CN110138694A - A kind of single carrier frequency domain equalization algorithm based on noise prediction - Google Patents

Abstract

The present invention relates to a single-carrier frequency domain equalization algorithm based on noise prediction, including: (1) using the correlation between the specific known sequence noise at the output end of the frequency domain equalizer and the noise contained in the unknown data sequence, and applying the Wiener filter principle to predict And offset the noise contained in the unknown data sequence, so as to obtain lower noise power at the output of the equalizer, thereby improving the system performance. (2) Improve the noise prediction algorithm's prediction inaccuracy, poor performance and high complexity when the specific sequence is short, so that the robustness of the frequency domain equalization system based on noise prediction proposed in this paper is enhanced, and the performance Compared with the noise prediction algorithm proposed in the original literature, it has been significantly improved. (3) The computational complexity has also been greatly reduced.

Description

A Single Carrier Frequency Domain Equalization Algorithm Based on Noise Prediction

technical field

The invention relates to the technical field of communication, and more specifically, to a method for improving the performance of a noise prediction frequency-domain equalizer in a single-carrier system.

Background technique

For frequency selective channels with large delay spread, single carrier frequency domain equalization (SC-FDE) is a very effective technique to overcome ISI. SC-FDE adopts low-complexity frequency-domain equalization technology. Compared with OFDM technology, SC-FDE has a smaller peak-to-average ratio (PAR), strong resistance to frequency selectivity, and lower sensitivity to phase noise. In addition, compared with time-domain equalization, SC-FDE has lower computational complexity while obtaining the same system performance. Therefore, the application of SC-FDE technology in wireless communication scenarios is further studied.

Existing frequency domain equalizers include traditional ZF (zero-forcing) equalizers, MMSE (minimum mean square error) equalizers, and MIMO-SCFDE (Multiple-Input and Multiple-Output Single Carrier Frequency Domain Equalization) systems for spatial multiplexing. Based on the zero-forcing (ZF) and minimum mean square error (MMSE) criteria, the noise-predictive ZF equalizer (ZF-NP-FDE) and the noise-predictive MMSE equalizer (MMSE-NP-FDE) are derived, respectively. Based on the algorithm of noise prediction, since the specific sequence as CP is fully known by the receiver, the noise contained in the estimated value of the specific sequence at the output of the frequency domain equalizer can be accurately calculated; secondly, the estimated value of the data at the output of the frequency domain equalizer contains The statistical correlation characteristics of the noise contained in the noise and the noise contained in the specific sequence estimation value, and the noise contained in the calculated specific sequence estimation value are used to predict and offset the noise contained in the data estimation. Compared with the traditional equalizer, the algorithm based on noise prediction improves system performance. However, this noise prediction algorithm is not accurate enough. When the inserted specific sequence (UW) is short and the data is long, the noise estimation of the obtained data part is rough, especially the noise estimation of the data part far away from UW may appear rough. Big deviation.

Contents of the invention

In order to overcome the deficiencies in the prior art, the present invention proposes a single-carrier ZF equalizer (ZF-NP-FDE) based on noise prediction of an improved algorithm and a single-carrier MMSE equalizer (MMSE-NP-FDE) of noise prediction It is used to reduce the power of the estimated data, reduce the mean square error, increase the signal-to-noise ratio, and improve the performance of the system.

In order to achieve the above object, the specific steps of the method proposed by the present invention are as follows:

S1. Analyze the single-input and single-output SC-FDE system, establish a system model and construct an unknown data symbol parameter vector d;

S2. Analyze the relationship between known noise and unknown data noise, and then write the relationship between ε _w and ε _d according to the correlation between noises;

S3. According to the Wiener filter criterion, find the optimal matrix W _{ZF of the noise figure, d} , W _{MMSE, d} ;

S4. Solve the noise value symbol by symbol according to the first symbol of the unknown data, and calculate the noise value of all unknown symbols by analogy;

S5. After ZF or MMSE equalization of the received data symbols, the obtained noise value of each symbol is subtracted and judged to obtain the transmitted data symbols.

The beneficial effects of the present invention are:

1) The method provided by the present invention proposes a single-carrier frequency-domain equalization algorithm applicable to multipath channels. Under 8psk modulation mode, taking deep fading channel simulation as an example, in the ZF frequency-domain equalizer, when the SER is 10 When -3, compared with the original algorithm, the improved noise prediction frequency domain equalizer can obtain about 6dB SNR gain; in the MMSE frequency domain equalizer, when the SER is 10-3, the improved noise prediction equalizer Compared with the original algorithm, an SNR gain of about 5.5dB can be obtained.

2) In the present invention, the accuracy of noise prediction is effectively improved through point-by-point noise prediction, and noise accumulation is avoided through symbol decision.

Description of drawings

Fig. 1 realization flowchart of the present invention

Figure 2 Amplitude-frequency response of deep fading channel

Figure 3 ZF frequency domain equalizer performance in deep fading channel

Figure 4 Deep fading channel MMSE frequency domain equalizer performance

Figure 5 Amplitude-frequency response of light fading channel

Figure 6 ZF frequency domain equalizer performance in light fading channel

Figure 7 Light fading channel MMSE frequency domain equalizer performance

Figure 8 Average performance of random channel ZF frequency domain equalizer

Figure 9 Average performance of random channel MMSE frequency domain equalizer

Detailed ways

The accompanying drawings are for illustrative purposes only and cannot be construed as limiting the patent;

The present invention will be further elaborated below in conjunction with the accompanying drawings and embodiments.

Example 1

As shown in Figure 1, the concrete steps of the method that the present invention proposes are as follows:

a) Analyze the single-input and single-output SC-FDE system, establish the system model and construct the unknown data sign parameter vector d.

Wherein, the specific method of step a) is:

The transmitter segments the data stream to be transmitted into a number of data packets of length P. A specific known sequence of length Q is inserted before each data packet, and a specific sequence (UW) is inserted before all transmitted data packets. In order to offset the interference between data packets, the length Q of a specific sequence is selected to be greater than the length of the channel impulse response. Each transmitted data packet can be expressed as

Among them, d is a data symbol vector of P×1, and w is a specific known sequence of Q×1.

The received data packets can be expressed as

y=Hx+n

Among them, n is an additive noise vector, and its elements are complex Gaussian random variables with independent and identical distribution, zero mean, and variance N ₀ . H is a circular matrix composed of channel impulse response, H=F ^H ΛF, F is a Fourier transform matrix, its dimension is N=P+Q; Λ is composed of the value obtained by DFT transformation of channel impulse response diagonal matrix.

The received signal y is used to detect the transmitted data d.

b) Analyze the relationship between known noise and unknown data noise, and then write the relationship between ε _w and ε _d according to the correlation between noises.

Wherein, the specific method for finding step b) is as follows:

For ZF equalizer:

The receiver of the single-carrier system inserted into UW does not need to delete the corresponding part of UW in the received signal, but directly performs serial/parallel conversion, which will Decomposed into two parts: data and UW:

in F _d is the matrix formed by the front P columns of the matrix F, and F _w is the matrix formed by the rear Q columns of the matrix F. Since w is completely known to the receiver, the noise vector n _w can be accurately estimated

For MMSE equalizer:

Through the inverse Fourier transform (IDFT), the time domain signal obtained can be expressed as

in is a diagonal matrix. Similar to ZF-NP-FDE, It can be decomposed into two parts: data and UW:

also, The estimated error of

Similarly, decomposing ε into two parts, we get and The estimation error of

c) According to the Wiener filtering criterion, the optimal matrix W _{ZF, d} , W _{MMSE, d} of the noise figure is obtained;

Wherein, the concrete method of seeking of step c) is as follows:

For ZF equalizer:

Since n _d and n _w are linear transformations of the same Gaussian noise n, the two are related. Consider predicting n _d from the accurately estimated n _w . According to the principle of Wiener filtering, select the matrix W _{ZF of P×Q, and d} is

By solving, we can get

The predicted value of n _d is

For MMSE equalizer:

According to the principle of Wiener filtering, the matrix W _{MMSE of P×Q is selected, and d} is

The solution to this problem is

The predicted value of noise ε _d is

d) Solve the noise value symbol by symbol according to the first symbol of the unknown data, and calculate the noise value of all unknown symbols by analogy.

Wherein, the concrete method of step d) is as follows:

For ZF equalizer:

After the noise vector n _w is known accurately, the noise prediction value of the first symbol of the data packet is calculated

in

F _d1 is a vector composed of elements in the first column of matrix F. offset noise and sign decision

dec{x} represents the sign decision for x. recalculate the noise value for this symbol

Merge it into the noise vector n _w as the known noise, and remove the first element of the vector n _w to become a new known noise vector n _w ′. The purpose of removing the first element of the vector is to keep the length of the noise vector and avoid excessive complexity caused by its length being too long. By analogy, the noise prediction value of the i-th symbol of the data packet is

Among them, n _w ′ is a new known noise vector obtained by merging the noise vector when estimating the i-1th symbol noise value and the recalculated symbol noise value after judging the i-1th symbol, and removing the first element ,

F _di is a vector composed of elements in column i of matrix F, and F _w ′ is a matrix composed of elements in column Q of matrix F corresponding to known noise vectors, assuming that known noise vector n _w ′ is expressed in formula (3-8) middle The noise of the n~n+Q elements of the matrix F, then F _W ′ is a matrix composed of elements in the n~n+Q columns of the matrix F.

For MMSE equalizer:

The noise prediction value of the i-th symbol of the data packet is

Where ε _w ′ is a new known noise vector obtained by merging the noise vector when estimating the i-1th symbol noise value and the recalculated symbol noise value after the i-1th symbol is judged, and removing the first element , estimating the noise vector of the first signed noise value to obtain

F _di is a vector composed of elements in column i of matrix F, and F _w ′ is a matrix composed of elements in column Q of matrix F corresponding to known noise vectors, assuming that known noise vector ε _w ′ is expressed as formula (3-9) middle The noise of the n~n+Q elements of the matrix F, then F _w ′ is a matrix composed of elements in the n~n+Q columns of the matrix F.

e) After ZF or MMSE equalization of the received data symbols, the calculated noise value of each symbol is subtracted and judged to obtain the transmitted data symbols.

Wherein, the concrete method of step e) is as follows:

For ZF equalizer:

Make a decision on the i-th symbol

recalculate the noise value for this symbol

Merge with n _w ′ and remove the first element to obtain a new known noise vector. The above steps are repeated to sequentially obtain the estimated noise value and the decision value of each symbol of the data packet.

For MMSE equalizer:

Make a decision on the i-th symbol

recalculate the noise value for this symbol

Merge with ε _w ′ and remove the first element to obtain a new known noise vector. The above steps are repeated to sequentially obtain the estimated noise value and the decision value of each symbol of the data packet.

Example 2

The present invention has carried out performance analysis and simulation to above-mentioned method, specifically as follows:

The length of the UW inserted in the transmitted data packet is 6, and the length of the data symbol vector is 58, so the dimension of the FFT is 64. The transmission symbols are modulated by 8PSK; the channel is a Rayleigh fading multipath channel, and the length of the channel impulse response is 6. Simulations are made in three sets of channel coefficients, namely the deep fading channel, the fading indistinct channel and the COST-207RA channel 10,000 six-path channels randomly generated by the model.

Figure 2 shows the amplitude-frequency response of a deep fading channel, and the channel coefficient is h=[0.6523-0.1627i 0.1449+0.8804i-0.4126+0.2606i -0.1432-0.09780i -0.1921+0.07379i 0.07459+0.07625i]. Figures 3 and 4 respectively show the SER performance of the ZF and MMSE frequency domain equalizers of the single-carrier system in this channel environment, where the original algorithm refers to the literature [Che Xiaolin, He Chen, Jiang Lingge. Based on noise prediction Frequency Domain Equalization of Single Carrier MIMO System [J]. Electronic Journal, 2009, 37(1): 43-47.] The proposed frequency domain equalization algorithm based on noise prediction, the improved algorithm is the improved algorithm performance curve.

Figure 5 shows the amplitude-frequency response of the light fading channel, and the channel coefficient is h=[0.98-0.002i 0.385+0.532i -0.189-0.168i 0.01+0.051i -0.106-0.0197i -0.0612+0.0614i]. Figures 6 and 7 respectively show the SER performance of the ZF and MMSE frequency domain equalizers of the single carrier system in this channel environment.

Figures 8 and 9 respectively show the average SER performance of the ZF and MMSE frequency domain equalizers of the single-carrier system under 10,000 six-path channels randomly generated by the COST-207RA channel model.

It can be seen from the above simulations of various channel environments that the frequency domain equalizer based on noise prediction, whether it is the original algorithm or the improved algorithm, has significantly better performance than the traditional frequency domain equalizer. This is because, through noise prediction and cancellation, the noise power or mean square error of data estimation is reduced, thereby improving system performance. Compared with the original algorithm of noise prediction frequency domain equalization proposed in literature [], the performance of the improved algorithm has been significantly improved, mainly because the accuracy of noise prediction is effectively improved by point-by-point noise prediction, and the symbol The decision avoids noise accumulation. Taking deep fading channel simulation as an example, in the ZF frequency domain equalizer, when the SER is 10 ^-3 , compared with the original algorithm, the improved noise prediction frequency domain equalizer can obtain about 6dB SNR gain; in the MMSE frequency domain In the equalizer, when the SER is 10 ^-3 , the improved noise prediction equalizer can obtain about 5.5dB SNR gain compared with the original algorithm.

Claims (1)

1. a single carrier frequency domain equalization algorithm based on noise prediction, is characterized in that, comprises the steps: S1. Analyze the single-input and single-output SC-FDE system, establish a system model and construct an unknown data symbol parameter vector d; S2. Analyze the relationship between known noise and unknown data noise, and then write the relationship between ε _w and ε _d according to the correlation between noises; S3. According to the Wiener filter criterion, find the optimal matrix W _{ZF of the noise figure, d} , W _{MMSE, d} ; S4. Solve the noise value symbol by symbol according to the first symbol of the unknown data, and calculate the noise value of all unknown symbols by analogy; S5. After ZF or MMSE equalization of the received data symbols, the obtained noise value of each symbol is subtracted and judged to obtain the transmitted data symbols.