阅读说明：本技术 一种基于空载波的ofdm系统频偏估计分析方法 (OFDM system frequency offset estimation analysis method based on null carrier ) 是由 陈芳炯 潘裕利 余华 季飞 于 2020-03-18 设计创作，主要内容包括：本发明属于无线通信领域,涉及一种基于空载波的OFDM系统频偏估计分析方法,包括：将发送的序列经过OFDM方案得到调制符号后,将调制符号经过瑞利信道进行发送,在接收端将利用瑞利信道和噪声的统计特性进行频偏估计均方误差的计算。频偏估计均方误差的理论值用包括瑞利信道响应系数和信道噪声两个随机变量的统计特性,结合检测出的非激活子载波与加性复高斯白噪声的统计特性直接进行计算；在计算频偏估计均方误差的理论值时,利用泰勒级数展开,进而得到更精确的频偏估计均方误差表达式。本发明利用瑞利信道的统计特性能得到频偏估计均方误差的理论值,并取其高阶近似作为结果,有效地提高了估计分析方法的通用性与准确性。(The invention belongs to the field of wireless communication, and relates to a method for estimating and analyzing frequency offset of an OFDM (orthogonal frequency division multiplexing) system based on a null carrier, which comprises the following steps: after the transmitted sequence is subjected to an OFDM scheme to obtain a modulation symbol, the modulation symbol is transmitted through a Rayleigh channel, and the calculation of the frequency offset estimation mean square error is carried out at a receiving end by utilizing the statistical characteristics of the Rayleigh channel and noise. The theoretical value of the frequency deviation estimation mean square error is directly calculated by combining the statistical properties of two random variables including a Rayleigh channel response coefficient and channel noise and the detected statistical properties of the inactive subcarrier and additive complex Gaussian white noise; and when the theoretical value of the frequency deviation estimation mean square error is calculated, taylor series expansion is utilized, and a more accurate frequency deviation estimation mean square error expression is obtained. The invention utilizes the statistical property of the Rayleigh channel to obtain the theoretical value of the frequency deviation estimation mean square error, and takes the high-order approximation as the result, thereby effectively improving the universality and the accuracy of the estimation analysis method.)

1. A frequency offset estimation analysis method of an OFDM system based on a null carrier is characterized in that:

the theoretical value of the frequency deviation estimation mean square error is directly calculated by combining the statistical properties of two random variables including a Rayleigh channel response coefficient and channel noise and the detected statistical properties of the inactive subcarrier and additive complex Gaussian white noise;

and when the theoretical value of the frequency deviation estimation mean square error is calculated, taylor series expansion is utilized, and a more accurate frequency deviation estimation mean square error expression is obtained.

2. The method of analyzing frequency offset estimation in OFDM system according to claim 1, wherein said method comprises:

before a sending end sends data, setting null subcarriers at fixed subcarrier positions in advance, and carrying modulation symbols on the rest subcarriers;

forming a frequency domain transmitting signal by a subcarrier carrying a modulation symbol and a preset null subcarrier, and adding a cyclic prefix larger than channel delay through IFFT to obtain a baseband time domain transmitting signal;

removing the cyclic prefix at a receiving end, and taking the obtained baseband time domain receiving signal as a random variable which changes along with a channel;

calculating an inverse discrete Fourier transform matrix by using the position and the number of null sub-carriers preset by a sending end;

combining the statistical characteristics of a Rayleigh channel, and equating a theoretical expression of mean square error of frequency offset estimation to be an expectation of a random variable function comprising a Rayleigh channel response coefficient and channel noise;

and performing Taylor series expansion on the theoretical expression of the frequency deviation estimation mean square error, performing second-order approximation on the expression of the expectation and the variance, and calculating to obtain a high-order approximation result of the frequency deviation estimation mean square error.

3. The OFDM system frequency offset estimation analysis method of claim 1 or 2, wherein the frequency offset estimation is performed by frequency offset estimationThe mean square error calculation method comprises the following steps:

wherein the content of the first and second substances,andrespectively, the target function g () is ═₀The first and second derivatives of (a).

4. The method of claim 3, wherein g () is calculated by the following formula:

where y denotes a received time-domain signal vector, y^HRepresenting the transposed conjugate of the received time-domain signal vector y, D () representing the matrix corresponding to the frequency offset, D^H() The transposed conjugate of D () is represented,representing an inverse discrete Fourier transform matrixProducts of conjugate transpose thereof, i.e.

5. The OFDM system frequency offset estimation analysis method of claim 4, wherein the received time domain signal vector y is calculated by the following formula:

wherein: x represents a frequency domain transmission symbol in the form of a diagonal matrix, W represents a discrete fourier transform matrix, h represents a time domain response of a rayleigh channel, and v represents additive complex gaussian white noise.

6. The method of claim 3, wherein the calculating of the mean square error of the frequency offset estimation comprises:

firstly, the first step is toIs written intoIs expected toSum varianceThen on expectationSum varianceThe expression of (a) is approximated by a Taylor series;

the calculation formula is as follows:

7. the OFDM system frequency offset estimation analysis method of claim 6,the calculation formula of (2) is as follows:

wherein the content of the first and second substances,andrespectively representAndin the expectation that the position of the target is not changed,to representAndthe covariance of (a) of (b),to representThe variance of (c).

8. The OFDM system frequency offset estimation analysis method of claim 6,the calculation formula of (2) is as follows:

wherein the content of the first and second substances,to representThe variance of (c).

Technical Field

The invention belongs to the field of wireless communication, and relates to a frequency offset estimation analysis method of an OFDM system based on a null carrier.

Background

Orthogonal Frequency Division Multiplexing (OFDM) is one of the most critical technologies in wireless communication systems due to its high spectrum utilization and strong resistance to multipath fading. Many common wireless communication systems employ OFDM technology. The OFDM technology can effectively overcome Intersymbol interference (ISI) in addition to high spectral efficiency and resistance to multipath fading, and can perform modulation and demodulation by using an IFFT/FFT fast algorithm. In an OFDM practical system, due to factors such as doppler effect, Carrier Frequency Offset (CFO) is often caused, which causes Frequency spectrum overlap between adjacent subcarriers, which destroys orthogonality, and thus Inter-Carrier Interference (ICI) is caused, and the effectiveness of system transmission performance is affected. Therefore, it is important to perform accurate estimation and compensation of CFO before demodulation. In the existing research, the estimation of CFO can be mainly divided into a training sequence-based method and a null subcarrier-based method.

Mounir Ghogho et al proposed in 2001 an OFDM carrier frequency offset estimation method based on null subcarrier detection under Rayleigh channel (see the literature: Ghogho M, Swami A, Giannakis G B. optimized null-subcarrier selection for CFO estimation in OFDM over frequency-selective channels [ C ]// IEEE Global communication conference. IEEE, 2001). The method is characterized in that CFO is accurately estimated by means of a maximum likelihood estimation method on an OFDM system by means of preset null sub-carriers, utilizing orthogonality among the sub-carriers and minimizing energy of the null sub-carriers at a receiving end, and a Cramer-Rao Bound (CRB) of carrier frequency offset estimation is given. Due to the complexity of the objective function, the algorithm does not relate to a theoretical calculation method of the mean square error of the CFO estimation value under the Rayleigh channel, namely the correctness of the estimation method cannot be well verified.

In 2018, researchers propose a CFO estimation and compensation method of an OFDM-IM system in a wireless fixed channel (see the Chinese patent application of the southern China's university for frequency offset estimation of an OFDM-IM system', published as 8.17.2018, published as CN108418772A), however, the fixed channel has great limitations, and the method has no generality in a complex and changeable channel environment and is difficult to popularize and apply.

Therefore, aiming at the defects of the existing CFO estimation performance analysis obtained by the above investigation, in order to more effectively apply the generalized CFO estimation performance analysis method to wireless communication, it is necessary to design a CFO estimation analysis algorithm which can effectively ensure the accuracy of CFO estimation, can effectively apply to a general rayleigh channel, has greater universality, and finally can effectively provide powerful theoretical support for simulation results.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides the OFDM system frequency offset estimation analysis method based on the empty carrier, which can effectively guarantee the accuracy of frequency offset estimation, can be effectively applied to a general Rayleigh channel, has higher universality and can effectively provide powerful theoretical support for a simulation result.

The invention is realized by adopting the following technical scheme:

a frequency offset estimation analysis method of an OFDM system based on null carriers comprises the following steps:

the theoretical value of the frequency offset estimation mean square error is characterized by comprising a Rayleigh channel response coefficient and channel noise: the statistical characteristics of two random variables of the noise are combined with the statistical characteristics of the detected inactive subcarriers and the additive complex Gaussian white noise to directly calculate;

and when the theoretical value of the frequency deviation estimation mean square error is calculated, taylor series expansion is utilized, and a more accurate frequency deviation estimation mean square error expression is obtained.

Further, a method for analyzing frequency offset estimation of an OFDM system based on a null carrier includes:

before a sending end sends data, setting null subcarriers at fixed subcarrier positions in advance, and carrying modulation symbols on the rest subcarriers;

forming a frequency domain transmitting signal by a subcarrier carrying a modulation symbol and a preset null subcarrier, and adding a cyclic prefix larger than channel delay through IFFT to obtain a baseband time domain transmitting signal;

removing the cyclic prefix at a receiving end, and taking the obtained baseband time domain receiving signal as a random variable which changes along with a channel;

calculating an inverse discrete Fourier transform matrix by using the position and the number of null sub-carriers preset by a sending end;

combining the statistical characteristics of a Rayleigh channel, and equating a theoretical expression of mean square error of frequency offset estimation to be an expectation of a random variable function comprising a Rayleigh channel response coefficient and channel noise;

and performing Taylor series expansion on the theoretical expression of the frequency deviation estimation mean square error, performing second-order approximation on the expression of the expectation and the variance, and calculating to obtain a high-order approximation result of the frequency deviation estimation mean square error.

Preferably, the frequency offset estimationThe mean square error calculation method comprises the following steps:

wherein the content of the first and second substances,andrespectively, the target function g () is ═₀The first and second derivatives of (a).

Preferably, the calculation formula of g () is:

where y denotes a received time-domain signal vector, y^HRepresenting the transposed conjugate of the received time-domain signal vector y, D () representing the matrix corresponding to the frequency offset, D^H() The transposed conjugate of D () is represented,representing an inverse discrete Fourier transform matrixProducts of conjugate transpose thereof, i.e.

Preferably, the calculation formula of the received time-domain signal vector y is:

wherein: x represents a frequency domain transmission symbol in the form of a diagonal matrix, W represents a discrete fourier transform matrix, h represents a time domain response of a rayleigh channel, and v represents additive complex gaussian white noise.

Preferably, the calculation process of the frequency offset estimation mean square error comprises:

firstly, the first step is toIs written intoIs expected toSum varianceThen on expectationSum varianceThe expression of (a) is approximated by a Taylor series;

the calculation formula is as follows:

preferably, the first and second electrodes are formed of a metal,the calculation formula of (2) is as follows:

wherein the content of the first and second substances,andrespectively representAndin the expectation that the position of the target is not changed,to representAndthe covariance of (a) of (b),to representThe variance of (c).

Preferably, the first and second electrodes are formed of a metal,meter (2)The calculation formula is as follows:

wherein the content of the first and second substances,to representThe variance of (c).

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

1. the invention aims at the generality of the Rayleigh channel, is not limited to a fixed channel, and uses a design idea of utilizing the channel statistical characteristics in an OFDM system on the performance analysis of frequency offset estimation. In the theoretical calculation of the frequency offset estimation mean square error, a time-varying channel is not required to be measured or estimated, but the statistical characteristics of expectation, variance and the like of Rayleigh channel response are directly utilized, and the statistical characteristics of the detected inactive subcarriers and additive complex Gaussian white noise are directly combined for calculation. The theoretical value of the frequency deviation estimation mean square error is obtained by utilizing the statistical property of the Rayleigh channel, and the high-order approximation of the theoretical value is taken as a result, so that the universality and the accuracy of the estimation analysis method are effectively improved.

2. The invention adopts the Taylor series to carry out the high-order approximation of the mean square error of the frequency deviation estimation, so the direct pair is not carried outAndthe expected values of the located numerator and denominator are respectively obtained, and a second-order term is obtained after the series expansion, so that the effect of improving the accuracy of the theoretical estimation performance is achieved.

Drawings

Fig. 1 is a simplified flow chart of a method for analyzing frequency offset estimation of an OFDM system according to an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to examples and drawings, but the embodiments of the present invention are not limited thereto.

The principle of the invention comprises: after the transmitted sequence is subjected to an OFDM scheme to obtain a modulation symbol, the modulation symbol is transmitted through a Rayleigh channel, and the calculation of the frequency offset estimation mean square error is carried out at a receiving end by utilizing the statistical characteristics of the Rayleigh channel and noise. When calculating the theoretical value of the frequency deviation estimation mean square error, firstly, taylor series expansion is utilized to carry out second order approximation on the expression of expectation and variance, and then more accurate frequency deviation estimation mean square error is obtained.

Specifically, as shown in fig. 1, a method for analyzing frequency offset estimation of an OFDM system based on null carriers includes:

before a sending end sends data, setting null subcarriers at fixed subcarrier positions in advance, and carrying modulation symbols on the rest subcarriers;

forming a frequency domain transmitting signal by a subcarrier carrying a modulation symbol and a preset null subcarrier, and adding a cyclic prefix larger than channel delay through IFFT to obtain a baseband time domain transmitting signal;

removing the cyclic prefix at a receiving end, and taking the obtained baseband time domain receiving signal as a random variable which changes along with a channel;

calculating an inverse discrete Fourier transform matrix by using the position and the number of null sub-carriers preset by a sending end

Combining the statistical characteristics of a Rayleigh channel, and equating a theoretical expression of frequency offset estimation mean square error to be an expectation of a random variable function about Rayleigh channel response h and noise v;

and performing Taylor series expansion on the theoretical expression of the frequency deviation estimation mean square error, and calculating to obtain a high-order approximate result of the frequency deviation estimation mean square error.

The invention is explained in more detail below by means of a preferred example.

A frequency offset estimation analysis method of an OFDM system based on null carriers comprises the following steps:

s1, at the transmitting end, a null subcarrier is set in advance at a fixed subcarrier position, then the transmitted sequence is modulated by the OFDM scheme, and the remaining subcarriers carry the modulated symbols.

And S2, obtaining a time domain received signal after the receiving end finishes operations such as removing cyclic prefix, IFFT and the like, and regarding the obtained time domain received signal as a random variable which changes along with a channel.

And S3, obtaining a mean square error expression of the frequency offset estimation according to the statistical characteristics of the Rayleigh channel and the additive complex Gaussian white noise.

In particular, frequency offset estimationThe mean square error calculation method comprises the following steps:

wherein the content of the first and second substances,andrespectively, the target function g () is ═₀The first and second derivatives of (a).

The formula for g () is:

where y denotes a received time-domain signal vector, y^HRepresenting the transposed conjugate of the received time-domain signal vector y, D () representing the matrix corresponding to the frequency offset, D^H() The transposed conjugate of D () is represented,representing an inverse discrete Fourier transform matrixProducts of conjugate transpose thereof, i.e.

The calculation formula of the received time domain signal vector y is:

wherein: x represents a frequency domain transmission symbol in the form of a diagonal matrix, W represents a discrete fourier transform matrix, h represents a time domain response of a rayleigh channel, and v represents additive complex gaussian white noise.

S4, expanding by Taylor seriesSum varianceAnd performing second-order approximation to obtain a more accurate mean square error expression of the frequency offset estimation, and calculating to obtain a high-order approximation result of the mean square error of the frequency offset estimation.

Specifically, first, the followingIs written intoIs expected toSum varianceThen on expectationSum varianceThe expression of (a) is approximated by a taylor series, and the calculation formula is:

the calculation formula of (2) is as follows:

wherein the content of the first and second substances,andrespectively representAndin the expectation that the position of the target is not changed,to representAndthe covariance of (a) of (b),to representThe variance of (c).

The calculation formula of (2) is as follows:

wherein the content of the first and second substances,to representThe variance of (c).

The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.