CN103441967B - Ofdm system channel estimation and signal detecting method based on basis expansion model - Google Patents

Abstract

The invention relates to an OFDM system channel estimation and signal detection method based on a base extension model, which belongs to the technical field of wireless and mobile communication. Specifically, the method includes the following steps: transmitting OFDM signal at the transmitting end, channel modeling at the receiving end, initialization, estimating base extension model coefficients, channel equalization and signal detection, iteration, and output. Channel modeling at the receiving end separates interference and useful information from the frequency domain signal at the receiving end. Initialization assumes that there is no cyclic prefix restriction, estimates the base expansion model coefficients and detects the current transmitted data symbols, and obtains the inter-symbol interference frequency response and The cyclic prefix reconstructs the frequency response of the part, thereby eliminating the impact of inter-symbol interference. The estimation method proposed by the present invention, on the one hand, can estimate the channel with obvious time variation, and can effectively eliminate the intersymbol interference introduced by the multipath time delay, and complete the channel estimation and signal detection of the OFDM system under the dual channel selection, and improve the system performance. performance.

Description

Channel Estimation and Signal Detection Method for OFDM System Based on Basis Extended Model

technical field

The invention belongs to the technical field of wireless and mobile communication, and specifically relates to an OFDM system joint channel estimation and signal detection algorithm based on the lack of cyclic prefix of the base extension model under the double-selection channel. From the perspective of the frequency domain, the inter-symbol interference elimination and the iteration are carried out. The reconstruction of the cyclic prefix largely overcomes the influence of inter-symbol interference caused by the absence of the cyclic prefix, and then achieves ideal channel estimation and signal detection performance.

Background technique

In the ground ultra-high-speed mobile environment, inter-carrier interference (Inter-Carrier Interference, ICI) caused by fast time-varying channels and inter-symbol interference (Inter-Symbol Interference, ISI) caused by multipath effects will destroy the transmission characteristics of OFDM systems, resulting in Rapid deterioration of system performance. Therefore, under such challenges, how to use comb pilots for effective channel estimation and improve system anti-interference ability is one of the core technologies of future wireless communication transmission systems.

In the face of the Inter-Carrier Interference (ICI) problem caused by fast time-varying channels, when the normalized maximum Doppler shift of the channel is greater than 20%, the parameters to be estimated on each separable path of the channel are one The length of the OFDM symbol, even if the channel has only one separable path, if we want to estimate a single-path fast-changing channel, all subcarriers at the origin of the OFDM system are required to be pilots, so we must use a model to equivalent fast-changing channels. The basis expansion model BEM (Basis Expansion Model) approximates the channel with mutually orthogonal basis functions, so that the parameters to be estimated on each separable path of the channel are reduced from the length of one OFDM symbol to the number of basis functions, so that the estimated parameters decrease very much. Technical Document 1 (K.A.D.Teo and S.Ohno, Optimal MMSE finite parameter model for doubly-selective channels[C], in IEEE Global Telecommunications Conference, 2005.GLOBECOM'05., 2005, 6(5):3502–3507) adopted DKL-BEM (Discrete Karhuen-Loeve BEM) is used to approximate the time-varying channel. This model uses the statistical characteristics of the channel to construct the BEM basis, and uses the main eigenvector of the channel autocorrelation function as the basis function vector. This model has a better estimation effect, but requires explicit knowledge of the statistical properties of the channel.

Facing the problem of Inter-Symbol Interference (ISI) caused by channel multipath effects, Technical Document 2 (Dukhyun Kim; Stuber, G.L. Residual ISI cancellation for OFDM with application to HDTV broadcasting, IEEE Trans.Commun., vol. 16, no.8, pp.1590-1599, Oct.1998; and Cheol-Jin Park; Gi-Hong Im; Efficient Cyclic Prefix Reconstruction for Coded OFDM Systems, IEEE Commun.lett., vol.8, no.5, pp .274-276, May.2004) transform it into OFDM system structure without cyclic prefix protection. Residual ISI cancellation algorithm (Residual ISIcancellation, RISIC) and cyclic prefix reconstruction (Cyclic Prefix Reconstruction, CPR) algorithm can effectively eliminate intersymbol interference and achieve effective detection of OFDM symbols. But this method is realized under the assumption that the channel is slowly changing.

It can be seen from the above that using the base extension model to model fast time-varying channels can effectively track the time-varying nature of the channel, and based on effective inter-symbol interference cancellation and cyclic prefix reconstruction can overcome the ISI caused by channel multipath, but when The channel presents a dual-selection characteristic, that is, when both are considered, how to perform channel estimation and signal detection in an OFDM system has not been discussed in literature so far, and the present invention is based on this.

Contents of the invention

The purpose of the present invention is to solve the existing problems of using the base extension model to estimate the fast-changing channel technology when it is applied to the OFDM system with missing cyclic prefix. System channel estimation and signal detection methods.

In order to achieve the above object, technical scheme of the present invention is:

The OFDM system channel estimation and signal detection method based on the base extension model, as shown in Figures 3 and 4, includes the following steps:

Step 1: Set the frequency-domain OFDM symbols mixed with pilot and data sent by the sender of the current OFDM system as X ⁱ , denoted as Among them, N represents the length of the OFDM symbol, and some subcarriers with certain positions in the frequency domain OFDM symbol ^Xi are assigned pilots, and others are data subcarriers; then the corresponding time domain OFDM symbol Xi currently sent by the ^sender can be written as And x ⁱ =F ^H X ⁱ , where F ^H represents the IFFT transformation matrix of N points, and i represents the ith OFDM symbol, that is, the index number of the OFDM symbol;

Step 2: Assuming that the time-domain OFDM symbol x ⁱ is double-selected through fast time-varying and multipath effect superimposition, the time-domain OFDM symbol received by the receiving end is

Using the complex exponent base extension model to describe the dual-choice channel h=[h ₀ ,h ₁ ,...,h _l ,...,h _L ], where h _l =[h _{0 ,l} ,h _1,l ,…,h _n,l ,…,h _N-1,l ] represent the impulse response of the lth path, if h _q (l) is used to represent the BEM coefficient corresponding to the lth path of the channel , b _q represents the basis function, then there are:

in, Represents rounding up, f _d represents the maximum Doppler frequency shift, and f _d =f _c v/c, and f _c represents the center frequency of the OFDM system carrier, v represents the relative motion speed between the transmitting end and the receiving end, c represents the speed of light, T _s represents the sampling period;

After the time-domain OFDM symbol ^xi is double-selected by fast time-varying and multipath effects, the time-domain OFDM symbol y ^received by the receiving end can be expressed as:

in, Indicates that the length of the cyclic prefix in the OFDM system is greater than the maximum multipath delay of the channel and the receiving end receives the i-th OFDM symbol, Represents the interference of the previous OFDM transmitted symbol x ^i-1 on the current OFDM received symbol y ⁱ , represents the refactored part of the cyclic prefix;

Transform the formula (20) into the frequency domain, then:

Step 3: Initialize;

Set the number of iterations I = 0, let so

Step 4: Estimating the corresponding channel base expansion model coefficients;

The pilot position observation Y ^p in the signal Y at the receiving end can be expressed as:

Among them, Y ^p represents the frequency response at the pilot position at the receiving end, Ph _eqv represents the frequency response generated by the pilot, D ^d S ^d _heqv represents the interference part of the OFDM symbol data subcarrier to the pilot subcarrier, and W ^p represents the receiving Frequency domain noise at the end pilot position;

Use the LS estimation criterion to estimate _heqv , then the estimation equation is:

Considering the accuracy of the inverse operation of the matrix P, a small disturbance is often added, where α is the disturbance factor. will estimate the resulting BEM coefficients Substituting into equation (15), the channel time-domain impulse response can be obtained

Step 5: Channel equalization and signal detection;

Using the estimated channel time-domain impulse response construct matrix Find the Channel Frequency Response Matrix Using the MMSE criterion to construct the frequency domain equalizer of the i-th frame OFDM data unit has Among them, σ ² is the noise variance, I _N is the identity matrix of N×N, and then the current frequency domain symbol vector of the sending end is detected

Step 6: Judgment; order:

I=I+1 (10)

If I≤M, M is the number of iterations whose value range is a natural number, execute step 7, otherwise, go to step 8;

Step seven: iteration;

Using the estimated channel time-domain impulse response construct matrix Plus the frequency domain symbol vector estimated at the previous moment and the current frequency-domain sign vector Substituting the time domain into the formula (25)(26) to obtain with After updating equation (24), go to step four;

Step 8: Detect and obtain the current frequency-domain symbol vector of the transmitting end Calculate the final estimator

The beneficial effects of the present invention are:

The present invention proposes a method for channel estimation and signal detection of an OFDM system based on a base-spreading model in the case of dual channel selection and signal prefix absence, using the base-spreading model to analyze the inter-symbol interference and the repetition of the cyclic prefix from the perspective of the frequency domain The frequency domain response introduced by the structural part, and through iteration to a large extent overcome the ISI impact caused by the lack of cyclic prefix, and then achieve the ideal channel estimation and signal detection performance.

Description of drawings

FIG. 1 is a schematic diagram of the processing flow at the sending end of the present invention.

FIG. 2 is a schematic diagram of a time-domain data structure model adopted in the present invention.

FIG. 3 is a schematic diagram of a processing flow at the receiving end of the present invention.

Fig. 4 is a schematic flow chart of specific algorithm steps of the present invention.

detailed description

The OFDM system channel estimation and signal detection method based on the base extension model, as shown in Figures 3 and 4, includes the following steps:

Step 1: Set the frequency-domain OFDM symbols mixed with pilot and data sent by the sender of the current OFDM system as X ⁱ , denoted as Among them, N represents the length of the OFDM symbol, and some subcarriers with certain positions in the frequency domain OFDM symbol ^Xi are assigned pilots, and others are data subcarriers; then the corresponding time domain OFDM symbol Xi currently sent by the ^sender can be written as And x ⁱ =F ^H X ⁱ , where F ^H represents the IFFT transformation matrix of N points, and i represents the ith OFDM symbol, that is, the index number of the OFDM symbol.

Step 2: Assuming that the time-domain OFDM symbol x ⁱ is double-selected through fast time-varying and multipath effect superimposition, the time-domain OFDM symbol received by the receiving end is Since the time-domain OFDM symbols at the transmitting end pass through dual channel selection, the time-domain OFDM symbols received at the receiving end will be subject to inter-symbol interference (ISI, as shown in the gray shaded part in Figure 2(b)) from adjacent OFDM symbols. ,so:

Among them, L represents the number of paths of the multipath channel, and l represents the lth path of the channel, Indicates the impulse response of the i-th OFDM symbol at the n-th sampling time of the l-th path, <nl>N means (nl) to find the remainder of N, x _<nl> means the sampling output value at the nl-th sampling time, Represents zero-mean time-domain additive white Gaussian noise with variance σ ² at the nth sampling moment.

Expressing formula (11) in vector form, we have:

in The expression is:

Using the complex exponent base extension model to describe the dual-choice channel h=[h ₀ ,h ₁ ,...,h _l ,...,h _L ], where h _l =[h _{0 ,l} ,h _1,l ,…,h _n,l ,…,h _N-1,l ] represent the impulse response of the lth path, if h _q (l) is used to represent the BEM coefficient corresponding to the lth path of the channel , b _q represents the basis function, then there are:

in, Represents rounding up, f _d represents the maximum Doppler frequency shift, and f _d =f _c v/c, and f _c represents the center frequency of the OFDM system carrier, v represents the relative motion speed between the transmitting end and the receiving end, c represents the speed of light, and T _s represents the sampling period.

Now assume that the length of the cyclic prefix in the OFDM system is greater than the maximum multipath delay of the channel. In this case, the i-th OFDM symbol received by the receiving end is Expressed as:

here Represents the time-domain channel matrix, by the time-varying channel impulse response coefficient The cyclic shift composition can be expressed as:

Comparing equations (12) and (18) shows that:

in,

here, Represents the interference of the previous OFDM transmitted symbol x ^i-1 on the current OFDM received symbol y ⁱ , Refactored part representing a cyclic prefix.

Transform the formulas (18) and (20) into the frequency domain, then the expressions of each component in the frequency domain are:

Simultaneous formulas (15) and (19) get:

where H _q is given by The cyclic symmetric matrix composed of is of the form:

Step 3: Initialize.

Set the number of iterations I = 0, let so

Step 4: Estimate the corresponding channel base expansion model coefficients.

Substituting formula (27) into (23), we have:

Among them, _FL represents the first L columns of the FFT transformation matrix F.

For the convenience of expression, the i superscript is omitted, and the pilot position observation Y ^p in the signal Y at the receiving end can be expressed as:

Among them, Y ^p represents the frequency response at the pilot position at the receiving end, Ph _eqv represents the frequency response generated by the pilot, D ^d S ^d _heqv represents the interference part of the OFDM symbol data subcarrier to the pilot subcarrier, and W ^p represents the receiving Frequency-domain noise at the end pilot locations; here:

h _eqv =[h ₀ ^T ,h ₁ ^T ,...,h _q ^T ,...h _Q ^T ] ^T (34)

h _q = [h _q (0), h _q (1)..., h _q (L)] ^T (35)

Similarly, the expressions of D ^d and S ^d can be written, and the index number p of the position of the pilot subcarrier is changed to the index number d of the position of the data subcarrier.

Use the LS estimation criterion to estimate _heqv , then the estimation equation is:

Considering the accuracy of the inverse operation of the matrix P, a small disturbance is often added, where α is the disturbance factor. will estimate the resulting BEM coefficients Substituting into equation (15), the channel time-domain impulse response can be obtained

Step five: channel equalization and signal detection.

Using the estimated channel time-domain impulse response construct matrix Find the Channel Frequency Response Matrix Using the MMSE criterion to construct the frequency domain equalizer of the i-th frame OFDM data unit has Among them, σ ² is the noise variance, I _N is the identity matrix of N×N, and then the current frequency domain symbol vector of the sending end is detected

Step Six: Judgment.

I=I+1 (37)

If I≤M, go to step 7, otherwise, go to step 8

Step Seven: Iterate.

Using the estimated channel time-domain impulse response construct matrix Plus the frequency domain symbol vector estimated at the previous moment and the current frequency-domain sign vector Substituting the time domain into the formula (25)(26), to obtain with After updating equation (24), go to step four.

Step 8: Detect and obtain the current frequency-domain symbol vector of the transmitting end Calculate the final estimator

Claims (1)

1. The OFDM system channel estimation and signal detection method based on the base extension model, comprising the following steps: Step 1: Set the frequency-domain OFDM symbols mixed with pilot and data sent by the sender of the current OFDM system as X ⁱ , denoted as Among them, N represents the length of the OFDM symbol, and some subcarriers with certain positions in the frequency domain OFDM symbol ^Xi are assigned pilots, and others are data subcarriers; then the corresponding time domain OFDM symbol Xi currently sent by the ^sender can be written as And x ⁱ =F ^H X ⁱ , where F ^H represents the IFFT transformation matrix of N points, and i represents the ith OFDM symbol, that is, the index number of the OFDM symbol; Step 2: Assuming that the time-domain OFDM symbol x ⁱ is double-selected through fast time-varying and multipath effect superimposition, the time-domain OFDM symbol received by the receiving end is Using Complex Exponential Base Extended Model to Describe Dual-choice Channels with Fast Time Variation and Superposition of Multipath Effects in Indicates the first diameter impulse response, if used Indicates the channel No. The BEM coefficient corresponding to the bar diameter, b _q represents the basis function, then there are: ${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; Q</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ in, Represents rounding up, f _d represents the maximum Doppler frequency shift, and f _d =f _c v/c, and f _c represents the center frequency of the OFDM system carrier, v represents the relative motion speed between the transmitting end and the receiving end, c represents the speed of light, T _s represents the sampling period; After the time-domain OFDM symbol ^xi is double-selected by fast time-varying and multipath effects, the time-domain OFDM symbol y ^received by the receiving end can be expressed as: ${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ in, Indicates that the length of the cyclic prefix in the OFDM system is greater than the maximum multipath delay of the channel and the receiving end receives the i-th OFDM symbol, Represents the interference of the previous OFDM transmitted symbol x ^i-1 on the current OFDM received symbol y ⁱ , represents the refactored part of the cyclic prefix; Transform the formula (4) into the frequency domain, then: ${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Y</span>}}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ Step 3: Initialize; Set the number of iterations I = 0, let so Step 4: Estimating the corresponding channel base expansion model coefficients; The pilot position observation Y ^p in the signal Y at the receiving end can be expressed as: $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Y</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Y</span>}}}^{\mathrm{<span\; class="notranslate">\; p</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; q</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; q</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Ph</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; q</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; q</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$ Among them, Y ^p represents the frequency response at the pilot position at the receiving end, Ph _eqv represents the frequency response generated by the pilot, D ^d S ^d _heqv represents the interference part of the OFDM symbol data subcarrier to the pilot subcarrier, and W ^p represents the receiving Frequency domain noise at the end pilot position; Use the LS estimation criterion to estimate _heqv , then the estimation equation is: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; q</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$ Consider the accuracy of the inverse operation of the matrix P, plus a small disturbance, where α is the disturbance factor; the estimated BEM coefficient Substituting into equation (1), the channel time-domain impulse response can be obtained Step 5: Channel equalization and signal detection; Using the estimated channel time-domain impulse response construct matrix Find the Channel Frequency Response Matrix Using the MMSE criterion to construct the frequency domain equalizer of the i-th frame OFDM data unit has Among them, σ ² is the noise variance, I _N is the identity matrix of N×N, and then the current frequency domain symbol vector of the sending end is detected Step 6: Judgment; order: I=I+1 (10) If I≤M, M is the number of iterations whose value range is a natural number, execute step 7, otherwise, go to step 8; Step seven: iteration; Using the estimated channel time-domain impulse response construct matrix Plus the frequency domain symbol vector estimated at the previous moment and the current frequency-domain sign vector Substituting the time domain into the formula (6)(7), to obtain with After updating equation (5), go to step four; Step 8: Detect and obtain the current frequency-domain symbol vector of the transmitting end Calculate the final estimator