阅读说明：本技术 OFDM系统中基于局部搜索Capon的CFO估计算法 (CFO estimation algorithm based on local search Capon in OFDM system ) 是由 陈曦 叶长波 张小飞 于 2019-10-28 设计创作，主要内容包括：本发明公开了OFDM系统中基于局部搜索Capon的CFO估计算法,本发明算法在全局搜索Capon算法的基础上进行改进,该方法首先建立接收信号的数学模型,然后通过接收信号的数学模型获得协方差矩阵,最后通过构造的谱函数进行局部搜索获得CFO估计结果。局部搜索大大降低了计算复杂度,且该发明算法解决了传统Capon算法在低信噪比情况下因为谱峰不明显或者谱峰缺失导致估计性能严重下降的问题。仿真证明了该方法的有效性。(The invention discloses a CFO estimation algorithm based on local search Capon in an OFDM system, which is improved on the basis of a global search Capon algorithm. The local search greatly reduces the calculation complexity, and the algorithm solves the problem that the estimation performance is seriously reduced due to unobvious spectral peaks or spectral peak loss of the traditional Capon algorithm under the condition of low signal-to-noise ratio. The simulation demonstrates the effectiveness of the method.)

The CFO estimation algorithm based on the local search Capon in the OFDM system is characterized by comprising the following steps:

step 1: establishing a mathematical model of a received signal;

step 2: calculating an estimated value of a covariance matrix of the received signal;

and step 3: the CFO estimate is obtained by a local spectral peak search.

2. The CFO estimation algorithm based on local search Capon as claimed in claim 1, wherein the specific step of step 3 includes:

step 3.1: constructing a Capon spatial spectrum function;

in the formula (I), the compound is shown in the specification,

step 3.2: carrying out local spectral peak search on the Capon space spectral function to obtain P spectral peaks;

step 3.3: calculating to obtain an estimated value of the real frequency offset according to the frequency offset values corresponding to the P spectral peaks;

in the formula (I), the compound is shown in the specification,

Technical Field

The invention relates to a CFO (Carrier Frequency offset) estimation algorithm based on local search Capon in an OFDM (orthogonal Frequency Division multiplexing) system, belonging to the technical field of wireless communication.

Background

OFDM, an orthogonal frequency division multiplexing technology, started in the nineties, and is characterized by taking full advantage of the orthogonality of subcarriers for multicarrier modulation. Currently, the OFDM system has been widely used in the fields of high definition television signal transmission, digital video transmission, wireless local area network, etc., and is applied to wireless wide area networks and fourth generation cellular communication networks. Compared with other systems, the OFDM system has many advantages, such as higher spectrum utilization rate, good resistance to frequency selective fading, and the like. However, the orthogonality of the OFDM system to the self-check of each subcarrier is very strict, and any Carrier Frequency Offset (CFO) affects the orthogonality between subcarriers. Therefore, accurate estimation and compensation of CFO in an OFDM system is required to ensure the performance of the system. CFO estimation methods currently fall into two categories: non-blind CFO estimation and blind CFO estimation. Non-blind CFO estimation methods include pilot frequency-based and cyclic prefix-based methods; the blind CFO estimation adopts the traditional spectrum estimation method, such as a MUSIC algorithm, an ESPRIT algorithm based on rotation-invariant signal parameter estimation, a CFO estimation algorithm based on kurtosis and the like. Compared with a non-blind CFO estimation method, the blind CFO estimation method has higher frequency band utilization rate, and certain algorithms have higher CFO estimation performance.

Compared with a non-blind estimation method, the global search Capon algorithm has better estimation performance, but the algorithm needs to search all subcarriers, so that the calculation complexity is higher. The local Capon algorithm provided by the invention is improved on the basis of global search, and only one subcarrier is searched, so that the calculation complexity is lower. According to simulation results, when the signal-to-noise ratio is high, the local Capon algorithm has CFO estimation performance close to that of a global search Capon algorithm on the basis of lower complexity. The problem that the CFO estimation performance of the global search Capon algorithm is poor when the signal to noise ratio is low is greatly improved.

Disclosure of Invention

The technical problem to be solved by the invention is to provide a CFO estimation algorithm based on local search Capon, and the method is improved on the basis of a global search Capon algorithm, so that the high complexity caused by the step of searching all P subcarriers by global search is reduced. Meanwhile, the algorithm of the invention adopts local search, so that the CFO estimation performance is approximately the same as that of the global search Capon algorithm when the signal-to-noise ratio is high. The CFO estimation performance is better than the global search Capon algorithm at low signal-to-noise ratio.

The invention adopts the following technical scheme for solving the problems:

a CFO estimation algorithm based on local search Capon in an OFDM system is basically characterized in that a mathematical model of a received signal is established, a covariance matrix of the received signal is calculated through the mathematical model of the received signal, and CFO estimation is obtained through local search.

Compared with the prior art, the invention adopting the technical scheme has the following beneficial effects:

① the algorithm of the invention adopts local spectral peak search, the search range is one subcarrier, while the traditional Capon algorithm adopts global search, the search range is all P subcarriers, the search range is large, and the calculation amount is large;

② the algorithm inherits the higher estimation performance of the traditional Capon algorithm and is better than the ESPRIT algorithm;

③ the algorithm superposes P spectral peaks during local search, which can effectively overcome the problem that the estimation performance is seriously reduced due to the unobvious spectral peaks or the missing spectral peaks in the low signal-to-noise ratio condition of the traditional Capon algorithm;

④ the method of the present invention can effectively perform CFO estimation in OFDM system.

Drawings

FIG. 1 is a flow chart of the algorithm of the present invention;

FIG. 2 is a graph of frequency offset estimation corresponding to the global search Capon algorithm when SNR is 0 dB;

FIG. 3 is a graph of frequency offset estimation corresponding to the global search Capon algorithm when SNR is 20 dB;

FIG. 4 is a graph of frequency offset estimation corresponding to the local search Capon algorithm when SNR is 0 dB;

FIG. 5 is a graph of frequency offset estimation corresponding to the local search Capon algorithm when SNR is 20 dB;

FIG. 6 is a comparison graph of CFO estimation performance for different algorithms;

FIG. 7 is a comparison graph of CFO estimation performance when N takes different values;

FIG. 8 is a comparison graph of CFO estimation performance when K takes different values;

FIG. 9 is a comparison graph of CFO estimation performance when P takes different values;

fig. 10 is a CFO estimation performance diagram for different CFO cases.

Detailed Description

The technical scheme of the invention is further described in detail by combining the drawings and the specific embodiments:

the symbols represent: in the invention, (.)^T，(·)^HAnd (·)^-1Denoted as transpose, conjugate transpose and inversion, respectively. Capital X represents a matrix, lowercase X (-) represents a vector, E [ ·]Indicating that it is desired. Re (. cndot.) represents the real part. diag (v) denotes the diagonal element as a diagonal matrix of vector v.

The parameters involved in the method of the invention are as follows: consider an uplink OFDM system. The system has N subcarriers, where P channels are used for data transmission and the remaining N-P channels are virtual carriers. And a cyclic prefix with the length L is used for eliminating the inter-channel interference caused by the multipath effect, wherein L is larger than the maximum time delay of the signal. Firstly, obtaining an expression of a received signal according to a mathematical model of the received signal, then calculating a signal covariance matrix estimation value, and finally obtaining CFO estimation through local spectral peak search. In this example, a CFO estimation algorithm based on local search Capon in the OFDM system is specifically implemented as follows:

step 1: establishing a mathematical model of a received signal

After inserting the cyclic prefix, the signal is transmitted through the multi-channel fading channel, and after removing the cyclic prefix, the received signal can be expressed as

x(k)＝EF_Pdiag(h)s(k)e^{j2πΔf(k-1)(N+L)}(1)

Wherein E ═ diag (1, E)^j2πΔf/N,...,e^{j2πΔf(N-1)/N}) Is a frequency offset matrix in the system; Δ f is a preset initial frequency offset; f_PThe first P columns of the inverse discrete Fourier transform matrix; h ═ H (1), H (2),.., H (p)]^T，

For frequency correspondence of different channels, s (k) ═ s₁(k),s₂(k),...,s_P(k)]^TAnd transmitting the kth data block for the P data transmission channels. From the formula (1)

X＝Adiag(h)B^T(2)

Wherein B ═ diag (1, e)^j2πΔf(N+L),...,e^{j2πΔf(K-1)(N+L)})S；S＝[s(1),s(2),...s(K)]^TAll K data blocks transmitted for the P channels; the matrix A has van der Mond properties

In the noisy case, the received signal may be represented as

Wherein W is noise during reception; s ═ diag (h) B^T。

Step 2: calculating an estimate of a signal covariance matrix

The basic algorithm of the method is a global search Capon algorithm, which comprises the following steps:

the Capon algorithm is also called Minimum Variance Method (MVM), and the optimization problem solved by the Capon algorithm can be expressed as:

with the constraint of

Wherein P (ω) ω^HE[XX^H]ω＝ω^HR omega is the power of the output signal, X represents a noise-free received signal matrix, and R represents a covariance matrix R-XX constructed from the noise-free received signals^H/K。

Capon's algorithm attempts to minimize the power of noise and interference contributions in the non-signal direction, while the power is constant in the signal direction. The optimal weighting vector can be solved by Lagrange multiplier method, and the result is

In the formula (I), the compound is shown in the specification,

is a received signal covariance matrix. For the data model represented by equation (3), the data covariance matrix can be estimated from equation (4). Substituting the formula (5) into the constraint condition to obtain the spatial spectrum of the Capon algorithm, wherein the CFO estimated value can be obtained by searching the spectrum peak of the spectrum function

In the formula (I), the compound is shown in the specification,

whereinRepresenting an angle search range, and performing global spectral peak search on the spectral function, wherein the search range is [0,2 pi P/N]P spectral peaks can be obtained, corresponding frequency shifts are respectively

As shown in fig. 3. Where Δ f represents a preset initial frequency offset.

The estimated value of the real frequency offset can be calculated and obtained according to the frequency offset values corresponding to the P spectral peaks

In the formula (I), the compound is shown in the specification,

and searching the angle value corresponding to the ith spectrum peak for the global condition. F represents global search trueThe real frequency deviation estimation value has the spectrum peak search range of [0,2 pi P/N]。

As can be seen from fig. 3, in the case of high signal-to-noise ratio, P distinct spectral peaks can be obtained, and then the frequency offset estimation value can be obtained according to equation (7). However, in the case of low signal-to-noise ratio, due to the interference of noise, the spectral peak is not obvious, and even the spectral peak is missing, as shown in fig. 2. Thus, the frequency offset estimation value obtained according to equation (7) has a large deviation from the actual frequency offset value. In addition, because a spectrum function needs to be searched globally, the traditional Capon algorithm has a large amount of operation and is not beneficial to being applied to actual CFO estimation.

And step 3: CFO estimation through local spectral peak search

In order to solve the problems of the conventional global search Capon algorithm, an improved local search method can be adopted to perform CFO estimation. It can be seen that the local search for P spectral peaks has the following relationship

Therefore, like equation (6), we can construct the following spectral function to obtain CFO estimation by local search

In the formula (I), the compound is shown in the specification,

the estimated value of the real frequency offset can be calculated and obtained according to the frequency offset values corresponding to the P spectral peaks

In the formula (I), the compound is shown in the specification,and searching the angle corresponding to the ith spectrum peak for the local part. F_LS-CaponRepresenting the local search of the real frequency deviation estimated value, the search range is [0,2 pi/N]。

As can be seen from the equations (8) and (9), the search range of the local search Capon algorithm is greatly reduced, so the computation amount is reduced. In addition, because the spectral function of the algorithm is formed by overlapping P spectral peaks, even if individual spectral peaks are not obvious or spectral peaks are missing, the true frequency offset in the obtained spectral function still corresponds to a unique spectral peak under the condition of low signal to noise ratio.

The algorithm computational complexity analysis of the invention is shown in table 1:

table 1 is a comparison table of complexity calculation of each algorithm, wherein N, P is the number of subcarriers and the number of channels used by the system, K is the number of fast beats, n is_gRepresenting the number of searches of the MUSIC algorithm or Capon global search, n_lRepresenting the number of searches of the local search Capon algorithm. The traditional Capon algorithm employs global spectral peak search, n_gLarge, high complexity; the Capon algorithm presented herein employs a local spectral peak search, n_lIs much less than n_gAnd the algorithm complexity is greatly reduced.

TABLE 1 comparison table for calculating complexity of each algorithm

Fig. 2 is a graph of frequency offset estimation corresponding to the global search Capon algorithm when SNR is 0 dB. As can be seen from the figure, when the signal-to-noise ratio is low, due to interference of noise, a spectrum peak may be not obvious, even a spectrum peak is absent, so that a large error exists between the frequency offset estimation value obtained according to equation (7) and the actual frequency offset. The frequency offset Δ f is 0.4, the number of subcarriers N is 32, the number of channels P used for transmission is 20, and the number of cyclic prefixes L is 8.

Fig. 3 is a graph of frequency offset estimation corresponding to the global search Capon algorithm when SNR is 20 dB. From the figure, P distinct spectral peaks can be obtained when the signal-to-noise ratio is high. The frequency offset Δ f is 0.4, the number of subcarriers N is 32, the number of channels P used for transmission is 20, and the number of cyclic prefixes L is 8.

Fig. 4 is a graph of frequency offset estimation corresponding to the local search Capon algorithm when SNR is 0 dB. From the figure, under the condition of low signal-to-noise ratio, the local search Capon algorithm can still obtain a relatively accurate frequency offset estimation value through local spectral peak search. The frequency offset Δ f is 0.4, the number of subcarriers N is 32, the number of channels P used for transmission is 20, and the number of cyclic prefixes L is 8.

Fig. 5 is a graph of frequency offset estimation corresponding to the local search Capon algorithm when SNR is 20 dB. The frequency offset Δ f is 0.4, the number of subcarriers N is 32, the number of channels P used for transmission is 20, and the number of cyclic prefixes L is 8.

FIG. 6 is a graph comparing the performance of the local search Capon algorithm, the ESPRIT algorithm, and the PM algorithm herein, from which it can be derived that the estimated performance of the algorithm of the present invention is much higher than the other two algorithms. Wherein, N is 32, P is 20, L is 8, K is 200, and the simulation times is 500.

Fig. 7 to 9 are performance graphs of the local search Capon algorithm under different parameters. Fig. 7 and fig. 8 show the estimation performance of the local search Capon algorithm under different subcarrier numbers N and different fast beat numbers K, respectively, and the estimation performance of CFO improves as K and N increase; fig. 9 shows the estimated performance of the algorithm at different channel numbers P, and it can be seen that the performance of the CFO algorithm decreases as P increases. Because as the number of channels increases, the interference between the channels increases, resulting in a deterioration of the CFO estimation performance.

Fig. 10 shows CFO estimation performance for different CFO cases. From the graph, the local search Capon algorithm has very close CFO estimation performance for different CFOs. Where N is 32, P is 20, K is 200, SNR is 20dB and CFO range is [0, ω ], ω is 2 pi/N is normalized subcarrier space.