Method for compensation of phase noise effect on data transmission in radio channel

Abstract

The present invention generally relates to the field of electrical communication and more specifically to apparatuses and methods of phase noise mitigation for signal transmission in wideband telecommunication systems. The method for compensation of the phase noise effect on the data transmission through a radio channel is based on a possibility to present the phase noise of a reference oscillator like a random process where the main spectral density is concentrated in the low-frequency region. Therefore, the number of estimated parameters can be reduced many times to several low-frequency spectral components instead of a direct estimation in the time domain. The advantage of the method is an improvement of the estimation accuracy and a reduction of the computational complexity.

Claims

1. A method for estimation and compensation of phase noise effect on data transmission comprising: a. Reception of a sequence of multiple signal samples; b. Estimation of phase noise in the sequence of multiple signal samples; c. Compensation of the phase noise in the sequence of multiple signal samples using a phase noise estimate, wherein the phase noise estimation comprises the successive steps of: b1. Selection of a sequence of several signal samples from a variety of signal samples; b2. Direct estimation of phase noise realization from the sequence of several signal samples; b3. Generation of a sequence of estimates of the phase noise realization; b4. Estimation and extraction of one or several phase noise low-frequency spectral components by a linear combination of the phase noise realization estimates with weighted coefficients; b5. Estimation of the phase noise in a sequence of multiple signal samples in a time domain using an inverse Fourier transform of the estimated low-frequency phase noise components.

2. The method according to claim 1, wherein a number of estimated spectral components is selected a priori to cover phase noise spectrum of used signal generators at a preliminarily specified level.

3. The method according to claim 1, wherein pilot signals a priori known to a receiver are used for direct estimation of the phase noise realization.

4. The method according to claim 1, wherein received and demodulated data symbols are used for direct estimation of the phase noise realization.

5. The method according to claim 1, wherein a combination of (i) pilot signals that are a priori known to a receiver and (ii) received and demodulated data symbols is used for direct estimation of the phase noise realization.

6. The method according to claim 1, wherein a Fast Fourier Transform (FFT) is used for estimation of the phase noise spectral components.

7. The method according to claim 1, wherein a method operating according to a minimum mean square error (MMSE) criterion is used for estimation of the phase noise spectral components.

8. The method according to claim 1, wherein the phase noise is preliminarily estimated and compensated via a linear interpolation of phase noise values between samples or groups of samples of pilot signals that are a priori known to a receiver.

9. The method according to claim 1, wherein a mean value of the phase noise calculated via averaging of phase noise values over samples of a pilot signal that is a priori known to a receiver is preliminarily estimated and compensated.

10. The method according to claim 1, wherein the phase noise estimation and compensation are performed before received signal equalization.

11. The method according to claim 1, wherein the phase noise estimation and compensation are performed after received signal equalization.

12. The method according to claim 1, wherein a block modulation with a single carrier and frequency domain equalization is used for the data transmission.

13. The method according to claim 12, wherein a length of a set of signal samples used for the phase noise estimation and compensation is a multiple of a signal modulation block length.

14. The method according to claim 1, which is applied in signal processing blocks of a digital modem for a wideband radio relay communication station.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further features and advantages of the present invention will become apparent from the following description of the preferred embodiments with reference to accompanying drawings.

(2) FIG. 1a top level diagram of a single carrier communication system with the traditional PLL-based phase noise estimation and compensation method applied to the equalized signal (prior art).

(3) FIG. 2a top level diagram of a single carrier communication system with the traditional PLL-based phase noise estimation and compensation method applied to the pre-equalized signal (prior art).

(4) FIG. 3a structure of the phase noise compensation apparatus disclosed in U.S. Pat. No. 7,409,024 (prior art).

(5) FIG. 4a structure of the phase noise compensation apparatus disclosed in U.S. Pat. No. 7,733,993 (prior art).

(6) FIG. 5an overall structure of a receiver including the phase noise compensation apparatus disclosed in U.S. Pat. No. 9,160,382 (prior art).

(7) FIG. 6a general scheme of the phase noise compensation apparatus disclosed in U.S. Pat. No. 9,160,382 (prior art).

(8) FIG. 7a receiver functional diagram containing the phase noise estimation and compensation scheme according to the present invention being applied to the signal after the equalization.

(9) FIG. 8a receiver functional diagram containing the phase noise estimation and compensation scheme according to the present invention being applied to the signal before the equalization

(10) FIG. 9a functional diagram of the phase noise estimation and compensation apparatus according to one embodiment of the present invention.

(11) FIG. 10a functional diagram of the phase noise estimation and compensation apparatus according to one embodiment of the present invention additionally applying the preliminary phase noise estimation and compensation scheme.

(12) FIG. 11an example of a time-domain phase noise realization and values of phase corrections applied to each signal sample and calculated by the linear interpolation, phase errors averaging, and the proposed method based on estimation of the spectral components.

(13) FIG. 12a dependence of the bit error probability on the signal-to-noise ratio for the data transmission in the additive white Gaussian noise channel for different methods of phase noise suppression in the received signal.

(14) The following reference numerals are used in the figures: 100a single carrier communication system 101a forward error correction encoder, 102a digital modulator, 103a digital-to-analog convertor, 104a transmitter mixer, 105a power amplifier, 106a transmitter antenna, 107a radio channel, 108a receiver antenna, 109a low-noise amplifier, 110a receiver mixer, 111an analog-to-digital converter, 112a frequency and time synchronization module, 113an equalizer, 114a phase errors compensator, 115a digital demodulator, 116a low-pass filter, 117a phase-locked loop, 118a forward error correction decoder, 200a single carrier communication system, 300a single carrier receiver, 301a frequency and time synchronization module, 302an equalizer, 303a phase noise estimation and compensation module, 304a demodulator, 305a decoder, 400a single carrier receiver, 500a phase noise estimation and compensation module, 501a signal delay line, 502a phase error detector, 503a phase noise spectral components estimator, 504an inverse Fourier Transform module, 505a phase error compensator, 600a phase noise estimation and compensation apparatus, 601a signal delay line, 602a preliminary phase noise estimator, 603a preliminary phase noise compensator, 604a phase error detector, 605a phase noise spectral components estimator, 606an inverse Fourier Transform module, 607a signal delay line, 608a phase error compensator

DETAILED DESCRIPTION OF THE INVENTION

(15) The present invention proposes a method for phase noise suppression in the received signal for data transmission in wireless communication systems which is characterized by a better efficiency and a lower computational complexity in comparison with known methods based on a linear interpolation or phase error averaging.

(16) The method is based on a possibility to present the phase noise of a reference oscillator like a random process where the main spectral density is concentrated in the low-frequency region. Therefore, due to estimation of a phase noise as several samples of the received signal in the frequency domain instead of the time domain, the number of estimated parameters can be reduced many times to several low-frequency spectral components instead of a direct estimation of the time domain realization.

(17) For a detailed description of the developed method, a mathematical model of the data transmission is considered where a signal s0(n) generated at the transmitter propagates through a channel with the additive white Gaussian noise (n) (AWGN) and is received at the receiver in presence of a phase noise of the reference oscillator (n), which causes phase changes for each received signal sample:
x(n)=s(n).Math.exp[j(n)]+(n)(1)

(18) The main goal of efficient phase noise suppression is to obtain the most accurate estimate of the time domain realization of (n) for each sample of the signal and to apply the obtained estimate for compensation of the received signal phase distortions. In the claimed invention estimation of the phase noise is provided by several samples constituting a subset with the length of N from the total number L of signal samples, observed at the receiver (NL). In the general case, selection of the signal samples for the phase noise estimation by the proposed method can be done arbitrarily so it is not necessary to select all values of the observed signal or sampling with any period. Let the indices of the signal samples that are included into the subset of samples form a set of I.sub.n={i,i[0,L1]} with the power of N. Then, the values included into the subset of samples of the received signal and can be represented in a vector form as:
x=S+(2)

(19) where X=[{x(m), mI.sub.n}].sup.T is a vector of the received signal samples included into the current subset, [{e.sup.j(m)}, mI.sub.n}].sup.T is a vector of a phase noise time domain realization, =[{(m), mI.sub.n}].sup.T is a vector of Gaussian noise samples, S=diag[{s(m), mI.sub.n}].sup.T) is a diagonal matrix in which nonzero elements of the main diagonal correspond to the transmitted signal samples from the subset.

(20) A frequency characteristic of the phase noise can be calculated from a subset of N samples of the entire phase noise realization of L signal samples. It is provided by the discrete Fourier transform (DFT) of the samples of the phase noise realization in the time domain corresponding to the signal elements and included into the subset:

(21) $\begin{array}{cc}J\left(k\right)=\underset{n{I}_n}{\overset{}{.Math.}}{e}^{j.Math.\left(n\right)}.Math.e^{j\frac{2\mathrm{nk}}{L}},k\left[0,L-1\right]J=F,& \left(3\right)\end{array}$

(22) where J=[J(0) . . . J(L1)] is a vector of the phase noise spectral characteristic for the entire observed signal, F is an LN shortened DFT matrix containing only the columns of the DFT matrix corresponding to the indices of the signal samples from the subset I.sub.n.

(23) In a vector form the frequency response of the phase noise realization for the entire observed signal can be represented as a sum of two components:
J=J.sub.u+J.sub.u(4)

(24) where J.sub.u=[J(0) . . . J(W/21),0, . . . 0, J (LW/2), J(L1)].sup.T is a vector of low-frequency spectral components of the phase noise realization, and J.sub.u=[0, . . . 0, J (W/2), J (LW/21), 0 . . . 0].sup.T is a vector of high-frequency spectral components of the phase noise realization.

(25) Due to the low-frequency nature of the phase noise, estimation of its spectral characteristics is provided by determining only the values of the vector Ju, and the vector J-u can be assumed equal to zero. The number of the estimated spectral components of the phase noise W (the length of the vector Ju) is chosen to cover the phase noise spectrum at a certain level. Characteristics of the phase noise power spectral density can be determined according to characteristics of the reference oscillator.

(26) The number of low-frequency spectral components W covering the required spectral region of the phase noise depends on a ratio of a duration of the subset of N samples of the signal to the received signal sample period. However, in most of the practical implementations the number W is chosen to be equal to 3, 5, 7.

(27) Estimation of the phase noise spectral components for the entire signal includes phase error detection from each sample of the subset of the received signal samples and forming a sequence of estimates of a time domain phase noise realization Y for the considered subset X, which is defined as:
Y=(S).sup.1.Math.X=F.sup.H.Math.J.sub.u+F.sup.H.Math.J.sub.u+(S).sup.1(5)

(28) Phase errors for each sample from the subset are calculated by dividing the received signal by the complex values of the transmitted signal samples (the diagonal elements of the matrix S). The transmitted signal samples can be determined both on a basis of a priori knowledge of pilot samples in the transmitted signal and from the received signal data samples by making hard decisions in the demodulator which consists in approximation of the received signal symbols by the signal constellation values situated at the shortest Euclidean distance. Phase error estimation of the data samples may be inaccurate due to demodulation errors leading to a degradation of the described method, however, this effect may be neglected for the purposes of the present description.

(29) Expression (5) can be reduced to the form:
Y=F.sup.H.Math.J.sub.u+E,(6)

(30) where E is a modified additive Gaussian noise that includes the receiver Gaussian noise and the phase noise spectral components J.sub.u, excluded from the further estimation.
E=F.sup.H.Math.J.sub.u+(S).sup.1(7)
Estimates of non-zero vector elements of the phase noise spectral components J.sub.u can be calculated by filtering the sequence of estimates of the phase noise realization Y:
.sub.u=M.Math.Y,(8)

(31) where M is a matrix of the phase noise spectral characteristics estimation with the size of WN. .sub.u=[(0) . . . (W/21), (LW/2), . . . (L/2)] is a vector of estimated spectral components including only W nonzero elements of the vector J.sub.u.

(32) In one embodiment, estimates of the first W phase noise spectral components can be calculated by the Fourier transform from all N samples of the subset. In that case, the filtering matrix M has the size of WN and is formed by rows of columns of the Fourier matrix F of the size of LL, corresponding to the estimated spectral components and indices of the signal samples I.sub.n included into the subset. This approach is the simplest way to calculate the required values but it does not consider autocorrelation properties of the phase noise spectral components and additionally requires the phase noise sampling to be periodical.

(33) In another embodiment, the criterion of minimum mean square error (MMSE) is used for calculation of elements of the filtering matrix M according to the equation:
M=R.sub.JuJu.Math.F(F.sup.H.Math.R.sub.JuJu.Math.F+R.sub.).sup.1,(9)

(34) where R.sub.JuJu is a correlation matrix of W low-frequency phase noise spectral components, whose elements depend on characteristics of the carrier frequency reference oscillator, R.sub. is a correlation matrix of residual noises, F is a Fourier matrix with the size of WN for calculation of W low-frequency phase noise spectral components from the signal samples of the subset and is formed as F={f.sub.j,i}, where f.sub.,j,I is an element of the Fourier matrix F with the size of LL such that j[0,W1], iI.sub.n. Estimation of the phase noise spectral components in this embodiment gives more optimal result compared to the estimation based on the Fourier transform, however, it requires an additional a priori knowledge of statistical characteristics of the estimated noise.

(35) An estimate of the time domain phase noise realization for all L samples of the received signal further used for the phase noise compensation can be calculated as an inverse discrete Fourier transform with the dimensions of WL from estimates of the phase noise spectral components J.sub.u:

(36) $\begin{array}{cc}\left(n\right)=\frac{1}{2N}\left(\underset{k=0}{\overset{W/2-1}{.Math.}}{\hat{J}}_u\left(k\right).Math.e^{-j\frac{2\mathrm{nk}}{L}}+\underset{k=L-W/2}{\overset{L-1}{.Math.}}{\hat{J}}_u\left(k-L+\frac{W}{2}\right).Math.e^{-j\frac{2\mathrm{nk}}{L}}\right)& \left(10\right)\end{array}$

(37) Thus, a method of phase noise compensation in a received signal based on estimation of the spectral components presented in this invention comprises the following steps:

(38) 1. Selection of a sequence of N signal samples S from a variety of L received signal samples s(n), forming a subset from which the estimation is performed;

(39) 2. Estimation of the phase noise realization Y in the sequence of N signal samples included into the current subset using knowledge of the pilot samples and the demodulated data samples;

(40) 3. Estimation of phase noise low-frequency spectral components .sub.u by a linear combination of the phase noise realization estimates Y with weighted filter coefficients M;

(41) 4. Calculation of an estimate of the time-domain phase noise realization for all L samples of the received signal via the inverse Fourier transform of the estimated phase noise low-frequency components .sub.u.

(42) 5. Using this estimate for the phase noise compensation in the received signal s(n).

(43) It should be noted that accuracy of the estimation of phase errors from the data samples strongly depends on a level of all noises in the received signal. Therefore, in order to improve the quality of the phase distortion estimation, a preliminary estimation and compensation of the phase noise for elimination of a common phase rotation of all signal samples included into the i-th subset can be additionally performed. This procedure is based on estimation of phase errors from the pilot samples of the received signal, which are known a priori. In one embodiment, a linear interpolation of the phase values between the estimates is performed to calculate the preliminary eliminated phase error for the data symbols. In another embodiment, the phase noise compensation for the data samples is performed with the average value of the phase errors calculated from the pilot samples of the signal.

(44) A general scheme of an embodiment of a single carrier receiver 300 used in single-carrier communication systems containing a phase noise suppression scheme implementing the developed method is shown in FIG. 7. The functional diagram includes the following components: a frequency and time synchronization module 301, an equalizer 302, a phase noise estimation and compensation module 303 using the claimed method of phase noise suppression, a received signal demodulator 304 and a forward error correction decoder 305. In the presented embodiment of the invention, the phase noise is estimated and compensated after the received signal equalization.

(45) A possible embodiment of the present invention is a single carrier receiver architecture 400 shown in FIG. 8, where the phase noise suppression is performed by a phase noise estimation and compensation module 303 before equalization of the received signal by a demodulator 304.

(46) A functional diagram of an embodiment of a digital phase noise estimation and compensation module 500 using the method presented above is shown in FIG. 9. In this embodiment, the sequence of the received signal samples is fed to a phase error detector 502, which calculates estimates of phase errors either based on a priori knowledge of the pilot samples or based on results of the signal demodulation using hard decisions or combining the both approaches. Then, the obtained sequence of estimates of the time-domain phase noise realization enters a phase noise spectral components estimator 503, which calculates an estimate W of the phase noise low-frequency spectral components for the current sequence of signal samples. The resulting estimate goes to an inverse Fourier Transform module 504, where a final estimation of the time-domain phase noise realization is calculated using the inverse Fourier transform, which is used to compensate phase errors in the input signal delayed by a signal delay line 501 by the time required to perform the calculations.

(47) FIG. 10 provides a functional diagram of one embodiment of a phase noise estimation and compensation apparatus 600, additionally using a preliminary phase noise estimation and compensation to improve accuracy of a phase error detector 604. The pre-suppression circuit consists of a preliminary phase noise estimator 602, a preliminary phase noise compensator 603 and a signal delay line 601 for the time required to calculate the sequence used in the pre-compensation procedure. A subsequent phase noise suppression circuit is similar to the architecture applied in the phase noise estimation and compensation module 500 and uses the previously presented blocks of a phase error detector 604, a phase noise spectral components estimator 605, an inverse Fourier Transform module 606, a signal delay line 607 and a phase error compensator 608 in a sequence of the received signal samples.

(48) In order to illustrate efficiency of the phase noise suppression, the proposed method was compared with the estimation and compensation schemes based on a linear interpolation and averaging of phase error estimates performed from pilot samples of the signal. FIG. 11 shows an example of a time-domain phase noise realization, as well as its estimates using the three considered methods. The phase noise realization is given for an integrated 60 GHz signal generator used in modern radio-relay communication systems. As it can be seen from the presented results, the proposed method provides a better estimation of the phase distortions for all samples of the received signal.

(49) The Bit Error Rate (BER) is one of the main characteristics of a data transmission quality in communication systems and is defined as a ratio of the number of incorrectly received bits to the total number of received bits. FIG. 12 shows an example of the impact of the phase noise on the BER value in a radio-relay communication system in the 60 GHz frequency band. The figure shows the results for three cases: no phase noise compensation for the received signal, compensation of the phase noise by the method of linear interpolation and compensation of the phase noise by the method proposed in the present invention. The presented results correspond to the case of uncoded data transmission with the 64-QAM digital modulation and demonstrate the dependence of the BER on the signal-to-noise ratio (SNR) in the channel in presence of the reference oscillator phase noise. The time-domain phase noise realization was set in the simulation according to a mathematical model of a free-running oscillator. The level of the power spectral density curve was chosen equal to 69 dBc/Hz at the 100 kHz offset from the carrier frequency. FIG. 12 additionally provides a BER curve for the case of absence of the phase noise for evaluation of the phase noise compensation efficiency for the considered methods.

(50) As can be seen from the presented examples of different phase noise compensation methods, in the case of absence of a phase noise suppression algorithm a complete system malfunction with a constant level of BER=0.08 is observed. The usage of the phase noise compensation for the two considered methods makes possible to achieve the BER level of 10-6. The gain of using the proposed method is 6 dB in terms of SNR, which is a significant advantage of this scheme compared to the liner interpolation method. In the claimed method a degradation of the SNR operating point due to the phase noise impact on the data transmission is only 1.2 dB at the level of BER 10-6 relative to the ideal case of absence of the phase noise. It is an acceptable value for modern communication systems.

(51) Computational complexity of the proposed method requires WN complex multiplications and 2W(N1) additions for estimation of phase noise spectral components, as well as WN complex multiplications and 2(W1)N additions of the multiplication results for calculation of the inverse discrete Fourier transform (DFT). The methods of phase noise estimation and compensation known from the prior art, based on the digital filtering procedure of a sequence of received signal samples, require performing NN complex multiplications and 2N(N1) additions of the multiplication results to estimate a phase noise realization on a sequence of N symbols. Since the size of N of the sequence from which the estimation is done is much larger than the number of estimated spectral components W, the computational complexity of the known analogues significantly exceeds the complexity of the method proposed in the present invention.

(52) The present invention is not limited to the embodiments disclosed in this description for illustrative purposes only and covers all modifications and variations that are not beyond the scope and essence of the invention as defined by the claims.