CN103346991A - Channel estimation and synchronization method based on cyclic prefixes - Google Patents

Abstract

The invention discloses a channel estimation and synchronization method based on cyclic prefixes, and relates to the channel estimation and synchronization method applied to a well logging telemetry system. The channel estimation and synchronization method based on the cyclic prefixes solves the problems that an existing channel estimation and synchronization method is low in accuracy, large in algorithm complexity and long in estimated time. The method includes the following steps: first, a sending end collects data from a sensor for modulation, and the modulated data are sent to a cable for transmission; second, a receiving end receives OFDM signals which are transmitted by channels and have the cyclic prefixes; third, for channel delay theta, the mth symbol is interfered by the (m-1)th symbol; fourth, a probability density function and a log-likelihood function of the mth symbol are calculated; fifth, the power of the received signals is calculated through the data of the received M OFDM symbols; sixth, in order to evaluate the power of N channels, a (N+NG)*N constant matrix A is set; seventh, the set operation is conducted on relevant sampling sites to infer the starting position of a DFT window. The channel estimation and synchronization method based on the cyclic prefixes is applied to the field of underground oil exploitation.

Description

A kind of channel estimating and method for synchronous based on Cyclic Prefix

Technical field

The present invention relates to a kind of channel estimating and method for synchronous that is applied to logging remote transmission system, especially a kind of channel estimating and method for synchronous based on OFDM technical data transmission system.

Background technology

Obtain down-hole oil reservoir information with the most reasonable logging mode efficiently in the oil exploitation, it is considerable carrying out oil-gas mining to greatest extent.Wireless well logging transmission technologys such as electromagnetic wave, sound wave, mud-pulse are quite paid close attention in oil reservoir logging, but too serious for long Distance Transmission signal attenuation, be difficult to guarantee data accuracy, and message transmission rate are difficult to improve.

In the oil reservoir logging field, normally utilize 4000～7000 meters cable that measuring instrument is transferred to the down-hole, various indexs and parameters such as the pressure on measurement stratum, density, when common electric power cable is transferred to the down-hole with measuring instrument to power devices, in addition can also be as the data transmission channel between aboveground and the downhole instrument.Single-core cable go into the well easily because of it and price lower, as transmission path, has very high reliability, utilize cable transmission data needn't lay telecommunication cable in addition, save cost and fortification, but utilize the transmission rate of seven core cable data transmission system to be no more than 500kbps at present, single-core cable communications speed is no more than 80kbps.

Channel estimating and estimation synchronously generally are separately to carry out, and through two module arithmetics, the someone discusses based on the channel estimating of the no inclined to one side consistent Estimation of pilot tone and synchronization combining algorithm.Be divided into the auxiliary and non-data-aided method of data by whether inserting data in addition.Existing channel estimating and the estimation synchronously methods that in channel, add the cyclic training sequence that adopt more, be the Schmild algorithm the earliest, estimated performance is better, but it is synchronous or finish judgement at receiving terminal and just can estimate with receiving terminal need to insert pilot tone, has reduced transmission rate; Non-data-aided method needn't be inserted data in addition, only handles receiving data, does not waste channel resource, and shortcoming is exactly that algorithm complex is big, and estimated time is long.

Synchronous estimation based on Cyclic Prefix, can obtain simultaneously regularly and the decimal frequency bias estimation as the Beek algorithm, but only be applicable to the gaussian sum flat fading channel, and accuracy of estimation is limited, algorithm on this basis generally is to improve its probability density metric function, generally has limitation.

Summary of the invention

The present invention will solve that existing channel is estimated and the synchronous estimation method transmission rate is low, and complexity is big, the problem that grow estimated time, and a kind of channel estimating based on Cyclic Prefix and method for synchronous are provided.

Channel estimating and method for synchronous based on Cyclic Prefix comprise following content:

One, the transmitting terminal collection is carried out (2,1,3) convolutional encoding as forward error correction FEC control from the data of downhole sensor, and coding is exported the input as 16QAM, and then is mapped to QAM data flow X _k=[X _{0, k}, X _{1, k}... X _{N-1, k}], 0≤k≤N-1, X _kRepresent the data on i subcarrier of k symbol;

The QAM data flow is carried out inverse discrete Fourier transform IDFT and parallel serial conversion successively, becomes OFDM symbol serial data stream x _n=[x _{0, n}, x _{1, n}... x _{N-1, n}];

Be N with the tail end length of each OFDM symbol serial data stream _GData Copy to OFDM symbol serial data stream front as Cyclic Prefix, be added with the Cyclic Prefix in OFDM System signal and be coupled on the single-core cable and transmit;

Two, receiving terminal receive channel transmission be added with the Cyclic Prefix in OFDM System signal, will be added with the Cyclic Prefix in OFDM System signal from the single-core cable decoupling zero and carry out power amplification through what channel transmitted then, sample frequency is identical with transmitting terminal, is designated as r (n), is modeled as:

$r\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)s(n-\mathrm{\θ})+\mathrm{\ω}\left(n\right)$

H (n, l) the expression impulse response of l subchannel of n constantly, 1≤l≤L, ω (n) expression zero-mean variance is σ _{2 ω}White Gaussian noise, θ are channel latency;

Wherein, definition transmitting terminal Cyclic Prefix data

With receiving terminal OFDM symbol serial data stream endian data

Correlation is carried out synchronously and channel estimating;

Three, for channel latency θ, m symbol is subjected to m-1 symbol-interference:

$r_m\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_{m-1}(n-l-\mathrm{\θ})+\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_m(n-l-\mathrm{\θ})+\mathrm{\ω}\left(n\right)---\left(1\right)$

n∈{θ，θ+1，…θ+N+N _G-1}

$r_m(n+N)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_m(n+N-l-\mathrm{\θ})+$ (2)

$\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_{m+1}(n+N-l-\mathrm{\θ})+\mathrm{\ω}(n+N)$

The correlation expectation and the coefficient correlation that are divided into mutually between two sampled values of N are respectively:

${\mathrm{\γ}}_n=E\left[r_m\left(n\right)r_m^{*}(n+N)\right]=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\σ}}_{h\left(l\right)}^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2---\left(3\right)$

${\mathrm{\ρ}}_n=\frac{E\left[r_m\left(n\right)r_m^{*}(n+N)\right]}{\sqrt{E\left[\right|r_m\left(n\right){|}^2]+E[\left|r_m(n+N){|}^2\right]}}---\left(4\right)$

Four, intercepted length is 2N+N _GThe region of search in, calculate m symbol probability density function and ask log-likelihood function to obtain following formula:

${\mathrm{\Λ}}_m=\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N+N_G}{\mathrm{\Π}}}\frac{f(r_m\left(n\right),r_m(n+N))}{f\left(r_m\left(n\right)\right)f\left(r_m(n+N)\right)}---\left(5\right)$

After receiving M symbol, based on relevant expectation γ _nWith coefficient correlation ρ _nLog-likelihood function become:

$\mathrm{\Λ}=\log \left(\underset{m}{\mathrm{\Π}}{\mathrm{\Λ}}_m\right)=M\underset{n}{\mathrm{\Σ}}\{\frac{2({\mathrm{\ρ}}_n\mathrm{\Ψ}\left(n\right)-{\mathrm{\ρ}}_n^2\mathrm{\Φ}\left(n\right))}{({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)(1-{\mathrm{\ρ}}_n^2)}-\log (1-{\mathrm{\ρ}}_n^2)\}---\left(6\right)$

Order

(7)

${\mathrm{\φ}}_n=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right)|+|r_m^{*}(n+N)\left|\right]$

(8)

$\mathrm{\Φ}\left(n\right)=\frac{1}{2M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right){|}^2+\left|r_m^{*}(n+N){|}^2\right]=\frac{{\mathrm{\φ}}_n}{2}$

θ≤n≤θ+N+N wherein _G-1, ask local derviation to obtain the coefficient correlation ρ of likelihood function Λ:

${\widehat{\mathrm{\ρ}}}_n=\frac{\mathrm{\Ψ}\left(n\right)}{\mathrm{\Φ}\left(n\right)}$ (9)

${\widehat{\mathrm{\γ}}}_n=\mathrm{\Ψ}\left(n\right)$

Thereby obtain the least-squares estimation vector of correlation:

$\hat{r}=[{\widehat{\mathrm{\γ}}}_0,{\widehat{\mathrm{\γ}}}_1,\·\·\·{\widehat{\mathrm{\γ}}}_{N+N_G-1}{]}^T---\left(10\right)$

Five, the power of the data computation reception signal by M OFDM symbol receiving:

Utilize received signal power (12) formula to ask for the coefficient correlation of whole channel:

$\mathrm{\ρ}=\frac{E\left[\right|r_m\left(n\right){|}^2-{\mathrm{\σ}}_{\mathrm{\ω}}^2}{E\left[\right|r_m\left(n\right){|}^2]}---\left(12\right)$

Six, estimate the power of L channel, establish (N+N _G) * N constant matrices A:

$A=[a\left(0\right),a\left(1\right),\·\·\·,a\left(N\right){]}_{(N+N_G)\×N}$

$a\left(0\right)=[a\left(\mathrm{0,0}\right),a\left(\mathrm{0,1}\right),\·\·\·,a(0,N+N_G-1){]}^T$

$={\left[\begin{array}{cc}{1}_{1\×N_G}& 0_{1\×N}\end{array}\right]}_{(N+N_G)\×1}^T---\left(13\right)$

a(i)＝[a(i，0)，a(i，1)，…，a(i，N+N _G-1)] ^T

a(i，j)＝a(0，(-i+j))mod(N+N _G)

It is mobile that element among a (i) just press the element among a (0) the i circulation, ring shift right, and with regard to confirmable constant matrix, the channel power on L subchannel is estimated as after determining for the useful symbol of OFDM and circulating prefix-length:

First sub-channel positions performance number is given up, and the power that obtains L=N channel is estimated A ⁺Be the pseudo inverse matrix of A,

Be the column matrix of N, namely finished channel estimating;

Seven, to correlated sampling point set algorithm development DFT window starting position, Λ _mBe the maximum likelihood function based on Cyclic Prefix of every frame data:

$\mathrm{\Λ}=\frac{1}{M}\underset{m}{\mathrm{\Σ}}{\mathrm{\Λ}}_m=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}{r}_m\left(n\right)r_m^{*}(n+N)$ (15)

$-\frac{\mathrm{\ρ}}{2}\frac{1}{M}\underset{m}{\mathrm{\Σ}}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}{\left|r\left(n\right)\right|}^2+|r^{*}(n+N){|}^2$

$\mathrm{\Λ}=\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}\frac{1}{M}\underset{m}{\mathrm{\Σ}}{r}_m\left(n\right)r_m^{*}\left(\text{n+N}\right)$ (16)

$-\frac{\mathrm{\ρ}}{2}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}\frac{1}{M}\underset{m}{\mathrm{\Σ}}|r\left(n\right){|}^2+|r^{*}(n+N){|}^2$

The maximum likelihood function of this step relative set is to M frame data N+N _GThe data of length are carried out correlation operation, i.e. two-dimensional search, and the accuracy of timing estimation is higher, tries to achieve the θ of maximum correspondence of likelihood function with regard to is-symbol timing estimation position, i.e. DFT window starting position:

Utilize the autocorrelation performance of Cyclic Prefix, this method obtains the sub-channel power estimation by the maximum likelihood algorithm of synchronous estimation, finish timing synchronization with the channel power results estimated conversely and estimate, namely finish channel estimating and method for synchronous based on Cyclic Prefix.

The invention effect:

The present invention is based on channel estimating and the signal-timing method of Cyclic Prefix, regularly separating the situation of carrying out with channel estimating and symbol compares, reduced the complexity of computing, utilize the symbol of channel estimation results regularly to calculate and belong to two-dimensional search, have higher estimated accuracy, can be applicable to most evil bad channel circumstance.For M sample, the multiplicative complexity of unified algorithm is M*NG, and most of is add operation, and obviously this algorithm complex is minimum.The present invention can realize that the single-core cable channel transmission rate is 80kbps, the spread of the rumours system of error rate 1e-4.

Description of drawings

Fig. 1 is flow chart of the present invention;

Fig. 2 is the ofdm system structure chart that is applied in the single-core cable;

Fig. 3 is the intrinsic behavioral illustrations figure of circulating prefix structure;

Fig. 4 is channel estimating and the timing synchronization algorithm block diagram based on Cyclic Prefix that proposes, ψ n and

Be that the M frame data are searched for by row, corresponding each n circulation stack computing,

Represent that two inputs pass through certain calculation.

Embodiment

Embodiment one: channel estimating and the method for synchronous based on Cyclic Prefix of present embodiment comprise following content:

Channel estimating and method for synchronous based on Cyclic Prefix comprise following content:

One, the transmitting terminal collection is carried out (2,1,3) convolutional encoding as forward error correction FEC control from the data of downhole sensor, and coding is exported the input as 16QAM, and then is mapped to QAM data flow X _k=[X _{0, k}, X _{1, k}... X _{N-1, k}], 0≤k≤N-1, X _kRepresent the data on i subcarrier of k symbol;

The QAM data flow is carried out inverse discrete Fourier transform IDFT and parallel serial conversion successively, becomes OFDM symbol serial data stream x _n=[x _{0, n}, x _{1, n}... x _{N-1, n}];

Be N with the tail end length of each OFDM symbol serial data stream _GData Copy to OFDM symbol serial data stream front as Cyclic Prefix, be added with the Cyclic Prefix in OFDM System signal and be coupled on the single-core cable and transmit;

Two, receiving terminal receive channel transmission be added with the Cyclic Prefix in OFDM System signal, will be added with the Cyclic Prefix in OFDM System signal from the single-core cable decoupling zero and carry out power amplification through what channel transmitted then, sample frequency is identical with transmitting terminal, is designated as r (n), is modeled as:

$r\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)s(n-\mathrm{\θ})+\mathrm{\ω}\left(n\right)$

H (n, l) the expression impulse response of l subchannel of n constantly, 1≤l≤L, ω (n) expression zero-mean variance is σ _{2 ω}White Gaussian noise, θ are channel latency;

Wherein, definition transmitting terminal Cyclic Prefix data With receiving terminal OFDM symbol serial data stream endian data

Correlation is carried out synchronously and channel estimating;

Three, for channel latency θ, m symbol is subjected to m-1 symbol-interference:

$r_m\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_{m-1}(n-l-\mathrm{\θ})+\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_m(n-l-\mathrm{\θ})+\mathrm{\ω}\left(n\right)$ (19)

n∈{θ，θ+1，…θ+N+N _G-1}

$r_m(n+N)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_m(n+N-l-\mathrm{\θ})+$ (20)

$\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_{m+1}(n+N-l-\mathrm{\θ})+\mathrm{\ω}(n+N)$

The correlation expectation and the coefficient correlation that are divided into mutually between two sampled values of N are respectively:

${\mathrm{\γ}}_n=E\left[r_m\left(n\right)r_m^{*}(n+N)\right]=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\σ}}_{h\left(l\right)}^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2---\left(21\right)$

${\mathrm{\ρ}}_n=\frac{E\left[r_m\left(n\right)r_m^{*}(n+N)\right]}{\sqrt{E\left[\right|r_m\left(n\right){|}^2]+E[\left|r_m(n+N){|}^2\right]}}---\left(22\right)$

Four, intercepted length is 2N+N _GThe region of search in, calculate m symbol probability density function and ask log-likelihood function to obtain following formula:

${\mathrm{\Λ}}_m=\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N+N_G}{\mathrm{\Π}}}\frac{f(r_m\left(n\right),r_m(n+N))}{f\left(r_m\left(n\right)\right)f\left(r_m(n+N)\right)}---\left(23\right)$

After receiving M symbol, based on relevant expectation γ _nWith coefficient correlation ρ _nLog-likelihood function become:

$\mathrm{\Λ}=\log \left(\underset{m}{\mathrm{\Π}}{\mathrm{\Λ}}_m\right)=M\underset{n}{\mathrm{\Σ}}\{\frac{2({\mathrm{\ρ}}_n\mathrm{\Ψ}\left(n\right)-{\mathrm{\ρ}}_n^2\mathrm{\Φ}\left(n\right))}{({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)(1-{\mathrm{\ρ}}_n^2)}-\log (1-{\mathrm{\ρ}}_n^2)\}---\left(24\right)$

Order

(25)

${\mathrm{\φ}}_n=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right)|+|r_m^{*}(n+N)\left|\right]$

(26)

$\mathrm{\Φ}\left(n\right)=\frac{1}{2M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right){|}^2+\left|r_m^{*}(n+N){|}^2\right]=\frac{{\mathrm{\φ}}_n}{2}$

θ≤n≤θ+N+N wherein _G-1, ask local derviation to obtain the coefficient correlation ρ of likelihood function Λ:

${\widehat{\mathrm{\ρ}}}_n=\frac{\mathrm{\Ψ}\left(n\right)}{\mathrm{\Φ}\left(n\right)}---\left(27\right)$

${\widehat{\mathrm{\γ}}}_n=\mathrm{\Ψ}\left(n\right)$

Thereby obtain the least-squares estimation vector of correlation:

$\hat{r}=[{\widehat{\mathrm{\γ}}}_0,{\widehat{\mathrm{\γ}}}_1,\·\·\·{\widehat{\mathrm{\γ}}}_{N+N_G-1}{]}^T---\left(28\right)$

Five, the power of the data computation reception signal by M OFDM symbol receiving:

Utilize received signal power (12) formula to ask for the coefficient correlation of whole channel:

$\mathrm{\ρ}=\frac{E\left[\right|r_m\left(n\right){|}^2-{\mathrm{\σ}}_{\mathrm{\ω}}^2}{E\left[\right|r_m\left(n\right){|}^2]}---\left(30\right)$

Six, estimate the power of L channel, establish (N+N _G) * N constant matrices A:

$A=[a\left(0\right),a\left(1\right),\·\·\·,a\left(N\right){]}_{(N+N_G)\×N}$

$a\left(0\right)=[a\left(\mathrm{0,0}\right),a\left(\mathrm{0,1}\right),\·\·\·,a(0,N+N_G-1){]}^T$

$={\left[\begin{array}{cc}{1}_{1\×N_G}& 0_{1\×N}\end{array}\right]}_{(N+N_G)\×1}^T---\left(31\right)$

a(i)＝[a(i，0)，a(i，1)，…，a(i，N+N _G-1)] ^T

a(i，j)＝a(0，(-i+j))mod(N+N _G)

It is mobile that element among a (i) just press the element among a (0) the i circulation, ring shift right, and with regard to confirmable constant matrix, the channel power on L subchannel is estimated as after determining for the useful symbol of OFDM and circulating prefix-length:

First sub-channel positions performance number is given up, and the power that obtains L=N channel is estimated A ⁺Be the pseudo inverse matrix of A,

Be the column matrix of N, namely finished channel estimating;

Seven, to correlated sampling point set algorithm development DFT window starting position, Λ _mBe the maximum likelihood function based on Cyclic Prefix of every frame data:

$\mathrm{\Λ}=\frac{1}{M}\underset{m}{\mathrm{\Σ}}{\mathrm{\Λ}}_m=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}{r}_m\left(n\right)r_m^{*}(n+N)$ (33)

$-\frac{\mathrm{\ρ}}{2}\frac{1}{M}\underset{m}{\mathrm{\Σ}}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}{\left|r\left(n\right)\right|}^2+|r^{*}(n+N){|}^2$

$\mathrm{\Λ}=\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}\frac{1}{M}\underset{m}{\mathrm{\Σ}}{r}_m\left(n\right)r_m^{*}\left(\text{n+N}\right)$ (34)

$-\frac{\mathrm{\ρ}}{2}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}\frac{1}{M}\underset{m}{\mathrm{\Σ}}|r\left(n\right){|}^2+|r^{*}(n+N){|}^2$

The maximum likelihood function of this step relative set is to M frame data N+N _GThe data of length are carried out correlation operation, i.e. two-dimensional search, and the accuracy of timing estimation is higher, tries to achieve the θ of maximum correspondence of likelihood function with regard to is-symbol timing estimation position, i.e. DFT window starting position:

Utilize the autocorrelation performance of Cyclic Prefix, this method obtains the sub-channel power estimation by the maximum likelihood algorithm of synchronous estimation, finish timing synchronization with the channel power results estimated conversely and estimate, namely finish channel estimating and method for synchronous based on Cyclic Prefix.

The present embodiment effect:

The present invention is based on channel estimating and the signal-timing method of Cyclic Prefix, regularly separating the situation of carrying out with channel estimating and symbol compares, reduced the complexity of computing, utilize the symbol of channel estimation results regularly to calculate and belong to two-dimensional search, have higher estimated accuracy, can be applicable to most evil bad channel circumstance.For M sample, the multiplicative complexity of unified algorithm is M*NG, and most of is add operation, and obviously this algorithm complex is minimum.The present invention can realize that the single-core cable channel transmission rate is 80kbps, the spread of the rumours system of error rate 1e-4.

Verify the present embodiment effect by following examples:

One, the transmitting terminal collection is at first carried out (2,1,3) convolutional encoding as forward error correction FEC control from the data of transducer, and coding output is mapped to QAM data flow X as the input of 16QAM _k=[X _{0, k}, X _{1, k}... X _{N-1, k}], 0≤k≤N-1 represents the data on i subcarrier of k symbol; Modulation signal carries out serial to parallel conversion, inverse discrete Fourier transform IDFT and parallel serial conversion successively, becomes serial data stream x _k=[x _{0, k}, x _{1, k}... x _{N-1, k}], be the data d of M with the tail end length of each OFDM symbol _k=[x _{N-M, k}, x _{N-M+1, k}... x _{N-1, k}] copy to the front as Cyclic Prefix, be added with the Cyclic Prefix in OFDM System signal and be coupled on the single-core cable and transmit;

Two, receiving terminal will be through the signal of channel transmission from the single-core cable decoupling zero and carry out power amplification, and sample frequency is identical with transmitting terminal, is designated as r (n), is modeled as:

$r\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)s(n-\mathrm{\θ})+\mathrm{\ω}\left(n\right)$

H (n, l) the expression impulse response of l subchannel of n constantly, 1≤l≤L, ω (n) expression zero-mean variance is σ _{2 ω}White Gaussian noise, θ are channel latency, at first according to Cyclic Prefix data z (n)=[r _{N-G (n)}, r _{N-G+1 (n)}... r _{N-1 (n)}] and OFDM symbol endian data y _(n)=[r _{N-G (n)}, r _{N-G+1 (n)}... r _{N-1 (n)}] correlation carries out synchronously and channel estimating;

Three, the foundation of channel estimating is that the symbol of the message segment correspondence position of a plurality of frames transmits at same subchannel, utilizing these symbol power and received signal power to estimate power on this subchannel, specifically is to make the maximized y of z (n) probability density function (n) and channel parameter:

$f\left(r_m\left(n\right)\right)=\frac{\exp (-\frac{\left|r_m\left(n\right)\right|}{{\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2})}{\mathrm{\π}({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)}$

For delayedchannel, m symbol is subjected to m-1 symbol-interference,

$r_m\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_{m-1}(n-l-\mathrm{\θ})+\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_m(n-l-\mathrm{\θ})+\mathrm{\ω}\left(n\right)$

n∈{θ，θ+1，…θ+N+N _G-1}

$r_m(n+N)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_m(n+N-l-\mathrm{\θ})+$

$\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_{m+1}(n+N-l-\mathrm{\θ})+\mathrm{\ω}(n+N)$

Associating Gaussian probability-density function between two sampled values:

$f(r_m\left(n\right),r_m(n+N))=\frac{\exp (-\frac{|r_m\left(n\right){|}^2-2{\mathrm{\ρ}}_n\mathrm{Re}\{r_m\left(n\right)r_m^{*}(n+N)+|r_m(n+N){|}^2}{({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)(1-{\mathrm{\ρ}}_n^2)})}{{\mathrm{\π}}^2{({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)}^2(1-{\mathrm{\ρ}}_n^2)}$

Wherein

${\mathrm{\σ}}_r^2\≡\underset{l}{\mathrm{\Σ}}{\mathrm{\σ}}_{h\left(l\right)}^2$

Coefficient correlation between the sampled value of two N of being separated by and correlation expectation:

${\mathrm{\ρ}}_n=\frac{E\left[r_m\left(n\right)r_m^{*}(n+N)\right]}{\sqrt{E\left[\right|r_m\left(n\right){|}^2]+E[\left|r_m(n+N){|}^2\right]}}$

${\mathrm{\γ}}_n=E\left[r_m\left(n\right)r_m^{*}(n+N)\right]=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\σ}}_{h\left(l\right)}^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2$

Four, intercepted length is 2N+N in frame data _GThe region of search in, calculate m symbol probability density function and ask log-likelihood function to obtain following formula:

${\mathrm{\Λ}}_m=\log \left(\underset{m}{\mathrm{\Π}}\frac{f(r_m\left(n\right),r_m(n+N))}{f\left(r_m\left(n\right)\right)f\left(r_m(n+N)\right)}\right)$

After receiving M symbol, based on relevant expectation γ _nBecome with the log-likelihood function of coefficient correlation ρ:

$\mathrm{\Λ}=M\underset{n}{\mathrm{\Σ}}\{\frac{2({\mathrm{\ρ}}_n\mathrm{\Ψ}\left(n\right)-{\mathrm{\ρ}}_n^2\mathrm{\Φ}\left(n\right))}{({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)(1-{\mathrm{\ρ}}_n^2)}-\log (1-{\mathrm{\ρ}}_n^2)\}$

Order

${\mathrm{\φ}}_n=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right)|+|r_m^{*}(n+N)\left|\right]$

$\mathrm{\Φ}\left(n\right)=\frac{1}{2M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right){|}^2+\left|r_m^{*}(n+N){|}^2\right]=\frac{{\mathrm{\φ}}_n}{2}$

θ≤n≤θ+N+N wherein _G-1, require the maximum of likelihood function Λ, to coefficient correlation ρ _nAsk local derviation:

$\mathrm{\Λ}\≡M\underset{n}{\mathrm{\Σ}}{\mathrm{\Λ}}_n$

$\frac{{\mathrm{d\Λ}}_n}{d{\mathrm{\ρ}}_n}=\frac{-2}{({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)(1-{\mathrm{\ρ}}_n^2)}\{({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2){\mathrm{\ρ}}_n^3-\mathrm{\Ψ}\left(n\right){\mathrm{\ρ}}_n^2+$

$[2\mathrm{\Φ}\left(n\right)-({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)]{\mathrm{\ρ}}_n+\mathrm{\Ψ}\left(n\right)\}$

Only need make following formula equal zero and just can obtain ρ _nEstimation, but unusual difficult the asking of its real root:

$({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2){\mathrm{\ρ}}_n^3-\mathrm{\Ψ}\left(n\right){\mathrm{\ρ}}_n^2+[2\mathrm{\Φ}\left(n\right)-({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)]{\mathrm{\ρ}}_n-\mathrm{\Ψ}\left(n\right)=0$

As can be seen

When especially M is bigger, so (33) formula becomes:

$({\mathrm{\ρ}}_n^2+1)(\mathrm{\Φ}\left(n\right){\mathrm{\ρ}}_n-\mathrm{\ψ}\left(n\right))=0$

Obtained the maximal possibility estimation of coefficient correlation with relevant expectation:

${\widehat{\mathrm{\ρ}}}_n=\frac{\mathrm{\Ψ}\left(n\right)}{\mathrm{\Φ}\left(n\right)}$

${\widehat{\mathrm{\γ}}}_n=\mathrm{\Ψ}\left(n\right)$

Thereby obtain the least-squares estimation vector of correlation:

$\hat{r}=[{\widehat{\mathrm{\γ}}}_0,{\widehat{\mathrm{\γ}}}_1,\·\·\·{\widehat{\mathrm{\γ}}}_{N+N_G-1}{]}^T$

Five, receive the power of signal by the data computation of the M frame OFDM symbol that receives:

Utilize received signal power (37) formula to ask for the coefficient correlation of whole channel:

$\mathrm{\ρ}=\frac{E\left[\right|r_m\left(n\right){|}^2-{\mathrm{\σ}}_{\mathrm{\ω}}^2}{E\left[\right|r_m\left(n\right){|}^2]}$

Six, estimate for the power of asking N+1 channel, establish (N+N _G) * N constant matrices A,

$A=[a\left(0\right),a\left(1\right),\·\·\·,a\left(N\right){]}_{(N+N_G)\×N}$

$a\left(0\right)=[a\left(\mathrm{0,0}\right),a\left(\mathrm{0,1}\right),\·\·\·,a(0,N+N_G-1){]}^T$

$={\left[\begin{array}{cc}{1}_{1\×N_G}& 0_{1\×N}\end{array}\right]}_{(N+N_G)\×1}^T$

a(i)＝[a(i，0)，a(i，1)，…，a(i，N+N _G-1)] ^T

a(i，j)＝a(0，(-i+j))mod(N+N _G)

Notice that the element among a (i) is the element among a (0) to be pressed the i circulation move ring shift right.Determine the back with regard to confirmable constant matrix for the useful symbol of OFDM and circulating prefix-length, then the channel power on L subchannel:

First sub-channel positions performance number is given up, and is estimated A by the power that can obtain L channel ⁺Be the pseudo inverse matrix of A,

Column matrix for N.This step has been finished channel estimating;

Seven, utilize the result of calculation of channel estimating that the symbol timing position is carried out two-dimensional search:

At first pair correlation function is derived:

$\mathrm{\Λ}=\frac{1}{M}\underset{m}{\mathrm{\Σ}}{\mathrm{\Λ}}_m=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}{r}_m\left(n\right)r_m^{*}(n+N)$

$-\frac{\mathrm{\ρ}}{2}\frac{1}{M}\underset{m}{\mathrm{\Σ}}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}{\left|r\left(n\right)\right|}^2+|r^{*}(n+N){|}^2$

$\mathrm{\Λ}=\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}\frac{1}{M}\underset{m}{\mathrm{\Σ}}{r}_m\left(n\right)r_m^{*}\left(\text{n+N}\right)$

$-\frac{\mathrm{\ρ}}{2}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}\frac{1}{M}\underset{m}{\mathrm{\Σ}}|r\left(n\right){|}^2+|r^{*}(n+N){|}^2$

Try to achieve the θ of maximum correspondence of likelihood function with regard to is-symbol timing estimation position, just DFT window starting position:

$\mathrm{\θ}=\arg \underset{\mathrm{\θ}}{\max }\left\{\mathrm{\Λ}\left(\mathrm{\θ}\right)\right\}$

The present embodiment effect:

Present embodiment is based on channel estimating and the signal-timing method of Cyclic Prefix, regularly separating the situation of carrying out with channel estimating and symbol compares, reduced the complexity of computing, utilize the symbol of channel estimation results regularly to calculate and belong to two-dimensional search, have higher estimated accuracy, can be applicable to most evil bad channel circumstance.For M sample, the multiplicative complexity of unified algorithm is M*NG, and most of is add operation, and obviously this algorithm complex is minimum.Present embodiment can realize that the single-core cable channel transmission rate is 80kbps, the spread of the rumours system of error rate 1e-4.

Verify the present embodiment effect by following examples:

One, at first the information of decoupling zero is carried out power amplification, suppose that sampling timing is accurate, receive the M frame data, every frame comprises a plurality of OFDM symbols, is modeled as:

$r\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)s(n-\mathrm{\θ})+\mathrm{\ω}\left(n\right)$

21, the M frame data that receive are pressed column count:

${\mathrm{\φ}}_n=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right)|+|r_m^{*}(n+N)\left|\right]$

Two or two, at first carry out channel estimating:

$\mathrm{\Φ}\left(n\right)=\frac{1}{2M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right){|}^2+\left|r_m^{*}(n+N){|}^2\right]=\frac{{\mathrm{\φ}}_n}{2}$

Two or three, receive the power of signal:

Two or four, obtain correlation function

${\widehat{\mathrm{\γ}}}_n=\mathrm{\Ψ}\left(n\right)$

$\hat{r}=[{\widehat{\mathrm{\γ}}}_0,{\widehat{\mathrm{\γ}}}_1,\·\·\·{\widehat{\mathrm{\γ}}}_{N+N_G-1}{]}^T$

Two or five, establish (N+N _G) * N constant matrices A, can calculate and store in advance:

$A=[a\left(0\right),a\left(1\right),\·\·\·,a\left(N\right){]}_{(N+N_G)\×N}$

$a\left(0\right)=[a\left(\mathrm{0,0}\right),a\left(\mathrm{0,1}\right),\·\·\·,a(0,N+N_G-1){]}^T$

$={\left[\begin{array}{cc}{1}_{1\×N_G}& 0_{1\×N}\end{array}\right]}_{(N+N_G)\×1}^T$

a(i)＝[a(i，0)，a(i，1)，…，a(i，N+N _G-1)] ^T

a(i，j)＝a(0，(-i+j))mod(N+N _G)

Two or six, calculating sub-channel power according to the estimation of (48), (49), (50) estimates:

31, by the coefficient correlation of the whole channel of power calculation that receives signal:

$\mathrm{\ρ}=\frac{E\left[\right|r_m\left(n\right){|}^2]-{\mathrm{\σ}}_{\mathrm{\ω}}^2}{E\left[\right|r_m\left(n\right){|}^2]}$

Three or two, the region of search being set in the emulation is 2N+N _G, to the data computation of circulating prefix-length, maximum likelihood correlation function tolerance:

The corresponding θ of its maximum is with regard to is-symbol timing estimation value:

Fig. 2 is the ofdm system structure chart that is applied in the present embodiment in the single-core cable, comprise convolutional encoding and decoding, constellation mapping and solution mapping, IFFT/FFT conversion, and add/go cyclic prefix module, receiving terminal at first carries out channel estimating by receiving data, carry out timing synchronization by estimated result, the subchannel estimating power can carry out the adaptive bit loading simultaneously, and each channel by its big or small assignment information bit that gains, is improved systematic function;

Fig. 3 is the intrinsic behavioral illustrations of circulating prefix structure in the present embodiment, and Cyclic Prefix is added in each OFDM symbol front end, and as can be seen from the figure the maximum likelihood function of probability density appears at the strongest data interval of correlation;

Fig. 4 is channel estimating and the timing synchronization algorithm block diagram based on Cyclic Prefix that proposes in the present embodiment, ψ n and

Be that the M frame data are searched for by row, corresponding each n circulation stack computing,

Represent that two inputs pass through certain calculation.

Claims (1)

1. channel estimating and method for synchronous based on a Cyclic Prefix is characterized in that comprising following content based on channel estimating and the method for synchronous of Cyclic Prefix:

One, the transmitting terminal collection is carried out (2,1,3) convolutional encoding as forward error correction FEC control from the data of downhole sensor, and coding is exported the input as 16QAM, and then is mapped to QAM data flow X _k=[X _{0, k}, X _{1, k}... X _{N-1, k}], 0≤k≤N-1, X _kRepresent the data on i subcarrier of k symbol;

The QAM data flow is carried out inverse discrete Fourier transform IDFT and parallel serial conversion successively, becomes OFDM symbol serial data stream x _n=[x _{0, n}, x _{1, n}... x _{N-1, n}];

Be N with the tail end length of each OFDM symbol serial data stream _GData

Copy to OFDM symbol serial data stream front as Cyclic Prefix, be added with the Cyclic Prefix in OFDM System signal and be coupled on the single-core cable and transmit;

Two, receiving terminal receive channel transmission be added with the Cyclic Prefix in OFDM System signal, will be added with the Cyclic Prefix in OFDM System signal from the single-core cable decoupling zero and carry out power amplification through what channel transmitted then, sample frequency is identical with transmitting terminal, is designated as r (n), is modeled as:

$r\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)s(n-\mathrm{\θ})+\mathrm{\ω}\left(n\right)$

H (n, l) the expression impulse response of l subchannel of n constantly, 1≤l≤L, ω (n) expression zero-mean variance is White Gaussian noise, θ are channel latency;

Wherein, definition transmitting terminal Cyclic Prefix data

With receiving terminal OFDM symbol serial data stream endian data

Correlation is carried out synchronously and channel estimating;

Three, for channel latency θ, m symbol is subjected to m-1 symbol-interference:

$r_m\left(n\right)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_{m-1}(n-l-\mathrm{\θ})+\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_m(n-l-\mathrm{\θ})+\mathrm{\ω}\left(n\right)---\left(1\right)$

$n\∈\{\mathrm{\θ},\mathrm{\θ}+1,...\mathrm{\θ}+N+N_G-1\}$

$r_m(n+N)=\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_m(n+N-l-\mathrm{\θ})+$ (2)

$\underset{l=0}{\overset{N}{\mathrm{\Σ}}}h(n,l)r_{m+1}(n+N-l-\mathrm{\θ})+\mathrm{\ω}(n+N)$

The correlation expectation and the coefficient correlation that are divided into mutually between two sampled values of N are respectively:

${\mathrm{\γ}}_n=E\left[r_m\left(n\right)r_m^{*}(n+N)\right]=\underset{l=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\σ}}_{h\left(l\right)}^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2---\left(3\right)$

${\mathrm{\ρ}}_n=\frac{E\left[r_m\left(n\right)r_m^{*}(n+N)\right]}{\sqrt{E\left[{\left|r_m\left(n\right)\right|}^2\right]+E\left[{\left|r_m(n+N)\right|}^2\right]}}---\left(4\right)$

Four, intercepted length is 2N+N _GThe region of search in, calculate m symbol probability density function and ask log-likelihood function to obtain following formula:

${\mathrm{\Λ}}_m=\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N+N_G}{\mathrm{\Π}}}\frac{f(r_m\left(n\right),r_m(n+N))}{f\left(r_m\left(n\right)\right)f\left(r_m(n+N)\right)}---\left(5\right)$

After receiving M symbol, based on relevant expectation γ _nWith coefficient correlation ρ _nLog-likelihood function become:

$\mathrm{\Λ}=\log \left(\underset{m}{\mathrm{\Π}}{\mathrm{\Λ}}_m\right)=M\underset{n}{\mathrm{\Σ}}\{\frac{2({\mathrm{\ρ}}_n\mathrm{\Ψ}\left(n\right)-{\mathrm{\ρ}}_n^2\mathrm{\Φ}\left(n\right))}{({\mathrm{\σ}}_r^2+{\mathrm{\σ}}_{\mathrm{\ω}}^2)(1-{\mathrm{\ρ}}_n^2)}-\log (1-{\mathrm{\ρ}}_n^2)---\left(6\right)$

Order

(7)

${\mathrm{\φ}}_n=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\left[\right|r_m\left(n\right)|+|r_m^{*}(n+N)\left|\right]$

(8)

$\mathrm{\Φ}\left(n\right)=\frac{1}{2M}\underset{m}{\mathrm{\Σ}}[{\left|r_m\left(n\right)\right|}^2+{\left|r_m^{*}(n+N)\right|}^2]=\frac{{\mathrm{\φ}}_n}{2}$

θ≤n≤θ+N+N wherein _G-1, ask local derviation to obtain the coefficient correlation ρ of likelihood function Λ:

${\widehat{\mathrm{\ρ}}}_n=\frac{\mathrm{\Ψ}\left(n\right)}{\mathrm{\Φ}\left(n\right)}---\left(9\right)$

${\widehat{\mathrm{\γ}}}_n=\mathrm{\Ψ}\left(n\right)$

Thereby obtain the least-squares estimation vector of correlation:

$\hat{r}={[{\widehat{\mathrm{\γ}}}_0,{\widehat{\mathrm{\γ}}}_1,...{\widehat{\mathrm{\γ}}}_{N+N_G-1}]}^T---\left(10\right)$

Five, the power of the data computation reception signal by M OFDM symbol receiving:

Utilize received signal power (12) formula to ask for the coefficient correlation of whole channel:

$\mathrm{\ρ}=\frac{E\left[{\left|r_m\left(n\right)\right|}^2\right]-{\mathrm{\σ}}_{\mathrm{\ω}}^2}{E\left[{\left|r_m\left(n\right)\right|}^2\right]}---\left(12\right)$

Six, estimate the power of L channel, establish (N+N _G) * N constant matrices A:

$A=[a\left(0\right),a\left(1\right),...,a\left(N\right){]}_{(N+N_G)\×N}$

$a\left(0\right)=[a\left(\mathrm{0,0}\right),a\left(\mathrm{0,1}\right),...,a(0,N+N_G-1){]}^T$

$=[1_{1\×N_G}{0}_{1\×N}{]}_{(N+N_G)\×1}^T---\left(13\right)$

a(i)＝[a(i，0)，a(i，1)，…，a(i，N+N _G-1)] ^T

a(i，j)＝a(0，(-i+j))mod(N+N _G)

It is mobile that element among a (i) just press the element among a (0) the i circulation, ring shift right, and with regard to confirmable constant matrix, the channel power on L subchannel is estimated as after determining for the useful symbol of OFDM and circulating prefix-length:

First sub-channel positions performance number is given up, and the power that obtains L=N channel is estimated A ⁺Be the pseudo inverse matrix of A,

Be the column matrix of N, namely finished channel estimating;

Seven, to correlated sampling point set algorithm development DFT window starting position, Λ _mBe the maximum likelihood function based on Cyclic Prefix of every frame data:

$\mathrm{\Λ}=\frac{1}{M}\underset{m}{\mathrm{\Σ}}{\mathrm{\Λ}}_m=\frac{1}{M}\underset{m}{\mathrm{\Σ}}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}{r}_m\left(n\right)r_m^{*}(n+N)$ (15)

$-\frac{\mathrm{\ρ}}{2}\frac{1}{M}\underset{m}{\mathrm{\Σ}}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}{\left|r\left(n\right)\right|}^2+{\left|r^{*}(n+N)\right|}^2$

$\mathrm{\Λ}=\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}\frac{1}{M}\underset{m}{\mathrm{\Σ}}{r}_m\left(n\right)r_m^{*}(n+N)$ (16)

$-\frac{\mathrm{\ρ}}{2}\underset{n=\mathrm{\θ}}{\overset{\mathrm{\θ}+N_G-1}{\mathrm{\Σ}}}\frac{1}{M}\underset{m}{\mathrm{\Σ}}{\left|r\left(n\right)\right|}^2+{\left|r^{*}(n+N)\right|}^2$

The maximum likelihood function of this step relative set is to M frame data N+N _GThe data of length are carried out correlation operation, i.e. two-dimensional search, and the accuracy of timing estimation is higher, tries to achieve the θ of maximum correspondence of likelihood function with regard to is-symbol timing estimation position, i.e. DFT window starting position:

Utilize the autocorrelation performance of Cyclic Prefix, this method obtains the sub-channel power estimation by the maximum likelihood algorithm of synchronous estimation, finish timing synchronization with the channel power results estimated conversely and estimate, namely finish channel estimating and method for synchronous based on Cyclic Prefix.

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