OFDM Transmitter and OFDM Receiver

Abstract

To suppress interfering electric power to OFDM signals and reduce a calculation volume to a practical level for the case where OP technology is utilized.SOLUTION: There is provided, an OFDM transmitter for generating an OFDM signal, from D information bit sequences and transmitting the OFDM signal. The OFDM transmitter comprises: a constellation modulation unit 11 for generating data symbols mapped to a constellation from the information bit sequences; a precoding processing unit 12 for multiplying an orthogonal precoder matrix to the data symbols outputted from the constellation modulation unit 11; an inverse Fourier transform unit 14 for applying inverse Fourier transformation to the modulated symbols outputted from the precoding processing unit 12 and thereby generating a baseband OFDM signal in which the D information bit sequences are multiplexed in a frequency direction; a serial-parallel conversion unit 16 for serial-parallel converting the baseband OFDM signal; and a transmission unit 17 for frequency converting to the serial-parallel converted OFDM signal into a signal in an RF band and transmitting the frequency converted signal.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to an OFDM transmitter that transmits an orthogonal frequency division multiplexing (OFDM) signal and an OFDM receiver that receives an OFDM signal. In particular, the present invention relates to an OFDM transmitter and an OFDM receiver suitable for accommodating more wireless systems within a frequency band by suppressing high interference power generated by an OFDM signal in an adjacent band.

Background Art

[0002] As a method for transmitting a digital signal, a modulation method conventionally called an orthogonal frequency division multiplexing (OFDM) method has been applied. In this OFDM method, a large number of orthogonal subcarriers are provided within a transmission band, data is assigned to the amplitude and phase of each subcarrier, and digital modulation is performed by PSK (Phase Shift Keying) or QAM (Quadrature Amplitude Modulation).

[0003] In this OFDM method, since the transmission band is divided by a large number of subcarriers, the band per subcarrier becomes narrow and the modulation rate does not become slow, but the total transmission rate has the characteristic of being the same as that of the conventional modulation method. In addition, the OFDM method has the characteristic that the symbol rate becomes slow because a large number of subcarriers are transmitted in parallel. For this reason, in this OFDM method, the relative time length of multipath with respect to the time length of a symbol can be shortened, and the resistance to a multipath transmission path can be enhanced. In addition, since data is assigned to a plurality of subcarriers in the OFDM method, an IFFT (Inverse Fast Fourier Transform) arithmetic circuit that performs an inverse Fourier transform at the time of modulation and an FFT (Fast Fourier Transform) arithmetic circuit that performs a Fourier transform at the time of demodulation are used, so that a transmission and reception circuit can be configured.

[0004] When transmitting information using such an OFDM system, it is necessary to suppress the interference power to the OFDM signal in order to prevent interference from adjacent channels. As such an interference power suppression technique, the OP (Orthogonal Precoding) technique has been conventionally proposed (see, for example, Non-Patent Document 1). This OP technique has an advantage in terms of the error rate compared to the interference power suppression method using a filter or a window function, and is also an excellent method having backward compatibility with a conventionally implemented OFDM system.

Prior Art Documents

Non-Patent Documents

[0005]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0006] However, the OP technology described in Non-Patent Document 1 has problems with expressing complex matrices for precoding, which results in a large amount of calculation, and therefore has problems in terms of implementation.Furthermore, the OP technology described in Non-Patent Document 1 also requires an increased amount of memory to store matrices, which makes it difficult to adapt to various environments by storing multiple matrices.

[0007] Therefore, the present invention has been devised in consideration of the above-mentioned problems, and its object is to provide an OFDM transmitter that transmits orthogonal frequency division multiplexing (OFDM) signals and an OFDM receiver that receives OFDM signals, which can suppress interference power to OFDM signals in particular, reduce the amount of calculation to a practical level when OP technology is used, and can accommodate more wireless systems within a frequency band by significantly reducing the memory required for matrix storage. [Means for solving the problem]

[0008] An OFDM transmission device according to a first aspect of the present invention is an OFDM transmission device that generates an orthogonal frequency division multiplexing (OFDM) signal from D information bit sequences and transmits the signal, the OFDM transmission device comprising: a constellation modulation unit that generates data symbols mapped to a constellation from the information bit sequence; a precoding processing unit that multiplies the data symbols output from the constellation modulation unit by an orthogonal precoder matrix P; an inverse Fourier transform unit that performs an inverse Fourier transform on the modulation symbols output from the precoding processing unit to generate a baseband OFDM signal in which the D information bit sequences are multiplexed in the frequency direction; a serial-to-parallel conversion unit that performs serial-to-parallel conversion on the baseband OFDM signal; and a transmission unit that frequency-converts the serial-to-parallel converted OFDM signal to an RF band signal and transmits the signal, wherein the precoding processing unit multiplies by an orthogonal precoder matrix P that satisfies the following equation: P×P H =I D P=φ×PB BP B =O Here, φ : Diagonal and unitary complex diagonal matrix P B : Real matrix of size K×D B: Real matrix of size K×(K - D) I D : D - th order identity matrix 0: Zero matrix of size (K - D)×K K: Number of sub - carriers D: Number of information data

[0009] The OFDM transmitter according to the second invention, in the first invention, the precoding processing unit multiplies an orthogonal precoder matrix P including a unitary complex diagonal matrix φ and a real matrix P represented by the following formula. B It is characterized by multiplying the orthogonal precoder matrix P including the following. φ is a diagonal and unitary matrix P B =E D -ΛΠΛ D T Here, E D : The last D rows of the K - th order identity matrix Λ: Real lower trapezoidal matrix of size K×(K - D) Λ D : The last D rows of Λ Π: Real diagonal matrix of size (K - D)×(K - D)

[0010] The OFDM receiver according to the third invention is an OFDM receiver that receives an orthogonal frequency - division multiplexing (OFDM) signal, a receiving unit that frequency - converts the received RF - band signal into a base - band OFDM signal, a serial - to - parallel conversion unit that performs serial - to - parallel conversion on the OFDM signal frequency - converted by the receiving unit, a Fourier - transform unit that performs Fourier - transform processing on the serially - to - parallel - converted OFDM signal, and an orthogonal post - decoder matrix P on the equalization symbol output from the Fourier - transform unit HA post - decoding processing unit that multiplies, and a constellation demodulation unit that generates a series of D information bits from the demodulated symbols output from the post - decoding processing unit. The post - decoding processing unit multiplies by an orthogonal post - decoder matrix P that satisfies the following equation H An OFDM receiver characterized by multiplying. P×P H =I D P = φ×P B BP B =O Here φ : A diagonal and unitary complex diagonal matrix B: A real - valued matrix P B : A real - valued matrix of size K×D B: A real - valued matrix of size K×(K - D) I D : The D - th identity matrix 0: A zero matrix of size (K - D)×K K: The number of sub - carriers D: The number of information data

[0011] The OFDM receiver according to the fourth invention, in the third invention, is characterized in that the post - decoding processing unit multiplies by an orthogonal post - decoder matrix PH including a real - valued matrix PB consisting of the following equation. φ is a diagonal and unitary matrix P B =E D -ΛΠΛ D T Here E D : The last D rows of the K - th identity matrix Λ: A real - valued lower trapezoidal matrix of size K×(K - D) Λ D : The last D rows of Λ Π: A real - valued diagonal matrix of size (K - D)×(K - D)

Advantages of the Invention

[0012] According to the present invention having the above-described configuration, it can be seen that the interference power in the targeted band can be effectively suppressed by forming the notch. It is also shown that the interference power with different bandwidths can be suppressed. By appropriately generating and selecting the matrix used in the precoding process, effective interference power suppression is possible even in wireless systems with different bandwidths.

[0013] Further, according to the present invention, when using the OP technology, the amount of calculation can be reduced to a practical level, and by significantly reducing the memory required for matrix storage, it becomes possible to accommodate more wireless systems within the frequency band.

Brief Description of the Drawings

[0014]

Figure 1

Figure 2

Figure 3

Figure 4

Embodiments for Carrying Out the Invention

[0015] FIG. 1 is a block diagram showing the configuration of an OFDM (Orthogonal Frequency Division Multiplexing) transmitter 1 to which the present invention is applied.

[0016] This OFDM transmitter 1 has a constellation modulation unit 11, a precoding processing unit 12, a subcarrier mapping unit 13, an inverse Fourier transform unit 14, a CP insertion unit 15, a serial-to-parallel conversion unit 16, and a transmission unit 17 connected in sequence.

[0017] The constellation modulation unit 11 performs constellation modulation on the input D information bit sequences according to a predetermined data modulation method such as QPSK modulation. As a result, in this constellation modulation unit 11, data symbols d i mapped to the constellation are generated from the information bit sequences. The constellation modulation unit 11 outputs the generated data symbols d i .

[0018] The precoding processing unit 12 multiplies the data symbols d i output from the constellation modulation unit 11 by the orthogonal precoder matrix P. Details of the orthogonal precoder matrix P to be multiplied will be described in detail later. The precoding processing unit 12 outputs the modulation symbol c i (= P×d i ) to the subcarrier mapping unit 13.

[0019] The subcarrier mapping unit 13 maps the precoded modulation symbol c i to the subcarriers used for transmission.

[0020] The inverse Fourier transform unit 14 performs IFFT (inverse Fourier transform) processing and synthesizes the modulation symbols as subcarrier samples input in parallel from the subcarrier mapping unit 13. Thereby, the inverse Fourier transform unit 14 can generate a baseband OFDM signal in which D information bit sequences are multiplexed in the frequency direction.

[0021] The CP insertion unit 15 inserts, as a cyclic prefix (CP), a length Tc from the end of the OFDM signal to the head of the OFDM signal so that the OFDM signal becomes cyclically longer by a predetermined length Tc.

[0022] The serial-to-parallel conversion unit 16 performs serial-to-parallel conversion on the OFDM signal output from the CP insertion unit 15.

[0023] The transmission unit 17 performs frequency conversion on the OFDM signal output from the serial-to-parallel conversion unit 16 into an RF-band signal, amplifies it as necessary, and transmits it via an antenna.

[0024] FIG. 2 is a block diagram showing the configuration of the OFDM receiver 2 to which the present invention is applied.

[0025] This OFDM receiver 2 has a constellation demodulation unit 21, a post-decoding processing unit 22, a sub-carrier demapping unit 23, a Fourier transform unit 24, a CP removal unit 25, a serial-to-parallel conversion unit 26, and a reception unit 27 connected in sequence.

[0026] The reception unit 27 frequency-converts the RF-band signal received via the antenna into a baseband OFDM signal.

[0027] The serial-to-parallel conversion unit 26 performs serial-to-parallel conversion on the OFDM signal output from the reception unit 27.

[0028] The CP removal unit 25 removes the CP inserted into the OFDM signal.

[0029] The Fourier transform unit 24 performs Fourier transform processing on the OFDM signal output from the CP removal unit 25. At this time, in the Fourier transform unit 24, channel equalization processing may be further performed on this OFDM signal.

[0030] The sub-carrier demapping unit 23 performs a process of demapping sub-carriers on the equalized symbol subjected to Fourier transform, thereby obtaining an equivalent symbol q i to obtain.

[0031] The post-decoding processing unit 22 multiplies the equalized symbol q i output from the sub-carrier demapping unit 23 by an orthogonal post-decoder matrix P H The post-decoding processing unit 22 multiplies the demodulated symbol r i(=P H ×q i ) is output to the constellation demodulation unit 21.

[0032] The constellation demodulation unit 21 performs constellation demodulation on the demodulated symbol r output from the post-decoding processing unit 22 i in accordance with a predetermined data modulation method such as QPSK modulation. Through this constellation demodulation, the constellation demodulation unit 21 generates a series of D information bits from the demodulated symbol r i .

[0033] The OFDM transmitter 1 and the OFDM receiver 2 having the above-described configuration can be similarly realized only by newly adding the precoding processing unit 12 and the post-decoding processing unit 22 to a conventional OFDM system that performs CP, frequency-domain equivalence, etc.

[0034] Next, the orthogonal precoder matrix P for multiplying the data symbol d i will be described in the precoding processing unit 12.

[0035] The precoding processing unit 12 multiplies by the orthogonal precoder matrix P that satisfies the following equation. Also, the post-decoding processing unit 22 multiplies by the orthogonal post-decoder matrix P H . P×P H =I D P = φ×P B BP B =O Here, φ : Diagonal and unitary complex diagonal matrix P B : Real matrix of size K×D B: Real matrix of size K×(K - D) I D : D-dimensional identity matrix 0: Zero matrix of size (K - D)×K K: Number of subcarriers D: Number of information data

[0036] The number of sub - carriers K mentioned here is the number of sub - carriers that are mapped in the sub - carrier mapping unit 13 or demapped in the sub - carrier demapping unit 23.

[0037] The OFDM receiver 2 performs post - decoding that is reversible with respect to the pre - coding executed on the OFDM transmitter 1 side. That is, the OFDM receiver 2 can achieve ideal error rate characteristics by performing an inverse operation with low computational complexity.

[0038] Any orthogonal precoder matrix P and orthogonal post - decoder matrix P that satisfy the above - mentioned conditions H may be used.

[0039] At this time, the pre - coding processing unit 12 may multiply by an orthogonal precoder matrix P including a unitary complex diagonal matrix φ and a real - number matrix P B satisfying the following formula. The post - decoding processing unit 22 may multiply by an orthogonal post - decoder matrix P B including a unitary complex diagonal matrix φ and a real - number matrix P H satisfying the following formula. φ is a diagonal and unitary matrix P B =E D -ΛΠΛ D T Here,[[]] E D : The last D rows of the K - th identity matrix Λ: A real - number lower trapezoidal matrix of size K×(K - D) Λ D : The last D rows of Λ Π: A real - number diagonal matrix of size (K - D)×(K - D)

[0040] According to the OFDM transmitter 1 and the OFDM receiver 2 having the above-described configuration, since a linear spectral precoding (SP) process with a low computational load can be performed, the interference power with respect to an adjacent band can be significantly suppressed.

[0041] Fig. 3(a) shows the interference power suppression effect at a system bandwidth of 3.0 MHz, and Fig. 3(b) similarly shows the interference power suppression effect at a system bandwidth of 10 MHz. In both cases, the horizontal axis is the offset frequency (MHz), and the vertical axis is the power spectral density (dBm / Hz). In Fig. 3, a comparison is made between normal OFDM, OFDM in related research to which a window function is applied, and the example of the present invention. Also, reference spectral mask of 55 dB from flat top in the figure means a 55-dB spectral mask provided at both ends of the transmission band with reference to the average power density within the system band.

[0042] As shown in Fig. 3, it can be seen that the interference power in the band targeted for notch formation through the present invention can be effectively suppressed. It is also shown that interference power with different bandwidths can be suppressed. By appropriately generating and selecting the matrix (precoder P) used in the precoding process, effective interference power suppression is possible even in wireless systems with different bandwidths.

[0043] Further, according to the present invention, as shown in Fig. 4, the required memory amount (real number amount) is DM + M(M + 1) / 2 + 2(D + M), and the computational load (number of real number multiplications) is 4DM + M(M + 1) + 4(D + M). Here, M is the number of notches. It is shown that this represents a reduction in the maximum order term coefficient by about half compared to the Compact WY representation base of Non-Patent Document 2, achieving a significant reduction in the computational load.

[0044] Post-decoding reversible with respect to the precoding executed on the OFDM transmitter 1 side is performed on the OFDM receiver 2 side. That is, the OFDM receiver 2 can achieve ideal error rate characteristics by performing an inverse operation with a low computational load.

[0045] Hereinafter, the calculation basis of the orthogonal precoder matrix P and the orthogonal post-decoder matrix P described above in the present invention will be described. H will be described.

[0046] The OFDM transmission signal in the complex equivalent baseband in the discrete time domain in the digital OFDM modulation method is represented in the form of block transmission as follows.

[0047]

Equation

[0048] Here, τ is the discrete time, S i [τ] is the i-th OFDM symbol, N is the OFDM symbol sample period, and L is the guard interval (GI) sample length. When inserting a cyclic prefix (CP) into the GI, S i [τ] is represented in the form of an inverse discrete Fourier transform (IDFT) of the following equation.

[0049]

Equation

[0050] Here, Σ is the summation operator, k ∈ {k0, k1,..., kK-1} and K is the number of subcarriers, ci,k ∈ C is the modulation symbol, e is the Napier number, j is the imaginary unit, π is the pi, and I[τ] is a rectangular window function such that I[τ]=1 for τ=-L, -L+1,..., N-1 and I[τ]=0 for other τ, without impairing the effective length of the CP. The calculation of equation (2) can be efficiently implemented by the FFT algorithm, and the number of FFT points coincides with N. The power spectral density (PSD) of equation (1) is represented as follows.

[0051]

Equation

[0052] Here, let f be the frequency and T be the OFDM symbol period, and the angular frequency ω = 2πfT / N, where Ns = N + L. Also, Pi(ω) is the power spectrum of the i-th OFDM symbol S i [τ], and is given by the following equation (4).

[0053]

Equation

[0054] Also, the following equation (5) is the Fourier transform of S i [τ], where F is the Fourier transform operator.

[0055]

Equation

[0056] By substituting equation (1) into equation (5), the following equation (6) can be obtained.

[0057]

Equation

Equation

Equation

[0058]

Equation

[0059] Also, equation (7) can be transformed as follows.

[0060]

Equation

[0061] Here, Ns = N + L. This equation (8) can be summarized by the following equations (9) and (10).

[0062] [Number] (9)

[0063] Here, the following equation (10) represents the cardinal sign.

[0064] [Number] (10)

[0065] Next, consider the pre-coding represented by the following equation (11).

[0066] [Number] (11)

[0067] Here, P ∈ C K×D is a matrix called a pre-coder, and d i = [d i,0 d i,1 ... d i , D-1 T is the data symbol for transmitting D information symbols {d i,l}. Also, the process of restoring d D-1 l=0 from cis defined as post-decoding. When the orthogonality of the following equation is satisfied, equation (11) is called orthogonal pre-coding, and P is called an orthogonal pre-coder. i from c i to d

[0068] [Number] (12)

[0069] Here, (·) H is an operator representing the complex conjugate transpose of (·), and I m ∈ {0} m×m is the identity matrix. From equations (11) and (12), the following equation holds.

[0070]

Number

[0071] From equation (13), for the orthogonal precoding shown in equation (11), the multiplication by P H becomes post - decoding. Therefore, at the receiving side, post - decoding is applied to the symbol q i ∈ C K×1 . That is, the transmitted data d i can be restored by calculating the following equation (14).

[0072]

Number

[0073] By calculating this (14), the transmitted data d i can be restored. By appropriately determining P, the characteristics of the OFDM signal can be improved. In particular, the method of using P to suppress the out - of - band emission (OOBE) of the OFDM signal and improve the spectral characteristics is called spectral precoding. Assuming that the constraint conditions for c i to suppress OOBE are represented by the following M - th order linear equation.

[0074]

Number

[0075] Here, 0 m ∈ {0} m×1 represents the zero vector. With the orthogonal precoding represented by equation (11), for any di For equation (15) to hold, it is a necessary and sufficient condition that the following equation holds.

[0076]

Number

Number

[0077] The present invention derives a more efficient Trapezoidal Block Reflector (TBR) representation for the orthogonal factors of a matrix than the conventional compact WY representation, and aims to suppress the OOBE of an OFDM signal using an orthogonal precoder based on this. Here, focusing on equation (6), for M corner frequencies {ω0, ω, ω1,..., ω M-1}, consider the following equation being satisfied for any i.

[0078]

Number

[0079] From equation (17), A for the linear equation of equation (15) can be determined by the following equation.

[0080]

Number

[0081] Regarding equation (18), with m and l as the indices of the rows and columns of A respectively, [A] m,l = a kl (ω m ) and focusing on equation (9), perform matrix decomposition as follows.

[0082]

Number

Number

Number

[0083]

Number

[0084]

Number

[0085] Real matrix B T ∈R K×M Define the TBR representation, which is more efficient than the conventional compact WY representation, for the orthogonal factor of the real matrix B. First, the thin QR decomposition of B T is expressed as follows.

Number

[0086]

Number

Number

Number

Number

Number

[0087] The square matrix Q of Equation (23) M,MThe singular value decomposition for is expressed as in equation (24).

[0088]

Number

[0089] Here, U ∈ R M×M and V ∈ R M×M are both orthogonal matrices, and Σ is a diagonal matrix with non - negative values arranged in the diagonal components. From equation (24), the real symmetric matrix of equation (25) is obtained.

[0090]

Number

[0091] The modified Cholesky decomposition for Z in equation (25) is expressed as in the following equation (26).

[0092]

Number

[0093] Here, Π ∈ R M×M is a diagonal matrix, Δ ∈ R M×M is a lower triangular matrix with all diagonal components equal to 1. Define the following as the TBR representation of the orthogonal factor for B T

[0094]

Number

[0095] Here, equation (28) is a lower trapezoidal matrix with all diagonal components equal to 1.

[0096]

Number

[0097] Q B ​Since it satisfies the following equation (29), B T is an orthogonal factor of

[0098]

Number

[0099] The real - type storage required for storing the TBR representation is only KM - 1 / 2M(M - 1) for storing Λ and Π. This is 1 / 2M(M - 1) less than the K 2 required when directly storing QB. Furthermore, for B T ∈R K×M , it is also less than the KM real - type storage required for the block reflector representation of the orthogonal factor and the compact WY representation adopted in the QR decomposition routine geqrt of the practical linear algebra library LAPACK. The ratio of the storage amount required for the TBR representation to that for the compact WY representation is e = 1 - 1 / 2(M - 1) / K, which indicates the storage reduction rate when using the TBR representation. When M = K (i.e., B is a square matrix), e = 0.5+1 / 2K, and it has been shown that when K is large enough, the required storage amount is approximately halved compared to the compact WY representation.

[0100] In the present invention, the following orthogonal precoder based on the TBR representation defined by equation (27) is used.

[0101]

Number

[0102] Here, P B satisfies the following equation (31).

[0103]

Number

[0104] Also, the expression (32) is a matrix for extracting the last D columns by multiplying from the right.

Number

[0105] Also, E D satisfies the following expression (33).

Number

[0106] Also, the following expression (34) is a matrix obtained by extracting the last D rows of the lower trapezoidal matrix L of the expression (28).

Number

[0107] φ in the expression (19) and Q in the expression (27) B both become unitary matrices. Also, since the expression (33) holds, the expression (30) satisfies the expression (12). Further, from the expression (29), the expression (30) also satisfies the expression (16).

[0108] The number of real multiplications of the real matrix PB of the expression (31) for a complex vector is 2MD + 2[MK - 1 / 2M(M - 1)] = 4MD + M(M + 1) by performing the multiplications in right-associative order. Further, the number of real multiplications of the complex diagonal matrix φ of the expression (19) for the complex vector that is its output is 4K = 4D + 4M. Therefore, the number of real multiplications required for the precoding of the expression (11) or the post-decoding of the expression (14) when using the orthogonal precoder of the expression (30) is both a total of c = 4(M + 1)D + M(M + 5). This is smaller than the number of real multiplications c0 = 8MD + 4M 2 required by the method of Non-Patent Document 2 by c - c0 = 4(M - 1)D + M(3M - 5) times.

Explanation of Signs

[0109] 1 Transmitting device 2 Receiving device 11 Constellation Modulation Unit 12 Pre - coding Processing Unit 13 Sub - carrier Mapping Unit 14 Inverse Fourier Transform Unit 15 CP Insertion Unit 16 Serial - to - Parallel Conversion Unit 17 Transmission Unit 21 Constellation Demodulation Unit 22 Post - decoding Processing Unit 23 Sub - carrier Demapping Unit 24 Fourier Transform Unit 25 CP Removal Unit 26 Parallel - to - Serial Conversion Unit 27 Reception Unit

Claims

1. In an OFDM transmitter that generates and transmits an orthogonal frequency division multiplexing (OFDM) signal from D information bit sequences, a constellation modulation unit that generates data symbols mapped to a constellation from the information bit sequences; a precoding processing unit that multiplies the data symbols output from the constellation modulation unit by an orthogonal precoder matrix P; an inverse Fourier transform unit that generates a baseband OFDM signal in which D information bit sequences are multiplexed in the frequency direction by performing an inverse Fourier transform on the modulation symbols output from the precoding processing unit; a serial-to-parallel conversion unit that performs serial-to-parallel conversion on the baseband OFDM signal; a transmission unit that frequency-converts the serially-parallel converted OFDM signal into an RF-band signal and transmits it, wherein the precoding processing unit multiplies by an orthogonal precoder matrix P that satisfies the following equation, characterized OFDM transmitter. P × P H = I D P = φ × P B BP B = O Here, φ: a diagonal and unitary complex diagonal matrix P B : A real matrix of size K×D B: a real matrix of size K×(K−D) I D : D-th order identity matrix 0: a zero matrix of size (K−D)×K K: the number of subcarriers D: the number of information data

2. The pre-coding processing unit multiplies an orthogonal pre-coder matrix P including a unitary complex diagonal matrix φ having the following formula and a real matrix P B The OFDM transmission apparatus according to claim 1, characterized by multiplying an orthogonal pre-coder matrix P including the above. φ is a diagonal and unitary matrix P B = E D - ΛΠΛ D T Here, E D : The last D rows of the K-th identity matrix Λ: a real lower trapezoidal matrix of size K×(K−D) Λ D : The last D lines of Λ Π: a real diagonal matrix of size (K−D)×(K−D)

3. In an OFDM receiver that receives an orthogonal frequency division multiplexing (OFDM) signal, a receiving unit that frequency-converts the received RF-band signal into a baseband OFDM signal; a parallel-to-serial conversion unit that performs parallel-to-serial conversion on the OFDM signal frequency-converted by the receiving unit; a Fourier transform unit that performs Fourier transform processing on the parallel-to-serial converted OFDM signal; A post-decoding processing unit that multiplies the equalization symbol output from the Fourier transform unit by an orthogonal post-decoder matrix P H and a constellation demodulation unit that generates D information bit sequences from the demodulation symbols output from the post-decoding processing unit, The post-decoding processing unit multiplies an orthogonal post-decoder matrix P defined by the following equation H This is an OFDM receiver characterized by the above. P × P H = I D P = φ × P B BP B =O where φ: a diagonal and unitary complex diagonal matrix B: a real matrix P B : A real matrix of size K×D B: a real matrix of size K×(K−D) I D : D-th unit matrix 0: a zero matrix of size (K−D)×K K: the number of subcarriers D: the number of information data

4. The post-decoding processing unit multiplies the orthogonal post-decoder matrix P including the real number matrix P represented by the following formula B The OFDM receiver according to claim 3, characterized by multiplying H by the orthogonal post-decoder matrix P φ is a diagonal and unitary matrix P B = E D - ΛΠΛ D T Here, E D : The last D rows of the K-th identity matrix Λ: a real lower trapezoidal matrix of size K×(K−D) Λ D : The last D lines of Λ Π: a real diagonal matrix of size (K−D)×(K−D)

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