JP2009130634A - Carrier frequency offset, and i/q imbalance compensation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a correction method based on SCA of an OFDM signal. <P>SOLUTION: Firstly, the OFDM signal under CFO and I/Q imbalance is expressed by matrix. Secondly, a new method is proposed, which is based on a sub-carrier arrangement (SCA) and capable of analytically obtaining an I/Q imbalance correction coefficient, based on a CFO estimation value acquired by maximum likelihood CFO estimation. Furthermore, the proposed method is extended to a blind correction method to be adapted to an OFDM symbol with an asymmetric SCA structure by utilizing relation between the CFO estimation value and the I/Q imbalance correction. Lastly, validity of the proposed method is verified by computer simulation. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a method for estimating and compensating for carrier frequency offset (CFO) and I / Q signal imbalance (I / Q imbalance) in a direct conversion receiver.

  Today, Orthogonal Frequency Division Multiplexing (OFDM) schemes are employed in various broadband wireless communication systems such as DAB, DVB, and IEEE 802.11a. In the OFDM system, the frequency is effectively used by using orthogonal subcarriers, and the speed is increased by using multilevel modulation.

  In addition, the OFDM system is more resistant to multipath than the single frequency system, but is vulnerable to radio frequency (RF) disturbances, particularly local oscillator (LOs) frequency shifts in the transceiver. CFO is a factor causing inter-carrier interference (ICI), which leads to significant deterioration of transmission characteristics in the OFDM system.

  On the other hand, in the highly competitive wireless communication market, direct conversion receivers (DCR) are attracting attention because of their low cost. DCR that directly converts to baseband signals without converting to an intermediate frequency when converting to baseband signals enables downsizing, cost reduction, and labor saving of receivers compared to conventional superheterodyne receivers. It has the characteristic of being.

  However, by directly converting the RF band signal to the baseband signal, DC offset, I / Q imbalance, and even-order distortion problems are newly generated.

  The I / Q imbalance is caused by distortion of the I-phase component and the Q-phase component from the ideal state. In DCR, an RF band carrier signal having a π / 2 phase difference is required to decompose a received signal into an I-phase component and a Q-phase component. However, it is difficult to provide an LO having an accurate phase shift amount π / 2 for a high-frequency signal, and a frequency non-selective I / Q imbalance occurs in which the I-phase component and the Q-phase component are distorted from an ideal state.

  In a broadband communication system, frequency selective I / Q imbalance also occurs due to a difference in characteristics of analog components such as filters installed in the I branch and the Q branch. Due to these I / Q imbalances, image interference occurs and the error rate characteristics are significantly degraded.

Here, the problem of correcting CFO and I / Q imbalance in a direct conversion OFDM receiver is addressed. There have been considerable reports on CFO estimation in OFDM communication systems (see Non-Patent Document 1). Non-Patent Document 2 proposes an effect of I / Q imbalance by a local transmitter in an OFDM communication system and a correction method. Non-Patent Documents 4 and 5 propose correction methods in the case where both CFO and I / Q imbalance exist.
P. H. Moose, “A technical for orthogonal frequency division multiplexing frequency correction noise,“ IEEE Trans. Commun. , Vol. 42, pp. 2908-2914, Oct. 1994. C. L. Liu, “Impacts of I / Q impulse on QPSK-OFDM-QAM detection,” IEEE Trans. Consumer Electron. , Vol. 44, pp. 984-989, Aug. 1998. F. Horlin, A.M. Bourdoux, E .; Lopez Estraviz, and L.L. Van der Perre, “Low-complexity EM-based joint CFO and IQ impulse acquisition,” Proc. IEEE ICC, Jun. 2007. E. Lopez Estraviz, S.M. De Rore, F.M. Horlin, and L.L. Van der Perre, “Optimal training sequence for joint channel and frequency-dependent IQ impulse estimation in OFDM-based receivers,“ Proc. IEEE [21] G. Xing, M.C. Shen, and H.H. Liu, “Frequency offset and I / Q imbalance compensation for direct-conversion receivers,” IEEE Trans. Wireless Commun. , Vol. 4, no. 2, pp. 673-680, Mar. 2005.

  However, in these documents, frequency selective I / Q imbalance has not been considered. The non-patent document 4 is studying the problem, but does not take CFO into consideration.

  To date, the only correction method that takes into account CFO and two types of I / Q imbalances is Non-Patent Document 5 using a modified periodic pilot.

  In an OFDM system, pilot symbols and data symbols including information are different from each other in subcarrier arrangement (SCA), and periodic pilot symbols can be considered as SCA having an evenly spaced structure. Focusing on this point, a new correction method based on the SCA of the OFDM signal is proposed.

  First, an OFDM signal under CFO and I / Q imbalance is expressed in a matrix. Next, a new technique based on SCA is proposed that can analytically determine the I / Q imbalance correction coefficient based on the CFO estimation value obtained from the maximum likelihood CFO estimation. Note that the proposed method can be regarded as a generalized pilot utilization method because it provides pilot symbol design criteria that can be applied when both CFO and I / Q imbalance exist.

  Furthermore, the relationship between CFO estimation and I / Q imbalance correction is used to extend the proposed method to a blind correction method that can be applied to OFDM symbols having an asymmetric SCA structure. Finally, the effectiveness of the proposed method is verified by computer simulation.

  In the present invention, the CFO and I / Q imbalance can be obtained by calculation by knowing a predetermined transmission protocol of the OFDM signal and the received signal itself. Therefore, no special signal processing is required, and the CFO and the I / Q imbalance can be compensated only with a simple correction circuit.

  In the present specification, large (small) bold letters are used as matrices (column vectors) in equations, and superscripts H, T, *, and crosses are used as Hermitian, transposed, conjugate, and pseudo-inverse matrices, respectively. . In addition, when expressing these matrices in a sentence, they are expressed as “matrix + character”. For example, when the letter “A” is represented in bold in the formula and is given the meaning of a matrix, it is represented as “matrix A” in the sentence.

In the formula, subscripts I and Q are used as in-phase (I branch) and quadrature (Q branch) components. The matrix I _N is an N × N order unit matrix, [•] _N is an operation in mode N, and a mark with “×” in a circle indicates a convolution operation. R (•) and N _l (•) denote the right range space and the left null space (LNS) of the matrix. Further, tr (•) indicates a matrix trace operation.

  First, the system model will be described. Hereinafter, CFO and I / Q imbalance in DCR are expressed as mathematical models.

において零であり、Ｂは帯域幅である。 FIG. 1 shows a generalized structure of DCR having I branch and Q branch signals generated by analog processing. FIG. 2 shows a mathematical model when an I / Q imbalance occurs. Here, the frequency non-selective I / Q imbalance caused by the local transmitter is characterized by the amplitude difference α and the phase difference φ, and the branch component mismatch is represented by G _I (f) and G _Q (f). Are modeled by two real coefficient low-pass filters (LPFs) having different frequency characteristics. However, G _I (f) and G _Q (f) are

Is zero and B is the bandwidth.

The CFO can be defined by the following received signal check r (t) in the RF band modulated by the intermediate frequency fc having the frequency offset Δf. Note that “check r (t)” is substituted when the term on the left side of equation (1) is used in a sentence.

  Where tilts r (t), s (t) and h (t) are baseband representations of received signals, transmitted signals and channel responses. Note that “tilt r (t)” is substituted when the term on the left side of equation (2) is used in the sentence. At this time, according to the derivation in Non-Patent Document 5, the down-converted baseband signal dash r (t) is expressed by the following equation. “Dash r (t)” is substituted when the term on the left side of the following equation is used in the sentence.

但し、以下の関係である。

However, the relationship is as follows.

The above equation is discretized by an AD converter having a cycle Ts that satisfies the Nyquist sampling theorem. At this time, if c ₁ (t), c ₂ (t) and h (t) have a spread of L ₁ T _s , L ₂ T _s and L _h T _s , a discrete-time signal of the following equation is obtained. .

および

明らかに、「左矢印ｒ（ｎ）」は所望信号成分であり、「右矢印ｒ（ｎ）」はＩ／Ｑ不均衡によるイメージ干渉成分である。なお、「左矢印ｒ（ｎ）」は（６）式の左辺の項を、「右矢印ｒ（ｎ）」は（７）式の左辺の項を文中で用いる場合に代用する。 However, there is the following relationship.

and

Obviously, the “left arrow r (n)” is the desired signal component, and the “right arrow r (n)” is the image interference component due to I / Q imbalance. Note that “left arrow r (n)” is used when the term on the left side of equation (6) is used, and “right arrow r (n)” is used when the term on the left side of equation (7) is used in the statement.

の間隔をもつＮ個のサブチャネルに分解すると、ナイキストのサンプリング周期は、

となる。 Next, matrix representation of the OFDM system will be described. In an OFDM system, bandwidth B is

Nyquist sampling period is divided into N subchannels with a spacing of

It becomes.

The transmitted signal is blocked in an inverse DFT (IDFT) module and a CP of length N _cp is added to avoid inter-block interference (IBI). Since CP guarantees circular convolution, it guarantees orthogonality between subcarriers. Here, it is assumed that the _NCP is long enough to include the combined channel for the left arrow r (n) and the right arrow r (n).

但し、以下の関係である。 S _m is the signal carried by the m th subcarrier, H _m is the frequency response of the m th subcarrier to the matrix h, ε is the CFO normalized by f ₀ , and the matrix F ^H is N × N An IDFT matrix is shown. At this time, the matrix expression of the left arrow r (n) after timing synchronization is as follows.

However, the relationship is as follows.

上式において、行列Ｆ^Ｈ _Ｌ１−１は行列Ｆ^Ｈの下側Ｌ_１−１行から構成される行列であり、ＣＦＯは初期位相零と仮定されている。なお、行列Ｆ^Ｈ _Ｌ１−１は式（８）の右辺第３項の行列式の上側の行列を表す。式（８）は、更に次式のように書き直すことができる。

In the above equation, the matrix F ^H _L1-1 is a matrix composed of the lower L ₁ -1 rows of the matrix F ^H , and the CFO is assumed to have an initial phase of zero. The matrix F ^H _L1-1 represents a matrix on the upper side of the determinant of the third term on the right side of Expression (8). Equation (8) can be further rewritten as:

但し、

行列二重線チルトＣ１（１３式右辺第２項）は、ｃ_１，ｌ を

に置換え、左側L_１−１列を右側L_１−１列に加えることにより、行列Ｃ_１から得られるＮ×Ｎ次元の循環行列である。

However,

Matrix doublet tilt C1 (13 Equation second term) _is a _{c 1, l}

And the left L ₁ −1 column is added to the right L ₁ −1 column to obtain an N × N-dimensional circular matrix obtained from the matrix C ₁ .

を得る。但し、式（１５）右辺の中括弧のｍ番目の項であるチルトＣ_１，ｍは次式の周波数応答に対応する。 However, here, the matrix C ₁ is substituted when the term on the left side of the equation (10) is used in the sentence. Since the circulant matrix can be diagonalized by multiplying (I) the DFT matrix from the right (left),

Get. However, the tilt C _{1, m} that is the m-th term in the braces on the right side of the equation (15) corresponds to the frequency response of the following equation.

従って、ｒ（ｎ）の合成チャネルは非特許文献５で示されている

ではなく、

となる。行列Ｆ^Ｈの共役が列ベクトルの再配置となることから、次式で与えられる右矢印ｒ（ｎ）に対する同様な結果を得る。

Therefore, the synthesis channel of r (n) is shown in Non-Patent Document 5.

not,

It becomes. Since the conjugate of the matrix F ^H becomes the rearrangement of column vectors, a similar result is obtained for the right arrow r (n) given by the following equation.

但し、式（１８）右辺の中括弧のｍ番目の項であるチルトＣ_２，ｍは次式の周波数応答に対応する。

However, the tilt C _{2, m} that is the m-th term in the braces on the right side of the equation (18) corresponds to the frequency response of the following equation.

行列・チルトＣ_１，ｍおよび行列・チルトＣ_２，ｍが、行列・左矢印ｈおよび｛行列・左矢印ｈ｝^＊に組み込まれるので、

となる。

Since the matrix / tilt C _{1, m} and the matrix / tilt C _{2, m} are incorporated into the matrix / left arrow h and {matrix / left arrow h} ^* ,

It becomes.

Note that “matrix / tilt C _{1, m} ” is a term on the left side of Equation (15), and “matrix / tilt C _{2, m} ” is a term on the left side of Equation (18). “Arrow h” is the term on the left side of Equation (12), and “{Matrix / Left Arrow h} ^* ” is the fourth term on the right side of Equation (17).

  As a result, due to the presence of CFO and I / Q imbalance, the received OFDM signal is composed of two signals with opposite frequency offsets.

Next, correction based on subcarrier arrangement (SCA) will be described.
In an actual OFDM system, there are some subcarriers that do not carry information, that is, null subcarriers (NSCs), and in the data OFDM symbol, in order to avoid aliasing and facilitate the filtering operation, the band edge and the DC part NSC.

  On the other hand, in the pilot OFDM symbol, NSCs are arranged at equal intervals in order to implement a special time expression, for example, to form a periodic short training sequence in 802.11a. In other words, the structure of pilot symbols and data symbols can be considered to differ from each other only in the arrangement of NSCs or SCA.

の列を並べ替え、変調サブキャリアとナルサブキャリアに相当する

と、

の２個の副行列に分解する。 Without loss of generality, assume that there are P modulation subcarriers and K = N−P null subcarriers. There subcarrier, since it corresponds to a column with a matrix F ^H,

Are rearranged to correspond to modulation subcarriers and null subcarriers.

When,

Is decomposed into two sub-matrices.

および

とした二個の指標集合

および

により、行列Ｆ^Ｈの列と行列Ｗ、行列Ｖの列との対応を図る。

and

Two indicator sets

and

Thus, correspondence between the columns of the matrix F ^{H and} the columns of the matrix W and the matrix V is achieved.

および

の関係を有する。 The matrix F ^H is an orthogonal matrix,

and

Have the relationship.

であることから、行列ｗ_ｐ１とｗ_ｐ２は直流キャリアを中心に対称であり、

の関係が成立する。

Therefore, the matrices w _p1 and w _p2 are symmetric around the DC carrier,

The relationship is established.

は帯域の端およびＤＣ部のサブキャリアに相当する。明らかに、行列ｆ_０および行列ｆ_Ｎ／２は自己対称である。 In particular,

Corresponds to the end of the band and the subcarrier in the DC part. Obviously, the matrix f ₀ and the matrix f _{N / 2} are self-symmetric.

で表すこととする。 Note that the distance between the subcarrier matrix f _i and the matrix f _j is

It shall be expressed as

となる。 Next, CFO estimation will be described.
When noise is expressed by a matrix z of N × 1D vectors, equation (20) becomes

It becomes.

In the above equation, the matrix / left arrow d and the matrix / right arrow d are two P × 1-dimensional vectors composed of P non-zero elements in the matrix / left arrow h and the matrix / right arrow h, respectively. As is clear from the equation (21), the SCA expressed by the matrix W or the matrix V is an important key for CFO estimation. In order to simplify the handling, let the matrix _z be additive white noise (AWGN) with variance “σ ² _z matrix I _N ”.

の最小化により得られ、非ＡＷＧＮの場合には非線形最小二乗（ＮＬＳ）推定となる。 When the tilt ε is an estimated value of ε, ML estimation of ε is

In the case of non-AWGN, nonlinear least squares (NLS) estimation is obtained.

で得られ、また、Ｊ_ＭＬに代入することにより次式が得られる。 Since the above equation can be separated into terms of the matrix A (ε) and the matrix d, it can be treated as an independent estimation problem consisting of two stages. First, by differentiating with respect to the matrix and tilt d to J _ML, the optimal solution for the matrix-tilt d by placing a zero,

Further, the following equation is obtained by substituting in _JML .

但し、

であり、

は

への直交射影として知られている。

However,

And

Is

Known as an orthogonal projection to.

の関係が成立する必要がある。 To apply equation (25), the matrix A (ε) is column regular, ie

The relationship needs to be established.

の実用範囲において、行列Ａ（ε）はε＝０
以外に対しては、フルランクのファンデルモンド行列である。

In the practical range of the matrix A (ε), ε = 0
For other than, it is a full-rank van der monde matrix.

のときには、

は、

と同一となり、Ｊ_ＭＬ（チルトε）はεと−εにおいて同一の最小値をもつことになる。 However,

When

Is

And J _ML (tilt ε) has the same minimum value in ε and −ε.

は行列Ｗが行列ｆ_ｉと行列ｆ_Ｎ−ｉのＰ／２対からなる自己対称構造をもつ行列であることを意味する。 Since the matrix W is a van dermond matrix,

Means that the matrix W is a matrix having a self-symmetric structure composed of P / 2 pairs of the matrix f _i and the matrix f _N−i .

である行列ｗ_ｐの一個が少なくとも必要である。更に、ε= 0のとき、行列Ａ（ε）がフルランクであるためには、行列Ｗの任意の２個の列ベクトルが対称であってはいけない。 To avoid permutation,

At least one matrix w _p is required. Furthermore, when ε = 0, in order for the matrix A (ε) to be full rank, any two column vectors of the matrix W must not be symmetric.

の条件を満たす行列Ｗを選べば、ＭＬ法によるＣＦＯ推定値は次式となる。 As a result, in I / Q imbalance,

If the matrix W satisfying the above condition is selected, the CFO estimated value by the ML method is as follows.

This CFO estimation range is half of the minimum distance between the column vector of the matrix W and the column vector of the matrix W ^* . In order to expand the estimation range, the number of subcarriers in the matrix W may be selected to be small.

およびＸ（ｆ）する。αをＧ_Ｑ（ｆ）の一部と見なせることから、 補正後には

の関係が成立する。 Next, I / Q imbalance correction will be described.
Actually, the frequency selectivity I / Q imbalance is not large and is corrected by placing the FIR filter in the I branch or the Q branch (Non-patent Document 5) [21]. The impulse and frequency response of the Q branch correction filter, respectively,

And X (f). The α since regarded as part of the G _{Q (f),} after correction

The relationship is established.

となる。 At this time, the equation (14) is

It becomes.

は、

の周波数応答であり、

はＧ_Ｉ（ｆ）のインパルス応答である。 However,

Is

Is the frequency response of

Is the impulse response of G _I (f).

のように書き直すことができる。 Similarly, equation (17) is

Can be rewritten as

である。ここで右辺の括弧の中のｍ番目の項を、「ハットＧ_ｍ」とする。ハットＧ_ｍは、

に対応する。 However,

It is. Here, the m-th term in the parenthesis on the right side is defined as “hat G _m ”. Hat G _m

Corresponding to

および

となる。 From the real coefficient of matrix g _I ,

and

It becomes.

および

が成立する。 as a result

and

Is established.

所望信号

は、

で得られ、その実部および虚部は次式となる。

Therefore, the received signal when the frequency selectivity I / Q imbalance does not occur is given by the following equation.

Desired signal

Is

The real part and the imaginary part are obtained by the following equation.

  The above two equations show asymmetric correction for a received signal with only LO imbalance corrected by two gain coefficients β and χ corresponding to tanφ and secφ. The overall structure taking the CFO correction of FIG. Obviously, since χ is built into x, the correction problem becomes an optimization problem for x and β.

により得られ、次式の最小化により求めることができる。 Since the MLCFO estimation is independent of the I / Q imbalance correction under an appropriate matrix W, the hat ε is obtained in advance. Since the matrix double dot r is an OFDM signal influenced by the CFO, by using the left null space, the optimal values of x and β are

Can be obtained by minimizing the following equation.

ここで、

と置き、

の関係を定義すれば、周波数選択性Ｉ／Ｑ不均衡補正後には

の関係をもつ。

here,

And put

If the relationship of frequency selectivity I / Q imbalance is corrected,

It has the relationship.

となることから、式（４１）を式（３８）に代入し、Ｊ（ｘ、β）をｘおよびβで微分すれば、

が得られる。 From Equations (35) and (36), the signal after frequency nonselective I / Q imbalance correction is

Therefore, if equation (41) is substituted into equation (38) and J (x, β) is differentiated by x and β,

Is obtained.

および

は、

の実部および虚部となる。 However,

and

Is

The real part and the imaginary part.

および

となる。 Obviously,

and

It becomes.

但し、

If equations (42) and (43) are set to zero and solved for x and β, the optimal solution is the analytical solution shown in the following equation.

However,

In summary, a pilot OFDM symbol is designed based on equation (26), and CFO and I / Q imbalance are corrected using the following four steps.
1) Estimate the hat ε using equation (27),
2) Deriving x and β from equation (44),
3) Correct the I / Q imbalance using the obtained x and β according to FIG.
4) Correct the CFO based on the hat ε.

がスカラであることから、 ブロック行列の逆行列定理により、

となる。 Next, calculation load reduction will be described.
The complexity of the correction method based on SCA lies in finding the hat ε, hat x, and hat β. In Equation (44), Λ is a (L _x +1) × (L _x +1) dimensional symmetric matrix, and

Is a scalar, the inverse matrix theorem of the block matrix

It becomes.

上式において、Λ1は小サイズのＬ_ｘ×Ｌ_ｘ次元の対称行列より、その逆行列を計算することは容易となる。 However,

In the above equation, Λ1 can be easily calculated from a small sized L _x × L _x dimensional symmetric matrix.

On the other hand, the overall complexity is dominated by CFO estimation value acquisition in Equation (27), which is an NLS problem and requires a one-dimensional search. Since J _ML (tilt ε) can be calculated using the eigenvector of the matrix B (tilt ε), the complexity can be reduced by selecting the matrix B (tilt ε) having a small rank.

より、固定されたＮにおいては、

すなわち、式（２６）に従って、ｉがゼロでない１個のサブキャリアｆｉのみの変調波であれば最小の複雑さとなる。更に、Ｎを減少させることにより複雑を低減化することができる。

From the fixed N,

That is, according to the equation (26), if the modulated wave is only one subcarrier fi where i is not zero, the complexity becomes minimum. Furthermore, complexity can be reduced by reducing N.

  When N = 2, there is no subcarrier that satisfies the equation (26), so the minimum value of N is 4. An N subcarrier OFDM symbol consisting of 4 identical blocks is equivalent to a 4 subcarrier OFDM system. Paying attention to this point, the pilot is given by the following equation.

但し、

However,

から構成された非対称ＳＣＡ構造をもつＮサブキャリアＯＦＤＭシステムとなる。Ｎ／４でダウンサンプリングすると、

The above pilot

N subcarrier OFDM system having an asymmetric SCA structure composed of When downsampling at N / 4,

  The above equation is a 4-subcarrier OFDM signal composed of one modulated wave matrix f1 according to equation (26). Consequently, the minimum complexity of CFO estimation can be realized by equation (50) and downsampling.

を取り除けば、探索範囲は

の範囲になる。 The minimum distance between this SCA and the conjugate of this SCA is 2, and the CFO estimation range of this pilot is in the range from −1 to −1. When a wide search is required, the number of subcarriers is reduced, for example, from equation (51)

The search range is

It becomes the range.

となる。 Next, blind correction will be described.
Once the CFO estimate is obtained, the above I / Q imbalance correction can be applied to OFDM symbols with null subcarriers. In order to obtain CFO using equation (27), the matrix A (tilt ε) must be column regular, ie, P must be smaller than N / 2. However, with normal data OFDM symbols

It becomes.

および

を得ることができる。 Fortunately, as apparent from the equation (44), the hat x and the hat β depend on the CFO estimated value hat ε, so that if the matrix V exists, for a certain CFO value tilt ε,

and

Can be obtained.

を用いて、ＣＦＯ推定値を

として求めることができる。 Therefore, formula (37) was rewritten

To calculate the CFO estimate

Can be obtained as

When the matrix W has a self-symmetric structure, J _b (tilt ε) is an even function of tilt ε (see Appendix I), so the P limit is relaxed, but to obtain an accurate CFO estimate An asymmetric structure of the matrix W is required.

Extending equation (53) to the sum over OFDM symbols in the considered interval, and if hat ε _b is obtained, using hat ε _b , x (hat ε _b ) and β (hat ε _b ), The correction structure of FIG. 3 is constructed. In fact, equation (54) provides blind CFO and I / Q imbalance correction for asymmetric SCA OFDM signals.

Next, simulation results will be described.
In order to prove the effectiveness of the proposed method, a simulation was conducted. The OFDM system used for the simulation was based on the 802.11a WLAN standard, and used carrier frequency of 5 GHz, B = 20 MHz, N = 64, N _CP = 16, and 16-QAM as a modulation scheme.

  The proposed preamble is an OFDM symbol composed of 80 samples including CP, and has P = 12 asymmetric subcarriers shown in Equation (26) and the time representation feature shown in Equation (50). Yes. Here, a data OFDM symbol composed of 52 modulated waves having an asymmetric structure in which 30 and 22 subcarriers at positive and negative frequencies are modulated is considered.

  In the method of Non-Patent Document 5, 128 samples of 4 pilot symbols each having 16 sample pilots and 16 samples CP are used for comparison. Ten data OFDM symbols are used for blind correction, and in the SCA-based approach, only the OFDM pilot consisting of 80 samples including the above-mentioned CP is used.

The frequency selective fading channel has 5 paths and has an exponentially decaying power profile. Two cases of I / Q imbalance in Non-Patent Document 5 are considered.
Case A) Frequency non-selectivity and frequency-selective imbalance consisting of α = 1 dB, φ = 5 °, matrix g _I = [1, 0, 1] ^T and matrix g _Q = [0, 1, 1] ^T.
Case B) Frequency nonselective imbalance consisting of α = 1 dB, φ = 5 ° and matrix g _I = matrix g _Q = [1, 0] ^T.

The normalized CFOε was set to 0.13, and the search range of ε was limited to (−0.48, 0.48) assuming a local transmitter of ± 30 ppm. In addition, the filter length of the correction filter is L _x = 5.

Figure 4 is a comparison of mean square error defined normalized CFO as E [(.epsilon. hat ε) ^2]. Compared with the method of Non-Patent Document 5, the proposed method based on SCA using a short preamble has slightly degraded characteristics. On the other hand, it can be seen that the blind method provides characteristics comparable to the pilot utilization method.

5 to 8 show the bit error rate (BER) with respect to the effective SNR (corrected SNR). For reference, the characteristics in the absence of CFO and I / Q imbalance (No CFO I / Q) are also shown. As can be seen from the figure, the proposed method is more effective than the method of Non-Patent Document 5 that causes an error flow at a high SNR in Case A.

  The reason for this is due to the difference in the optimization method for determining the correction coefficient. The method of Non-Patent Document 5 corrects the phase difference caused by CFO between adjacent pilots. Correction is performed based on the frequency arrangement of pilot OFDM symbols when no imbalance occurs.

  This makes optimization rigorous and effective. Furthermore, since the method of Non-Patent Document 5 removes the GI, it is necessary to add zero to the matrix to be expressed as a convolution, and an accurate expression cannot be obtained because the expression is not accurate.

FIG. 9 shows an evaluation function J _b (tilt ε) for CFO estimation by a blind method using a self-symmetric matrix W composed of 52 subcarriers. As is clear from FIG. 6, J _b (tilt ε) is an even function of tilt ε, which suggests the necessity of the matrix W having an asymmetric structure in order to obtain an accurate blind CFO.

  In summary, we present a CFO and I / Q imbalance correction problem in a direct conversion OFDM receiver. First, a matrix representation of OFDM signals under CFO and I / Q imbalance, and between SCA and MLCFO estimation Clarified the relationship.

  Next, in an appropriate SCA structure, MLCFO estimation under I / Q imbalance is performed, and the obtained CFO estimates are used to calculate correction coefficients for frequency nonselectivity and frequency selective I / Q imbalance correction. We proposed a new method based on SCA that can obtain analytical solutions.

  Furthermore, by using the relationship between CFO estimation and I / Q imbalance correction, the proposed method is extended to an OFDM symbol blind correction method with an asymmetric SCA structure. Finally, the effectiveness of the compensation method of the present invention was verified by computer simulation.

について証明を示しておく。 In the matrix W having self-symmetry,

Let me show you the proof.

および

はそれぞれ、行列ＶＶ^Ｈの実部および虚部である。

and

Are the real and imaginary parts of the matrix VV ^H , respectively.

すなわち、

および

となる。 At this time, when the matrix W has self-symmetry, the matrix V also has self-symmetry,

That is,

and

It becomes.

となる。 Furthermore, since the matrix Γ (tilt ε) is a diagonal matrix,

It becomes.

および

より、

および

であることは明らかである。

and

Than,

and

Obviously.

を導くことができる。 From the equations (41), (44), (45) and (46),

Can guide you.

となる。但し、行列ｒは任意のＮ×１次元ベクトルである。
At this time, when the matrix V has self-symmetry,

It becomes. However, the matrix r is an arbitrary N × 1D vector.

と置くと、式（５３）および（５５）より

となるので、

であることが証明される。

From the formulas (53) and (55)

So,

It is proved that.

  The present invention can be suitably used for a receiver that receives an OFDM signal.

It is a figure which shows the receiver of a direct conversion system. It is a figure showing the mathematical model of I / Q imbalance of a direct conversion system. It is a figure which shows the structure of a compensation circuit. It is a graph which shows the relationship between SNR of a received signal, and a mean square error. It is a graph which shows the relationship between SNR of a received signal, and effective SNR. 7 is a graph showing a relationship between SNR and BER of a received signal in case A. 10 is a graph showing a relationship between an SNR of a received signal and an effective SNR in case B. 7 is a graph showing a relationship between SNR and BER of a received signal in case B. It is a graph which shows the relationship between CFO and an evaluation function.

Claims (1)

A receiver for receiving an OFDM signal,
(27) or (28) is used to estimate the CFO,
X and β are obtained by the equation (44),
The sum of the signal obtained by multiplying the I-side signal of the received signal by β and the signal obtained by multiplying the Q-side signal of the received signal by x is defined as a new Q-side signal.
A method of compensating for CFO and IQ imbalance by adding to the I-side signal.

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