MIMO-OFDM channel estimation method and device based on Natural interpolation

Abstract

The present invention discloses a MIMO-OFDM channel estimation method and device based on natural interpolation. The method comprises: obtaining a channel coefficient at a pilot signal based on least squares channel estimation; assigning weights to the channel coefficients at several pilot signals near each interpolation point according to the size of the Voronoi diagram grid area based on the natural interpolation method, and obtaining an interpolation formula at the interpolation point by weighted summation; and performing natural interpolation on each interpolation point using the interpolation formula to obtain a MIMO-OFDM channel estimation result. The method applies natural interpolation to channel estimation, and obtains a channel frequency response estimate at the interpolation point by weighting the values ​​at several pilot signals near the interpolation point. This method can simultaneously utilize the time and frequency correlation of the channel, significantly improve the channel estimation accuracy, reduce the channel estimation error, and have a smoother interpolation effect and better interpolation performance.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a MIMO-OFDM channel estimation method and device based on Natural interpolation. Background Art

[0002] Orthogonal frequency division multiplexing (OFDM) divides a channel into mutually orthogonal subchannels, each of which can be viewed as flat fading. Multiple-input, multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) can further increase channel capacity and transmission rates, multiplying spectrum efficiency without increasing bandwidth or transmit power.

[0003] MIMO-OFDM systems require channel estimation for space-time code decoding and equalization. Pilot-assisted non-blind, blind, and semi-blind channel estimation are commonly used channel estimation methods. Pilot-assisted non-blind estimation is widely adopted due to its simple principle. This method first inserts a known pilot sequence into each OFDM symbol at the transmitter. The receiver estimates the channel frequency response (CFR) at the pilot location using methods such as least squares (LS). The CFR at the pilot location is then interpolated to obtain the complete channel response for all subcarrier locations. Interpolation, as a key step in non-blind channel estimation, is crucial for improving system performance.

[0004] At present, the commonly used interpolation methods include one-dimensional linear interpolation, two-dimensional linear interpolation, cubic polynomial interpolation, spline interpolation and DFT time domain interpolation.

[0005] However, one-dimensional linear interpolation uses only two adjacent data points for each interpolation point, which doesn't effectively exploit the channel's time and frequency correlation. Furthermore, the channel frequency response varies nonlinearly in the time-frequency dimension, making linear interpolation inadequate for characterizing channel characteristics. Two-dimensional linear interpolation relies heavily on one-dimensional linear interpolation, specifically on the subcarrier or OFDM symbol dimension where pilot signals are placed. Furthermore, two-dimensional linear interpolation is based on triangulation, resulting in uneven interpolation results. Cubic polynomial interpolation is not ideal in high-speed scenarios. Spline interpolation constructs a spline function for each segment, which doesn't address the vertical tangent problem. When the second-order derivative is discontinuous, the fitted curve fluctuates dramatically. DFT time-domain interpolation diffuses the noise within the maximum multipath delay to other subcarriers through interpolation, resulting in poor performance at high signal-to-noise ratios.

[0006] In summary, for MIMO-OFDM systems, existing interpolation schemes have the problems of low accuracy and performance degradation under high signal-to-noise ratio. Summary of the Invention

[0007] In order to solve the above problems existing in the prior art, the present invention provides a MIMO-OFDM channel estimation method and device based on Natural interpolation. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0008] The present invention provides a MIMO-OFDM channel estimation method based on Natural interpolation, comprising:

[0009] Obtain the channel coefficient at the pilot frequency based on the least squares channel estimation;

[0010] Based on the Natural interpolation method, the channel coefficients at several pilot channels near each interpolation point are weighted according to the size of the Voronoi diagram grid area, and the interpolation formula at the interpolation point is obtained by weighted summation;

[0011] The interpolation formula is used to perform Natural interpolation on each interpolation point to obtain a MIMO-OFDM channel estimation result.

[0012] A second aspect of the present invention provides a MIMO-OFDM channel estimation device based on Natural interpolation, comprising:

[0013] A first estimation module, configured to obtain a channel coefficient at a pilot frequency based on least squares channel estimation;

[0014] The second estimation module is used to assign weights to the channel coefficients at several pilot channels near each interpolation point according to the size of the Voronoi diagram grid based on the Natural interpolation method, and obtain the interpolation formula at the interpolation point by weighted summation;

[0015] The interpolation module is used to perform Natural interpolation on each interpolation point using the interpolation formula to obtain a MIMO-OFDM channel estimation result.

[0016] Beneficial effects of the present invention:

[0017] 1. The MIMO-OFDM channel estimation method based on natural interpolation proposed in this paper applies natural interpolation to channel estimation. Based on the unstructured grid Voronoi diagram, the channel frequency response estimate at the interpolation point is obtained by weighting the values ​​of several pilot signals near the interpolation point. This method can simultaneously utilize the time and frequency correlation of the channel, significantly improve the channel estimation accuracy, reduce the channel estimation error, and achieve smoother interpolation effect and better interpolation performance.

[0018] 2. When the present invention uses Natural interpolation, the pilot interval is small, so only a small number of weight groups need to be calculated, and the channel estimation results of all interpolation points can be obtained through translation or mirroring. The algorithm complexity is low and easy to implement in engineering.

[0019] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram of a pilot pattern for two transmitting antennas provided in an embodiment of the present invention;

[0021] Figure 2 A schematic diagram of a flow chart of a MIMO-OFDM channel estimation method based on Natural interpolation provided in an embodiment of the present invention;

[0022] Figure 3 Another flowchart of a MIMO-OFDM channel estimation method based on Natural interpolation provided by an embodiment of the present invention;

[0023] Figure 4 The original Voronoi diagram drawn based on 6 pilot points provided in an embodiment of the present invention;

[0024] Figure 5 For Figure 4 A new Voronoi diagram is drawn by adding an interpolation point on the basis of ;

[0025] Figure 6 A schematic diagram of the Natural interpolation weights for different data symbols provided in an embodiment of the present invention;

[0026] Figure 7 The system BER curves using different interpolation algorithms in an NLOS environment with a Doppler frequency shift of fd = 4.17 Hz are shown;

[0027] Figure 8 The system BER curves using different interpolation algorithms in an NLOS environment with a Doppler frequency shift of fd = 250 Hz are shown;

[0028] Figure 9 It is the local data cloud diagram of the real channel frequency response at the pilot;

[0029] Figure 10 It is a local data cloud of the estimated value of the channel frequency response at the pilot obtained by LS estimation;

[0030] Figures 11(a)-11(c) The following are the true channel frequency response and the total frequency response estimation value diagram obtained by two-dimensional linear interpolation and Natural interpolation respectively;

[0031] Figure 12 The NMSE curves of channel frequency response estimated using different interpolation algorithms in an NLOS environment with a Doppler frequency shift of fd = 4.17 Hz are shown;

[0032] Figure 13 The NMSE curves of channel frequency response estimated using different interpolation algorithms in an NLOS environment with Doppler frequency shift fd = 250 Hz are shown;

[0033] Figure 14 is the sum of squares of the interference terms caused by the channel frequency response estimation error in the NLOS environment with Doppler frequency shift fd = 4.17 Hz;

[0034] Figure 15 is the sum of squares of the interference terms caused by the channel frequency response estimation error in the NLOS environment with Doppler frequency shift fd = 250 Hz;

[0035] Figure 16 This is a structural block diagram of a MIMO-OFDM channel estimation device based on Natural interpolation provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0037] Example 1

[0038] This embodiment considers a 2-transmit 2-receive MIMO-OFDM system and uses a two-dimensional pilot. Pilot symbols are inserted at intervals in both the time and frequency domains. The two-dimensional pilot combines the characteristics of the comb pilot and the block pilot, and has strong adaptability to dual-dispersion channels. Figure 1 , Figure 1 Schematic diagram of two transmitting antenna pilot patterns provided by an embodiment of the present invention, wherein (a) is the time-frequency resource of transmitting antenna 1, and (b) is the time-frequency resource of transmitting antenna 2, with a frequency domain interval of n. f , the time domain interval is n t The idle symbol is a silent symbol set to avoid mutual interference between the pilot signals of the two antennas.

[0039] It should be noted that inserting a pilot in the time-frequency domain is equivalent to sampling the frequency response (CFR) of the channel. The pilot insertion interval needs to satisfy the Nyquist sampling theorem in order to recover the complete channel information, that is, the interval n in the time domain t To be smaller than the coherence time, the frequency domain spacing n f is smaller than the coherence bandwidth, as shown below:

[0040]

[0041] Among them, f m is the maximum Doppler shift, T symbol is the symbol period, Δf is the subcarrier spacing, τ m The maximum delay extension.

[0042] for Figure 1 For channel estimation, the two-dimensional pilots shown require interpolation in both the time (row) and frequency (column) dimensions. This is typically achieved by cascading two one-dimensional interpolators. One-dimensional interpolation methods include one-dimensional linear interpolation, cubic polynomial interpolation, spline interpolation, and DFT time-domain interpolation. Two-dimensional linear interpolation is a representative example of two-dimensional interpolation. The two cascaded one-dimensional interpolators can use different interpolation orders (time domain interpolation followed by frequency domain interpolation, or frequency domain interpolation followed by time domain interpolation) to obtain a channel frequency response estimate for each carrier frequency point on each OFDM symbol. However, when interpolating columns with pilots, only the channel frequency response estimates for a limited number of pilots before and after the interpolation point are used. This makes the interpolation result unreliable when noise causes significant deviations in the channel frequency response estimates for pilots adjacent to the interpolation point. However, for slow-fading channels, the channel characteristics remain essentially unchanged within the coherence time. Two-dimensional interpolation utilizes the channel frequency response estimates of adjacent OFDM symbols during frequency domain interpolation, thereby achieving a certain degree of noise suppression. Two-dimensional linear interpolation is based on triangulation, using three points to define a plane. Specifically, the channel frequency response estimates at three pilot signals are used to interpolate the data within the three points.

[0043] The Natural Neighbor Interpolation (NNI) algorithm, also known as the Natural interpolation method, was first proposed by Sibson and is widely used in fields such as geographic modeling and fluid dynamics gridding. This interpolation method can automatically adjust for irregular distribution and uneven density of data points in space. The first-order derivative of its interpolation function is continuous everywhere except the original point. These characteristics make Natural Neighbor Interpolation suitable for interpolating irregular spatial data.

[0044] Based on this, this embodiment introduces Natural interpolation into MIMO-OFDM channel estimation and proposes a MIMO-OFDM channel estimation method based on Natural interpolation. This method utilizes the channel frequency response estimates at multiple pilot frequencies near the interpolation point, assigning appropriate weights based on their area, and then performing a weighted summation. This method exploits the fact that the channel characteristics remain essentially unchanged within the coherence time. Furthermore, compared to other interpolation methods, Natural interpolation utilizes more pilot frequency information when interpolating each data carrier frequency point.

[0045] See Figure 2-3 , Figure 2 This is a flow chart of a MIMO-OFDM channel estimation method based on Natural interpolation provided by an embodiment of the present invention; Figure 3 1 is another flow chart of a MIMO-OFDM channel estimation method based on Natural interpolation provided by an embodiment of the present invention; the method mainly includes the following steps:

[0046] Step 1: Obtain the channel coefficients at the pilot frequency based on the least squares channel estimation.

[0047] Specifically, the channel coefficient at the pilot frequency is calculated based on the transmit channel frequency response and the receive channel frequency response. The calculation formula is:

[0048]

[0049] Where, The channel coefficient at the kth pilot in the frequency domain and the nth pilot in the time domain, also known as the LS estimate of the [k,n]th pilot channel frequency response, is Y(l k ,p n ) represents the receiving channel frequency response, X(l k ,p n ) represents the transmit channel frequency response (l k ,p n ) indicates the lth position where the [k,n] pilot is located k subcarriers and the pth n OFDM symbol positions.

[0050] It is understandable that other methods may also be used to implement the channel coefficient estimation at the pilot signal.

[0051] Step 2: Based on the Natural interpolation method, weights are assigned to the channel coefficients at several pilot channels near each interpolation point according to the size of the Voronoi diagram grid area, and the interpolation formula at the interpolation point is obtained based on the weights.

[0052] 21) Draw the original Voronoi diagram based on the pilot points.

[0053] Specifically, this embodiment takes six pilot points α1, α2, α3, α4, α5, and α6 as an example to draw the original Voronoi diagram. Figure 4 , Figure 4 This is the original Voronoi diagram drawn based on 6 pilot points provided by an embodiment of the present invention.

[0054] First, for each pilot point, draw the Delaunay triangulation; when any four points are not cocircular, the Delaunay triangulation is unique, such as Figure 4 As shown by the dotted line in .

[0055] Then, the original Voronoi diagram is obtained by making a perpendicular bisector for each edge of each triangle in the Delaunay triangulation, such as Figure 4 As shown by the solid line in .

[0056] Here, we need to introduce several concepts. The Voronoi diagram divides the plane where the pilot point is located into several grid cells (Voronoi Cell), namely Figure 4 β1, β2, β3, β4, β5 and β6 in each Voronoi Cell contain only one data point. The data points with common adjacent edges in the Voronoi Cell are called natural neighbors (NN). For example, the natural neighbors of α2 are α1, α3 and α5.

[0057] 22) Add interpolation points to the original Voronoi diagram and draw a new Voronoi diagram; wherein the Voronoi cell where the interpolation point is located is divided into several parts by the original Voronoi diagram, and the pilot point corresponding to each part is used as a natural neighbor of the interpolation point.

[0058] Specifically, in Figure 4 On the basis of , add the interpolation point α and obtain the new Voronoi diagram according to the drawing process in step 21).

[0059] See Figure 5 , Figure 5 is Figure 4 The new Voronoi diagram is drawn by adding an interpolation point to the original Voronoi diagram. The Voronoi cell where the interpolation point α is located is divided into N = 6 parts by the original Voronoi diagram. The pilot point corresponding to each part is a natural neighbor of the interpolation point. That is, the interpolation point α has 6 natural neighbors, namely α1, α2, α3, α4, α5 and α6.

[0060] 23) The weight of the corresponding natural neighboring point is determined by the area size of each part.

[0061] Let the area of ​​each part be S i , i=1,2,...,N, S is the sum of their areas, that is, the area of ​​the Voronoi Cell where the interpolation point is located, and the weight calculation formula is as follows:

[0062]

[0063] Where k i Represents the weight of the i-th natural neighbor point, and N represents the total number of data neighbors of the interpolation point.

[0064] 24) Perform weighted summation on the channel coefficients at the corresponding pilot points based on the weights to obtain an interpolation formula at the interpolation point.

[0065] For Natural interpolation, the value of the interpolation point is related to its natural neighboring points. The interpolation point α has N natural neighboring points α1, α2, ..., α N , the interpolation formula is as follows:

[0066]

[0067] In the formula, α represents the interpolation point, f(α) is the estimated value of the channel coefficient at the interpolation point α, and α i represents the natural neighbor of the interpolation point α, k i represents the natural neighbor α i The corresponding weight, f(α i ) is the natural neighbor α i The interpolation result at , that is, the estimated value of the channel coefficient.

[0068] Step 3: Use the interpolation formula to perform Natural interpolation on each interpolation point to obtain the MIMO-OFDM channel estimation result.

[0069] It should be noted that for Figure 1 For the two-dimensional pilot pattern shown, since the data symbol positions have a translation and mirror symmetry relationship, it is only necessary to calculate the number of weight groups, and then calculate each group of weights according to the above method, and then the interpolation processing of all interpolation points can be achieved by translation and mirroring.

[0070] In this embodiment, the calculation formula for the number of weight groups is:

[0071]

[0072] Where K represents the number of weight groups, Indicates rounding down, n t and n f They represent the time domain interval and frequency domain interval of the two-dimensional pilot respectively.

[0073] It is understandable that since the subcarriers at the edge of the two-dimensional pilot and the data symbols on the OFDM symbol are in the process of natural interpolation, it is equivalent to one-dimensional linear interpolation. In reality, in order to ensure the accuracy of channel estimation, the pilot interval will not be too large, so the number of weight groups will not be too many, the algorithm complexity will be low, and it will be easy to implement in engineering.

[0074] Specifically, for Figure 1 The two-dimensional pilot pattern shown, n f =7,n t=2, except for the edge subcarriers and edge OFDM symbols, one-dimensional linear interpolation is performed. According to the calculation formula of the number of weight groups, the Natural interpolation on the data symbol only needs to calculate 9 groups of weights, such as Figure 6 As shown, the blue solid circles are the pilot data points, the circles with black crosses are the time-frequency resource locations that are kept silent to avoid inter-antenna interference, and the black hollow circles are the data points (including the orange and green filled locations). Figure 6 The weights of the 9 data points in the black dotted box and the weights of the other data points all belong to this weight set. In the weight calculation, the data points in the black dotted box and the other data points are in a translation and mirror symmetric relationship (that is, the weights of the orange-filled data points outside the black dotted box can be obtained by translating the weights of the orange-filled data points inside the black dotted box, and the weights of the green-filled data points can be obtained by mirror symmetry of the weights of the orange-filled data points). Therefore, the weights do not need to be calculated repeatedly, and it is easy to implement in hardware.

[0075] Table 1 below gives the Figure 1 All weights of the two-dimensional pilot pattern Natural interpolation shown, pilot point α i Corresponding to its corresponding weight k i The relationship between the subscript and the pilot position is starting from the upper left corner and rotating clockwise one by one.

[0076] Table 1 Weight list

[0077]

[0078]

[0079] The above method can be used to interpolate the CFR of the pilot position at the receiving end. For systems with multiple transmitting ends, multiple interpolation processes can be performed to obtain the complete channel response of all subcarrier positions.

[0080] The MIMO-OFDM channel estimation method based on Natural interpolation proposed in the present invention applies Natural interpolation to channel estimation. Based on the unstructured grid Voronoi diagram, the channel frequency response estimation value at the interpolation point is obtained by weighting the values ​​at several pilot signals near the interpolation point, thereby being able to simultaneously utilize the time and frequency correlation of the channel, significantly improving the channel estimation accuracy and reducing the mean square error.

[0081] In order to verify the effectiveness of the method proposed in the present invention, the Natural interpolation method proposed in the present invention is simulated by computer and compared with the existing linear interpolation, second-order interpolation, cubic spline interpolation and DFT interpolation.

[0082] 1. Simulation conditions:

[0083] This simulation targets a 2-transmit, 2-receive MIMO-OFDM system, employing the Alamouti-STBC diversity scheme for channel estimation. The channel model uses the 6-path VA (urban) model specified in ITU-R M.1225, taking into account Doppler shift. MRC combining is used at the receiver, the channel frequency response at the pilot position is estimated using the LS method, and the detection algorithm uses ZF detection. The simulation parameters are shown in Table 2 below:

[0084] Table 2 Simulation parameter settings

[0085]

[0086]

[0087] 2. Simulation content and result analysis

[0088] Experiment 1: Simulating the BER curve of the system using different interpolation methods

[0089] See Figure 7 , Figure 7 The following is a system BER curve diagram using different interpolation algorithms in an NLOS environment with a Doppler frequency shift of fd = 4.17 Hz. Figure 7 It can be seen that when the Doppler frequency shift fd = 4.17 Hz, spline interpolation has the worst performance. Cubic polynomial interpolation performs better than spline interpolation, one-dimensional linear interpolation performs better than two-dimensional linear interpolation, and DFT time-domain interpolation performs better than linear interpolation. The performance of the Natural interpolation of the present invention is the best. When the bit error rate is large, Natural interpolation shows a significant improvement of about 0.6 dB compared to DFT time-domain interpolation.

[0090] Figure 8 This is the system BER curve using different interpolation algorithms in the NLOS environment with Doppler frequency shift fd = 250Hz. Figure 7 , the DFT time domain interpolation performance deteriorates, and the DFT time domain interpolation performance is inferior to the linear interpolation. The Natural interpolation performance of the present invention is also the best, which can bring about 1.6dB performance improvement compared with the one-dimensional linear interpolation.

[0091] The above analysis demonstrates that, in several typical channel scenarios, the channel estimation method based on Natural interpolation proposed in this invention significantly improves performance compared to existing channel estimation methods based on other interpolation methods. Furthermore, once the pilot pattern is determined, the Natural interpolation coefficients can also be determined accordingly, making it very easy to implement in engineering.

[0092] Experiment 2: Simulating the interpolation effect of Natural interpolation

[0093] In the LOS environment with Doppler frequency shift fd = 83.3Hz, a frequency domain channel frequency response data cloud diagram of multiple adjacent OFDM symbols in a frame is drawn. The amplitude size is represented by color, which intuitively shows the interpolation effect of Natural interpolation and two-dimensional linear interpolation. The results are as follows: Figure 9 and Figure 10 As shown, Figure 9 H11 is the real channel frequency response at the pilot P Local data cloud diagram of (real part), Figure 10 estH11 is the channel frequency response estimate at the pilot obtained by LS estimation P (real part) of the local data cloud diagram. Figure 9 and Figure 10 In the figure, each rectangular grid represents a subcarrier position, where the one marked with "P" represents the pilot subcarrier position. It can be seen that due to the influence of factors such as noise, the channel frequency response estimate estH11 at the pilot estimated by LS is P With the real channel frequency response H11 P There is a deviation.

[0094] Figures 11(a)-11(c) is the true channel frequency response H11 and the total frequency response estimation values ​​obtained by two-dimensional linear interpolation and Natural interpolation, among which Figure 11(a) shows the true channel frequency response H11, and Figure 11(b) shows the estH11 P The total frequency response estimate estH11 obtained by two-dimensional linear interpolation 2Dlinear , Figure 11(c) shows the P The total frequency response estimate estH11 obtained by Natural interpolation Natural The rectangular grids marked with "P" in the figure are the pilot subcarrier positions, and the other rectangular grids are the data subcarrier positions. Since two-dimensional linear interpolation is based on linear interpolation of triangulation, one-dimensional linear interpolation is performed on the edges of the triangles (that is, on the rows or columns with pilots), the interpolation result appears as uneven stripes. Overall, the result of Natural interpolation is more uniform than that of two-dimensional linear interpolation.

[0095] For two-dimensional pilots, a large part of two-dimensional linear interpolation is one-dimensional linear interpolation, and one-dimensional linear interpolation only uses two adjacent data points for interpolation. When the value deviation of two adjacent data points is large, the interpolation result of the segment will be unreliable. Natural interpolation is a weighted summation of the values ​​at natural neighboring points. Figure 1In the pilot pattern shown, the interpolation of any data point (except the edge subcarriers and OFDM symbols of a frame) requires data from at least six nearby pilot points. The weight of each pilot point is obtained by dividing the Voronoi cell area. This enables Natural interpolation to more fully and reasonably utilize the correlation of the channel in the time and frequency domains, suppress noise, and improve the interpolation accuracy of the channel frequency response. Therefore, Natural interpolation achieves better interpolation effect when performing channel frequency response interpolation.

[0096] Experiment 3: Simulating the system NMSE curve using different interpolation methods

[0097] Specifically, the NMSE performance of Natural interpolation is compared with other interpolation methods in NLOS channel environments with Doppler frequency shift fd = 4.17 Hz and nLOS channel environments with fd = 250 Hz. Figure 12 The NMSE curves for estimating the channel frequency response using different interpolation algorithms in an NLOS environment with a Doppler frequency shift of 4.17 Hz are presented. It can be seen that spline interpolation performs the worst. Cubic polynomial interpolation outperforms spline interpolation, one-dimensional linear interpolation outperforms two-dimensional linear interpolation, and DFT time-domain interpolation outperforms one-dimensional linear interpolation. Natural interpolation performs the best, with the NMSE of Natural interpolation reduced by 50% compared to two-dimensional linear interpolation.

[0098] Figure 13 The NMSE curves of channel frequency response estimated by different interpolation algorithms in nLOS environment with Doppler frequency shift fd = 250Hz are given. Figure 12 , the performance of DFT time domain interpolation deteriorates in this channel environment, that is, DFT time domain interpolation has performance deterioration under high signal-to-noise ratio, while the NMSE of Natural interpolation is still the smallest.

[0099] Experiment 4: Simulating the Channel Estimation Error Interference Term Using Different Interpolation Algorithms

[0100] Specifically, assuming that the total number of subcarriers in the OFDM system is N, the matrix form of the received signal is expressed as:

[0101] Y=HX+N;

[0102] Where X is the N×1 transmitted signal vector, Y is the N×1 received signal vector, N is the additive white Gaussian noise vector, and H is the N×N channel frequency response matrix, which is a diagonal matrix. The elements on the diagonal are the fast Fourier transform (FFT) of the channel impulse response h.

[0103] The system adopts the Alamouti-STBC diversity scheme. Assume that the two adjacent OFDM symbol sequences of the input are X1=[x1(0),x1(1),...,x1(N-1)] T ,X2=[x2(0),x2(1),...,x2(N-1)] T , encode the two symbol sequences in the following form:

[0104]

[0105] in,(·) * It represents the complex conjugate of the symbol. For the sake of simplicity, only a single receiving antenna is used for derivation. Assuming that the channel remains unchanged in two consecutive symbol periods, the received signal is expressed as:

[0106]

[0107] Where H1 and H2 represent the channel matrices from transmit antenna 1 and transmit antenna 2 to receive antenna 1, respectively. Zero-forcing (ZF) detection is widely used due to its simple principle. This involves taking the complex conjugate of the above equation and multiplying both sides by the Hermitian transpose of the estimated channel matrix. To facilitate detection, the channel is usually assumed to be quasi-static. Assuming the channel remains unchanged within two OFDM symbol periods, we have:

[0108]

[0109] Furthermore, multiply the above formula on the left by After that, the right side of the equation is usually used as the ZF test result:

[0110]

[0111] Focus on the interference term generated by the channel frequency response estimation error under each OFDM symbol, that is, the second term in the above formula, recorded as Right now:

[0112]

[0113] The closer the interpolated channel frequency response estimate is to the true value, the greater the interference term The smaller it is, the better the detection result. Therefore, the interpolation accuracy has a significant impact on the system performance.

[0114] The following plots the interference term generated by the channel frequency response estimation error under different interpolation methods. The sum of the squares of the moduli . Figure 14 and Figure 15 According to The interference term generated by the channel frequency response estimation error within one frame under two channel environments drawn by the formula The sum of squares of the modulus of , focusing on the comparison between Natural interpolation and one-dimensional linear interpolation. Figure 14 The corresponding Doppler frequency shift fd = 4.17 Hz, Figure 15 The corresponding Doppler frequency shift fd = 250Hz.

[0115] Depend on Figure 14-15 It can be seen that in the two channel environments, Natural interpolation is better than the one-dimensional linear interpolation interference term. The sum of squared moduli is smaller, that is, the channel frequency response estimation value obtained by Natural interpolation is closer to the true value of the channel frequency response, so the detection result will be more accurate.

[0116] In summary, the present invention addresses the problems existing in the pilot-assisted non-blind channel estimation interpolation algorithm in existing MIMO-OFDM systems, such as low interpolation accuracy and performance degradation under high signal-to-noise ratios. A MIMO-OFDM channel estimation method based on Natural interpolation is proposed, and compared with commonly used one-dimensional linear interpolation, two-dimensional linear interpolation, cubic polynomial interpolation, spline interpolation, and DFT time-domain interpolation. Simulation results show that the Natural interpolation method proposed in the present invention can more fully utilize the correlation of the channel in the time and frequency domains, thereby suppressing noise. Based on the area calculation weight, more pilot information can be used when interpolating each data carrier frequency point, and the interpolation result is more uniform, thereby obtaining a more accurate channel estimate. During detection, the more accurate channel estimation result reduces the interference term generated by the channel frequency response estimation error, thereby improving detection accuracy. Therefore, the method proposed in the present invention has better performance.

[0117] In addition, since Natural interpolation can interpolate randomly scattered data, it is suitable for complex pilot design.

[0118] Example 2

[0119] Based on the above embodiment 1, this embodiment provides a MIMO-OFDM channel estimation device based on Natural interpolation. Figure 16 , Figure 16 A structural block diagram of a MIMO-OFDM channel estimation device based on Natural interpolation provided in an embodiment of the present invention, the device comprising:

[0120] A first estimation module, configured to obtain a channel coefficient at a pilot frequency based on least squares channel estimation;

[0121] The second estimation module is used to assign weights to the channel coefficients at several pilot channels near each interpolation point according to the size of the Voronoi diagram grid based on the Natural interpolation method, and obtain the interpolation formula at the interpolation point by weighted summation;

[0122] The interpolation module is used to perform Natural interpolation on each interpolation point using the interpolation formula to obtain a MIMO-OFDM channel estimation result.

[0123] The device provided in this embodiment can implement the method provided in the above embodiment 1. For detailed process, please refer to the above embodiment 1. Therefore, the device can also significantly improve the channel estimation accuracy, reduce the channel estimation error, and have a smoother interpolation effect and better interpolation performance.

[0124] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A MIMO-OFDM channel estimation method based on Natural interpolation, characterized in that: include: Obtain the channel coefficient at the pilot frequency based on the least squares channel estimation; Based on the Natural interpolation method, the channel coefficients at several pilot channels near each interpolation point are weighted according to the size of the Voronoi diagram grid area, and the interpolation formula at the interpolation point is obtained by weighted summation; Performing Natural interpolation on each interpolation point using the interpolation formula to obtain a MIMO-OFDM channel estimation result; The channel coefficients at the pilot frequency are obtained based on the least squares channel estimation, including: The channel coefficient at the pilot is calculated based on the transmit channel frequency response and the receive channel frequency response. The calculation formula is: ； Where, Indicates the frequency domain k In the time domain n The channel coefficient at the pilot frequency, represents the receiving channel frequency response, Indicates the transmit channel frequency response express The pilot frequency is located at subcarriers and the OFDM symbol positions; Among them, based on the Natural interpolation method, the channel coefficients at several pilot channels near each interpolation point are weighted according to the size of the Voronoi diagram grid area, and the interpolation formula at the interpolation point is obtained by weighted summation, including: Draw the original Voronoi diagram based on the pilot points; Adding interpolation points to the original Voronoi diagram to draw a new Voronoi diagram; wherein the Voronoi cell where the interpolation point is located is divided into several parts by the original Voronoi diagram, and the pilot point corresponding to each part is used as a natural neighbor of the interpolation point; The weight of the corresponding natural neighbor point is determined by the area size of each part; Performing weighted summation on the channel coefficients at the corresponding pilot points based on the weights to obtain an interpolation formula at the current interpolation point; Among them, the original Voronoi diagram is drawn based on the pilot points, including: Draw the Delaunay triangulation based on the pilot points; Draw a perpendicular bisector for each side of each triangle in the Delaunay triangulation to obtain the original Voronoi diagram; The formula for determining the weight of the corresponding natural neighbor point by the area size of each part is: ； Where, Indicates the i The weight of the natural neighbors, represents the total number of natural neighboring points of the interpolation point, Indicates the i The area of ​​the part, Indicates the total area; The interpolation formula at the interpolation point is expressed as: ； Where, represents the interpolation point, Indicates interpolation points The estimated channel coefficient at Indicates interpolation points The natural neighbors of Represents natural neighbors The corresponding weights, Represents natural neighbors The channel coefficient at ; Before performing Natural interpolation on each interpolation point using the interpolation formula to obtain the MIMO-OFDM channel estimation result, the method further includes: The number of weight groups is calculated based on the pilot pattern. The calculation formula is: ； Where, represents the number of weight groups, Indicates rounding down. and Respectively represent the time domain interval and frequency domain interval of the two-dimensional pilot; The interpolation formula is used to perform Natural interpolation on each interpolation point to obtain the MIMO-OFDM channel estimation result, including: Based on the number of weight groups, all interpolation points are interpolated according to the interpolation formula in a translation and mirroring manner to obtain a MIMO-OFDM channel estimation result.

2. A MIMO-OFDM channel estimation device based on Natural interpolation, characterized in that: include: A first estimation module, configured to obtain a channel coefficient at a pilot frequency based on least squares channel estimation; The second estimation module is used to assign weights to the channel coefficients at several pilot channels near each interpolation point according to the size of the Voronoi diagram grid based on the Natural interpolation method, and obtain the interpolation formula at the interpolation point by weighted summation; An interpolation module, configured to perform Natural interpolation on each interpolation point using the interpolation formula to obtain a MIMO-OFDM channel estimation result; The channel coefficients at the pilot frequency are obtained based on the least squares channel estimation, including: The channel coefficient at the pilot is calculated based on the transmit channel frequency response and the receive channel frequency response. The calculation formula is: ； Where, Indicates the frequency domain k In the time domain n The channel coefficient at the pilot frequency, represents the receiving channel frequency response, Indicates the transmit channel frequency response express The pilot frequency is located at subcarriers and the OFDM symbol positions; Among them, based on the Natural interpolation method, the channel coefficients at several pilot channels near each interpolation point are weighted according to the size of the Voronoi diagram grid area, and the interpolation formula at the interpolation point is obtained by weighted summation, including: Draw the original Voronoi diagram based on the pilot points; Adding interpolation points to the original Voronoi diagram to draw a new Voronoi diagram; wherein the Voronoi cell where the interpolation point is located is divided into several parts by the original Voronoi diagram, and the pilot point corresponding to each part is used as a natural neighbor of the interpolation point; The weight of the corresponding natural neighbor point is determined by the area size of each part; Performing weighted summation on the channel coefficients at the corresponding pilot points based on the weights to obtain an interpolation formula at the current interpolation point; Among them, the original Voronoi diagram is drawn based on the pilot points, including: Draw the Delaunay triangulation based on the pilot points; Draw a perpendicular bisector for each side of each triangle in the Delaunay triangulation to obtain the original Voronoi diagram; The formula for determining the weight of the corresponding natural neighbor point by the area size of each part is: ； Where, Indicates the i The weight of the natural neighbors, represents the total number of natural neighboring points of the interpolation point, Indicates the i The area of ​​the part, Indicates the total area; The interpolation formula at the interpolation point is expressed as: ； Where, represents the interpolation point, Indicates interpolation points The estimated channel coefficient at Indicates interpolation points The natural neighbors of Represents natural neighbors The corresponding weights, Represents natural neighbors The channel coefficient at ; Before performing Natural interpolation on each interpolation point using the interpolation formula to obtain the MIMO-OFDM channel estimation result, the method further includes: The number of weight groups is calculated based on the pilot pattern. The calculation formula is: ； Where, represents the number of weight groups, Indicates rounding down. and Respectively represent the time domain interval and frequency domain interval of the two-dimensional pilot; The interpolation formula is used to perform Natural interpolation on each interpolation point to obtain the MIMO-OFDM channel estimation result, including: Based on the number of weight groups, all interpolation points are interpolated according to the interpolation formula in a translation and mirroring manner to obtain a MIMO-OFDM channel estimation result.

Images