CN104601518A - SFO and CFO combined estimation method based on maximum likelihood estimation - Google Patents

Abstract

The invention discloses an SFO and CFO combined estimation method based on maximum likelihood estimation, and aims to solve the problems that the computational complexity is high due to two-dimensional global search, and the high-SNR (Signal Noise Ratio) error floor estimation accuracy cannot continue to converge in the existing SFO and CFO combined estimation method. The technical solution is that the method comprises the following steps: determining a range of SFO, transforming the range of SFO into a range of variable t, using first-order Legendre polynomial to approximate a formula I shown in the description to obtain first-order Legendre polynomial approximant, substituting the approximant into a formula II shown in the description to obtain t; transforming a final estimation value eta' of SFO by t; obtaining an estimation value epsilon' of CFO by the eta'. The SFO and CFO combined estimation method based on maximum likelihood estimation does not require the two-dimensional global search, so that the computational complexity is reduced greatly, meanwhile, the problem of error floor in high SNR in the existing estimation method is eliminated, and the estimation accuracy is improved.

Description

Based on sampling frequency offset and the carrier wave frequency deviation combined estimation method of maximal possibility estimation

Technical field

The present invention relates generally to the synchronous estimation field in wireless communication system base band signal process, aims to provide a kind of computation complexity is low, estimated accuracy is high sampling frequency offset (SFO) and carrier wave frequency deviation (CFO) combined estimation method.

Background technology

OFDM (OFDM) technology is widely used in modern wireless communication systems because of its high spectrum utilization, is adopted by multiple communication protocol such as IEEE 802.11a, IEEE 802.16a, DVB-T and DRM etc.But OFDM technology is quite responsive to synchronous error, the performance of its receiver is caused significantly to reduce.SFO and CFO is synchronous error main in ofdm system.In order to improve the performance of receiver, needing to estimate the value of SFO and CFO in receivers, and compensating to received signal according to estimated value.

SFO and CFO is not mated by the sampling clock of transmitter and receiver to cause with factors such as Doppler frequency shifts.Traditional synchronous estimation method is estimated respectively by SFO and CFO, then compensates.In recent years, the combined estimation method of SFO and CFO is proposed in succession.2004, M.M.Freda etc. propose SFO and the CFO combined estimation method of time domain the earliest in " Joint channel estimation and synchronizationfor OFDM systems " (" in ofdm system joint channel estimation and synchronous method "), but the method needs extra inversefouriertransform parts, adds the complexity of receiver synchronization module, in order to reduce the complexity of system, 2009, the people such as H.Nguyen-Le are at " RLS-based jointestimation and tracking of channel response, sampling, and carrier frequency offsetsfor OFDM " (" based on the channel of recurrence least square in ofdm system, sampling frequency offset and carrier wave frequency deviation Combined estimator and tracking ") in propose a kind of SFO and CFO combined estimation method utilizing in frequency domain two identical long training sequences to carry out maximal possibility estimation, but, because in the method, the impact of a weight factor makes its estimated accuracy be restricted, 2011, the people such as Y.-H.Kim by improving the cost function of people's combined estimation methods such as H.Nguyen-Le, make estimated accuracy greatly improve in " Joint maximum likelihood estimation of carrier and samplingfrequency offsets for OFDM systems " (" sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation ").Above-mentioned various combined estimation methods all need to carry out two-dimentional global search to the cost function of SFO and CFO, computing time is increased greatly, particularly when high s/n ratio, restriction due to step-size in search makes to there is error floor to the Combined estimator of SFO and CFO, and estimated accuracy cannot continue convergence.As shown in Figure 1, SFO and CFO combined estimation method that the people such as Y.-H.Kim proposes in " Joint maximum likelihoodestimation of carrier and sampling frequency offsets for OFDM systems " (" sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation ") is mainly divided into the following steps:

The first step: obtain two long training sequence R from the symbol flow data that receiver receives ₀(k) and R ₁(k);

Second step: by CFO in span [-0.5,0.5] be divided into 100 parts in interval, the step-size in search by CFO is defined as 0.01, by SFO in span [-0.0015,0.0015] be divided into 100 parts in, the step-size in search by SFO is defined as 0.00003;

3rd step: the cost function according to (1) formula performs two-dimentional global search in the interval described in CFO and SFO, and find out the SFO value and CFO value that make cost function minimum, as respective estimated value;

Wherein, R ₀(k) first frequency domain long training sequence for receiving, R ₁(k) second frequency domain long training sequence for receiving, ε represents that the value that CFO is possible, η represent the value that SFO is possible, represent the estimated result that CFO is final, represent the estimated result that SFO is final, represent the final estimated value of ε and η value when making cost function $ (ε, η) get minimum value as CFO and SFO.

The core of the method performs two-dimentional global search to cost function $ (ε, η) in SFO and CFO span, finds the estimated value of η and ε when making cost function get minimum value as SFO and CFO.There are following two shortcomings in this combined estimation method.

1. the global search of two dimension makes amount of calculation significantly increase, and adds computation complexity, has made Combined estimator need longer computing time;

2. the precision of this combined estimation method depends on the step-size in search of two-dimensional search, and contribute to improving estimated accuracy although reduce step-size in search, computation complexity also increases thereupon.So step-size in search can only seek compromise between estimated accuracy and computation complexity, and which results in when high s/n ratio (SNR), this combined estimation method exists error floor, estimated accuracy cannot continue convergence.

Summary of the invention

The technical problem to be solved in the present invention is: the computation complexity brought for two-dimentional global search in existing SFO and CFO combined estimation method is high, and the problem that error floor estimated accuracy cannot continue convergence is there is when high SNR, a kind of SFO and CFO combined estimation method based on maximal possibility estimation is proposed.Combined estimation method of carrying does not need to carry out two-dimentional global search, therefore greatly reduces computation complexity, eliminates existing method of estimation exists error floor problem when high SNR simultaneously, improves estimated accuracy.

Feature of the present invention comprises the following steps:

The first step: the span determining SFO in real system;

Be [-20 × 10 by the SFO tolerance limit of IEEE 802.11a agreement defined ^-6,+20 × 10 ^-6], namely need to make the SFO of communication system drop on [-20 × 10 ^-6,+20 × 10 ^-6] in scope, in proposed combined estimation method, in order to make all SFO values drop within the span of estimation, the tolerance limit of setting SFO be the β of IEEE 802.11a agreement tolerance limit doubly, namely make the variable η of SFO drop on [-2 β × 10 ^-5, 2 β × 10 ^-5] in scope, β is positive integer, general recommendation is greater than 3.

Second step: the span span of SFO being transformed to t, makes t ∈ [-1,1];

Owing to requiring when Legnedre polynomial is approached that the variable of approximated function belongs to interval [-1,1], therefore the variable η of SFO is multiplied by 10 ⁵/ 2 β transform to variable t, and this variations per hour t ∈ [-1,1], meets the condition that Legnedre polynomial is approached.

3rd step: use single order Legnedre polynomial to approach

Wherein, N is the sum (being 64 in IEEE 802.11a agreement) of communication system sub-carriers, N _mfor communication system sub-carriers sum adds the length (being 80 in IEEE 802.11a agreement) of Cyclic Prefix, p and q is the natural number being less than N.

4th step: will single order Legnedre polynomial approach substitution (2) formula, solve the linear function about t, obtain the value of t;

$0=\underset{p>q}{\mathrm{\Σ}}(p-q)\mathrm{Im}\left(R\left(p\right){R\left(q\right)}^{*}{e}^{j\frac{{2\mathrm{\πN}}_m}{N}(p-q)2\mathrm{\β}\×{10}^{-5}\×t}\right)---\left(2\right)$

Wherein, Im (x) represents the imaginary part of plural x, R (q) ^*represent the conjugation of plural R (q).

5th step: the estimated value being obtained SFO by t

The final estimated value of SFO by the known t of second step 10 ⁵/ 2 β times, therefore the t value the 4th step obtained is divided by 10 ⁵/ 2 β are the estimated value finally estimating the SFO obtained

6th step: by the estimated value of the SFO that the 5th step obtains (3) formula of substitution, obtains the estimated value of CFO

$\widehat{\mathrm{\ϵ}}=-\frac{\mathrm{N\θ}}{{2\mathrm{\πN}}_m(1+\widehat{\mathrm{\η}})}---\left(3\right)$

Wherein, θ is (4) formula phase place, in parameter K represent the sub-carrier number (being 52 in IEEE802.11a agreement) used in communication system, k is more than or equal to the positive integer that-K/2 is less than K/2-1,

$g\left(\widehat{\mathrm{\η}}\right)=\underset{k=-K/2}{\overset{K/2-1}{\mathrm{\Σ}}}{R_1}^{*}\left(k\right)R_0\left(k\right)e^{j\frac{{2\mathrm{\πN}}_m}{N}\mathrm{k\η}}---\left(4\right)$

Compared with prior art, advantage of the present invention is just:

1. the present invention does not need the global search of two dimension, two the long training sequence R received by receiver ₀(k) and R ₁k () just can solve the estimated value of SFO with the estimated value of CFO significantly reduce computation complexity; 2. because the present invention does not need the global search carrying out two dimension, therefore when high SNR, there is not error floor in combined estimation method that the present invention carries, and comparing tradition needs the combined estimation method of two-dimensional search to have higher precision.

Accompanying drawing explanation

Fig. 1 is SFO and the CFO combined estimation method flow chart that the people such as Y.-H.Kim propose;

Fig. 2 is SFO and CFO combined estimation method flow chart of the present invention;

Fig. 3 represents the mean square error comparison diagram of SFO and the CFO combined estimation method estimation sampling frequency offset that the people such as SFO and the CFO combined estimation method that the people such as the present invention and H.Nguyen-Le proposes and Y.-H.Kim proposes;

Fig. 4 represents the mean square error comparison diagram of SFO and the CFO combined estimation method estimation carrier wave frequency deviation that the people such as SFO and the CFO combined estimation method that the people such as the present invention and H.Nguyen-Le proposes and Y.-H.Kim proposes.

Embodiment

Fig. 2 is flow chart of the present invention, the present invention includes following steps:

The first step: in IEEE 802.11a agreement, the typical error tolerance of SFO is [-20 × 10 ^-6,+20 × 10 ^-6], therefore when carrying out single order Legnedre polynomial and approaching, the span arranging SFO is η ∈ [-2 β × 10 ^-5, 2 β × 10 ^-5] be enough to meet the scope of η value in real system;

Second step: make t=(10 ⁵/ 2 β) η, then t ∈ [-1,1], therefore known:

Due to the 3rd step carry out Legnedre polynomial approach time, the independent variable of approximated function needs to be positioned in interval [-1,1], therefore needs to be multiplied by 10 to η ⁵/ 2 β are transformed to t, carry out Legnedre polynomial approach the function containing variable t.

3rd step: right in t ∈ [-1,1] interval, carry out single order Legnedre polynomial approach;

3.1 establish p ₀(t)=1, p ₁(t)=t;

Wherein, p ₀(t) and p ₁t () is respectively constant term that single order Legnedre polynomial approaches and once item, right ask single order Legnedre polynomial to approach, next will obtain the coefficient of constant term and once item respectively;

3.2 calculate (p ₀, p ₀), (p ₁, p ₁), (y, p ₀), (y, p ₁);

Wherein, (x, y) represents the inner product of x and y;

$(p_0,p_0)={\∫}_{-1}^{1}1\mathrm{dt}=2$

$(p_1,p_1)={\∫}_{-1}^1{t}^2\mathrm{dt}=\frac{2}{3}$

$(y,p_0)={\∫}_{-1}^1{e}^{\mathrm{jat}}\mathrm{dt}=2\frac{\sin a}{a}$

$(y,p_1)={\∫}_{-1}^1{\mathrm{te}}^{\mathrm{jat}}\mathrm{dt}=-2j\frac{a\cos a-\sin a}{a^2}$

Wherein

$a=\frac{{2\mathrm{\πN}}_m}{N}(p-q)\×2\mathrm{\β}\×{10}^{-5}$

The coefficient a of 3.3 acquisition single order Legnedre polynomial constant terms and once item ₀, a ₁;

$a_0=\frac{1}{(p_0,p_0)}(y,p_0)=\frac{\sin a}{a}$

$a_1=\frac{1}{(p_1,p_1)}(y,p_1)=3j\frac{\sin a-a\cos a}{a^2}$

3.4 obtain single order Legnedre polynomial approach;

$e^{j\frac{{2\mathrm{\πN}}_m}{N}(p-q)\×2\mathrm{\β}\×{10}^{-5}t}=a_0+a_{1}t---\left(5\right).$

4th step: (5) formula is substituted into (2) formula and solves linear function about t, two long training sequences that can obtain receiving when receiver are R ₀(k) and R ₁t value time (k), the expression of t is such as formula shown in (6);

$t=-\frac{\underset{p>q}{\mathrm{\Σ}}(p-q)\mathrm{Im}\left\{R\left(p\right){R\left(q\right)}^{*}\frac{\sin a}{a}\right\}}{\underset{p>q}{\mathrm{\Σ}}(p-q)\mathrm{Im}\left\{3\mathrm{jR}\left(p\right){R\left(q\right)}^{*}\frac{\sin a-a\cos a}{a^2}\right\}}---\left(6\right)$

5th step: according to the relation of estimated value η and the t of SFO in second step, the final estimated value of known SFO following formula can be expressed as by t;

$\widehat{\mathrm{\η}}=2\mathrm{\β}\×{10}^{-5}t---\left(7\right)$

6th step: by the estimated value of SFO substitution formula (3) can obtain the estimated value obtaining CFO

$\widehat{\mathrm{\ϵ}}=-\frac{\mathrm{N\θ}}{{2\mathrm{\πN}}_m(1+\widehat{\mathrm{\η}})}---\left(8\right)$

Wherein, namely θ is phase place

In matlab, establish base band signal process link based on IEEE 802.11a wireless communication protocol, use the present invention carry combined estimation method and traditional combined estimation method carries out Combined estimator to the sampling frequency offset SFO in this link and carrier wave frequency deviation CFO respectively.When sampling frequency offset η is set to 0.000112, when carrier wave frequency deviation ε is set to 0.212 time, SNR various combined estimation method in [0dB, 50dB] scope result as shown in Figure 3 and Figure 4.In Fig. 3 and Fig. 4 during the emulation of SFO and CFO Combined estimator, CFO is set to 0.212, SFO and is set to 0.000112, each simulation parameter is with reference to IEEE 802.11a standard, OFDM total number of sub-carriers is 64, and the OFDM subcarrier number employed is 52, and circulating prefix-length is 16.In Fig. 3 and Fig. 4, the curve of roundel is article " RLS-based joint estimation and tracking of channelresponse, sampling, and carrier frequency offsets for OFDM " (" based on the channel of recurrence least square in ofdm system, sampling frequency offset and carrier wave frequency deviation Combined estimator and tracking ") in put forward the result curve of combined estimation method, the curve of target cross in article " Joint maximum likelihood estimation of carrier andsampling frequency offsets for OFDM systems " (" sampling frequency offset and carrier wave frequency deviation combined estimation method based on maximal possibility estimation ") put forward the result curve of combined estimation method, the curve of five-pointed star mark puies forward by the present invention the result curve that combined estimation method obtains.

The abscissa of Fig. 3 and Fig. 4 is SNR, unit is dB, ordinate is mean square error, then observe Fig. 3 with Fig. 4 known: when identical SNR, the present invention carry the below that combined estimation method result curve is positioned at classical joint method of estimation curve, namely, under identical state of signal-to-noise, institute of the present invention extracting method has less mean square error, so the present invention has higher estimated accuracy.Particularly when high s/n ratio, this advantage will be more obvious.

Compared to traditional combined estimation method, SFO and the CFO combined estimation method that the present invention carries does not need the global search carrying out two dimension, so the present invention also has the low advantage of computation complexity.

Claims (5)

1., based on sampling frequency offset and the carrier wave frequency deviation combined estimation method of maximal possibility estimation, it is characterized in that comprising the following steps:

The first step: the span determining SFO in real system, method is: the tolerance limit of setting SFO be the β of IEEE 802.11a agreement tolerance limit doubly, β is positive integer, the marginal range namely making the variable η of SFO be greater than agreement to specify, then η ∈ [-2 β × 10 ^-5, 2 β × 10 ^-5];

Second step: the span span of SFO being transformed to variable t, make t ∈ [-1,1], meet the condition that Legnedre polynomial is approached, method is:

Make t=(10 ⁵/ 2 β) η, then t ∈ [-1,1], $e^{j\frac{2\mathrm{\π}{N}_m}{N}(p-q)\mathrm{\η}}=e^{j\frac{2\mathrm{\π}{N}_m}{N}(p-q)\×2\mathrm{\β}\×{10}^{5}t};$

Wherein, N is the sum of communication system sub-carriers, N _mfor communication system sub-carriers sum adds the length of Cyclic Prefix, p and q is the natural number being less than N;

3rd step: use single order Legnedre polynomial to approach obtain single order Legnedre polynomial approach as shown in (5) formula:

$e^{j\frac{2\mathrm{\π}{N}_m}{N}(p-q)\×2\mathrm{\β}\×{10}^{-5}t}=a_0+a_{1}t---\left(5\right)$

4th step: (5) formula is substituted into (2) formula,

$0=\underset{p>q}{\mathrm{\Σ}}(p-q)\mathrm{Im}\left(R\left(p\right)R{\left(q\right)}^{*}{e}^{j\frac{2\mathrm{\π}{N}_m}{N}(p-q)2\mathrm{\β}\×{10}^2\×t}\right)---\left(2\right)$

Wherein, Im (x) represents the imaginary part of plural x, R (q) ^*represent the conjugation of plural R (q), solve the linear function about t, obtain the expression of t as shown in (6) formula;

$t=-\frac{\underset{p>q}{\mathrm{\Σ}}(p-q)\mathrm{Im}\left\{R\right(p\left)R{\left(q\right)}^{*}\frac{\sin a}{a}\right\}}{\underset{p>q}{\mathrm{\Σ}}(p-q)\mathrm{Im}\left\{3\mathrm{jR}\left(p\right)R{\left(q\right)}^{*}\frac{\sin a-a\cos a}{a^2}\right\}}---\left(6\right)$

5th step: according to the relation of estimated value η and the t of SFO in second step, the final estimated value of known SFO following formula can be expressed as by t:

$\widehat{\mathrm{\η}}=2\mathrm{\β}\×{10}^{-5}t---\left(7\right)$

6th step: by the estimated value of the SFO that the 5th step obtains (3) formula of substitution, obtains the estimated value of CFO

$\widehat{\mathrm{\ϵ}}=-\frac{\mathrm{N\θ}}{2\mathrm{\π}{N}_m(1+\widehat{\mathrm{\η}})}---\left(3\right)$

Wherein, namely θ is phase place,

$g\left(\widehat{\mathrm{\η}}\right)=\underset{k=-K/2}{\overset{K/2-1}{\mathrm{\Σ}}}{R_1}^{*}\left(k\right)R_0\left(k\right)e^{j\frac{2\mathrm{\π}{N}_m}{N}\mathrm{k\η}}---\left(4\right),$

K represents the sub-carrier number used in communication system, and k is more than or equal to the positive integer that-K/2 is less than K/2-1.

2. a kind of sampling frequency offset based on maximal possibility estimation and carrier wave frequency deviation combined estimation method as claimed in claim 1, is characterized in that the total N of communication system sub-carriers is 64, and communication system sub-carriers sum adds the length N of Cyclic Prefix _mbe 80.

3. a kind of sampling frequency offset based on maximal possibility estimation and carrier wave frequency deviation combined estimation method as claimed in claim 1, is characterized in that using single order Legnedre polynomial to approach method be:

3.1 establish p ₀(t)=1, p ₁(t)=t;

Wherein, p ₀(t) and p ₁t () is respectively constant term that single order Legnedre polynomial approaches and once item;

3.2 calculate (p ₀, p ₀), (p ₁, p ₁), (y, p ₀), (y, p ₁);

Wherein, (x, y) represents the inner product of x and y;

$(p_0,p_0)={\∫}_{-1}^{1}1\mathrm{dt}=2$

$(p_1,p_1)={\∫}_{-1}^1{t}^2\mathrm{dt}=\frac{2}{3}$

$(y,p_0)={\∫}_{-1}^1{e}^{\mathrm{jat}}\mathrm{dt}=2\frac{\sin a}{a}$

$(y,p_1)={\∫}_{-1}^1{\mathrm{te}}^{\mathrm{jat}}\mathrm{dt}=-2j\frac{a\cos a-\sin a}{a^2}$

Wherein

$a=\frac{2\mathrm{\π}{N}_m}{N}(p-q)\×2\mathrm{\β}\×{10}^{-5};$

3.3 obtain single order Legendre polynomials number a ₀, a ₁;

$a_0=\frac{1}{(p_0,p_0)}(y,p_0)=\frac{\sin a}{a}$

$a_1=\frac{1}{(p_1,p_1)}(y,p_1)=3j\frac{\sin a-a\cos a}{a^2}$

3.4 obtain single order Legnedre polynomial approach as shown in (5) formula.

4. a kind of sampling frequency offset based on maximal possibility estimation and carrier wave frequency deviation combined estimation method as claimed in claim 1, is characterized in that in parameter K be 52.

5. a kind of sampling frequency offset based on maximal possibility estimation and carrier wave frequency deviation combined estimation method as claimed in claim 1, is characterized in that β is greater than 3.