JP2008306605A - Apparatus and method for separating mixed signal, and device and method for ofdm reception - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a mixed signal separating apparatus capable of solving a problem of component permutation or scale indetermination that may occur when independent component analysis (ICA) is applied. <P>SOLUTION: A mixed symbol is separated by a separate matrix W obtained by ICA and a separate symbol u is obtained. For components of the separate symbol u, a vector in which only a k<SP>th</SP>component u<SB>k</SB>is kept as it is while the other components are made into "0", is multiplied by an inverse matrix W<SP>-1</SP>, thereby creating a divided vector ξ<SB>k</SB>. An order l(k) of a maximum component in the divided vector ξ<SB>k</SB>is defined as the order of the divided vector ξ<SB>k</SB>, and the divided vector is permutated, so that component permutation caused by ICA is calibrated. Furthermore, since each divided vector ξ<SB>k</SB>has no scale indetermination, the problem of scale indetermination caused by ICA is concurrently solved. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a reception technique in an Orthogonal Frequency Division Multiplexing (OFDM) communication system, and more particularly to a reception technique for estimating an unknown channel interference state and a transmission symbol by an independent component analysis method.

  In recent years, OFDM communication systems are used in a wide range of fields such as wireless LAN, terrestrial digital broadcasting, and power line carrier communications, and are also attracting attention as technologies for realizing next-generation mobile communications.

  OFDM uses a large number of orthogonal carrier waves (subcarriers) so that the phase of the signal wave to be modulated is orthogonal between adjacent subcarriers, and the frequency bands are effectively used by partially overlapping the subcarrier bands. It is a communication method.

  Fig. 1 shows the basic configuration of an OFDM communication system. In FIG. 1, the OFDM communication system includes an OFDM transmitter 100 and an OFDM receiver 120, and the two are coupled by a communication channel 140.

  The OFDM transmitter 100 includes an encoder 101, an interleaver 102, a mapper 103, a serial-parallel converter 104, an inverse discrete Fourier transformer 105, a parallel-serial converter 106, a digital / analog converter 107, a low-pass filter 108, and a carrier wave generator 109. And an up-converter 110.

  In OFDM transmitter 100, first, in order to enable error correction for a random error, encoder 101 encodes data to be transmitted. Next, in order to enable error correction for the burst error, the interleaver 102 replaces the transmission bits so that adjacent bits of the transmission bit string before encoding are separated as much as possible in the transmission bit string after encoding. Is done. Next, in the mapper 103, the transmission bit string is associated with the complex symbol s [n] (n = 0, 1,...). Hereinafter, the complex symbol s [n] is referred to as “transmission symbol”, and the symbol time of each transmission symbol is referred to as Ts.

Next, in the serial-parallel converter 104, the transmission symbol s [n] is serial-parallel converted every N data blocks. Here, N is the total number of subcarriers. The time of the data block is denoted as m (m = 0, 1,...). In a data block at time m, a serial transmission symbol s [n] is expressed by the following equation for a parallel transmission vector s [m] = (s ₀ [m],..., S _N-1 [m]) ^T Is converted as follows.

Here, s _i [m] is a parallel transmission symbol, i = 1, 2,..., N−1 is a subcarrier number, and m is a data block number. The symbol time (hereinafter referred to as “OFDM symbol time”) T _p of each transmission symbol s _i [m] that is parallelized is represented by the following equation.

Also, the frequency f _i = i · f ₀ is assigned to the _i -th subcarrier. f ₀ is a subcarrier interval (bandwidth), and f ₀ = 1 / T _p = 1 / NT _s .

Next, the inverse discrete Fourier transformer 105 performs an inverse discrete Fourier transform on the transmission vector s [m]. s _i [m] = s (f _i ; m) (f _i = i · f ₀ ) as a function of frequency space, b _k [m] = b (t _k ; m) (t _k = k · T _s , k = 1,2, ..., N-1) as a function of time space,

とすると、b_k[m]は次式のように表される。

Then, b _k [m] is expressed as follows.

b _k [m] is called a “modulation symbol” and is a multi-carrier baseband OFDM signal

をt_k＝k・T_sで標本化して得られる標本値と同じである。

Is the same as the sample value obtained by sampling with t _k = k · T _s .

Next, in the parallel-serial converter 106, b _k [m] is parallel-serial converted as follows.

Next, the serialized modulation symbol b [n] is converted into an analog signal b (t _n ) (t _n = n · T _s ) by the digital / analog converter 107 and then passes through the low-pass filter 108. To do. For simplicity, if the low-pass filter 108 is an ideal linear filter, the modulated signal b (t _n ) is converted to a baseband OFDM signal s _Tm (t) by the low-pass filter 108 as follows: Is done.

ここで、h_t(t)はローパス・フィルタ108のインパルス応答を表す。

Here, h _t (t) represents the impulse response of the low-pass filter 108.

Finally, in the up-converter 110, the baseband OFDM signal s _Tm (t) is multiplied by the sine wave exp (j2πf _c t) output from the carrier oscillator 109 to obtain a passband OFDM signal as shown in the following equation. Up-converted to s _T (t) and transmitted to communication channel 140.

In the communication channel 140, the passband OFDM signal s _T (t) is affected by distortion and noise. Therefore, the received signal s _R (t) received by the OFDM receiver 120 is as follows.

ここで、h_c(t)はチャネルのインパルス応答、n(t)は負荷雑音である。負荷雑音は、白色でガウス分布に従うものとする。

Here, h _c (t) is the impulse response of the channel, and n (t) is the load noise. The load noise is white and follows a Gaussian distribution.

  The OFDM receiver 120 includes a carrier wave generator 121, a down converter 122, a low-pass filter 123, an analog-digital converter 124, a serial-parallel converter 125, an inverse discrete Fourier transformer 126, a parallel-serial converter 127, a demapper 128, A deinterleaver 129 and a decoder 130 are provided.

The received signal s _R (t) is first down-converted by the down converter 122 by the sine wave exp (−j2πf _c t) output from the carrier oscillator 121 to down-convert to the baseband OFDM signal s _Rm (t). Is done. Further, the transmission symbol s [n] is restored by the processing up to the low-pass filter 123, the analog-digital converter 124, the serial-parallel converter 125, the discrete Fourier transformer 126, and the parallel-serial converter 127, and then the demapper 128, The processing of the deinterleaver 129 and the decoder 130 is performed.

However, when the carrier frequency f _{c of} the sine wave exp (−j2πf _c t) output from the carrier oscillator 121 is shifted to f _c −Δf during the down conversion, the baseband OFDM signal s _Rm (t) is Distorted under the influence of the frequency offset Δf, and becomes the following formula (note that the phase offset does not affect the essential discussion about the estimation of the frequency offset thereafter, so it will not be considered here) .

  Therefore, the modulated signal c (t) after passing through the low-pass filter 123 is expressed by the following equation.

ここで、h_r(t)はローパス・フィルタ123のインパルス応答である。また、ノイズ項n’(t)は省略した。

Here, h _r (t) is an impulse response of the low-pass filter 123. Also, the noise term n ′ (t) is omitted.

  Due to the influence of the frequency offset Δf, the transmission symbol s [n] is not accurately restored even if the subsequent processing is performed, and the symbol error rate increases.

  Therefore, in order to evaluate the influence of the frequency offset Δf in more detail, the following inter-carrier interference problem (ICI: Inter Carrier Interference) is considered. In the following, for the sake of simplicity, there is no distortion in the transmission path including the low-pass filters 108 and 123 of the OFDM transmitter 100 and the OFDM receiver 120 and the communication channel 140, and symbol synchronization and sampling synchronization are appropriately performed. Assume that Also, the term due to the additional noise n (t) in the equation is omitted.

Based on the above assumption, the modulated signal c (t) is sampled as c (t _n ) = c [n] (t _n = n · T _s ), and further c [mN + k] → c _k [ Series] like [m]. Since it is assumed that there is no distortion in the transmission line, it may be assumed that the frequency response h (t) of the transmission line satisfies the Nyquist criterion, so h (t _k ) is expressed by the following equation.

Accordingly, the parallel received symbol c _k [m] is expressed by the following equation.

  Here, ε is a normalized frequency offset defined by the following equation.

c_k[m]＝c(t_k;m),x_l[m]＝x(f_l;m),f_l＝l・f₀,f₀＝1/T_p＝1/NT_sとすると、離散フーリエ変換器126において並列受信シンボルc_k[m]を離散フーリエ変換して得られる混合シンボルx_l[m]は、次式のように表される。

c _k [m] = c (t _k ; m), x _l [m] = x (f _l ; m), f _l = l · f ₀ , f ₀ = 1 / T _p = 1 / NT _s The mixed symbol x _l [m] obtained by performing the discrete Fourier transform on the parallel received symbol c _k [m] in the discrete Fourier transformer 126 is expressed by the following equation.

ここで、α_l,iは「干渉度」と呼び、次式で定義される未知の値である。

Here, α _{l, i} is called “interference degree” and is an unknown value defined by the following equation.

As can be seen from the equation (18), the mixed symbol x _l [m] includes not only the desired symbol amount α _ll · s _l [m] of the subcarrier but also interference components α _{l, i} from other subcarriers. S _i [m] (i ≠ l) is also included.

  Actually, from equations (18) and (19), if Δf = 0 (ε = 0),

となって、x_l[m]＝s_l[m]となる。一方、Δf≠0(ε≠0)の場合、α_l,i≠0(∀l,i)となるため、x_l[m]≠s_l[m]となる。従って、周波数オフセットがある場合には、混合シンボルx_l[m]は送信シンボルs_l[m]とは同じにならない。これが、OFDMシステムにおけるICI問題である。

Thus, x _l [m] = s _l [m]. On the other hand, when Δf ≠ 0 (ε ≠ 0), α _{l, i} ≠ 0 (∀l, i), so x _l [m] ≠ s _l [m]. Therefore, when there is a frequency offset, the mixed symbol x _l [m] is not the same as the transmitted symbol _sl [m]. This is the ICI problem in OFDM systems.

  By the way, when Expression (18) is expressed in matrix expression, it is expressed as the following expression.

ここで、ブロック番号を表す添字mは省略した。sは送信ベクトル、xは混合ベクトル、Aは「干渉行列」という。OFDM受信機120においては、混合ベクトルx及び干渉行列Aは未知である。

Here, the subscript m representing the block number is omitted. s is a transmission vector, x is a mixed vector, and A is an “interference matrix”. In the OFDM receiver 120, the mixed vector x and the interference matrix A are unknown.

  In such a situation, an independent component analysis (ICA) method is known as a method for estimating the interference matrix A. ICA is a method of separating an original signal source from only signals (mixed signals) observed by mixing when the signal sources are statistically independent. The signal separated by ICA is called “separated signal”.

  As a technique for estimating the interference matrix A by ICA in an OFDM receiver, the MIMO receivers described in Patent Documents 1 and 2 are known.

In ICA, (a) transmission symbols s _i (i = 0, ..., N-1) are statistically independent, (b) have an average value of 0, and (c) have a non-Gaussian probability distribution. Assume. Assuming in (a) is _{E [s 0, ..., s} N-1] = E [s 0] ... means E [s _N-1]. Assuming (b), generality will not be lost if DC removal processing is performed in advance. The assumption (c) means that the transmission symbol sequence s [n] is not a complete random sequence.

  Under this assumption, the separation matrix W is estimated so that each element of the separation vector u represented by the following equation is independent.

W＝A^-1であれば、u＝sとなり、干渉の除去された送信ベクトルを推定することができる。特許文献1には、この分離行列Wの推定に関して、自然勾配アルゴリズムを用いて解く方法、最尤推定アルゴリズムを用いて解く方法、Jutten and Heraultのアルゴリズムを用いて解く方法などが記載されている。尚、分離行列Wを推定するアルゴリズムとしては、そのほかにBell and Sejnowskiのアルゴリズム、Amari et. al.のアルゴリズム、Cardoso and Laheldのアルゴリズムなど、種々のアルゴリズムが考案されている(非特許文献1参照)。通常は、自然勾配アルゴリズムや最尤推定アルゴリズムを用いて解く方法がよく使用される。自然勾配アルゴリズムでは、分離行列Wは、次式のような逐次更新によって求められる。

If W = A− ¹ , u = s, and the transmission vector from which interference is removed can be estimated. Patent Document 1 describes a method of solving the separation matrix W using a natural gradient algorithm, a method of solving using a maximum likelihood estimation algorithm, a method of solving using a Jutten and Herault algorithm, and the like. In addition, various algorithms such as Bell and Sejnowski's algorithm, Amari et. Al. Algorithm, and Cardoso and Laheld algorithm have been devised as algorithms for estimating the separation matrix W (see Non-Patent Document 1). . Usually, a method of solving using a natural gradient algorithm or a maximum likelihood estimation algorithm is often used. In the natural gradient algorithm, the separation matrix W is obtained by sequential updating as in the following equation.

ここで、ηは更新係数である。F(x｜W(t))は推定関数と呼ばれ、任意の非線形可測関数φ(u)を用いて以下のように表される。

Here, η is an update coefficient. F (x | W (t)) is called an estimation function, and is expressed as follows using an arbitrary nonlinear measurable function φ (u).

ここで、E[・]は期待値、Iは単位行列、・^H は共役転置を表す。

Here, E [•] is an expected value, I is a unit matrix, and • ^H is a conjugate transpose.

  Assuming that the probability density function p (s) of the signal source is already known, the maximum likelihood estimation algorithm is applied to the estimation function F (x | W (t)) and is solved as follows: be able to.

JP 2006-186804 A JP 2006-191187 A Noboru Murata, “Introduction to Independent Component Analysis”, Tokyo Denki University Press, July 2004, pp. 66-104, pp. 144-150. Yuan Liu and Wasfy Mikhael, "A Blind Intercarrier Interference Cancellation Approach in Differential Modulation OFDM Communication Systems", Proc. IASTED International Conference on Circuits, Signals, and Systems, pp.178-181, 2004.

  However, even if the separation matrix W is obtained by the algorithm as described above and the separation vector u is estimated, the separation vector u is not necessarily equal to the transmission vector s due to ICA-specific component replacement and scale indefinite problems. .

  The component replacement problem is a problem that the i-th component of the separation vector u does not necessarily correspond to the i-th component of the transmission vector s, and the order of the components may be changed. Therefore, to emphasize that the components are replaced in the separation vector u, the components of the separation vector u are

のように、成分番号を表す添字のiにチルダ(tilde)を付けて表記し、

Like the subscript i indicating the component number, with a tilde (tilde),

と定義する(尚、以下の明細書中で式(35)をテキスト表記する場合には(i)~と記すことにする)。

(In the following specification, when formula (35) is expressed in text, it is written as (i) ~).

Supplementally, the separated symbol u _(i), which is the (i) -th component of the separated vector u, is one of N transmission symbols {s ₀ , s ₁ ,..., S _N-1 }. Although it corresponds exclusively, it is unknown which transmission symbol corresponds. That is, the set {u _{(0) ~} , u _{(1) ~} , ..., u _{(N-1) ~} } has a one _- to-one correspondence with the set {s ₀ , s ₁ , ..., s _N-1 } The specific correspondence of which corresponds to which is unknown.

In addition, the problem of indefinite scale is that even if the specific correspondence between the transmission symbol s _i and the separation symbol u _{(i) ~} can be specified,

のように送信シンボルs_iはd_i倍されて、しかもd_iとiとは独立に不規則な値をとるため、倍率(スケール)d_iが定まらない、という問題である。

Thus, the transmission symbol s _i is multiplied by d _i , and d _i and i take an irregular value independently, so that the magnification (scale) d _i is not determined.

That is, the estimated value of the separation matrix W does not necessarily converge to A- ¹ , but generally converges to W = PDA- ¹ . Here, the matrix D is a diagonal matrix for converting the scale, and is expressed as D = diag (d ₀ , d ₁ ,..., D _N-1 ). The matrix P is a permutation matrix, with one “1” in each row and column element, and the other components being zero.

  In Patent Document 1, in order to solve this problem of component replacement, known information such as an IP address is included in advance in a transmission symbol, and the order of the components of the separation vector u is corrected based on the known symbol. Is configured to do.

However, in this case, since it is necessary to previously have known information in common on the transmitter side and the receiver side, there is a limitation in applying to general-purpose communication. In addition, the MIMO receiver of Patent Document 1 does not take measures against the problem of indefinite scale. Therefore, it is not possible to determine the interference matrix A directly, in the case where the inter-carrier interference problems described above (ICI) occurs occurs may be difficult to accurately estimate the transmitted symbols s _l.

On the other hand, in Non-Patent Document 2, it is considered that the separation matrix W corresponds to the inverse matrix A ⁻¹ of the interference matrix A, and A is a circulant matrix and α _{i, i} > α _{l, i} ( l ≠ i) (this will be described later), it is assumed that the relationship w _{i, i} > w _{l, i} (l ≠ i) holds for the elements w _{l, i} of W. We are trying to solve the component replacement on the grounds.

However, this assumption holds if W = A ⁻¹ , but generally W is not A ⁻¹ as described above. Also, Non-Patent Document 2 does not solve the problem of indefinite scale.

  Therefore, the conventional technique has a problem that the modulation scheme applicable to each subcarrier is limited to the DPSK or PSK type and cannot be applied to the QAM type modulation scheme.

  Therefore, an object of the present invention is to provide a mixed signal separation technique capable of solving the problem of component replacement and the indefinite scale that occur when ICA is applied.

  It is another object of the present invention to provide an OFDM reception technique that can be applied to a QAM type modulation scheme in an OFDM receiver that separates mixed signals by independent component analysis.

In the following, first, the basic principle of the present invention will be described, and then the configuration and operation of the present invention will be described.
[1] Basic Principle [1-1] Nature of Interference Degree First, the nature of the interference degree α _{l, i} that is an element of the interference matrix A will be described. As can be seen from the equation (19) _{, the} interference degree α _{l, i} does not depend on the individual values of i and l, but depends on (il) mod N and the normalized frequency offset ε. Therefore,

と表記を改める。α_i-lについて、規格化周波数オフセットがε＝0.2のときの値をプロットすると、図2のようになる。図2より、α_i-lの実部と虚部は両方とも、i≠lの場合の値に比べてi＝lの場合の値が際立って大きな値をとって最大となることが分かる。すなわち、

Change the notation. For α _il , the values when the normalized frequency offset is ε = 0.2 are plotted as shown in FIG. From FIG. 2, it can be seen that both the real part and the imaginary part of α _il are maximized, with the value when i = 1 being markedly greater than the value when i ≠ l. That is,

のように当該サブキャリアでの干渉成分が最も大きく、他のサブキャリアからの干渉成分は小さい。

As described above, the interference component in the subcarrier is the largest, and the interference component from other subcarriers is small.

[1-2] Correction of Component Replacement The separation vector u obtained by the equation (25) is generally replaced by the component and is expressed as the equation (36). The elements u _{(i) ˜} ((i) ˜ = (0) ˜, (1) ˜,..., (N−1) ˜) of the separation vector u are called “separation symbols”. For each of the N separated symbols u _{(i) ~} ((i) ~ = (0) ~, (1) ~, ..., (N-1) ~), the (i) ~ component is u _{( An} N-dimensional vector in which the other components are 0 in _{i) ~} is introduced, and this is denoted as u _{(i) ~} .

Furthermore, a vector obtained by applying an inverse matrix W ⁻¹ of the separation matrix _{to the} N-dimensional vector u _(i) is called a “partition vector”,

と記す。また、分割ベクトルξ_(i)~の各要素ξ_l,(i)~を「分割シンボル」と呼ぶ。定義より、各分割ベクトルξ_(i)~は次式のように表される。

. Further, each element ξ _{l, (i) ˜} of the divided vector ξ _{(i) ˜} is referred _to as “divided symbol”. By definition, each divided vector ξ _{(i) ˜} is expressed as follows:

  At this time, the following theorem holds.

[Theorem 1]
The following relationship is established between the transmission symbol s _i , the divided symbols ξ _{l, (i) ˜} , and the interference degree α _{l, i} .

(定理1終わり)

(End of Theorem 1)

(Proof)
S = (s ₀ , s ₁ ,..., S _N−1 ) ^T , and a mixed vector consisting of a permutation of mixed symbols is x = (x _0). , x ₁ ,..., x _N−1 ) ^T and the separation vector obtained by ICA is u = (u _{(0) ˜} ,..., u _{(N−1) ˜} ) ^T. At this time, the separation vector is expressed as follows.

  Here, the matrix D is a diagonal matrix representing the indefiniteness of the scale. The matrix P is a permutation matrix, with one “1” in each row and column element, and the other components being zero.

  On the other hand, when the interference matrix is A and the separation matrix is W, the separation vector u is related as follows.

  When both sides of Expression (46) are expanded, the following expression is obtained.

The (i) -th separated symbol u _(i) -is obtained by subjecting the i-th transmitted symbol s _i to component replacement.

と得られたものと仮定する。このとき、第i番目の送信シンボルs_iのみが活性(s_i≠0)で、その他は不活性(s_n≠i＝0)とすると式(47)より、次式のような関係が得られる。

It is assumed that At this time, if only the i-th transmission symbol s _i is active (s _i ≠ 0) and the others are inactive (s _{n ≠ i} = 0), the following relationship is obtained from equation (47). It is done.

Further, a divided vector ξ _{(i) ~} derived from the (i) ~ th separated symbol u _{(i) ~}

と定義すると、式(49),(50)より次式が成立する。

Then, the following equation is established from equations (49) and (50).

  When this is displayed as an element,

となり、式(43)が成り立つことが証明される。
(証明終わり)

And it is proved that Equation (43) holds.
(End of proof)

The separation symbol u _{(i) ~} is calculated as the (i) ~ th element by changing the order of the i-th transmission symbol s _i in the separation vector u as described above. (i) ~ is unknown. That is, with reference to FIG. 3, it is not clear which of the transmission symbols s _{i corresponds} to {u _{(0) ~} , ..., u _{(N-1) ~} }, but for the time being, it corresponds. The separation symbol is written as u _{(i) ~} . Therefore, the (i) -th divided vector ξ _{(i) ~} derived from the separated symbol u _{(i) ~} as shown in Equation (42) also specifically corresponds to what number of transmitted symbols. It is unknown whether it is.

However, even specific correspondence between the order i split vector xi] _(i) the order (i) - of _- the transmitted symbol s _i were unknown, Equation (43) is split vector xi] _{(i) -} Suggests the following properties.

(Property 1)
The divided vector elements ξ _{l, (i) ˜} are interferences from the transmission symbol s _i (i-th subcarrier) to each mixed symbol (subcarrier) (l = 0, 1,..., N−1). Represents the minute (in contrast to equation (18)).

(Property 2)
Even if the second subscripts of ξ _{l, (i) ˜} and α _{l, i} differ between i and (i) ˜ by component replacement, the first subscript takes the same l. That is, even if there is a component replacement, the first subscript l of ξ _{l, (i) ˜} inherits the order of the first subscript l of α _{l, i} as it is (see FIG. 3).

(Property 3)
The degree of interference (α _{l, i} ) from the transmission symbol s _i to each mixed symbol x _l (l = 0,1,..., N−1) is determined from the separated symbols u _{(i) to} each element ξ _{l , (i) to} (l = 0, 1,..., N−1) are directly reflected in the size (α _{l, i} ) when they are generated (see FIG. 3).

The above (property 2) and (property 3) are expressed in terms of subcarriers.In other words, the interference mechanism from the i-th subcarrier to each subcarrier (l = 0, 1, ..., N-1) is separated. The symbols u _{(i) ˜} are inherited by the generation mechanism of the divided symbols ξ _{l, (i) ˜} (l = 0, 1,..., N−1).

  On the other hand, substituting Equation (43) into Equation (39) yields the following relational expression.

From equation (53), it can be seen that ξ _{l, (i) ˜} has the maximum absolute value when the first subscript l becomes l = i.
From the above, it is possible to estimate (i) to which has been unknown so far as follows.
That is, the absolute value of the divided symbols ξ _{l, (i) ~} (l = 0,1, ..., N-1) belonging _to the divided vector ξ _{(i) ~} Number l of what is the largest

とすれば、(i)~＝(i)^となって、分割ベクトルξ_(i)~に対応する送信シンボルをs_(i)^に特定することができる。この手順をすべての分割ベクトルξ_(i)~((i)~＝(0)~,(1)~,…,(N-1)~)に対して行えば、成分置換の問題は解消されることになる。

Then, (i) ~ = (i) ^, and the transmission symbol corresponding to the divided vector ξ _{(i) ~} can be specified as s _{(i) ^} . If this procedure is performed for all divided vectors ξ _{(i) ~} ((i) ~ = (0) ~, (1) ~, ..., (N-1) ~), the problem of component replacement is eliminated. Will be.

(Example 1)
For example, as shown in FIG. 4, split vector _{ξ (i) ~ = (ξ} 0, (i) ~, ξ 1, (i) ~, ..., ξ N-1, (i) ~) of elements of ^T Among these, the element indicated by the thick arrow is the element having the maximum absolute value. The result of equation (54) is (0) ^ = 2, (1) ^ = 3, (2) ^ = 0, (3) ^ = 1, and the correspondence between the division vector and the transmission symbol is It can be specified that ξ _{(0) ˜ corresponds} to s ₂ , ξ _{(1) ˜ corresponds} to s ₃ , ξ _{(2) ˜ corresponds} to s ₀ , and ξ _{(3) ˜} corresponds to s ₁ . Based on this correspondence, the split vectors are (ξ _{(2) ~} , ξ _{(3) ~} , ξ _{(0) ~} , ξ _{(1) ~} ), and the separation symbols are (u _{(2) ~} , u _{(3) ~} , u _{(0) ~} , u _{(1) ~} ), the order matches the order of the transmission vectors (s ₀ , s ₁ , s ₂ , s ₃ ), and the problem of component replacement is solved Is done.
(End of example)

[1-3] Elimination of scale ambiguity As described above, the problem of component replacement has been solved, and the notation of the division vector that has been clearly associated with the order of each transmitted symbol has been renewed.

と記す。また、各送信シンボルの順番との対応付けが明確となった分離ベクトルuの表記を改めて

. In addition, the notation of the separation vector u, which has been clearly associated with the order of each transmission symbol, has been revised.

と記す。また、式(43)及び式(37)の表記を、それぞれ

. In addition, the notation of formula (43) and formula (37)

と書き改める。

And rewrite.

At this time, the separated symbol (u) ^ _i is obtained by multiplying the transmission symbol s _i by d _i . However, since d _i takes a random value independently of i, the scale is not the same for all i (i = 0, 1,..., N−1). Therefore, even if the component replacement is corrected, the separation symbol (u) ^ _i still has an indefinite scale problem.

On the other hand, the divided symbol (ξ) ^ _{l, i} is obtained by multiplying the transmission symbol s _i by α _{l, i} . Here, α _{l, i} is not a random value but takes a regular value depending on (il) as shown in equation (19). Therefore, there is no scale indefiniteness in the divided symbol (ξ) ^ _{l, i} whose component replacement has been corrected.

  This will be described in detail as follows. First, from equation (38), equation (57) is equivalent to the following equation.

Therefore, when the receiving side subcarrier is a subcarrier having the same number as that of the transmitting side (that is, when l = i), the transmission symbol s _i is multiplied by α ₀ on the receiving side and expressed by the following equation: .

If the subcarrier number is the same on the transmitting side and the receiving side, the scale is α ₀ times for all subcarriers, and the divided symbol (ξ) ^ _{i, i} has no scale indefiniteness. It means that.

  Also for crosstalk to adjacent subcarriers,

となって、すべてのiについてスケールは同一となることが分かる。

Thus, the scale is the same for all i.

  More generally, crosstalk from the i-th subcarrier to the i-th subcarrier

についても、αi-lが式(19)によって(i-l)の関数として一意的に決定される。以上のことから、分割シンボル(ξ)^_i,iにはスケールの不定性がないと結論づけられる。

Also, αi-l is uniquely determined as a function of (il) by equation (19). From the above, it can be concluded that the divided symbol (ξ) ^ _{i, i} has no scale indefiniteness.

[1-4] Estimation of normalized frequency offset Next, the normalized frequency offset ε is calculated using the divided symbols (ξ) ^ _{l, i} obtained by correcting the component permutation and the indeterminacy of the scale as described above. presume.

First, the ratio r _{l, i} of the i-th element (ξ) ^ _{i, i} and the l-th element (ξ) ^ _{l, i} of the divided vector (ξ) ^ _i is called the “divided symbol ratio”. r _{l, i} = (ξ) ^ _{i, i} / (ξ) ^ _{l, i} . This divided symbol ratio r _{l, i} can be expressed as an interference ratio as shown in the following equation from equation (43).

  Substituting equation (19) into equation (64) leads to the following equation:

When the equation (65) is solved for ε and it is expressed as ε _{l, i} as a normalized frequency offset for l, i (l ≠ i), ε _{l, i} becomes as follows.

Actually, since the value of the divided symbol ratio r _{l, i} obtained by ICA varies including an error, the value of the normalized frequency offset ε _{l, i} also varies. Therefore, a method for robustly estimating the normalized frequency offset ε with as little variation due to error as possible is required.

Here, the division symbol ratio r _{l, i} depends on (il) mod N, as is apparent from the equation (65). Therefore, as it becomes clear if we _write r _il = r _{l, i} ,

と巡回性を持つ。そのため、何れのr_i-lについても、集合{r_l,i｜i,l=0,1,…,N-1}からN個の値が得られる。従って、各r_i-lについてN個の値を平均すれば、誤差によるばらつきの問題は緩和することができる。

And has a patrol. Therefore, for any r _il , N values are obtained from the set {r _{l, i} | i, l = 0,1,..., N−1}. Therefore, if N values are averaged for each r _il , the problem of variation due to errors can be alleviated.

As for the average, the harmonic average is more effective than the normal arithmetic average when the variation of samples is large. Therefore, the harmonic mean (r) ^ _il defined by the following equation is adopted as the estimated value of the divided symbol ratio _ril .

The right side of equation (66) is theoretically a real number, but in reality, even if (r) ^ _il is substituted, it does not become a real value. Therefore, the normalized frequency offset ε _{l, i} that should be a real value is estimated as a complex value. Therefore, the normalized frequency offset ε _{l, i} in equation (66) is redefined as ε (r _il ), and the estimated value (r) ^ _il of the divided symbol ratio is substituted into this, and the following equation is obtained: (ε) ^ is adopted as an estimate of the normalized frequency offset.

[1-5] Transmission Symbol Recovery Finally, the transmission vector s is recovered based on the normalized frequency offset (ε) ^ estimated by the equation (69).

  First, by substituting (ε) ^ obtained by Equation (69) into Equation (19), the estimated value of the interference is obtained.

として求める。

Asking.

Next, this is assigned to each element of the interference matrix A to obtain an estimated value (A) ^ of the interference matrix. Finally, an inverse matrix (A) ^ ^-1 of the estimated value (A) ^ of the interference matrix is obtained, and an estimated value (s) ^ of the transmission vector s is obtained by the following equation.

  As a result, the transmission vector s is restored from the distorted mixed vector x without distortion.

[2] Configuration and operation of the present invention The first configuration of the present invention related to the mixed signal separation device is that N (N ≧ 2) independent transmission symbols s _i (i = 1,..., N−1) A mixed signal separation device that restores each of the original transmission symbols s _i based on N mixed symbols x _j (j = 1,..., N−1) generated by mixing in a transmission path. ,
Separation matrix calculation for calculating the separation matrix W for converting the N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) by independent component analysis. Means,
Inverse matrix calculating means for calculating an inverse matrix W ⁻¹ of the separation matrix W;
Separation vector calculating means for calculating N separation symbols u _k based on the N mixed symbols x _j and the separation matrix W;
Corresponding to each of the N separation symbols u _k , an N-dimensional vector u _{k in} which the k-th component is u _k and the other components are 0 is transformed by the inverse matrix W ⁻¹ of the separation matrix Division vector calculation means for calculating a division vector ξ _k obtained by
Corresponding to each of the N divided vectors ξ _k , the maximum component order l (k) = arg max _l {ξ _{l, k} } among the N components ξ _{l, k} of the divided vector is An order search means for searching;
By resetting the order k of each of the N separated symbols u _k and / or the N divided vectors ξ _k to the order l (k) searched by the order searching means, independent components are obtained. Component replacement correction means for correcting component replacement in the analysis;
The N separated symbols u _{l (k)} (k = 1,..., N−1) or the N divided vectors ξ _{l (k)} (k = 1,..., N-1) based on transmission symbol estimation means for estimating the original transmission symbols s _i ,
It is provided with.

With this configuration, the component replacement correction means directly corrects the component replacement based on the components of the divided vector ξ _k that directly reflects the interference matrix A and has no scale indefiniteness. Even if it converges, it becomes possible to correct the component replacement accurately. That is, it is possible to solve the problem of component replacement that occurs when ICA is applied. Then, based on the separated symbol u _{l (k)} (k = 1,..., N−1) or the divided vector ξ _{l (k)} (k = 1,. by estimating each transmitted symbol s _i with high accuracy it becomes possible to restore each transmitted symbol s _i of the original.

  In addition to the OFDM communication system, the mixed signal separation apparatus of the present invention can also be used to separate components transmitted from each transmission antenna in a general MIMO communication system.

According to a second configuration of the present invention relating to a mixed signal separation device, in the first configuration, the transmission symbol estimation means includes:
For each of the N divided vectors ξ _{l (k)} (k = 1,..., N−1) whose order has been reset by the component replacement correcting means, the l (k) th of the divided vectors. The divided symbol ratio r _{l, l (k)} = ξ _, which is the ratio of the ith component ξ _{l (k), l (k)} to the other components ξ _{l, l (k)} (l ≠ l (k)) divided symbol ratio calculating means for calculating _{l (k), l (k)} / ξ _{l, l (k)} ;
Each divided symbol ratio r _{l, l (k)} is _converted into two components α _{l (k), l (k) of} an interference matrix A = (α _{j, i} ) that generates a mixed symbol x _j from transmission symbols s _i. , α _{l, l (k)} ratio α _{l (k), l (k)} / α _{l, l (k)} as an interference degree estimating means for estimating the interference matrix A,
Restored symbol calculation means for calculating each transmission symbol s _i restored from each mixed symbol x _j based on the estimated interference matrix A;
It is provided with.

According to this configuration, the transmission symbol estimation means, component xi] _{l, l (k)} interference matrix on the basis of the A = (α _{j, i)} of the scale ambiguity no split vector xi] _{l (k)} components (interference Therefore _, the value of each interference degree α _{j, i} can be accurately estimated without being affected by the indefiniteness of the scale generated in ICA. That is, the problem of indefinite scale that occurs when ICA is applied can be solved. Then, by calculating each transmission symbol s _i using the estimated interference matrix A, it is possible to restore each original transmission symbol s _i with high accuracy.

In the first configuration of the present invention related to the mixed signal separation method, N (N ≧ 2) independent transmission symbols s _i (i = 1,..., N−1) are mixed and generated in the transmission path. A mixed signal separation method for restoring each of the original transmission symbols s _i based on N mixed symbols x _j (j = 1,..., N−1),
Separation matrix calculation for calculating the separation matrix W for converting the N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) by independent component analysis. Steps,
An inverse matrix calculating step of calculating an inverse matrix W ⁻¹ of the separation matrix W;
A separation vector calculation step of calculating N separation symbols u _k based on the N mixed symbols x _j and the separation matrix W;
Corresponding to each of the N separation symbols u _k , an N-dimensional vector u _{k in} which the k-th component is u _k and the other components are 0 is transformed by the inverse matrix W ⁻¹ of the separation matrix A divided vector calculating step for calculating a divided vector ξ _k obtained by
Corresponding to each of the N divided vectors ξ _k , the maximum component order l (k) = arg max _l {ξ _{l, k} } among the N components ξ _{l, k} of the divided vector is An order search step for searching;
By resetting the order k of each of the N separated symbols u _k and / or the N divided vectors ξ _k to the order l (k) searched in the order searching step, independent components A component replacement correction step for correcting component replacement in the analysis;
The N separated symbols u _{l (k)} (k = 1,..., N−1) or N divided vectors ξ _{l (k)} (k = 1, ..., N-1), a transmission symbol estimation step for estimating each of the original transmission symbols s _i ;
It is provided with.

According to a second configuration of the present invention related to the mixed signal separation method, in the first configuration, the transmission symbol estimation step includes:
For each of the N divided vectors ξ _{l (k)} (k = 1,..., N−1) whose order has been reset in the component replacement correction step, the l (k) th of the divided vector The divided symbol ratio r _{l, l (k)} = ξ _, which is the ratio of the ith component ξ _{l (k), l (k)} to the other components ξ _{l, l (k)} (l ≠ l (k)) a division symbol ratio calculating step for calculating _{l (k), l (k)} / ξ _{l, l (k)} ;
Each divided symbol ratio r _{l, l (k)} is _converted into two components α _{l (k), l (k) of} an interference matrix A = (α _{j, i} ) that generates a mixed symbol x _j from transmission symbols s _i. , α _{l, l (k)} ratio α _{l (k), l (k)} / α _{l, l (k)} as an interference degree estimation step for estimating the interference matrix A,
A restored symbol calculation step of calculating each transmission symbol s _i restored from each mixed symbol x _j based on the estimated interference matrix A;
It is provided with.

In the first configuration of the present invention related to the OFDM receiver, after the transmission symbols s _i (i = 1,..., N−1) independent on the transmission side are OFDM-modulated and transmitted and mixed in the transmission path, In the OFDM communication system received at the receiving side and demodulated as N mixed symbols x _j (j = 1,..., N−1), the mixed symbols x _j (j = 1,. An OFDM receiver that restores each of the original transmission symbols s _i based on:
Separation matrix calculation for calculating the separation matrix W for converting the N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) by independent component analysis. Means,
Inverse matrix calculating means for calculating an inverse matrix W ⁻¹ of the separation matrix W;
Separation vector calculating means for calculating N separation symbols u _k based on the N mixed symbols x _j and the separation matrix W;
Corresponding to each of the N separation symbols u _k , an N-dimensional vector u _{k in} which the k-th component is u _k and the other components are 0 is transformed by the inverse matrix W ⁻¹ of the separation matrix Division vector calculation means for calculating a division vector ξ _k obtained by
Corresponding to each of the N divided vectors ξ _k , the maximum component order l (k) = arg max _l {ξ _{l, k} } among the N components ξ _{l, k} of the divided vector is An order search means for searching;
By resetting the order k of each of the N separated symbols u _k and / or the N divided vectors ξ _k to the order l (k) searched by the order searching means, independent components are obtained. Component replacement correction means for correcting component replacement in the analysis;
The N separated symbols u _{l (k)} (k = 1,..., N−1) or the N divided vectors ξ _{l (k)} (k = 1,..., N-1) based on transmission symbol estimation means for estimating the original transmission symbols s _i ,
It is provided with.

With this configuration, the component replacement correction unit directly corrects the component replacement based on the component of the divided vector ξ _k that directly reflects the interference matrix A and has no scale indefiniteness, so the separation matrix W has converged to any state. However, it becomes possible to correct the component replacement accurately. That is, the problem of component replacement that occurs when ICA is applied to an OFDM receiver can be solved. Then, based on the separated symbol u _{l (k)} (k = 1,..., N−1) or the divided vector ξ _{l (k)} (k = 1,. by estimating each transmitted symbol s _i with high accuracy it becomes possible to restore each transmitted symbol s _i of the original.

The second configuration of the present invention related to an OFDM receiver is the first configuration, wherein the transmission symbol estimation means is:
For each of the N divided vectors ξ _{l (k)} (k = 1,..., N−1) whose order has been reset by the component replacement correcting means, the l (k) th of the divided vectors. The divided symbol ratio r _{l, l (k)} = ξ _, which is the ratio of the ith component ξ _{l (k), l (k)} to the other components ξ _{l, l (k)} (l ≠ l (k)) divided symbol ratio calculating means for calculating _{l (k), l (k)} / ξ _{l, l (k)} ;
Each divided symbol ratio r _{l, l (k)} is _converted into two components α _{l (k), l (k) of} an interference matrix A = (α _{j, i} ) that generates a mixed symbol x _j from transmission symbols s _i. , α _{l, l (k)} ratio α _{l (k), l (k)} / α _{l, l (k)} as an interference degree estimating means for estimating the interference matrix A,
Restored symbol calculation means for calculating each transmission symbol s _i restored from each mixed symbol x _j based on the estimated interference matrix A;
It is provided with.

According to this configuration, the component (interference degree) of the interference matrix A = (α _{j, i} ) is estimated based on the components ξ _{l, l (k)} of the divided vector ξ _{l (k)} without scale indefiniteness. Therefore _, the value of each interference degree α _{j, i} can be estimated with high accuracy. That is, the problem of indefinite scale that occurs when ICA is applied to an OFDM receiver can be solved. Then, by calculating each transmission symbol s _i using the estimated interference matrix A, it is possible to restore each original transmission symbol s _i with high accuracy. Therefore, in addition to DPSK and PSK type modulation schemes, it is also possible to apply QAM type modulation schemes.

According to a third configuration of the present invention relating to an OFDM receiver, in the second configuration, the interference degree estimation means,
For each of the divided symbol ratios r _{l, l (k)} , a division for calculating an average divided symbol ratio r _{l (k) -l} , which is an average value of the indexes having the same absolute value difference | l (k) −l | Symbol ratio averaging means;
Normalized frequency offset calculation that calculates a normalized frequency offset ε based on the N-1 average divided symbol ratio r _{l (k) -l} (l (k) -l = 1,..., N−1). Means,
Interference degree calculating means for calculating each component α _{j, i} (i, j = 0,..., N−1) of the interference matrix A based on the estimated value ε of the normalized frequency offset;
It is provided with.

With this configuration, even when a normalized frequency offset occurs due to a shift between the carrier frequency on the transmitter side and the transmission frequency on the receiver side during down conversion on the receiver side, estimating accurately the interference matrix a, precisely it is possible to restore each transmitted symbol s _i of the original.

According to a fourth configuration of the present invention relating to an OFDM receiver, in the third configuration, the division symbol ratio averaging means performs an average division symbol ratio r _{l (k ) -l} is calculated.

With this configuration, even when there is a variation in the divided symbol ratio calculated from the components of each divided vector ξ _{l (k)} due to an error, the variation is suppressed by harmonic averaging, and the stable average divided symbol ratio r with high accuracy is achieved. _{l (k) -l} can be calculated.

  According to a fifth configuration of the present invention relating to an OFDM receiver, in the third configuration, the normalized frequency offset calculating means calculates the normalized frequency offset ε by performing the calculations of equations (73) and (74). It is characterized by calculating.

With this configuration, even if the normalized frequency offset calculated from the components of each divided vector ξ _{l (k)} due to errors has variations or imaginary parts, the variations can be suppressed by realization and averaging, and the accuracy is high. A stable normalized frequency offset ε can be calculated.

According to a sixth configuration of the present invention relating to an OFDM receiver, in the third configuration, the interference degree calculation means performs each of the components α _{j, i} ( i, j = 0,..., N−1) is calculated.

  With this configuration, when a normalized frequency offset occurs, the interference matrix A can be calculated with high accuracy in consideration of the normalized frequency offset.

In the first configuration of the present invention related to the OFDM reception method, after independent transmission symbols s _i (i = 1,..., N−1) are OFDM-modulated and transmitted on the transmission side and mixed in the transmission path, In the OFDM communication system received at the receiving side and demodulated as N mixed symbols x _j (j = 1,..., N−1), the mixed symbols x _j (j = 1,. Based on an OFDM reception method for recovering each of the original transmission symbols s _i , comprising:
Separation matrix calculation for calculating the separation matrix W for converting the N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) by independent component analysis. Steps,
An inverse matrix calculating step of calculating an inverse matrix W ⁻¹ of the separation matrix W;
A separation vector calculation step of calculating N separation symbols u _k based on the N mixed symbols x _j and the separation matrix W;
Corresponding to each of the N separation symbols u _k , an N-dimensional vector u _{k in} which the k-th component is u _k and the other components are 0 is transformed by the inverse matrix W ⁻¹ of the separation matrix A divided vector calculating step for calculating a divided vector ξ _k obtained by
Corresponding to each of the N divided vectors ξ _k , the maximum component order l (k) = arg max _l {ξ _{l, k} } among the N components ξ _{l, k} of the divided vector is An order search step for searching;
By resetting the order k of each of the N separated symbols u _k and / or the N divided vectors ξ _k to the order l (k) searched in the order searching step, independent components A component replacement correction step for correcting component replacement in the analysis;
The N separated symbols u _{l (k)} (k = 1,..., N−1) or N divided vectors ξ _{l (k)} (k = 1, ..., N-1), a transmission symbol estimation step for estimating each of the original transmission symbols s _i ;
It is provided with.

In the second configuration of the present invention related to the OFDM reception method, in the first configuration, in the transmission symbol estimation step,
For each of the N divided vectors ξ _{l (k)} (k = 1,..., N−1) whose order has been reset in the component replacement correction step, the l (k) th of the divided vector The divided symbol ratio r _{l, l (k)} = ξ _, which is the ratio of the ith component ξ _{l (k), l (k)} to the other components ξ _{l, l (k)} (l ≠ l (k)) a division symbol ratio calculating step for calculating _{l (k), l (k)} / ξ _{l, l (k)} ;
Each divided symbol ratio r _{l, l (k)} is _converted into two components α _{l (k), l (k) of} an interference matrix A = (α _{j, i} ) that generates a mixed symbol x _j from transmission symbols s _i. , α _{l, l (k)} ratio α _{l (k), l (k)} / α _{l, l (k)} as an interference degree estimation step for estimating the interference matrix A,
A restored symbol calculation step of calculating each transmission symbol s _i restored from each mixed symbol x _j based on the estimated interference matrix A;
It is provided with.

In the third configuration of the present invention related to the OFDM receiving method, in the second configuration, in the interference degree estimation step,
For each of the divided symbol ratios r _{l, l (k)} , a division for calculating an average divided symbol ratio r _{l (k) -l} , which is an average value of the indexes having the same absolute value difference | l (k) −l | A symbol ratio averaging step;
Normalized frequency offset calculation that calculates a normalized frequency offset ε based on the N-1 average divided symbol ratio r _{l (k) -l} (l (k) -l = 1,..., N−1). Steps,
An interference degree calculating step of calculating each component α _{j, i} (i, j = 0,..., N−1) of the interference matrix A based on the normalized frequency offset estimate ε;
It is provided with.

In the fourth configuration of the present invention related to the OFDM reception method, in the third configuration, in the divided symbol ratio averaging step, an average divided symbol ratio r _{l ( k) -l} is calculated.

  The fifth configuration of the present invention related to the OFDM reception method is the normalized frequency offset ε by performing the calculations of equations (73) and (74) in the normalized frequency offset calculation step in the third configuration. Is calculated.

The sixth configuration of the present invention related to the OFDM reception method is the third configuration, wherein in the interference degree calculation step, each component α _{j, i of the} interference matrix A is calculated by performing the calculation of equation (75). (i, j = 0,..., N−1) is calculated.

As described above, according to the present invention, the component replacement is corrected based on the component of the divided vector ξ _k that directly reflects the interference matrix A and has no scale indefiniteness. Even if it converges to, it becomes possible to correct the component replacement accurately. Accordingly, it is possible to provide a mixed signal separation device and a mixed signal separation method capable of solving the problem of component replacement that occurs when ICA is applied.

Further, since the component (interference degree) of the interference matrix A = (α _{j, i} ) is estimated based on the components ξ _{l, l (k)} of the divided vector ξ _{l (k)} without scale indefiniteness, the ICA It is possible to accurately estimate the value of each interference degree α _{j, i} and restore the transmission symbol s _i with high accuracy without being affected by the indefiniteness of the scale generated in FIG. Accordingly, it is possible to provide a mixed signal separation device and a mixed signal separation method capable of solving the problem of indefinite scale that occurs when ICA is applied.

Further, by using the mixed signal separation method in an OFDM receiver, without being affected by the problem and scale indefinite permutation can be restored accurately transmitted symbol s _i. Therefore, it is possible to provide an OFDM receiver and an OFDM reception method that can be applied to a QAM type modulation scheme in an OFDM receiver that separates mixed signals by independent component analysis.

  The best mode for carrying out the present invention will be described below with reference to the drawings.

FIG. 5 is a block diagram of the OFDM receiver 1 described in Embodiment 1 of the present invention.
The OFDM receiver 1 of this embodiment includes an antenna 2, a carrier wave transmitter 3, a down converter 4, a low-pass filter 5, an analog / digital converter 6, a serial-parallel converter 7, a discrete Fourier transformer 8, and a transmission symbol restoration. And a parallel-serial converter 10, a demapper 11, a deinterleaver 12, and a decoder 13. Of these components, the portions other than the transmission symbol reconstructor 9 are the same as those of the OFDM receiver 120 of FIG.

  The OFDM receiver 1 of the present embodiment is characterized by including a transmission symbol reconstructor 9 that estimates and reconstructs transmission symbols by removing interference between subcarriers after the discrete Fourier transformer 8. .

  FIG. 6 is a block diagram showing a configuration of transmission symbol reconstructor 9 of FIG. The transmission symbol restorer 9 includes a separation matrix calculator 21, an inverse matrix calculator 22, a separation vector calculator 23, a divided vector generator 24, an order determiner 25, a divided symbol ratio calculator 26, and a normalized frequency offset calculator 27. An averager 28, an interference matrix generator 29, an inverse matrix calculator 30, and a restoration vector generator 31.

  Here, in the present embodiment, the separation matrix calculator 21 is a separation matrix calculator, the inverse matrix calculator 22 is an inverse matrix calculator, the separation vector calculator 23 is a separation vector calculator, and the divided vector generator 24 is a divided vector calculator. Means, order determiner 25, order finding means and component replacement correcting means, divided symbol ratio calculator 26, divided symbol ratio calculator, normalized frequency offset calculator 27, averager 28 and interference matrix generator 29, interference. The degree estimation means, the inverse matrix calculator 30 and the restoration vector generator 31 correspond to restoration symbol calculation means.

Separation matrix calculator 21 calculates a separation matrix W for converting N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) using ICA. To do.

The inverse matrix calculator 22 generates an inverse matrix W ⁻¹ of the separation matrix W generated by the separation matrix calculator 21.

Separator vector calculator 23, based on the separating matrix W and mixed vector x, and calculates a separation vector u of N separate symbols u _k.

The division vector generator 24 is defined by Expression (42) based on each separation symbol u _k output from the separation vector calculator 23 and the inverse matrix W ⁻¹ of the separation matrix output from the inverse matrix calculator 22. N divided vectors ξ _{(i) ˜} ((i) ˜ = (0) ˜, (1) ˜,..., (N−1) ˜) are generated.

The order determiner 25 determines the order (i) ˜ = (i) ^ of each divided vector ξ _{(i) ˜} output from the divided vector generator 24 according to the equation (54).

The division symbol ratio calculator 26 is defined by Expression (64) based on each component of the division vector (ξ) ^ _i = ξ _{(i) ^} in which the order (i) ^ is determined by the order determiner 25. The divided symbol ratios r _{l ,, i} (i, l = 0,1, ..., N-1) are calculated, and (N-1) divided symbol ratios r _il defined by the equation (68) are calculated. Calculate the estimated value (r) ^ _il .

The normalized frequency offset calculator 27 calculates the normalized frequency offset ε ((() by the calculation of Expression (66) for each of the (N−1) divided symbol ratios r _il output from the divided symbol ratio calculator 26. r) ^ _il ) = ε _{l ,, i} calculates the real part Re [ε ((r) ^ _il )].

The averager 28 calculates the average of the real part Re [ε ((r) ^ _il )] of the (N-1) standardized frequency offsets output from the standardized frequency offset calculator 27, and outputs this average. As an estimated value (ε) ^ of a standardized frequency offset.

The interference matrix generator 29 calculates each interference degree α _{l, i} (i, l = 0,1,..., N of the interference matrix A according to the equation (19) based on the estimated value (ε) ^ of the normalized frequency offset. -1) is calculated.

The inverse matrix calculator 30 calculates an inverse matrix A ⁻¹ of the interference matrix A output from the interference matrix generator 29.

Based on the inverse matrix A- ¹ of the interference matrix output from the inverse matrix calculator 30 and the mixed vector x, the restoration vector generator 31 calculates the estimated value (s) ^ of the transmission vector s by the calculation of equation (71). This is output to the parallel-serial converter 10.

  The operation of the transmission symbol reconstructor 9 of the OFDM receiver 1 of the present embodiment configured as described above will be described below. FIG. 7 is a flowchart showing the operation of the transmission symbol reconstructor 9 of FIG.

First, the mixed vector x output from the discrete Fourier transformer 8 is input to the separation matrix calculator 21. The mixed vector x is a vector composed of the N mixed symbols x _j that are parallelized.

In step S1, the separation matrix calculator 21 converts the N mixed symbols _xj into statistically independent N separation symbols u _k (k = 1,..., N−1). Is calculated by ICA. Here, as an algorithm for the separation matrix W by ICA, it is generally easy to use the natural gradient method, but as described above, various known methods other than the natural gradient method can also be used. is there.

In step S2, the inverse matrix calculator 22 generates an inverse matrix W ⁻¹ of the separation matrix W generated by the separation matrix calculator 21. As the inverse matrix generation algorithm, a known method such as the Gauss-Jordan method is used.

On the other hand, in step S3, the separation vector calculator 23, based on the mixed vector x and the separating matrix W, the operation of Equation (46), to calculate the separation vector u of N separate symbols u _k. The separation vector u is a vector obtained by decomposing the mixed vector x into statistically independent components.

  In step S4, the divided vector generator 24 initializes an index number i, which is an internal variable register, to 0.

In step S5, split vector generator 24, by performing the following calculation, split vector _{ξ (i) ~ = (ξ} 0, (i) ~, ξ 1, (i) ~, ..., ξ N- _{1, (i) ~} ) ^T is calculated.

ここで、w^(-1) _l,iは分離行列の逆行列W^-1の第(l,i)成分を表す。

Here, w ⁽⁻¹⁾ _{l, i} represents the (l, i) component of the inverse matrix W ⁻¹ of the separation matrix.

Subsequently, in step S6, the order determination unit 25, split vector xi] _(i) element of _{~ {ξ 0, (i)} ~, ξ 1, (i) ~, ..., ξ N-1, (i) ~ } Having the maximum absolute value ξ _{l, (i) ˜} is searched, and its index number l = (i) ^ is determined as the order (i) ˜ of the divided vectors ξ _{(i) ˜} . That is,

のように分割ベクトルξ_(i)~の順番(i)~を決定する。

Split vector xi] _(i) the order of _- (i) as to determine the ~.

In step S6, the divided vector generator 24 determines whether i = N−1. If i <N−1, i is incremented by 1 (S8), and the process returns to step S5. In the case of i = N−1, the order determiner 25 rearranges the order of each element of each divided vector ξ _{(i) ^} according to the determined order, and corrects the N component replacements. Generate split vectors (ξ) ^ ₀ , (ξ) ^ ₁ , ..., (ξ) ^ _N-1 . These are output to the divided symbol ratio calculator 26, and the process proceeds to step S9.

In step S9, the divided symbol ratio calculator 26 calculates each component of the divided vectors (ξ) ^ ₀ , (ξ) ^ ₁ ,..., (Ξ) ^ _N−1 whose component replacement has been corrected by the order determiner 25. Based on the above, the division symbol ratio r _{l ,, i} (i, l = 0,1,..., N−1) is calculated by performing the calculation of Expression (64). Then, the divided symbol ratio calculator 26 performs the calculation of the equation (68) to obtain an estimated value (r) ^ _il (il = 1, 2,..., (N−1) divided symbol ratios r _il , N-1) is calculated.

In step S10, the normalized frequency offset computing unit 27 _applies each of the (N-1) divided symbol ratios r _il (il = 1, 2,..., N-1) output from the divided symbol ratio computing unit 26. On the other hand _, the real part Re [ε ((r) ^ _il )] of the normalized frequency offset ε ((r) ^ _il ) = ε _{l ,, i} is calculated by performing the operation of equation (66). . Then, the averager 28 calculates the average of the real part Re [ε ((r) ^ _il )] of (N−1) standardized frequency offsets output from the standardized frequency offset computing unit 27, Is output as an estimated value (ε) ^ of the final normalized frequency offset.

In step S11, the interference matrix generator 29, based on the estimated value (ε) ^ of the normalized frequency offset, the interference degree α _{l, i} (i, l = 0,1, ..., N-1) is calculated.

In step S12, the inverse matrix calculator 30 calculates an inverse matrix A ⁻¹ of the interference matrix A output from the interference matrix generator 29.

Finally, in step S13, the restored vector generator 31 performs the calculation of Expression (71) based on the inverse matrix A- ¹ of the interference matrix output from the inverse matrix calculator 30 and the mixed vector x, and the transmission vector Calculate the estimated value (s) ^ of s. The calculated estimated value (s) ^ of the transmission vector is output to the parallel-serial converter 10.

It is a block diagram showing the basic composition of an OFDM communication system. It is a figure showing the relationship between the difference of an interference degree and a carrier number. It is a figure showing the production | generation of a division | segmentation symbol and inheritance of an interference characteristic. It is a figure showing a response | compatibility (N = 4) with a transmission symbol and a division | segmentation symbol. 1 is a block diagram of an OFDM receiving apparatus described in Example 1 of the present invention. FIG. 6 is a block diagram showing a configuration of a transmission symbol decompressor in FIG. 7 is a flowchart showing the operation of the transmission symbol reconstructor in FIG.

Explanation of symbols

1 OFDM receiver
2 Antenna
3 Carrier transmitter
4 Down converter
5 Low-pass filter
6 Analog to digital converter
7 Series-parallel converter
8 Discrete Fourier Transform
9 Transmit symbol restorer
10 Parallel to serial converter
11 Demapper
12 Deinterleaver
13 Decoder
21 Separation matrix calculator
22 Inverse matrix calculator
23 Separate vector calculator
24 split vector generator
25 Sequencer
26 division symbol ratio calculator
27 Normalized frequency offset calculator
28 Averager
29 Interference matrix generator
30 Inverse matrix calculator
31 Restored vector generator
100 OFDM transmitter
101 encoder
102 Interleaver
103 Mapper
104 series-parallel converter
105 Inverse discrete Fourier transformer
106 Parallel to serial converter
107 Digital-to-analog converter
108 Low-pass filter
109 Carrier wave transmitter
110 Up Converter
120 OFDM receiver
121 Carrier transmitter
122 Down Converter
123 Low-pass filter
124 Analog to digital converter
125 series-parallel converter
126 Discrete Fourier Transform
127 Parallel converter
128 Demapper
129 Deinterleaver
130 decoder
140 communication channels

Claims (16)

N mixed symbols x _j (j = 1,..., N) generated by mixing N (N ≧ 2) independent transmission symbols s _i (i = 1,..., N−1) in the transmission path. -1), a mixed signal separation device for restoring the original transmission symbols s _i ,
Separation matrix calculation for calculating the separation matrix W for converting the N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) by independent component analysis. Means,
Inverse matrix calculation means for calculating an inverse matrix W ⁻¹ of the separation matrix W;
And separating vector calculating means for calculating the N pieces of the separating symbol u _k based on the N of the mixed symbols x _j and the separating matrix W,
Corresponding to each of the N separation symbols u _k , an N-dimensional vector u _{k in} which the k-th component is u _k and the other components are 0 is converted by the inverse matrix W ⁻¹ of the separation matrix. A divided vector calculating means for calculating a divided vector ξ _k obtained by:
Corresponding to each of the N divided vectors ξ _k , the maximum component order l (k) = arg max _l {ξ _{l, k} } among the N components ξ _{l, k} of the divided vector. An order search means for searching;
By resetting the order k of each of the N separated symbols u _k and / or the N divided vectors ξ _k to the order l (k) searched by the order searching means, independent components Component replacement correction means for correcting component replacement in the analysis;
N separated symbols u _{l (k)} (k = 1,..., N−1) or N divided vectors ξ _{l (k)} (k = 1,..., N-1), a transmission symbol estimation means for estimating each of the original transmission symbols s _i ;
A mixed signal separating apparatus. The transmission symbol estimation means includes
For each of the N divided vectors ξ _{l (k)} (k = 1,..., N−1) whose order has been reset by the component replacement correcting means, the l (k) th of the divided vectors. The divided symbol ratio r _{l, l (k)} = ξ _, which is the ratio of the ith component ξ _{l (k), l (k)} to the other components ξ _{l, l (k)} (l ≠ l (k)) divided symbol ratio calculating means for calculating _{l (k), l (k)} / ξ _{l, l (k)} ;
Each divided symbol ratio r _{l, l (k)} is _converted into two components α _{l (k), l (k) of} an interference matrix A = (α _{j, i} ) that generates a mixed symbol x _j from the transmission symbol s _i. , Α _{l, l (k)} ratio α _{l (k), l (k)} / α _{l, l (k)} as an interference degree estimating means for estimating the interference matrix A;
Restored symbol calculation means for calculating each transmission symbol s _i restored from each mixed symbol x _j based on the estimated interference matrix A;
The mixed signal separating apparatus according to claim 1, further comprising: N mixed symbols x _j (j = 1,..., N) generated by mixing N (N ≧ 2) independent transmission symbols s _i (i = 1,..., N−1) in the transmission path. -1), a mixed signal separation method for restoring the original transmission symbols s _i ,
Separation matrix calculation for calculating the separation matrix W for converting the N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) by independent component analysis. Steps,
An inverse matrix calculating step of calculating an inverse matrix W ⁻¹ of the separation matrix W;
A separation vector calculation step of calculating the N of the separation symbol u _k based on the N of the mixed symbols x _j and the separating matrix W,
Corresponding to each of the N separation symbols u _k , an N-dimensional vector u _{k in} which the k-th component is u _k and the other components are 0 is converted by the inverse matrix W ⁻¹ of the separation matrix. A divided vector calculation step for calculating a divided vector ξ _k obtained by:
Corresponding to each of the N divided vectors ξ _k , the maximum component order l (k) = arg max _l {ξ _{l, k} } among the N components ξ _{l, k} of the divided vector. An order search step for searching;
By resetting the order k of each of the N separated symbols u _k and / or the N divided vectors ξ _k to the order l (k) searched in the order searching step, the independent component A component replacement correction step for correcting component replacement in the analysis;
The N separated symbols u _{l (k)} (k = 1,..., N−1) or N divided vectors ξ _{l (k)} (k = 1,..., N−1), a transmission symbol estimation step for estimating each of the original transmission symbols s _i ;
A mixed signal separation method. The transmission symbol estimation step includes:
For each of the N divided vectors ξ _{l (k)} (k = 1,..., N−1) whose order has been reset in the component replacement correction step, the l (k) th of the divided vectors. The divided symbol ratio r _{l, l (k)} = ξ _, which is the ratio of the ith component ξ _{l (k), l (k)} to the other components ξ _{l, l (k)} (l ≠ l (k)) a divided symbol ratio calculating step for calculating _{l (k), l (k)} / ξ _{l, l (k)} ;
Each divided symbol ratio r _{l, l (k)} is _converted into two components α _{l (k), l (k) of} an interference matrix A = (α _{j, i} ) that generates a mixed symbol x _j from the transmission symbol s _i. , Α _{l, l (k)} ratio α _{l (k), l (k)} / α _{l, l (k)} to estimate the interference matrix A,
A restored symbol calculation step of calculating each transmission symbol s _i restored from each mixed symbol x _j based on the estimated interference matrix A;
The mixed signal separation method according to claim 3, further comprising: Independent transmission symbols s _i (i = 1,..., N−1) are OFDM-modulated and transmitted on the transmission side, mixed on the transmission path, and then received on the reception side, where N mixed symbols x _j (j = 1,..., N-1), the original transmission symbols s _i are restored based on the mixed symbols x _j (j = 1,..., N−1). An OFDM receiver that
Separation matrix calculation for calculating the separation matrix W for converting the N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) by independent component analysis. Means,
Inverse matrix calculation means for calculating an inverse matrix W ⁻¹ of the separation matrix W;
And separating vector calculating means for calculating the N pieces of the separating symbol u _k based on the N of the mixed symbols x _j and the separating matrix W,
Corresponding to each of the N separation symbols u _k , an N-dimensional vector u _{k in} which the k-th component is u _k and the other components are 0 is converted by the inverse matrix W ⁻¹ of the separation matrix. A divided vector calculating means for calculating a divided vector ξ _k obtained by:
Corresponding to each of the N divided vectors ξ _k , the maximum component order l (k) = arg max _l {ξ _{l, k} } among the N components ξ _{l, k} of the divided vector. An order search means for searching;
By resetting the order k of each of the N separated symbols u _k and / or the N divided vectors ξ _k to the order l (k) searched by the order searching means, independent components Component replacement correction means for correcting component replacement in the analysis;
N separated symbols u _{l (k)} (k = 1,..., N−1) or N divided vectors ξ _{l (k)} (k = 1,..., N-1), a transmission symbol estimation means for estimating each of the original transmission symbols s _i ;
An OFDM receiver comprising: The transmission symbol estimation means includes
For each of the N divided vectors ξ _{l (k)} (k = 1,..., N−1) whose order has been reset by the component replacement correcting means, the l (k) th of the divided vectors. The divided symbol ratio r _{l, l (k)} = ξ _, which is the ratio of the ith component ξ _{l (k), l (k)} to the other components ξ _{l, l (k)} (l ≠ l (k)) divided symbol ratio calculating means for calculating _{l (k), l (k)} / ξ _{l, l (k)} ;
Each divided symbol ratio r _{l, l (k)} is _converted into two components α _{l (k), l (k) of} an interference matrix A = (α _{j, i} ) that generates a mixed symbol x _j from the transmission symbol s _i. , Α _{l, l (k)} ratio α _{l (k), l (k)} / α _{l, l (k)} as an interference degree estimating means for estimating the interference matrix A;
Restored symbol calculation means for calculating each transmission symbol s _i restored from each mixed symbol x _j based on the estimated interference matrix A;
6. The OFDM receiver according to claim 5, further comprising: The interference degree estimation means includes
For each of the divided symbol ratios r _{l, l (k)} , a division for calculating an average divided symbol ratio r _{l (k) -l} , which is an average value of the indices having the same absolute value difference | l (k) −l | Symbol ratio averaging means;
Normalized frequency offset calculation for calculating a normalized frequency offset ε based on the N−1 average divided symbol ratio r _{l (k) -l} (l (k) -l = 1,..., N−1). Means,
Interference degree calculating means for calculating each component α _{j, i} (i, j = 0,..., N−1) of the interference matrix A based on the estimated value ε of the normalized frequency offset;
The OFDM receiver according to claim 6, further comprising: 8. The OFDM receiver according to claim 7, wherein the divided symbol ratio averaging means calculates an average divided symbol ratio r _{l (k) -l} by performing a harmonic average calculation of equation (1).

8. The OFDM receiving apparatus according to claim 7, wherein the standardized frequency offset calculating unit calculates the standardized frequency offset ε by performing the calculations of equations (2) and (3).

The interference degree calculating means calculates each component α _{j, i} (i, j = 0,..., N−1) of the interference matrix A by performing an operation of Equation (4). Item 8. The OFDM receiver according to Item 7.

Independent transmission symbols s _i (i = 1,..., N−1) are OFDM-modulated and transmitted on the transmission side, mixed on the transmission path, and then received on the reception side, where N mixed symbols x _j (j = 1,..., N-1), the original transmission symbols s _i are restored based on the mixed symbols x _j (j = 1,..., N−1). An OFDM reception method for
Separation matrix calculation for calculating the separation matrix W for converting the N mixed symbols x _j into statistically independent N separation symbols u _k (k = 1,..., N−1) by independent component analysis. Steps,
An inverse matrix calculating step of calculating an inverse matrix W ⁻¹ of the separation matrix W;
A separation vector calculation step of calculating the N of the separation symbol u _k based on the N of the mixed symbols x _j and the separating matrix W,
Corresponding to each of the N separation symbols u _k , an N-dimensional vector u _{k in} which the k-th component is u _k and the other components are 0 is converted by the inverse matrix W ⁻¹ of the separation matrix. A divided vector calculation step for calculating a divided vector ξ _k obtained by:
Corresponding to each of the N divided vectors ξ _k , the maximum component order l (k) = arg max _l {ξ _{l, k} } among the N components ξ _{l, k} of the divided vector. An order search step for searching;
By resetting the order k of each of the N separated symbols u _k and / or the N divided vectors ξ _k to the order l (k) searched in the order searching step, the independent component A component replacement correction step for correcting component replacement in the analysis;
The N separated symbols u _{l (k)} (k = 1,..., N−1) or N divided vectors ξ _{l (k)} (k = 1,..., N−1), a transmission symbol estimation step for estimating each of the original transmission symbols s _i ;
An OFDM receiving method comprising: In the transmission symbol estimation step,
For each of the N divided vectors ξ _{l (k)} (k = 1,..., N−1) whose order has been reset in the component replacement correction step, the l (k) th of the divided vectors. The divided symbol ratio r _{l, l (k)} = ξ _, which is the ratio of the ith component ξ _{l (k), l (k)} to the other components ξ _{l, l (k)} (l ≠ l (k)) a divided symbol ratio calculating step for calculating _{l (k), l (k)} / ξ _{l, l (k)} ;
Each divided symbol ratio r _{l, l (k)} is _converted into two components α _{l (k), l (k) of} an interference matrix A = (α _{j, i} ) that generates a mixed symbol x _j from the transmission symbol s _i. , Α _{l, l (k)} ratio α _{l (k), l (k)} / α _{l, l (k)} to estimate the interference matrix A,
A restored symbol calculation step of calculating each transmission symbol s _i restored from each mixed symbol x _j based on the estimated interference matrix A;
The OFDM reception method according to claim 11, further comprising: In the interference degree estimation step,
For each of the divided symbol ratios r _{l, l (k)} , a division for calculating an average divided symbol ratio r _{l (k) -l} , which is an average value of the indices having the same absolute value difference | l (k) −l | A symbol ratio averaging step;
Normalized frequency offset calculation for calculating a normalized frequency offset ε based on the N−1 average divided symbol ratio r _{l (k) -l} (l (k) -l = 1,..., N−1). Steps,
An interference degree calculating step of calculating each component α _{j, i} (i, j = 0,..., N−1) of the interference matrix A based on the estimated value ε of the normalized frequency offset;
13. The OFDM receiving method according to claim 12, further comprising: The OFDM reception method according to claim 13, wherein in the division symbol ratio averaging step, an average division symbol ratio r _{l (k) -l} is calculated by performing a harmonic average calculation of equation (1).   14. The OFDM receiving method according to claim 13, wherein in the normalized frequency offset calculating step, the normalized frequency offset ε is calculated by performing calculations of equations (2) and (3). In the interference degree calculation step, each component α _{j, i} (i, j = 0,..., N−1) of the interference matrix A is calculated by performing the calculation of Expression (4). The OFDM receiving method according to claim 13.

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