 1}SOPICISO , and an element (m, k) of P_ICi is expressed as

P_mk=^∑(n-(N-l)/2)e-^j2^-^k)/N .

8. An OFDM system comprising an OFDM transmitter in accordance with one of claims 1 through 7, and an OFDM receiver, wherein the OFDM receiver comprises a guard interval remover, a FFT and an ICI cancellation decoder, the ICI cancellation decoder receiving a FFT output vector outputted from the FFT so as to output elements corresponding to an input symbol vector of even elements and odd elements of the FFT output vector.

9. An encoding method comprising steps of:

(a) preparing an encoding matrix;

(b) generating a redundant symbol vector obtained by- multiplying the encoding matrix to an input symbol vector; and

(c) multiplexing the input symbol vector and the redundant symbol vector to generate an encoded symbol vector, where the encoding matrix is one of Q₀ and Q_E expressed as

Qo ⁼ "(SEPICISO ) SEPICISE I QE ^{= ~} (SOPICISE ) SQPICISO , an element (m, k) of P_ICi is expressed as

_Pmk=^∑(n-(N-\)/2)e-^j2m( m-k)IN

S_E is expressed as

S₀ is expressed as

10. The method in accordance with claim 9, wherein the multiplexer maps symbols included in the input symbol vector to even symbols of the encoded symbol vector, and maps symbols included in the redundant symbol vector to odd symbols of the encoded symbol vector when the redundant symbol generator generates the redundant symbol vector obtained by multiplying the input symbol vector to the Q₀ in the step (c) .

11. The method in accordance with claim 9, wherein the multiplexer maps symbols included in the input symbol vector to odd symbols of the encoded symbol vector, and maps symbols included in the redundant symbol vector to even symbols of the encoded symbol vector when the redundant symbol generator generates the redundant symbol vector obtained by multiplying the input symbol vector to the Q_E in the step (c) .